diff --git a/.github/workflows/python-publish.yml b/.github/workflows/python-publish.yml index 869d7a9..d51cde4 100644 --- a/.github/workflows/python-publish.yml +++ b/.github/workflows/python-publish.yml @@ -38,6 +38,12 @@ jobs: python -m pip install --upgrade pip pip install build pip install -e .[dev] + - name: Install SolidsPy + run: | + pip install --upgrade pip + pip install --index-url https://test.pypi.org/simple/ \ + --extra-index-url https://pypi.org/simple \ + SolidsPyKevin - name: Run tests with coverage run: | @@ -168,4 +174,14 @@ jobs: # run: | # for pkg in dist/*/*.tar.bz2; do # conda run -n base anaconda upload "$pkg" --force - # done \ No newline at end of file + # done + - name: Create GitHub Release + uses: actions/create-release@v1 + with: + tag_name: "v${{ env.VERSION }}" + release_name: "v${{ env.VERSION }}" + body: "Automated release for version ${{ env.VERSION }}" + draft: false + prerelease: false + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} \ No newline at end of file diff --git a/LICENSE b/LICENSE index afca776..f9697a0 100644 --- a/LICENSE +++ b/LICENSE @@ -1,6 +1,6 @@ MIT License -Copyright (c) 2015 - 2018 Kevin Sepúlveda-García and Nicolás Guarín-Zapata +Copyright (c) 2025 - 2027 Kevin Sepúlveda-García and Nicolás Guarín-Zapata Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the diff --git a/README.md b/README.md new file mode 100644 index 0000000..5906567 --- /dev/null +++ b/README.md @@ -0,0 +1,125 @@ +# SolidsPy: 2D/3D-Finite Element Analysis with Python + +| ![Animation 1](assets/anim1.gif) | ![Animation 2](assets/anim2.gif) | +|----------------------------------|----------------------------------| + +[![PyPI version](https://img.shields.io/pypi/v/solidspy.svg)](https://pypi.python.org/pypi/solidspy-opt) +[![Documentation Status](https://readthedocs.org/projects/solidspy-opt/badge/?version=latest)](https://solidspy-opt.readthedocs.io/en/latest/) +[![Downloads frequency](https://img.shields.io/pypi/dm/solidspy)](https://pypistats.org/packages/solidspy-opt) + +A simple topology optimization code for 2D/3D elasticity problems. **SolidsPy-Opt** uses as input easy-to-create text files (or Python data structures) defining a model in terms of nodal, element, material, and load data. It extends or modifies functionality from the original [SolidsPy](https://github.com/AppliedMechanics-EAFIT/SolidsPy) to support topology optimization workflows. + +- Documentation: http://solidspy-opt.readthedocs.io +- GitHub: https://github.com/AppliedMechanics-EAFIT/SolidsPy-Opt +- PyPI: https://pypi.org/project/solidspy-opt/ +- Free and open source software: [MIT license](http://en.wikipedia.org/wiki/MIT_License) + +## Features + +* Built upon an open-source Python ecosystem. +* Easy to use and modify for **topology optimization** tasks. +* Extends SolidsPy features to include optimization of material layout (topology optimization). +* Created with academic and research goals in mind. +* Can be used to teach or illustrate: + - Computational Modeling + - Topology Optimization + - Other advanced engineering topics + +## Installation + +The code is written in Python, depending on `numpy`, `scipy`, and `SolidsPy`. It has been tested under Windows, Mac and Linux. + +To install *SolidsPy-Opt*, open a terminal and type: + +```bash +pip install solidspy-opt +``` + +For generating mesh files from [Gmsh](http://gmsh.info/), install [meshio](https://github.com/nschloe/meshio): + +```bash +pip install meshio +``` + +## How to run a simple model + +Below is a minimal example showing how you might set up and run a 2D topology optimization analysis in *SolidsPy-Opt*. + +```python +import numpy as np +import matplotlib.pyplot as plt + +from solidspy_opt.optimize import ESO_stress +from solidspy_opt.utils import structure_3d, structures + +# Define the load directions and positions on the top face +load_directions_3d = np.array([ + [0, 1, 0], # Load in the Y direction + [1, 0, 0], # Load in the X direction + [0, 0, -1] # Load in the negative Z direction +]) +load_positions_3d = np.array([ + [5, 5, 9], # Position near the center of the top face + [1, 1, 9], # Position near one corner of the top face + [8, 8, 9] # Position near another corner of the top face +]) + +# Generate the nodes, materials, elements, loads, and BC indexes +nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L=10, # length in X + H=10, # length in Y + W=10, # length in Z + E=206.8e9, # Young's modulus + v=0.28, # Poisson's ratio + nx=10, # number of divisions in X + ny=10, # number of divisions in Y + nz=10, # number of divisions in Z + dirs=load_directions_3d, + positions=load_positions_3d +) + +# Run the ESO optimization +els_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = ESO_stress( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=200, + RR=0.005, # Initial removal ratio + ER=0.05, # Removal ratio increment + volfrac=0.5, # Target volume fraction + plot=True, # Whether to plot with solidspy's 3D plot function + dim_problem=3, + nnodes=8 # 8-node hexahedron +) +``` + +Save the script (for example, as `example_solidspy_opt.py`) and run it: + +```bash +python example_solidspy_opt.py +``` + +## License + +This project is licensed under the [MIT license](http://en.wikipedia.org/wiki/MIT_License). All documentation is licensed under the [Creative Commons Attribution License](http://creativecommons.org/licenses/by/4.0/). + +## Citation + +If you use **SolidsPy-Opt** in your research or publications, please cite it. A BibTeX entry for LaTeX users might look like: + +```bibtex +@software{solidspy_opt, + title = {SolidsPy-Opt: 2D/3D-Finite Element and Topology Optimization Analysis with Python}, + author = {Sepúlveda-García, Kevin and Guarin-Zapata, Nicolas}, + year = 2025, + version = {0.1.0}, + keywords = {finite-elements, scientific-computing, deep learning, topology, optimization}, + license = {MIT License}, + url = {https://github.com/AppliedMechanics-EAFIT/SolidsPy-Opt}, + abstract = {SolidsPy-Opt is a Python package designed to perform + topology optimization of 2D/3D solids by leveraging SolidsPy + finite-element package and advanced computational tools.} +} +``` \ No newline at end of file diff --git a/README.rst b/README.rst index e3f8ff5..27830fa 100644 --- a/README.rst +++ b/README.rst @@ -1,8 +1,16 @@ -SolidsPy-Opt: 2D Topology Optimization with Python -================================================== +SolidsPy: 2D/3D-Finite Element Analysis with Python +=================================================== -.. figure:: https://raw.githubusercontent.com/AppliedMechanics-EAFIT/SolidsPy/master/docs/img/wrench.png - :alt: Wrench under bending. +.. list-table:: + :header-rows: 0 + :widths: 50 50 + + * - .. image:: assets/anim1.gif + :alt: Animation 1 + :width: 300px + - .. image:: assets/anim2.gif + :alt: Animation 2 + :width: 300px .. image:: https://img.shields.io/pypi/v/solidspy.svg :target: https://pypi.python.org/pypi/solidspy-opt @@ -16,8 +24,8 @@ SolidsPy-Opt: 2D Topology Optimization with Python :target: https://pypistats.org/packages/solidspy-opt :alt: Downloads frequency -A simple finite element analysis (FEA) and topology optimization code for -2D elasticity problems. **SolidsPy-Opt** uses as input easy-to-create text +A simple opology optimization code for +2D/3D elasticity problems. **SolidsPy-Opt** uses as input easy-to-create text files (or Python data structures) defining a model in terms of nodal, element, material, and load data. It extends or modifies functionality from the original `SolidsPy `__ @@ -36,20 +44,14 @@ Features * Easy to use and modify for **topology optimization** tasks. -* Handles 2D elasticity, displacement, strain, and stress solutions, and - extends these workflows to include optimization of material layout +* Extends SolidsPy features to include optimization of material layout (topology optimization). -* Organized in independent modules for pre-processing, assembly, optimization, - and post-processing, allowing the user to easily modify or add new - features (e.g., new elements or custom optimization strategies). - * Created with academic and research goals in mind. * Can be used to teach or illustrate: - Computational Modeling - - Finite Element Methods - Topology Optimization - Other advanced engineering topics @@ -58,9 +60,7 @@ Installation ------------ The code is written in Python, depending on ``numpy``, ``scipy``, and -``sympy`` (and possibly other libraries if your optimization approach -requires them). It has been tested under Windows, Mac, Linux, and Android -environments. +``SolidsPy``. It has been tested under Windows, Mac and Linux. To install *SolidsPy-Opt*, open a terminal and type: @@ -68,13 +68,6 @@ To install *SolidsPy-Opt*, open a terminal and type: pip install solidspy-opt -If you also need an interactive GUI for file selection, you can install -`easygui `__: - -:: - - pip install easygui - For generating mesh files from `Gmsh `__, install `meshio `__: @@ -88,76 +81,57 @@ How to run a simple model ------------------------- Below is a minimal example showing how you might set up and run a -2D finite element + topology optimization analysis in *SolidsPy-Opt*. -(Adapt it to your actual code structure and function names.) +2D topology optimization analysis in *SolidsPy-Opt*. .. code:: python import numpy as np import matplotlib.pyplot as plt - # Hypothetical module import for SolidsPy-Opt: - from solidspy_opt.solids_GUI import solids_opt_auto - - # Define the data (nodes, constraints, elements, materials, loads, etc.) - nodes = np.array([ - [0, 0.00, 0.00], - [1, 2.00, 0.00], - [2, 2.00, 2.00], - [3, 0.00, 2.00], - [4, 1.00, 0.00], - [5, 2.00, 1.00], - [6, 1.00, 2.00], - [7, 0.00, 1.00], - [8, 1.00, 1.00]]) - - cons = np.array([ - [0, -1], - [0, -1], - [0, 0], - [0, 0], - [-1, -1], - [0, 0], - [0, 0], - [0, 0], - [0, 0]]) - - elements = np.array([ - [0, 1, 0, 0, 4, 8, 7], - [1, 1, 0, 4, 1, 5, 8], - [2, 1, 0, 7, 8, 6, 3], - [3, 1, 0, 8, 5, 2, 6]]) - - mats = np.array([[1.0, 0.3]]) - - loads = np.array([ - [2, 0.0, 1.0], - [3, 0.0, 1.0], - [6, 0.0, 2.0]]) - - data = { - "nodes": nodes, - "cons": cons, - "elements": elements, - "mats": mats, - "loads": loads - # Potentially additional data for optimization: - # "vol_frac": 0.5, - # "penal": 3.0, - # "filter_radius": 1.2, - # etc. - } - - # Run the simulation + topology optimization - disp, topo_density = solids_opt_auto(data) - - # Plot results - plt.figure() - # Hypothetical function that plots the density distribution - plt.imshow(topo_density.reshape(2,2)) - plt.title("Topology Density") - plt.colorbar() - plt.show() + from solidspy_opt.optimize import ESO_stress + from solidspy_opt.utils import structure_3d, structures + + # Define the load directions and positions on the top face + load_directions_3d = np.array([ + [0, 1, 0], # Load in the Y direction + [1, 0, 0], # Load in the X direction + [0, 0, -1] # Load in the negative Z direction + ]) + load_positions_3d = np.array([ + [5, 5, 9], # Position near the center of the top face + [1, 1, 9], # Position near one corner of the top face + [8, 8, 9] # Position near another corner of the top face + ]) + + # Generate the nodes, materials, elements, loads, and BC indexes + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L=10, # length in X + H=10, # length in Y + W=10, # length in Z + E=206.8e9, # Young's modulus + v=0.28, # Poisson's ratio + nx=10, # number of divisions in X + ny=10, # number of divisions in Y + nz=10, # number of divisions in Z + dirs=load_directions_3d, + positions=load_positions_3d + ) + + # Run the ESO optimization + els_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = ESO_stress( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=200, + RR=0.005, # Initial removal ratio + ER=0.05, # Removal ratio increment + volfrac=0.5, # Target volume fraction + plot=True, # Whether to plot with solidspy's 3D plot function + dim_problem=3, + nnodes=8 # 8-node hexahedron + ) Save the script (for example, as ``example_solidspy_opt.py``) and run it: @@ -184,14 +158,14 @@ A BibTeX entry for LaTeX users might look like: .. code:: bibtex @software{solidspy_opt, - title = {SolidsPy-Opt: 2D-Finite Element and Topology Optimization Analysis with Python}, + title = {SolidsPy-Opt: 2D/3D-Finite Element and Topology Optimization Analysis with Python}, author = {Sepúlveda-García, Kevin and Guarin-Zapata, Nicolas}, - year = 2024, + year = 2025, version = {0.1.0}, keywords = {finite-elements, scientific-computing, deep learning, topology, optimization}, license = {MIT License}, url = {https://github.com/AppliedMechanics-EAFIT/SolidsPy-Opt}, abstract = {SolidsPy-Opt is a Python package designed to perform - topology optimization of 2D solids by leveraging - finite-element methods and advanced computational tools.} + topology optimization of 2D/3D solids by leveraging SolidsPy + finite-element package and advanced computational tools.} } diff --git a/assets/anim1.gif b/assets/anim1.gif new file mode 100644 index 0000000..8e25677 Binary files /dev/null and b/assets/anim1.gif differ diff --git a/assets/anim2.gif b/assets/anim2.gif new file mode 100644 index 0000000..359322c Binary files /dev/null and b/assets/anim2.gif differ diff --git a/docs/advanced.rst b/docs/advanced.rst deleted file mode 100644 index 1b19301..0000000 --- a/docs/advanced.rst +++ /dev/null @@ -1,12 +0,0 @@ -Advanced tutorials -==================== - -Here we show some advanced tutorials for SolidsPy. - -.. toctree:: - :maxdepth: 2 - :caption: Contents: - - advanced/membrane_vibration - - diff --git a/docs/advanced/img/membrane_eigs.png b/docs/advanced/img/membrane_eigs.png deleted file mode 100644 index b51672c..0000000 Binary files a/docs/advanced/img/membrane_eigs.png and /dev/null differ diff --git a/docs/advanced/img/membrane_mode1.png b/docs/advanced/img/membrane_mode1.png deleted file mode 100644 index e6c5fd7..0000000 Binary files a/docs/advanced/img/membrane_mode1.png and /dev/null differ diff --git a/docs/advanced/membrane_vibration.rst b/docs/advanced/membrane_vibration.rst deleted file mode 100644 index ee500c1..0000000 --- a/docs/advanced/membrane_vibration.rst +++ /dev/null @@ -1,278 +0,0 @@ -Creation of new elements -======================== - -SolidsPy supports user elements, that is, you can pass a function that -returns the mass and stiffness matrices for your element to the assembly -operator. - -This example shows how to create an element for membrane deflection. - -Equation to solve ------------------ - -We want to find the vibration modes of vibration modes of a thin -membrane. This is described by the Helmholtz equation - -.. math:: \nabla^2 u + k^2 u = 0\quad \forall \mathbf{x} \in \Omega\, . - -The weak form for this problem is - -.. math:: - - - \int_\Omega \nabla u \cdot \nabla u \mathrm{d}\Omega - = k^2 \int_\Omega u^2 \mathrm{d}\Omega\, . - -And the discretized system is given by - -.. math:: [K]\{U\} = k^2[M]\{U\}\, . - -The following snippets assume that the following imports are made. - -.. code:: ipython3 - - import numpy as np - import matplotlib.pyplot as plt - from scipy.sparse.linalg import eigsh - import meshio - import solidspy.assemutil as ass - import solidspy.femutil as fem - import solidspy.gaussutil as gau - import solidspy.postprocesor as pos - -Elemental matrices ------------------- - -We approximate the solution as - -.. math:: u \approx \mathbf{N}^T \mathbf{u}\, , - -where :math:`\mathbf{N}^T = [N_0(x, y), N_1(x, y), \cdots, N_n(x, y)]` -is the matrix with interpolators, -:math:`\mathbf{u}^T = [u_0(x, y), u_1(x, y), \cdots, u_n(x, y)]` the -matrix with displacements, and :math:`n` is the number of nodes in each -element. - -The local mass and stiffness matrices are given by - -.. math:: - - \begin{align} - &[M_e] = \int_{\Omega_e} \mathbf{N} \mathbf{N}^T \mathrm{d}x \mathrm{d}y\, ,\\ - &[K_e] = \int_{\Omega_e} \mathbf{B} \mathbf{B}^T \mathrm{d}x \mathrm{d}y\, , - \end{align} - -:math:`\mathbf{B}` is the matrix with the gradient of function at each -node. - -The function ``acoust_diff`` returns the interpolation matrix -:math:`\mathbf{N}`, the interpolation derivatives matrix -:math:`\mathbf{B}`, and determinant for an element evaluated at a point -in local coordinates :math:`(r, s)`. - -.. code:: ipython3 - - def acoust_diff(r, s, coord, element): - """ - Interpolation matrices for elements for acoustics - - Parameters - ---------- - r : float - Horizontal coordinate of the evaluation point. - s : float - Vertical coordinate of the evaluation point. - coord : ndarray (float) - Coordinates of the element. - - Returns - ------- - H : ndarray (float) - Array with the shape functions evaluated at the point (r, s) - for each degree of freedom. - B : ndarray (float) - Array with the gradient matrix evaluated - at the point (r, s). - det : float - Determinant of the Jacobian. - """ - N, dNdr = element(r, s) - N.shape = 1, N.shape[0] - det, jaco_inv = fem.jacoper(dNdr, coord) - dNdx = jaco_inv @ dNdr - return N, dNdx, det - -Using the function ``acoust_diff`` we could compute local mass and -stiffness matrices. The function ``acoust_tri6`` returns these local -matrices for a quadratic triangular element (6 nodes). As input -arguments is take the coordinates of the nodes and material parameters, -speed of the wave in this case. - -.. code:: ipython3 - - def acoust_tri6(coord, params): - """ - Triangular element with 6 nodes for acoustics under - axisymmetric conditions. - - Parameters - ---------- - coord : coord - Coordinates of the element. - params : list - List with material parameters in the following order: - [Speed]. - - Returns - ------- - stiff_mat : ndarray (float) - Local stifness matrix. - mass_mat : ndarray (float) - Local mass matrix. - """ - - speed = params - stiff_mat = np.zeros((6, 6)) - mass_mat = np.zeros((6, 6)) - gpts, gwts = gau.gauss_tri(order=3) - for cont in range(gpts.shape[0]): - r = gpts[cont, 0] - s = gpts[cont, 1] - H, B, det = acoust_diff(r, s, coord, fem.shape_tri6) - factor = det * gwts[cont] - stiff_mat += 0.5 * speed**2 * factor * (B.T @ B) - mass_mat += 0.5 * factor * (H.T @ H) - return stiff_mat, mass_mat - -Assembly of system of equations -------------------------------- - -We need to read the mesh that is in the file ``square.msh``. - -.. code:: ipython3 - - mesh = meshio.read("square.msh") - points = mesh.points - cells = mesh.cells - tri6 = cells["triangle6"] - line3 = cells["line3"] - npts = points.shape[0] - nels = tri6.shape[0] - -We define the nodes array. - -.. code:: ipython3 - - nodes = np.zeros((npts, 3)) - nodes[:, 1:] = points[:, 0:2] - -And the constraints array. - -.. code:: ipython3 - - line_nodes = list(set(line3.flatten())) - cons = np.zeros((npts, 1), dtype=int) - cons[line_nodes, :] = -1 - -For the elements array we don’t need to use the first three columns -since we are going to tell the assembly function to use our own function -to compute the matrices. - -.. code:: ipython3 - - elements = np.zeros((nels, 9), dtype=int) - elements[:, 1] = 2 - elements[:, 3:] = tri6 - -.. code:: ipython3 - - mats = np.array([[1.0]]) - -.. code:: ipython3 - - assem_op, bc_array, neq = ass.DME(cons, elements, - ndof_node=1, ndof_el_max=6) - -.. code:: ipython3 - - stiff_mat, mass_mat = ass.assembler(elements, mats, nodes, neq, - assem_op, uel=acoust_tri6) - -Solution of the eigenvalue problem ----------------------------------- - -.. code:: ipython3 - - eigvals, eigvecs = eigsh(stiff_mat, M=mass_mat, k=10, which="LM", - sigma=1e-6) - eigvals - - -.. code:: - - array([ 2.00000007, 5.00000066, 5.0000012 , 8.0000045 , 10.00000638, - 10.00000638, 13.00001214, 13.00002403, 17.00002827, 17.00002928]) - - - -This problem has as analytical solution - -.. math:: k^2 = m^2 + n^2\quad \forall m, n\in \mathbb{N}\, . - -.. code:: ipython3 - - eigvals_exact = np.array(sorted([m**2 + n**2 - for m in range(1, 10) - for n in range(1, 10)])[:10]) - eigvals_exact - - -.. code:: - - array([ 2, 5, 5, 8, 10, 10, 13, 13, 17, 17]) - -We can compare them in a plot. - -.. code:: ipython3 - - plt.plot(eigvals_exact, "ko") - plt.plot(eigvals, "r.") - plt.xlabel("Eigenvalue number") - plt.ylabel("Eigenvale") - -.. figure:: img/membrane_eigs.png - :alt: Analytic vs. numerical results. - :width: 800 px - - -Visualization -------------- - -Let us visualize the first vibration mode. For that we first need to -complete the solution vector with ``pos.complete_disp`` and then -``pos.plot_node_field``. - -.. code:: ipython3 - - sol = pos.complete_disp(bc_array, nodes, eigvecs[:, 0], ndof_node=1) - -.. code:: ipython3 - - pos.plot_node_field(sol[:, 0], nodes, elements) - -.. figure:: img/membrane_mode1.png - :alt: First vibration mode for the membrane. - :width: 800 px - -Finally, we can complete all the eigenvectors and export the results to -a VTK file. - -.. code:: ipython3 - - for cont in range(10): - aux = pos.complete_disp(bc_array, nodes, eigvecs[:, cont], - ndof_node=1) - mesh.point_data["mode_%d" % cont] = aux - - meshio.write("membrane.vtk", mesh) - diff --git a/docs/conf.py b/docs/conf.py index 35be3c7..62cb8fc 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -71,7 +71,7 @@ # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. -language = None +language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. diff --git a/docs/index.rst b/docs/index.rst index e4b7c99..73ef95b 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -3,7 +3,7 @@ You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. -Welcome to SolidsPy's documentation! +Welcome to SolidsPy-Opt's documentation! ==================================== .. toctree:: @@ -14,14 +14,12 @@ Welcome to SolidsPy's documentation! tutorial installation usage - advanced contributing authors modules history - Indices and tables ================== diff --git a/docs/installation.rst b/docs/installation.rst index 7ff6542..d0cbda2 100644 --- a/docs/installation.rst +++ b/docs/installation.rst @@ -1,25 +1,100 @@ Installation ============ -The code is written in Python and it depends on ``numpy``, ``scipy`` and -``sympy``. It has been tested under Windows, Mac, Linux and Android. +This page describes how to install **SolidsPy-Opt** and its dependencies. -To install *SolidsPy* open a terminal and type: -:: +Basic Installation +------------------ - pip install solidspy +If you already have Python 3.8+ and the standard scientific stack (Numpy, Scipy, etc.) installed, you can install **SolidsPy-Opt** from the Python Package Index (PyPI) with: -To specify through a GUI the folder where the input -files are stored you will need to install `easygui `__. +.. code-block:: bash -To easily generate the required SolidsPy text files out of a -`Gmsh `__ model you will need -`meshio `__. + pip install solidspy-opt -These two can be installed with: +This will download and install the package along with any missing dependencies. -:: +Alternatively, you can install **SolidsPy-Opt** into a **virtual environment** (via `venv` or `conda` environments) to keep dependencies isolated: - pip install easygui - pip install meshio +.. code-block:: bash + + python -m venv venv + source venv/bin/activate + pip install --upgrade pip + pip install solidspy-opt + + +Optional Dependencies +--------------------- + +**SolidsPy-Opt** relies on some key packages for full functionality: + +- **`numpy`** (Array computations) +- **`scipy`** (Sparse linear algebra, solver utilities) +- **`matplotlib`** (Plotting, visualizations) +- **`meshio`** (Reading/writing Gmsh and other mesh formats, pinned at version 5.3.5) +- **`tensorflow`** (Potential usage in advanced or neural-based workflows) +- **`easygui`** (GUI usage in some interactive features) + +Some of these are optional, but recommended for a complete experience. By default, installing from PyPI attempts to install them if they are not present. + +If you need to generate complex geometries or 3D meshes, ensure that **`meshio`** is installed: + +.. code-block:: bash + + pip install meshio==5.3.5 + + +Development Installation +------------------------ + +If you want the **latest** code or to contribute, clone the GitHub repository and install in editable mode: + +.. code-block:: bash + + git clone https://github.com/AppliedMechanics-EAFIT/SolidsPy-Opt.git + cd SolidsPy-Opt + pip install --upgrade pip setuptools wheel + pip install -e . + +This will link your local copy so that any changes you make are immediately reflected in the installed package. + + +Installing from Test PyPI +------------------------- + +If you have a **test** version of **SolidsPy-Opt** or a custom fork (e.g., ``SolidsPyKevin``) published on Test PyPI, you can install it with: + +.. code-block:: bash + + pip install --index-url https://test.pypi.org/simple/ \ + --extra-index-url https://pypi.org/simple \ + SolidsPyKevin + +This ensures that non-Test-PyPI dependencies can still be pulled from the main PyPI index. + + +Verifying Installation +---------------------- + +After installing, open a Python shell or Jupyter notebook and try: + +.. code-block:: python + + import solidspy_opt + from solidspy_opt.optimize import ESO_stress + + print("SolidsPy-Opt installed successfully!") + +If no error is raised, your installation is ready. + + +Troubleshooting +--------------- + +- **Missing Dependencies**: Ensure that you have the correct versions of `numpy`, `scipy`, and other core libraries installed. +- **Path Issues**: If you are using a virtual environment, confirm that you have **activated** it before installing. +- **Conflicts**: Old versions of packages can lead to conflicts. Try `pip install --upgrade ` to update them. + +If you encounter any issue, please check the `GitHub Issues `_ for existing reports or open a new issue describing your problem. diff --git a/docs/modules.rst b/docs/modules.rst index f20701f..e6d61f3 100644 --- a/docs/modules.rst +++ b/docs/modules.rst @@ -3,42 +3,12 @@ SolidsPy reference SolidsPy have the following modules: - - ``solids_GUI.py``: The main program; - - ``preprocesor.py``: Pre-processing subroutines including - `Gmsh `__ convertion functions using - `meshio `__ - - ``assemutil.py``: Assembly of elemental stiffness matrices ; - - ``femutil.py``: Shape functions, its derivatives and general - finite element method subroutines; - - ``uelutil.py``: Elemental or local matrix subroutines for - different elements; and - - ``postprocesor.py``: Several results handling subroutines. + - ``models.py``: Modal analysis subroutines; + - ``optimize.py``: Optimization algorithms; -.. automodule:: solids_GUI +.. automodule:: solidspy_opt.models :members: -.. automodule:: assemutil - :members: - -.. automodule:: femutil - :members: - -.. automodule:: gaussutil - :members: - -.. automodule:: preprocesor - :members: - -.. automodule:: postprocesor - :members: - -.. automodule:: solutil - :members: - -.. automodule:: uelutil - :members: - - - - +.. automodule:: solidspy_opt.optimize + :members: \ No newline at end of file diff --git a/docs/tutorial.rst b/docs/tutorial.rst index 40f411c..c6c65e6 100644 --- a/docs/tutorial.rst +++ b/docs/tutorial.rst @@ -1,23 +1,14 @@ -SolidsPy's tutorials -==================== +Tutorials +========= -Here we show through simple examples how to conduct analyses using -SolidsPy. - -First we describe the structure of the text files for the -problem of small 2×2 square plate under axial loading. In the second part -of the documents we describe the creation of a -SolidsPy model with the aid of `Gmsh `__. This is -necessary when conducting analysis in large and complex geometries. In -this case the Gmsh files need to be converted into text files using -subroutines based upon `meshio `__. +Below is a collection of tutorials for **SolidsPy-Opt**. Each tutorial illustrates a different optimization technique and provides step-by-step instructions, along with example code. .. toctree:: :maxdepth: 2 - :caption: Contents: - - tutorials/square_example - tutorials/geometry_gmsh - tutorials/brazilian_test - + :caption: Tutorials + + tutorials/tutorial_eso_stress + tutorials/tutorial_eso_stiff + tutorials/tutorial_beso + tutorials/tutorial_simp diff --git a/docs/tutorials/brazilian_test.rst b/docs/tutorials/brazilian_test.rst deleted file mode 100644 index b02c5a0..0000000 --- a/docs/tutorials/brazilian_test.rst +++ /dev/null @@ -1,539 +0,0 @@ -========================================================================== -Geometry in Gmsh and solution with SolidsPy -========================================================================== - -:Author: Nicolás Guarín-Zapata -:Date: September, 2018 - -This document is a tutorial on how to generate a (specific) geometry -using Gmsh [Gmsh2009]_ and its subsequent processing for the generation -of input files for a Finite Element program in Python. This document -does not pretend to be an introduction to the management of Gmsh, -for this we suggest the official tutorial [Gmsh_tut]_ -(for text mode) or the official screencasts [Gmsh_scr]_ -(for the graphical interface). - -Model -===== - -The example to be solved corresponds to the determination of -Efforts in a cylinder in the *Brazilian Test*. The Brazilian Test -is a technique that is used for the indirect measurement of the resistance of -rocks It is a simple and effective technique, and therefore it is commonly used -for rock measurements. Sometimes this test is also used -for concrete [D3967-16]_. - -The following figure presents a scheme of the model to solve. Since the -original model may present rigid body movements, it -decides to use the symmetry of the problem. Then, the problem to -solve is a quarter of the original problem and the surfaces lower e -left present restrictions of *roller*. - -.. figure:: img/Prueba_brasilera.svg - :alt: Schematic of the problem to be solved. - :width: 400 px - - Schematic of the problem to be solved. - -Creation of the geometry and mesh in Gmsh -========================================= - -As a first step, it is suggested to create a new file in Gmsh, as -It shows in the following figure. - -.. figure:: img/Nuevo_archivo.png - :alt: Creation of a new file in Gmsh. - :width: 800 px - - Creation of a new file in Gmsh. - -When creating a new document it is possible [1]_ for Gmsh to ask about which -geometry kernel to use. We will not dwell on what the differences are -and we will use ``built-in``. - -.. figure:: img/Motor_geometrico.png - :alt: Pop-up window asking for the geometry kernel. - :width: 400 px - - Pop-up window asking for the geometry kernel. - -To create a model, we initially create the points. For that, let's go -to the option: ``Geometry> Elementary Entities> Add> Point``, as -shown in the following figure. Then, the coordinates of the -points in the pop-up window and "Add". Finally we can close the -pop-up window and press ``e``. - -.. figure:: img/Agregar_puntos.png - :alt: Agregar puntos al modelo. - :width: 800 px - - Agregar puntos al modelo. - -Later we create lines. For this, we go to the option: -`` Geometry> Elementary Entities> Add> Straight line``, as -shown in the following figure, and we select the initial points and -endings for each line. At the end, we can press ``e``. - -.. figure:: img/Agregar_lineas.png - :alt: Add straight lines to the model. - :width: 800 px - - Add straight lines to the model. - -We also create the circle arcs. For this, we go to the -option: ``Geometry> Elementary Entities> Add> Circle Arc``, as -shown in the following figure, and we select the initial points, -central and final for each arc (in that order). At the end, we can -press ``e``. - -.. figure:: img/Agregar_arcos.png - :alt: Add arcs to the model. - :width: 800 px - - Add arcs to the model. - -Since we already have a closed contour, we can define a surface. -For this, we go to the option: -``Geometry> Elementary Entities> Add> Plane Surface``, as -shown in the following figure, and we select the contours in order. -At the end, we can press `` e``. - -.. figure:: img/Agregar_superficie.png - :alt: Add surfaces. - :width: 800 px - - Add surfaces. - -Now, we need to define *physical groups*. Physical groups allow us to -associate names to different parts of the model such as lines and -surfaces. This will allow us to define the region in which we will resolve -the model (and we will associate a material), the regions that have -restricted movements (boundary conditions) and the regions -on which we will apply the load. In our case we will have 4 groups -physical: - -- Region of the model, where we will define a material; - -- Bottom edge, where we will restrict the displacement in :math:`y`; - -- Left edge, where we will restrict the displacement in :math:`x`; and - -- Top point, where we will apply the point load. - -To define the physical groups we are going to -``Geometry> Physical groups> Add> Plane Surface``, as shown in the -next figure. In this case, we can leave the field of `` Name`` empty -and allow Gmsh to name the groups for us, which will be -numbers that we can then consult in the text file - -.. figure:: img/Agregar_linea_fisica.png - :alt: Add physical groups. - :width: 800 px - - Add physical groups. - -After (slightly) editing the text file (``.geo``) this looks like this - -.. code:: C - - L = 0.1; - - // Points - Point(1) = {0, 0, 0, L}; - Point(2) = {1, 0, 0, L}; - Point(3) = {0, 1, 0, L}; - - // Lines - Line(1) = {3, 1}; - Line(2) = {1, 2}; - Circle(3) = {2, 1, 3}; - - // Surfaces - Line Loop(1) = {2, 3, 1}; - Plane Surface(1) = {1}; - - // Physical groups - Physical Line(1) = {1}; - Physical Line(2) = {2}; - Physical Point(3) = {3}; - Physical Surface(4) = {1}; - -We added a parameter ``L``, which we can vary to -to change the size of the elements when creating the -mesh. - -Now, we proceed to create the mesh. To do this, we go to ``Mesh> 2D``. -As we see in the figure below. - -.. figure:: img/Mallar_2D.png - :alt: Create the mesh. - :width: 800 px - - Create the mesh. - -Additionally, we can change the configuration so that it shows the elements -of the mesh in colors. For this, we are going to -``Tools> Options> Mesh`` and mark the box that indicates -``Surface faces``. - -.. figure:: img/Ver_superficie_malla.png - :alt: Create the mesh. - :width: 800 px - - Create the mesh. - -We can then refine the mesh going to -``Mesh> Refine by Splitting``, or by modifying the ``L`` parameter in the -input file (.geo). As a last step, we want to save the mesh. -To do this, go to ``Mesh> Save``, or ``File> Save Mesh``, as -shows below. - -.. figure:: img/Guardar_malla.png - :alt: Save the ``.msh`` file. - :width: 800 px - - Save the ``.msh`` file. - -Python script to generate input files -===================================== - -We need to create files with the information of the nodes (``nodes.txt``), -elements (``eles.txt``), loads (``loads.txt``) and materials -(``mater.txt``). - -The following code generates the necessary input files for -Run the finite element program in Python. - -.. code-block:: python - - import meshio - import numpy as np - - mesh = meshio.read("Prueba_brasilera.msh") - points = mesh.points - cells = mesh.cells - point_data = mesh.point_data - cell_data = mesh.cell_data - - # Element data - eles = cells["triangle"] - els_array = np.zeros([eles.shape[0], 6], dtype=int) - els_array[:, 0] = range(eles.shape[0]) - els_array[:, 1] = 3 - els_array[:, 3::] = eles - - # Nodes - nodes_array = np.zeros([points.shape[0], 5]) - nodes_array[:, 0] = range(points.shape[0]) - nodes_array[:, 1:3] = points[:, :2] - - # Boundaries - lines = cells["line"] - bounds = cell_data["line"]["gmsh:physical"] - nbounds = len(bounds) - - # Loads - id_cargas = cells["vertex"] - nloads = len(id_cargas) - load = -10e8 # N/m - loads_array = np.zeros((nloads, 3)) - loads_array[:, 0] = id_cargas - loads_array[:, 1] = 0 - loads_array[:, 2] = load - - # Boundary conditions - id_izq = [cont for cont in range(nbounds) if bounds[cont] == 1] - id_inf = [cont for cont in range(nbounds) if bounds[cont] == 2] - nodes_izq = lines[id_izq] - nodes_izq = nodes_izq.flatten() - nodes_inf = lines[id_inf] - nodes_inf = nodes_inf.flatten() - nodes_array[nodes_izq, 3] = -1 - nodes_array[nodes_inf, 4] = -1 - - # Materials - mater_array = np.array([[70e9, 0.35], - [70e9, 0.35]]) - maters = cell_data["triangle"]["gmsh:physical"] - els_array[:, 2] = [1 for mater in maters if mater == 4] - - # Create files - np.savetxt("eles.txt", els_array, fmt="%d") - np.savetxt("nodes.txt", nodes_array, - fmt=("%d", "%.4f", "%.4f", "%d", "%d")) - np.savetxt("loads.txt", loads_array, fmt=("%d", "%.6f", "%.6f")) - np.savetxt("mater.txt", mater_array, fmt="%.6f") - - -Now, let's discuss the different parts of the code to see what it does -each. - -Header and reading the ``.msh`` file ------------------------------------- - -The first part loads the necessary Python modules and reads the file -of mesh that in this case is called ``Prueba_brasilera.msh`` (line 6 and -7). In order for Python to be able to read the file, it must be in the -same directory as the Python file that will process it. - -.. code:: python - - import meshio - import numpy as np - - - mesh = meshio.read("Prueba_brasilera.msh") - points = mesh.points - cells = mesh.cells - point_data = mesh.point_data - cell_data = mesh.cell_data - -Element data ------------- - -The next section of the code creates the data for elements. The line -18 creates a variable `` eles`` with the information of the nodes that -make up each triangle. Line 11 creates an array (filled with zeros) -with the number of rows equal to the number of elements -(``eles.shape[0]``) and 6 columns [2]_. Then we assign a number to -each element, what we do on line 12 with ``range(eles.shape[0])`` -and this we assign to column 0. All -elements are triangles, that's why we should put 3 in column 1. Last, -in this section, we assign the nodes of each element to the array -with (line 19), and this assignment is made from column 3 to -final with ``els_array[:, 3::]``. - -.. code:: python - - # Element data - eles = cells["triangle"] - els_array = np.zeros([eles.shape[0], 6], dtype=int) - els_array[:, 0] = range(eles.shape[0]) - els_array[:, 1] = 3 - els_array[:, 3::] = eles - -Nodes data ----------- - -In the next section we create the information related to the -nodes. To do this, on line 17 we created an array ``nodes_array`` -with 5 columns and as many rows as there are points in the model -(``points.shape[0]``). Then, we assign the -element type on line 18. And finally, we assign the -information on the coordinates of the nodes on line 19 with -``nodes_array[:, 1:3] = points[:, :2]``, where we are adding the -information in columns 1 and 2. - -.. code:: python - - # Nodes - nodes_array = np.zeros([points.shape[0], 5]) - nodes_array[:, 0] = range(points.shape[0]) - nodes_array[:, 1:3] = points[:, :2] - -Boundary data -------------- - -In the next section we find the line information. For this, -we read the ``cells`` information in position ``line`` [3]_ -(line 22). The array ``lines`` -will then have the information of the nodes that form each -line that is on the border of the model. Then, we read the information -of the physical lines (line 23), and we calculate how many lines belong -to the physical lines (line 24). - -.. code:: python - - # Boundaries - lines = cells["line"] - bounds = cell_data["line"]["gmsh:physical"] - nbounds = len(bounds) - -Load data ---------- - -In the next section we must define the information of loads. -In this case, the loads are assigned in a single point that we define as a -physical group. On line 27 we read the nodes (in this case, one). -Then, we create an array that has as many rows as loads (``nloads``) and 3 -columns Assign the number of the node to which each load belongs -(line 31), the charges in :math: `x` (line 32) and the loads in :math:`y` and -(line 33) - -.. code:: python - - # Loads - id_cargas = cells["vertex"] - nloads = len(id_cargas) - load = -10e8 # N/m - loads_array = np.zeros((nloads, 3)) - loads_array[:, 0] = id_cargas - loads_array[:, 1] = 0 - loads_array[:, 2] = load - -Boundary conditions -------------------- - -Now, we will proceed to apply the boundary conditions, that is, the -model regions that have restrictions on displacements. -Initially, we identify which lines have an identifier 1 -(which would be the left side) with - -.. code:: python - - id_izq = [cont for cont in range(nbounds) if bounds[cont] == 1] - -This creates a list with the numbers (``cont``) for which the -condition (``bounds[cont] == 1``). On line 46 we get the nodes that belong to -these lines, however, this array has as many rows as lines -on the left side and two columns. First we return this array as -a one-dimensional array with ``nodes_izq.flatten()``. Later, on line 42, -we assign the value of -1 in the third column of the array for -nodes that belong to the left side. In the same way, this process -is repeated for the nodes at the bottom line. - -.. code:: python - - # Boundary conditions - id_izq = [cont for cont in range(nbounds) if bounds[cont] == 1] - id_inf = [cont for cont in range(nbounds) if bounds[cont] == 2] - nodes_izq = lines[id_izq] - nodes_izq = nodes_izq.flatten() - nodes_inf = lines[id_inf] - nodes_inf = nodes_inf.flatten() - nodes_array[nodes_izq, 3] = -1 - nodes_array[nodes_inf, 4] = -1 - -Materials ---------- - -In the next section we assign the corresponding materials to each -element. In this case, we only have one material. However, it -present the example as if there were two different ones. First, we created a -array with the material information where the first column -represents the Young's module and the second the Poisson's relation (line -46). Then, we read the information of the physical groups of surfaces -on line 48. Finally, we assign the value of 0 to the materials that -have as physical group 4 (see file ``.geo`` above) and 1 to the -others, which in this case will be zero (line 49). This information goes in the -column 2 of the arrangement. - -.. code:: python - - # Materials - mater_array = np.array([[70e9, 0.35], - [70e9, 0.35]]) - maters = cell_data["triangle"]["gmsh:physical"] - els_array[:, 2] = [1 for mater in maters if mater == 4] - -Export files ------------- - -The last section uses the ``numpy`` function to export the -files. - -.. code:: python - - # Create files - np.savetxt("eles.txt", els_array, fmt="%d") - np.savetxt("nodes.txt", nodes_array, - fmt=("%d", "%.4f", "%.4f", "%d", "%d")) - np.savetxt("loads.txt", loads_array, fmt=("%d", "%.6f", "%.6f")) - np.savetxt("mater.txt", mater_array, fmt="%.6f") - -Solution using SolidsPy -======================= - -To solve the model, we can type [4]_ - -.. code:: python - - from solidspy import solids_GUI - disp = solids_GUI() - -After running this program it will appear -a pop-up window as shown below. In this window -the directory we should locate the folder with the input files -generated previously. Keep in mind that the appearance of -this window may vary between operating systems. Also, we have -notef that sometimes the pop-up window may be hidden -by other windows on your desktop. - -.. figure:: img/solids_GUI-ventana.png - :alt: Pop-up window to locate folder with input files. - :width: 600 px - - Pop-up window to locate folder with input files. - - -At this point, the program must solve the model. If the -input files are used without modifications the program should print -a message similar to the following. - -:: - - Number of nodes: 123 - Number of elements: 208 - Number of equations: 224 - Duration for system solution: 0:00:00.086983 - Duration for post processing: 0:00:00 - Analysis terminated successfully! - -the times taken to solve the system can change a bit -from one computer to another. - -As a last step, the program generates graphics with the fields of -displacements, deformations and stresses, as shown in the -next figures. - -.. figure:: img/Prueba_brasilera_ux.svg - :alt: Horizontal displacement. - :width: 400 px - - Horizontal displacement. - -.. figure:: img/Prueba_brasilera_uy.svg - :alt: Vertical displacement. - :width: 400 px - - Vertical displacement. - -References -========== - -.. [D3967-16] - ASTM D3967–16 (2016), Standard Test Method for Splitting Tensile - Strength of Intact Rock Core Specimens, ASTM - International, `www.astm.org `__. - -.. [Gmsh2009] - Geuzaine, Christophe, y Jean-François Remacle (2009), *Gmsh: A 3-D - finite element mesh generator with built-in pre-and post-processing - facilities*. International Journal for Numerical Methods in Engineering, - 79.11. - -.. [Gmsh_tut] - Geuzaine, Christophe, y Jean-François Remacle (2017), Gmsh Official - Tutorial. Accessed: April 18, 2018 - http://gmsh.info/doc/texinfo/gmsh.html#Tutorial. - -.. [Gmsh_scr] - Geuzaine, Christophe, y Jean-François Remacle (2017), Gmsh Official - Screencasts. Accessed: April 18, 2018de - http://gmsh.info/screencasts/. - - -.. [1] - If the version is 3.0 or higher, this pop-up window will appear. - -.. [2] - For quadrilateral elements, 7 columns would be used, since each - Element is defined by 4 nodes. - -.. [3] - ``cells`` is a dictionary and allows to store information associated - with some keywords, in this case it is ``lines``. - -.. [4] - To make use of the graphical interface it must be installed - ``easygui``. diff --git a/docs/tutorials/geometry_gmsh.rst b/docs/tutorials/geometry_gmsh.rst deleted file mode 100644 index 552b793..0000000 --- a/docs/tutorials/geometry_gmsh.rst +++ /dev/null @@ -1,54 +0,0 @@ -Creation of a simple geometry using Gmsh -======================================== - -:Author: Juan Gómez -:Date: October 2017 - -We want to create a mesh for the following geometry - -.. figure:: ../img/template_schematic.png - :alt: Bilayer model. - - Bilayer model. - -The ``.geo`` file for this model is the following - -.. code:: c - - // Parameters - L = 2.0; - H = 1.0; - h_1 = H/2; - h_2 = H/2; - lado_elem = 0.1; - - - // Points - Point(1) = {0.0, 0.0, 0, lado_elem}; - Point(2) = {L, 0.0, 0, lado_elem}; - Point(3) = {L, h_2, 0, lado_elem}; - Point(4) = {L, H, 0, lado_elem}; - Point(5) = {0, H, 0, lado_elem}; - Point(6) = {0, h_2, 0, lado_elem}; - - // Lines - Line(1) = {1, 2}; - Line(2) = {2, 3}; - Line(3) = {3, 4}; - Line(4) = {4, 5}; - Line(5) = {5, 6}; - Line(6) = {6, 1}; - Line(7) = {3, 6}; - - // Surfaces - Line Loop(8) = {1, 2, 7, 6}; - Plane Surface(9) = {8}; - Line Loop(10) = {-7, 5, 4, 3}; - Plane Surface(11) = {10}; - - // Physical groups - Physical Surface(100) = {9}; // Material superior - Physical Surface(200) = {11}; // Material inferior - Physical Line(300) = {5, 6, 3, 2}; // Lineas laterales - Physical Line(400) = {1}; // Linea inferior - Physical Line(500) = {4}; // Linea superior (cargas) diff --git a/docs/tutorials/img/Agregar_arcos.png b/docs/tutorials/img/Agregar_arcos.png deleted file mode 100644 index a27bc04..0000000 Binary files a/docs/tutorials/img/Agregar_arcos.png and /dev/null differ diff --git a/docs/tutorials/img/Agregar_linea_fisica.png b/docs/tutorials/img/Agregar_linea_fisica.png deleted file mode 100644 index c2288aa..0000000 Binary files a/docs/tutorials/img/Agregar_linea_fisica.png and /dev/null differ diff --git a/docs/tutorials/img/Agregar_lineas.png b/docs/tutorials/img/Agregar_lineas.png deleted file mode 100644 index 168d7d9..0000000 Binary files a/docs/tutorials/img/Agregar_lineas.png and /dev/null differ diff --git a/docs/tutorials/img/Agregar_puntos.png b/docs/tutorials/img/Agregar_puntos.png deleted file mode 100644 index ccd10fb..0000000 Binary files a/docs/tutorials/img/Agregar_puntos.png and /dev/null differ diff --git a/docs/tutorials/img/Agregar_superficie.png b/docs/tutorials/img/Agregar_superficie.png deleted file mode 100644 index 0fae68e..0000000 Binary files a/docs/tutorials/img/Agregar_superficie.png and /dev/null differ diff --git a/docs/tutorials/img/Guardar_malla.png b/docs/tutorials/img/Guardar_malla.png deleted file mode 100644 index 3d10822..0000000 Binary files a/docs/tutorials/img/Guardar_malla.png and /dev/null differ diff --git a/docs/tutorials/img/Mallar_2D.png b/docs/tutorials/img/Mallar_2D.png deleted file mode 100644 index 7ce058c..0000000 Binary files a/docs/tutorials/img/Mallar_2D.png and /dev/null differ diff --git a/docs/tutorials/img/Motor_geometrico.png b/docs/tutorials/img/Motor_geometrico.png deleted file mode 100644 index 0ff3589..0000000 Binary files a/docs/tutorials/img/Motor_geometrico.png and /dev/null differ diff --git a/docs/tutorials/img/Nuevo_archivo.png b/docs/tutorials/img/Nuevo_archivo.png deleted file mode 100644 index b391da1..0000000 Binary files a/docs/tutorials/img/Nuevo_archivo.png and /dev/null differ diff --git a/docs/tutorials/img/Prueba_brasilera.pdf b/docs/tutorials/img/Prueba_brasilera.pdf deleted file mode 100644 index 4583d02..0000000 Binary files a/docs/tutorials/img/Prueba_brasilera.pdf and /dev/null differ diff --git a/docs/tutorials/img/Prueba_brasilera.svg b/docs/tutorials/img/Prueba_brasilera.svg deleted file mode 100644 index c3a8d81..0000000 --- a/docs/tutorials/img/Prueba_brasilera.svg +++ /dev/null @@ -1,259 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - image/svg+xml - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q - Q - Q - - diff --git a/docs/tutorials/img/Prueba_brasilera_ux.svg b/docs/tutorials/img/Prueba_brasilera_ux.svg deleted file mode 100644 index d2fb3b4..0000000 --- a/docs/tutorials/img/Prueba_brasilera_ux.svg +++ /dev/null @@ -1,408 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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-Until version 1.2.8 the data for a simulation was stored in 4 files - -- ``nodes.txt`` - -- ``eles.txt`` - -- ``mater.txt`` - -- ``loads.txt`` - -As shown below. - -- ``nodes.txt`` - -:: - - 0 0.00 0.00 0 -1 - 1 2.00 0.00 0 -1 - 2 2.00 2.00 0 0 - 3 0.00 2.00 0 0 - 4 1.00 0.00 -1 -1 - 5 2.00 1.00 0 0 - 6 1.00 2.00 0 0 - 7 0.00 1.00 0 0 - 8 1.00 1.00 0 0 - -- ``eles.txt`` - -:: - - 0 1 0 0 4 8 7 - 1 1 0 4 1 5 8 - 2 1 0 7 8 6 3 - 3 1 0 8 5 2 6 - -- ``mater.txt`` - -:: - - 1.0 0.3 - -- ``loads.txt`` - -:: - - 3 0.0 1.0 - 6 0.0 2.0 - 2 0.0 1.0 - -Run it in Python as follows: - -.. code:: python - - import matplotlib.pyplot as plt # load matplotlib - from solidspy import solids_GUI # import our package - disp = solids_GUI() # run the Finite Element Analysis - plt.show() # plot contours \ No newline at end of file diff --git a/docs/tutorials/square_example.rst b/docs/tutorials/square_example.rst deleted file mode 100644 index 70571eb..0000000 --- a/docs/tutorials/square_example.rst +++ /dev/null @@ -1,197 +0,0 @@ -Start here: 2×2 square with axial load -====================================== - -:Author: Nicolás Guarín-Zapata -:Date: May, 2017 - -In this document we briefly describe the use of SolidsPy, through a -simple example corresponding to a square plate under point loads. - -Input files ------------ - -The code requires the domain to be input in the form of text files -containing the nodes, elements, loads and material information. These -files must reside in the same directory and must have the names -``eles.txt``, ``nodes.txt``, ``mater.txt`` and ``loads.txt``. Assume -that we want to find the response of the 2×2 square under unitary -vertical point loads shown in the following figure. Where one corner is -located at (0,0) and the opposite one at (2,2). - -.. figure:: ../img/square-4_elements.png - :alt: 4-element solid under point loads. - - 4-element solid under point loads. - -The file ``nodes.txt`` is composed of the following fields: - -- Column 0: Nodal identifier (integer). -- Column 1: x-coordinate (float). -- Column 2: y-coordinate (float). -- Column 3: Boundary condition flag along the x-direction (0 free, -1 - restrained). -- Column 4: Boundary condition flag along the y-direction (0 free, -1 - restrained). - -The corresponding file has the following data - -:: - - 0 0.00 0.00 0 -1 - 1 2.00 0.00 0 -1 - 2 2.00 2.00 0 0 - 3 0.00 2.00 0 0 - 4 1.00 0.00 -1 -1 - 5 2.00 1.00 0 0 - 6 1.00 2.00 0 0 - 7 0.00 1.00 0 0 - 8 1.00 1.00 0 0 - -The file ``eles.txt`` contain the element information. Each line in the -file defines the information for a single element and is composed of the -following fields: - -- Column 0: Element identifier (integer). -- Column 1: Element type (integer): - - - 1 for a 4-noded quadrilateral. - - 2 for a 6-noded triangle. - - 3 for a 3-noded triangle. - -- Column 2: Material profile for the current element (integer). -- Column 3 to end: Element connectivity, this is a list of the nodes - conforming each element. The nodes should be listed in - counterclockwise orientation. - -The corresponding file has the following data - -:: - - 0 1 0 0 4 8 7 - 1 1 0 4 1 5 8 - 2 1 0 7 8 6 3 - 3 1 0 8 5 2 6 - -The file ``mater.txt`` contain the material information. Each line in -the file corresponds to a material profile to be assigned to the -different elements in the elements file. In this example, there is one -material profile. Each line in the file is composed of the following -fields: - -- Column 0: Young's modulus for the current profile (float). -- Column 1: Poisson's ratio for the current profile (float). - -The corresponding file has the following data - -:: - - 1.0 0.3 - -The file ``loads.txt`` contains the point loads information. Each line -in the file defines the load information for a single node and is -composed of the following fields - -- Column 0: Nodal identifier (integer). -- Column 1: Load magnitude for the current node along the x-direction - (float). -- Column 2: Load magnitude for the current node along the y-direction - (float). - -The corresponding file has the following data - -:: - - 3 0.0 1.0 - 6 0.0 2.0 - 2 0.0 1.0 - -Executing the program ---------------------- - -After installing the package, you can run the program in a Python -terminal using - -:: - - >>> from solidspy import solids_GUI - >>> solids_GUI() - -In Linux and you can also run the program from the terminal using - -:: - - $ python -m solidspy - -If you have ``easygui`` installed a pop-up window will appear for you to -select the folder with the input files - -.. figure:: ../img/Folder_selection.png - :width: 400px - :alt: Folder selection window. - - Folder selection window. - -select the folder and click ok. - -If you don't have ``easygui`` installed the software will ask you for -the path to your folder. The path can be absolute or relative. - -:: - - Enter folder (empty for the current one): - - -Then, you will see some information regarding your analysis - -:: - - Number of nodes: 9 - Number of elements: 4 - Number of equations: 14 - Duration for system solution: 0:00:00.006895 - Duration for post processing: 0:00:01.466066 - Analysis terminated successfully! - -And, once the solution is achieved you will see displacements and stress -solutions as contour plots, like the following - -.. image:: ../img/square-4_elements-horizontal_disp.png - :width: 400px - -.. image:: ../img/square-4_elements-vertical_disp.png - :width: 400px - - -Interactive execution -~~~~~~~~~~~~~~~~~~~~~ - -You can also run the program interactively using a Python terminal, a -good option is `IPython `__. - -In IPython you can run the program with - -.. code:: python - - In [1]: from solidspy import solids_GUI - - In [2]: UC = solids_GUI() - -After running the code we have the nodal variables for post-processing. -For example, we can print the displacement vector - -.. code:: python - - In [3]: np.set_printoptions(threshold=np.nan) - - In [4]: print(np.round(UC, 3)) - [ 0.6 -0.6 -0.6 4. 0.6 4. -0.6 2. -0. 4. 0.6 2. -0. 2. ] - -where we first setup the printing option for IPython to show the full -array and then rounded the array to 3 decimal places. - -.. code:: python - - In [5]: U_mag = np.sqrt(UC[0::2]**2 + UG[1::2]**2) - - In [6]: print(np.round(U_mag, 3)) - [ 0.849 4.045 4.045 2.088 4. 2.088 2. ] diff --git a/docs/tutorials/template.geo b/docs/tutorials/template.geo deleted file mode 100755 index 0cefe08..0000000 --- a/docs/tutorials/template.geo +++ /dev/null @@ -1,38 +0,0 @@ -// Parameters -L = 2.0; -H = 1.0; -h_1 = H/2; -h_2 = H/2; -lado_elem = 0.1; - - -// Points -Point(1) = {0.0, 0.0, 0, lado_elem}; -Point(2) = {L, 0.0, 0, lado_elem}; -Point(3) = {L, h_2, 0, lado_elem}; -Point(4) = {L, H, 0, lado_elem}; -Point(5) = {0, H, 0, lado_elem}; -Point(6) = {0, h_2, 0, lado_elem}; - -// Lines -Line(1) = {1, 2}; -Line(2) = {2, 3}; -Line(3) = {3, 4}; -Line(4) = {4, 5}; -Line(5) = {5, 6}; -Line(6) = {6, 1}; -Line(7) = {3, 6}; - -// Surfaces -Line Loop(8) = {1, 2, 7, 6}; -Plane Surface(9) = {8}; -Line Loop(10) = {-7, 5, 4, 3}; -Plane Surface(11) = {10}; - -// Physical groups -Physical Surface(100) = {9}; // Material superior -Physical Surface(200) = {11}; // Material inferior -Physical Line(300) = {5, 6, 3, 2}; // Lineas laterales -Physical Line(400) = {1}; // Linea inferior -Physical Line(500) = {4}; // Linea superior (cargas) - diff --git a/docs/tutorials/template.msh b/docs/tutorials/template.msh deleted file mode 100755 index 92ab41e..0000000 --- a/docs/tutorials/template.msh +++ /dev/null @@ -1,880 +0,0 @@ -$MeshFormat -2.2 0 8 -$EndMeshFormat -$Nodes -291 -1 0 0 0 -2 2 0 0 -3 2 0.5 0 -4 2 1 0 -5 0 1 0 -6 0 0.5 0 -7 0.09999999999979931 0 0 -8 0.1999999999996293 0 0 -9 0.2999999999994072 0 0 -10 0.3999999999991157 0 0 -11 0.4999999999988242 0 0 -12 0.5999999999985328 0 0 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-535 2 2 200 11 51 52 275 -536 2 2 200 11 213 243 263 -537 2 2 200 11 198 263 243 -538 2 2 200 11 74 255 75 -539 2 2 200 11 45 46 256 -540 2 2 200 11 196 237 284 -541 2 2 200 11 204 265 231 -542 2 2 200 11 212 234 260 -543 2 2 200 11 214 261 235 -544 2 2 200 11 204 231 275 -545 2 2 200 11 51 275 231 -546 2 2 200 11 195 241 257 -547 2 2 200 11 196 258 242 -548 2 2 200 11 70 279 71 -549 2 2 200 11 189 284 237 -550 2 2 200 11 49 50 272 -551 2 2 200 11 72 273 73 -552 2 2 200 11 47 48 274 -553 2 2 200 11 198 242 263 -554 2 2 200 11 216 281 271 -555 2 2 200 11 206 271 281 -556 2 2 200 11 207 274 289 -557 2 2 200 11 209 273 287 -558 2 2 200 11 208 288 272 -559 2 2 200 11 4 34 291 -560 2 2 200 11 4 291 33 -561 2 2 200 11 192 287 286 -562 2 2 200 11 224 286 287 -563 2 2 200 11 193 289 288 -564 2 2 200 11 223 288 289 -565 2 2 200 11 61 290 62 -566 2 2 200 11 206 286 279 -567 2 2 200 11 187 241 278 -568 2 2 200 11 199 247 268 -569 2 2 200 11 53 276 253 -570 2 2 200 11 56 254 277 -571 2 2 200 11 52 253 275 -572 2 2 200 11 61 247 290 -573 2 2 200 11 204 275 253 -574 2 2 200 11 205 277 254 -575 2 2 200 11 204 253 276 -576 2 2 200 11 70 271 279 -577 2 2 200 11 189 281 284 -578 2 2 200 11 62 290 250 -579 2 2 200 11 206 279 271 -580 2 2 200 11 216 284 281 -$EndElements diff --git a/docs/tutorials/template_input.py b/docs/tutorials/template_input.py deleted file mode 100755 index 6e4b62e..0000000 --- a/docs/tutorials/template_input.py +++ /dev/null @@ -1,77 +0,0 @@ -# -*- coding: utf-8 -*- -""" -Template to generate the input files for the FEM code SolidsPy. -The script uses meshio to read a GMSH mesh and produce -text files nodes.txt, eles.txt , mater.txt and loads.txt - -@authors: Juan Gomez - Nicolas Guarin-Zapata -""" -import meshio -import numpy as np -# -# Read the GMSH file using meshio -# -mesh = meshio.read("template.msh") -points = mesh.points -cells = mesh.cells -point_data = mesh.point_data -cell_data = mesh.cell_data - - -# Process element data. In this case we have used 3-noded triangles. -# (In SolidsPy 1 stands for quad; 2 for triangle6; 3 for triangle) -eles = cells["triangle"] -els_array = np.zeros([eles.shape[0], 6], dtype=int) -# Asigns element id -els_array[:, 0] = range(eles.shape[0]) -# Assigns element type according to SolidsPy -els_array[:, 1] = 3 -# Assign element connectivities -els_array[:, 3::] = eles -# Creates the materials array and assigns a profile (either 0 or 1) to -# each element according to the physical surface -mater_array = np.array([[1.0, 0.30], - [5.0, 0.30]]) -maters = cell_data["triangle"]["gmsh:physical"] -els_array[:, 2] = [0 if mater == 100 else 1 for mater in maters] - -# Process nodal data -nodes_array = np.zeros([points.shape[0], 5]) -nodes_array[:, 0] = range(points.shape[0]) # Assigns nodal id -nodes_array[:, 1:3] = points[:, :2] # Assigns space coordinates - -# Process physical lines to assign displacement boundary conditions -# and nodal point loads -# -# Displacement boundary conditions -lines = cells["line"] -# Bounds contains data corresponding to the physical line. -bounds = cell_data["line"]["gmsh:physical"] -# (-1 means a restraint degree of freedom) -id_frontera_lat = [cont for cont in range(len(bounds)) if bounds[cont] == 300] -nodes_frontera_lat = lines[id_frontera_lat] -nodes_frontera_lat = nodes_frontera_lat.flatten() -nodes_frontera_lat = list(set(nodes_frontera_lat)) -nodes_array[nodes_frontera_lat, 3] = -1 -id_frontera_abajo = [cont for cont in range(len(bounds)) if bounds[cont] == 400] -nodes_frontera_abajo = lines[id_frontera_abajo] -nodes_frontera_abajo = nodes_frontera_abajo.flatten() -nodes_frontera_abajo = list(set(nodes_frontera_abajo)) -nodes_array[nodes_frontera_abajo, 4] = -1 -# Nodal point loads -id_carga = [cont for cont in range(len(bounds)) if bounds[cont] == 500] -nodes_carga = lines[id_carga] -nodes_carga = nodes_carga.flatten() -nodes_carga = list(set(nodes_carga)) -ncargas = len(nodes_carga) -carga_total = -2.0 -cargas = np.zeros((ncargas, 3)) -cargas[:, 0] = nodes_carga -cargas[:, 2] = carga_total/ncargas - -# Write the model .txt files -np.savetxt("eles.txt" , els_array , fmt="%d") -np.savetxt("loads.txt", cargas, fmt=("%d", "%.6f", "%.6f")) -np.savetxt("nodes.txt", nodes_array , fmt=("%d", "%.4f", "%.4f", "%d", "%d")) -np.savetxt("mater.txt", mater_array , fmt="%.6f") diff --git a/docs/tutorials/tutorial_beso.rst b/docs/tutorials/tutorial_beso.rst new file mode 100644 index 0000000..f1ad93a --- /dev/null +++ b/docs/tutorials/tutorial_beso.rst @@ -0,0 +1,59 @@ +Bi-directional ESO (BESO) Tutorial +================================== + +**Bi-directional Evolutionary Structural Optimization (BESO)** refines the standard ESO concept by not only removing material in low-stress/sensitivity regions, but also allowing selective *adding* of material in some steps. + +Process +------- + +1. **Sensitivity analysis**: Evaluate element-level sensitivity (stress, strain energy, etc.). +2. **Element removal**: Remove the lowest-sensitivity elements (like ESO). +3. **Element addition**: Potentially restore some elements in high-sensitivity areas if the design is too coarse or if a certain criterion is triggered. +4. **Iterations**: Repeat until final volume fraction or iteration limit is achieved. + +Minimal Example +-------------- + +Below is a 2D usage snippet of the **`BESO`** function: + +.. code-block:: python + + import numpy as np + from solidspy_opt.optimize import BESO + from solidspy_opt.utils import structures + + # A small 2D example + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) + positions = np.array([[4, 1]]) + nodes, mats, els, loads, idx_BC = structures(L, H, nx, ny, dirs, positions, n=1) + + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = BESO( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, + t=0.0001, # target stress ratio + ER=0.001, # ratio increment + volfrac=0.5, + plot=False, + dim_problem=2, + nnodes=4 + ) + +Explanation of Parameters +------------------------- + +- **`t`** (Float): The *target stress ratio* for adding or removing elements. +- **`ER`**: Increment of that ratio each iteration. +- **`volfrac`**: Target volume fraction. BESO attempts to keep or converge near this fraction, possibly toggling add/remove to refine the shape. +- **`niter`**: Maximum number of iterations. + +Further Reading +-------------- + +- Huang, Xie (2009) for BESO fundamentals. +- `examples/beso.ipynb` or `docs/advanced/membrane_vibration.rst` references if you have advanced examples. diff --git a/docs/tutorials/tutorial_eso_stiff.rst b/docs/tutorials/tutorial_eso_stiff.rst new file mode 100644 index 0000000..76c1a0a --- /dev/null +++ b/docs/tutorials/tutorial_eso_stiff.rst @@ -0,0 +1,64 @@ +ESO by Stiffness Tutorial +========================= + +**Evolutionary Structural Optimization (ESO)** can also be driven by *stiffness-based* criteria, removing elements with the lowest “sensitivity” or “stiffness contribution.” + +Function Overview +----------------- + +**`ESO_stiff`** follows a similar flow to **`ESO_stress`**, but instead of the von Mises stress for removal, it evaluates an element stiffness (or strain energy) sensitivity criterion. + +Quick Example +------------ + +.. code-block:: python + + import numpy as np + from solidspy_opt.optimize import ESO_stiff + from solidspy_opt.utils import structures + + # 2D Example + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) # downward load + positions = np.array([[4, 1]]) + nodes, mats, els, loads, idx_BC = structures( + L=L, H=H, nx=nx, ny=ny, dirs=dirs, positions=positions, n=1 + ) + + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stiff( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, + RR=0.1, + ER=0.1, + volfrac=0.5, + plot=False, + dim_problem=2, + nnodes=4 + ) + +Explanation of Key Steps +------------------------ + +1. **System Assembly and Solution**: As with other approaches, it forms and solves :math:`K \, u = f`. +2. **Sensitivity Calculation**: Each element's stiffness contribution or strain-energy-based sensitivity is computed. +3. **Element Removal**: Elements with the lowest sensitivity are removed. +4. **Re-Meshing**: The algorithm may remove nodes if they become orphaned (no longer connected to any element). +5. **Iteration**: The process repeats until the desired volume fraction is reached or iteration count is exceeded. + +Parameter Notes +-------------- + +- **`RR`** (Removal Ratio): Threshold below which elements are removed. +- **`ER`** (Removal Ratio Increment): Increases the threshold each iteration. +- The rest of the parameters are akin to **`ESO_stress`** (see :ref:`tutorial_eso_stress`). + +See Also +-------- + +- `examples/eso_stiff.ipynb` for a more advanced demonstration. +- Xie and Steven, 1993, for original ESO references. diff --git a/docs/tutorials/tutorial_eso_stress.rst b/docs/tutorials/tutorial_eso_stress.rst new file mode 100644 index 0000000..ad58df6 --- /dev/null +++ b/docs/tutorials/tutorial_eso_stress.rst @@ -0,0 +1,86 @@ +ESO by Stress Tutorial +====================== + +In this tutorial, we demonstrate how to perform **Evolutionary Structural Optimization (ESO)** based on stress criteria using **SolidsPy-Opt**. This method iteratively removes elements with low relative stress until a target volume fraction is reached. + +Overview +-------- + +The **`ESO_stress`** function uses nodal and element data to: + +1. Assemble and solve the linear system. +2. Compute element von Mises stresses. +3. Remove elements below a certain stress threshold. +4. Repeat until the desired volume fraction or iteration limit is reached. + +Example Code +------------ + +Below is a minimal **2D** usage example. You can adapt it for **3D** as well. + +.. code-block:: python + + import numpy as np + import matplotlib.pyplot as plt + + # Import the ESO_stress solver and utility functions + from solidspy_opt.optimize import ESO_stress + from solidspy_opt.utils import structures + + # Define geometry, mesh, and loading + L, H = 60, 60 + nx, ny = 60, 60 + dirs = np.array([[0, -1]]) # single downward load + positions = np.array([[15, 1]]) # near top edge + nodes, mats, els, loads, idx_BC = structures( + L=L, H=H, + nx=nx, ny=ny, + dirs=dirs, + positions=positions, + n=1 + ) + + # Run ESO based on stress + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stress( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=200, # number of iterations + RR=0.001, # initial removal ratio + ER=0.01, # removal ratio increment + volfrac=0.5, # target volume fraction + plot=True, + dim_problem=2, + nnodes=4 + ) + +Description of Arguments +------------------------ + +- **`nodes`**: Numpy array with node coordinates and boundary conditions. +- **`els`**: Numpy array with element connectivity. +- **`mats`**: Numpy array with material properties. +- **`loads`**: Numpy array listing node loads (forces). +- **`idx_BC`**: Array of node indices for boundary conditions. +- **`niter`**: Maximum number of optimization iterations. +- **`RR`**, **`ER`**: Initial removal ratio and its increment. +- **`volfrac`**: Fraction of initial volume (area in 2D, volume in 3D) to remain after optimization. +- **`plot`**: Boolean to enable the SolidSpy-based plotting. +- **`dim_problem`**: 2 or 3 (2D or 3D). +- **`nnodes`**: Number of nodes per element (3 or 4 in 2D, 4 or 8 in 3D). + +Tips & Notes +------------ + +- Ensure your mesh is fine enough to capture meaningful stress distributions. +- For 3D usage, call :code:`structure_3d(...)` from **`solidspy_opt.utils`**. +- Plotting relies on SolidSpy's postprocessing modules. + + +Further Reading +-------------- + +- **Xie and Steven**, 1993, on the original ESO approach. +- `ESO_stress` docstring or `examples/eso_stress.ipynb` in the **examples/** directory. diff --git a/docs/tutorials/tutorial_simp.rst b/docs/tutorials/tutorial_simp.rst new file mode 100644 index 0000000..9323a16 --- /dev/null +++ b/docs/tutorials/tutorial_simp.rst @@ -0,0 +1,70 @@ +SIMP Tutorial +============= + +The **Solid Isotropic Material with Penalization (SIMP)** method is a classic topology optimization technique that penalizes intermediate densities to encourage “0 or 1” (void or solid) solutions. + +Basic Workflow +-------------- + +1. **Initialize** element densities (:math:`\rho_i`) to the volume fraction :math:`V_f`. +2. **Assemble and Solve** for displacements. +3. **Compute Sensitivities**: Typically compliance is used (minimize :math:`\int \sigma \epsilon`). +4. **Update Densities**: Using an **Optimality Criteria** or **Method of Moving Asymptotes** approach. +5. **Repeat** until convergence or iteration limit. + +Example +------- + +Here is a 2D usage snippet of **`SIMP`**: + +.. code-block:: python + + import numpy as np + from solidspy_opt.optimize import SIMP + from solidspy_opt.utils import structures + + # 2D domain + L, H = 60, 60 + nx, ny = 60, 60 + dirs = np.array([[0, -1]]) + positions = np.array([[15, 1]]) + nodes, mats, els, loads, idx_BC = structures( + L=L, H=H, nx=nx, ny=ny, + dirs=dirs, positions=positions, n=1 + ) + + rho, nodes_opt, UC, E_nodes, S_nodes = SIMP( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=100, + penal=3.0, # penalization factor + volfrac=0.5, + dimensions=[nx, ny], # needed for 2D plotting if you want to reshape densities + plot=True, + dim_problem=2, + nnodes=4 + ) + +Key Parameters +-------------- + +- **`penal`**: Penalization exponent (typical range 2–5). +- **`volfrac`**: Target volume fraction. +- **`dimensions`**: For 2D, pass `[nx, ny]` so the final density array can be reshaped and plotted. +- **`niter`**: Maximum iterations. + +Important Notes +--------------- + +- SIMP typically relies on a stable update scheme (Optimality Criteria or MMA). +- For 3D, pass `dim_problem=3` and optionally `nnodes=4` (tetra) or `nnodes=8` (brick). +- The code in `SIMP` may apply additional filtering or steps to ensure stable solutions. + +References +---------- + +- Bendsøe and Sigmund, 1999, for the original SIMP approach. +- `examples/simp.ipynb` for a comprehensive notebook demonstration. diff --git a/docs/usage.rst b/docs/usage.rst index 4b0929f..1fce5b1 100644 --- a/docs/usage.rst +++ b/docs/usage.rst @@ -1,6 +1,153 @@ Usage ------ +===== -.. todo:: +This page guides you through a basic **SolidsPy-Opt** workflow: creating or loading a mesh, defining materials and loads, and then running a chosen optimization algorithm. - Write comprehensive usage docs. +Basics +------ + +**SolidsPy-Opt** is designed to build on top of the original SolidSpy approach, but integrates topology optimization methods. In general, you will: + +1. **Import** the needed modules (e.g., from ``solidspy_opt.optimize``). +2. **Create or load** a mesh: by using the utility functions in ``solidspy_opt.utils`` or by reading external files (e.g., via meshio). +3. **Define material properties** and boundary/loading conditions. +4. **Call** an optimization function (e.g., **`ESO_stress`**, **`ESO_stiff`**, **`BESO`**, or **`SIMP`**). +5. **Process or visualize** the results. + +A Simple 2D Example +------------------- + +Below is an outline for a **2D** topology optimization using **`ESO_stress`**. This is a direct script version of what you might run in a Jupyter notebook. + +.. code-block:: python + + import numpy as np + import matplotlib.pyplot as plt + + from solidspy_opt.optimize import ESO_stress + from solidspy_opt.utils import structures + + # 1. Set up geometry and loading + L, H = 60, 60 # domain dimensions + nx, ny = 60, 60 # number of divisions in X and Y + dirs = np.array([[0, -1]]) # direction: downward load + positions = np.array([[15, 1]]) # near the top-left corner + n = 1 # single load + + # 2. Build the mesh and boundary conditions + nodes, mats, els, loads, idx_BC = structures( + L=L, H=H, nx=nx, ny=ny, + dirs=dirs, positions=positions, n=n + ) + + # 3. Run the ESO_stress optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stress( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=200, # maximum iterations + RR=0.001, # initial removal ratio + ER=0.01, # increment for removal ratio each iteration + volfrac=0.5, # target volume fraction + plot=True, # enable plotting via SolidSpy + dim_problem=2, # 2D + nnodes=4 # 4-node quadrilaterals + ) + + # 4. The optimization function returns: + # ELS_opt: the optimized elements array + # nodes_opt: the updated nodes array + # UC: full nodal displacements + # E_nodes, S_nodes: strain and stress at the nodes + + plt.show() + +Interpreting Results +-------------------- + +When you enable ``plot=True``, **SolidsPy-Opt** uses *SolidSpy* postprocessing routines to visualize: + +- **Deformed Mesh**: showing nodal displacements. +- **Stress Fields**: color contour of von Mises or principal stresses in the mesh. +- **Element Removal**: final shape after removing or adding elements (depending on the optimization). + +You can retrieve numeric data directly from the returned arrays: + +- **`ELS_opt`**: a 2D array with remaining elements and their connectivity. +- **`nodes_opt`**: the updated list of nodes and boundary flags after removal of orphaned nodes. +- **`UC`**: an array of nodal displacements that you can further post-process or plot. + +Advanced 3D Usage +----------------- + +For 3D, you can follow a similar pattern but use: + +- **`structure_3d`** from ``solidspy_opt.utils`` to create a cubic or rectangular 3D domain. +- **`dim_problem=3`** and **`nnodes=4`** (tetra) or **`nnodes=8`** (brick), as supported by your chosen routine. + +For example: + +.. code-block:: python + + from solidspy_opt.utils import structure_3d + from solidspy_opt.optimize import ESO_stress + + load_dirs = np.array([[0, 0, -1]]) # downward load in Z + load_pos = np.array([[5, 5, 9]]) # near top center (for a 10x10x10 domain) + + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L=10, H=10, W=10, E=210e9, v=0.3, nx=10, ny=10, nz=10, + dirs=load_dirs, positions=load_pos + ) + + ELS_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = ESO_stress( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=100, + RR=0.005, + ER=0.02, + volfrac=0.5, + plot=False, # disable plotting if you prefer + dim_problem=3, + nnodes=8 + ) + +Switching Between Optimization Methods +------------------------------------- + +If you want to switch from **`ESO_stress`** to, for example, **`BESO`** or **`SIMP`**, you only need to change the import and function call: + +.. code-block:: python + + # from solidspy_opt.optimize import BESO + # ... + # ELS_opt, nodes_opt, UC, E_nodes, S_nodes = BESO( + # nodes=..., els=..., ... + # ) + +Be mindful that each method has slightly different parameters (e.g., `t` and `ER` for BESO, or `penal` for SIMP). + +Integration with External Meshes +------------------------------- + +Though you can rely on **`structures()`** or **`structure_3d()`** to create simple rectangular/square meshes, you can also load meshes from Gmsh or other external generators: + +1. Install **meshio** (already in dependencies) to handle reading `.msh` or `.xml` formats, etc. +2. Convert that mesh into the format required by SolidSpy / SolidsPy-Opt (a combination of nodal coordinates, element connectivity, boundary conditions, etc.). + +For advanced geometry or boundary definitions, see the official SolidSpy or meshio documentation. + +Summary +------- + +This **Usage** guide has walked you through: +- Building or loading a mesh via **`structures()`** or **`structure_3d()`**. +- Calling the various optimization routines in **SolidsPy-Opt** (e.g., **`ESO_stress`**). +- Retrieving and plotting the optimized shape and solution fields. + +Explore the :ref:`tutorials ` section for deeper examples and step-by-step instructions on each solver (ESO, BESO, SIMP, etc.). If you run into trouble, open an issue on `GitHub `_. diff --git a/examples/beso.ipynb b/examples/beso.ipynb new file mode 100644 index 0000000..89fac89 --- /dev/null +++ b/examples/beso.ipynb @@ -0,0 +1,175 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **Bi-directional Evolutionary Structural Optimization (BESO) Examples**\n", + "\n", + "This notebook provides examples on how to use the `BESO` function from the `solidspy_opt.optimize` module for:\n", + "1. A 3D cubic structure.\n", + "2. A 2D square/rectangular structure.\n", + "\n", + "We will also use the helper functions `structure_3d` and `structures` from the `solidspy_opt.utils` module to create the respective meshes and boundary/loads arrays.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "imports" + ] + }, + "outputs": [], + "source": [ + "%matplotlib widget\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Import the BESO solver and utility functions from your package\n", + "from solidspy_opt.optimize import BESO\n", + "from solidspy_opt.utils import structure_3d, structures\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1: 3D Structure\n", + "In this example, we create a 3D 10×10×10 cubic mesh with some loads applied on its top face. We will run the BESO for up to 200 iterations, with a target volume fraction (`volfrac`) of 0.5. We also specify a small target stress ratio (`t`) and increment (`ER`).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "3D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions on the top face\n", + "load_directions_3d = np.array([\n", + " [0, 1, 0], # Load in the Y direction\n", + " [1, 0, 0], # Load in the X direction\n", + " [0, 0, -1] # Load in the negative Z direction\n", + "])\n", + "load_positions_3d = np.array([\n", + " [5, 5, 9], # Position near the center of the top face\n", + " [1, 1, 9], # Position near one corner of the top face\n", + " [8, 8, 9] # Position near another corner of the top face\n", + "])\n", + "\n", + "# Generate the nodes, materials, elements, loads, and BC indexes\n", + "nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d(\n", + " L=10, # length in X\n", + " H=10, # length in Y\n", + " W=10, # length in Z\n", + " E=206.8e9, # Young's modulus\n", + " v=0.28, # Poisson's ratio\n", + " nx=10, # number of divisions in X\n", + " ny=10, # number of divisions in Y\n", + " nz=10, # number of divisions in Z\n", + " dirs=load_directions_3d,\n", + " positions=load_positions_3d\n", + ")\n", + "\n", + "# Run the BESO optimization\n", + "els_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = BESO(\n", + " nodes=nodes_3d,\n", + " els=els_3d,\n", + " mats=mats_3d,\n", + " loads=loads_3d,\n", + " idx_BC=idx_BC_3d,\n", + " niter=200,\n", + " t=0.0001, # Target stress ratio\n", + " ER=0.005, # Stress ratio increment\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True, # Whether to plot with SolidSpy's 3D plot function\n", + " dim_problem=3,\n", + " nnodes=8 # 8-node hexahedron\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2: 2D Structure\n", + "In this example, we generate a 2D 60×60 square mesh, with a single load applied in the negative Y direction near the top of the structure. We run BESO for up to 200 iterations, again with a `volfrac` of 0.5, a small `t` value, and a moderate increment `ER`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "2D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions for the 2D example\n", + "load_directions_2d = np.array([[0, -1]])\n", + "load_positions_2d = np.array([[15, 1]]) # near the middle of the top edge\n", + "\n", + "# Generate the 2D structure\n", + "nodes_2d, mats_2d, els_2d, loads_2d, idx_BC_2d = structures(\n", + " L=60, # length in X\n", + " H=60, # length in Y\n", + " nx=60, # number of divisions in X\n", + " ny=60, # number of divisions in Y\n", + " dirs=load_directions_2d,\n", + " positions=load_positions_2d,\n", + " n=1 # Single load\n", + ")\n", + "\n", + "# Run the BESO optimization in 2D\n", + "els_opt_2d, nodes_opt_2d, UC_2d, E_nodes_2d, S_nodes_2d = BESO(\n", + " nodes=nodes_2d,\n", + " els=els_2d,\n", + " mats=mats_2d,\n", + " loads=loads_2d,\n", + " idx_BC=idx_BC_2d,\n", + " niter=200,\n", + " t=0.0001, # Target stress ratio\n", + " ER=0.005, # Stress ratio increment\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=False, # Disable plotting in 2D example to speed up execution\n", + " dim_problem=2,\n", + " nnodes=4 # 4-node quadrilateral\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes:\n", + "- The plotting functionality (with `plot=True`) will use **SolidSpy**'s plotting utilities under the hood.\n", + "- If you are running this in a non-interactive environment, you may need to change or remove `%matplotlib widget`.\n", + "- If you want to disable plotting in 3D, simply set `plot=False` in the call to `BESO`.\n", + "\n", + "### References:\n", + "- **Bi-directional Evolutionary Structural Optimization** (BESO) [Huang & Xie, 2009].\n", + "- [**SolidSpy** GitHub](https://github.com/AppliedMechanics-EAFIT/SolidSpy).\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + }, + "name": "example_beso" + }, + "nbformat": 4, + "nbformat_minor": 5 +} + diff --git a/examples/eso_stiff.ipynb b/examples/eso_stiff.ipynb index b78267e..616dc34 100644 --- a/examples/eso_stiff.ipynb +++ b/examples/eso_stiff.ipynb @@ -1,127 +1,175 @@ { - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "plaintext" + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **Evolutionary Structural Optimization (ESO) Based on Stiffness**\n", + "\n", + "This notebook provides examples on how to use the `ESO_stiff` function from the `solidspy_opt.optimize` module for:\n", + "1. A 3D cubic structure.\n", + "2. A 2D square/rectangular structure.\n", + "\n", + "We will also use the helper functions `structure_3d` and `structures` from the `solidspy_opt.utils` module to create the respective meshes and boundary/loads arrays.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "imports" + ] + }, + "outputs": [], + "source": [ + "%matplotlib widget\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Import the ESO solver and utility functions from your package\n", + "from solidspy_opt.optimize import ESO_stiff\n", + "from solidspy_opt.utils import structure_3d, structures\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1: 3D Structure\n", + "In this example, we create a 3D 10×10×10 cubic mesh with some loads applied on its top face. We run the ESO for up to 200 iterations, with a target volume fraction (`volfrac`) of 0.5. We use a small initial removal ratio and increment it with each iteration.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "3D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions on the top face\n", + "load_directions_3d = np.array([\n", + " [0, 1, 0], # Load in the Y direction\n", + " [1, 0, 0], # Load in the X direction\n", + " [0, 0, -1] # Load in the negative Z direction\n", + "])\n", + "load_positions_3d = np.array([\n", + " [5, 5, 9], # Position near the center of the top face\n", + " [1, 1, 9], # Position near one corner of the top face\n", + " [8, 8, 9] # Position near another corner of the top face\n", + "])\n", + "\n", + "# Generate the nodes, materials, elements, loads, and BC indexes\n", + "nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d(\n", + " L=10, # length in X\n", + " H=10, # length in Y\n", + " W=10, # length in Z\n", + " E=206.8e9, # Young's modulus\n", + " v=0.28, # Poisson's ratio\n", + " nx=10, # number of divisions in X\n", + " ny=10, # number of divisions in Y\n", + " nz=10, # number of divisions in Z\n", + " dirs=load_directions_3d,\n", + " positions=load_positions_3d\n", + ")\n", + "\n", + "# Run the ESO optimization\n", + "els_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = ESO_stiff(\n", + " nodes=nodes_3d,\n", + " els=els_3d,\n", + " mats=mats_3d,\n", + " loads=loads_3d,\n", + " idx_BC=idx_BC_3d,\n", + " niter=200,\n", + " RR=0.0001, # Initial removal ratio\n", + " ER=0.001, # Removal ratio increment\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True, # Whether to plot with solidspy's 3D plot function\n", + " dim_problem=3,\n", + " nnodes=8 # 8-node hexahedron\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2: 2D Structure\n", + "In this example, we generate a 2D 60×60 square mesh, with a single load applied in the negative Y direction near the top of the structure. We run the ESO for up to 200 iterations, with the same target volume fraction of 0.5.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "2D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions for the 2D example\n", + "load_directions_2d = np.array([[0, -1]])\n", + "load_positions_2d = np.array([[15, 1]]) # near the middle of the top edge\n", + "\n", + "# Generate the 2D structure\n", + "nodes_2d, mats_2d, els_2d, loads_2d, idx_BC_2d = structures(\n", + " L=60, # length in X\n", + " H=60, # length in Y\n", + " nx=60, # number of divisions in X\n", + " ny=60, # number of divisions in Y\n", + " dirs=load_directions_2d,\n", + " positions=load_positions_2d,\n", + " n=1 # Single load\n", + ")\n", + "\n", + "# Run the ESO optimization in 2D\n", + "els_opt_2d, nodes_opt_2d, UC_2d, E_nodes_2d, S_nodes_2d = ESO_stiff(\n", + " nodes=nodes_2d,\n", + " els=els_2d,\n", + " mats=mats_2d,\n", + " loads=loads_2d,\n", + " idx_BC=idx_BC_2d,\n", + " niter=200,\n", + " RR=0.0001, # Initial removal ratio for 2D\n", + " ER=0.001, # Removal ratio increment for 2D\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True,\n", + " dim_problem=2,\n", + " nnodes=4 # 4-node quadrilateral\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes:\n", + "- The plotting functionality (with `plot=True`) will use **solidspy**'s plotting utilities under the hood.\n", + "- If you are running this in a non-interactive environment, you may need to change or remove `%matplotlib widget`.\n", + "- If you want to disable plotting, simply set `plot=False` in the call to `ESO_stiff`.\n", + "\n", + "### References:\n", + "- **Evolutionary Structural Optimization** [Xie and Steven, 1993].\n", + "- [**SolidSpy** GitHub](https://github.com/AppliedMechanics-EAFIT/SolidSpy).\n" + ] } - }, - "outputs": [], - "source": [ - "from solidspy_opt.optimize import ESO_stiff\n", - "from solidspy_opt.utils import beam_3d" - ] + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + }, + "name": "example_eso_stiff" }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "plaintext" - } - }, - "outputs": [], - "source": [ - "nodes, mats, els, loads, idx_BC = beam_3d(\n", - " L=10, \n", - " H=10, \n", - " W=10, \n", - " E=206.8e9, \n", - " v=0.28, \n", - " nx=10, \n", - " ny=10, \n", - " nz=10, \n", - " dirs=load_directions, \n", - " positions=load_positions\n", - ")\n", - "\n", - "els, nodes, UC = ESO_stress(\n", - " nodes=nodes, \n", - " els=els, \n", - " mats=mats, \n", - " loads=loads, \n", - " idx_BC=idx_BC, \n", - " niter=200, \n", - " RR=0.005, \n", - " ER=0.05, \n", - " volfrac=0.5, \n", - " plot=False,\n", - " dim_problem=3, \n", - " nnodes=8)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "vscode": { - "languageId": "plaintext" - } - }, - "outputs": [], - "source": [ - "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "def plot_3d_hexahedral_mesh(nodes, elements, values=None):\n", - " \"\"\"\n", - " Plot a 3D hexahedral mesh using Matplotlib.\n", - "\n", - " Parameters\n", - " ----------\n", - " nodes : ndarray of shape (n_nodes, 3)\n", - " Node coordinates.\n", - " elements : ndarray of shape (n_elements, 8)\n", - " Indices of the nodes forming each hexahedron.\n", - " values : ndarray of shape (n_nodes,), optional\n", - " Values at the nodes to color the mesh. If None, a uniform color is used.\n", - " \"\"\"\n", - " fig = plt.figure()\n", - " ax = fig.add_subplot(111, projection='3d')\n", - "\n", - " # Default values for uniform color\n", - " if values is None:\n", - " values = np.ones(nodes.shape[0])\n", - "\n", - " # Define hexahedron faces for visualization\n", - " faces = [\n", - " [0, 1, 2, 3], # Bottom\n", - " [4, 5, 6, 7], # Top\n", - " [0, 1, 5, 4], # Front\n", - " [2, 3, 7, 6], # Back\n", - " [0, 3, 7, 4], # Left\n", - " [1, 2, 6, 5], # Right\n", - " ]\n", - "\n", - " # Plot each element\n", - " for el in elements:\n", - " for face in faces:\n", - " verts = [nodes[el[node], :] for node in face]\n", - " poly = Poly3DCollection([verts], edgecolor='k', alpha=0.6)\n", - " face_value = values[el].mean() # Average value for face coloring\n", - " poly.set_facecolor(plt.cm.viridis(face_value))\n", - " ax.add_collection3d(poly)\n", - "\n", - " ax.set_xlabel(\"X\")\n", - " ax.set_ylabel(\"Y\")\n", - " ax.set_zlabel(\"Z\")\n", - " ax.auto_scale_xyz(nodes[:, 0], nodes[:, 1], nodes[:, 2])\n", - " plt.show()\n", - "\n", - "values = np.random.rand(nodes.shape[0]) # Example values\n", - "\n", - "plot_3d_hexahedral_mesh(nodes[:,1:4], els[:,3:], values)\n" - ] - } - ], - "metadata": { - "language_info": { - "name": "python" - } - }, - "nbformat": 4, - "nbformat_minor": 2 + "nbformat": 4, + "nbformat_minor": 5 } + diff --git a/examples/eso_stress.ipynb b/examples/eso_stress.ipynb new file mode 100644 index 0000000..4574d25 --- /dev/null +++ b/examples/eso_stress.ipynb @@ -0,0 +1,174 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **Evolutionary Structural Optimization (ESO) Examples**\n", + "This notebook provides examples on how to use the `ESO_stress` function from the `solidspy_opt.optimize` module for:\n", + "1. A 3D cubic structure.\n", + "2. A 2D square/rectangular structure.\n", + "\n", + "We will also use the helper functions `structure_3d` and `structures` from the `solidspy_opt.utils` module to create the respective meshes and boundary/loads arrays.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "imports" + ] + }, + "outputs": [], + "source": [ + "%matplotlib widget\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Import the ESO solver and utility functions from your package\n", + "from solidspy_opt.optimize import ESO_stress\n", + "from solidspy_opt.utils import structure_3d, structures\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1: 3D Structure\n", + "In this example, we create a 3D 10×10×10 cubic mesh with some loads applied on its top face. We will run ESO for up to 200 iterations, with a target volume fraction (`volfrac`) of 0.5.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "3D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions on the top face\n", + "load_directions_3d = np.array([\n", + " [0, 1, 0], # Load in the Y direction\n", + " [1, 0, 0], # Load in the X direction\n", + " [0, 0, -1] # Load in the negative Z direction\n", + "])\n", + "load_positions_3d = np.array([\n", + " [5, 5, 9], # Position near the center of the top face\n", + " [1, 1, 9], # Position near one corner of the top face\n", + " [8, 8, 9] # Position near another corner of the top face\n", + "])\n", + "\n", + "# Generate the nodes, materials, elements, loads, and BC indexes\n", + "nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d(\n", + " L=10, # length in X\n", + " H=10, # length in Y\n", + " W=10, # length in Z\n", + " E=206.8e9, # Young's modulus\n", + " v=0.28, # Poisson's ratio\n", + " nx=10, # number of divisions in X\n", + " ny=10, # number of divisions in Y\n", + " nz=10, # number of divisions in Z\n", + " dirs=load_directions_3d,\n", + " positions=load_positions_3d\n", + ")\n", + "\n", + "# Run the ESO optimization\n", + "els_opt_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = ESO_stress(\n", + " nodes=nodes_3d,\n", + " els=els_3d,\n", + " mats=mats_3d,\n", + " loads=loads_3d,\n", + " idx_BC=idx_BC_3d,\n", + " niter=200,\n", + " RR=0.005, # Initial removal ratio\n", + " ER=0.05, # Removal ratio increment\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True, # Whether to plot with solidspy's 3D plot function\n", + " dim_problem=3,\n", + " nnodes=8 # 8-node hexahedron\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2: 2D Structure\n", + "In this example, we generate a 2D 60×60 square mesh, with a single load applied in the negative Y direction near the top of the structure. We will again run ESO to remove around half of the material by adjusting our `volfrac`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "2D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions for the 2D example\n", + "load_directions_2d = np.array([[0, -1]])\n", + "load_positions_2d = np.array([[15, 1]]) # near the middle of the top edge\n", + "\n", + "# Generate the 2D structure\n", + "nodes_2d, mats_2d, els_2d, loads_2d, idx_BC_2d = structures(\n", + " L=60, # length in X\n", + " H=60, # length in Y\n", + " nx=60, # number of divisions in X\n", + " ny=60, # number of divisions in Y\n", + " dirs=load_directions_2d,\n", + " positions=load_positions_2d,\n", + " n=1 # Single load\n", + ")\n", + "\n", + "# Run the ESO optimization in 2D\n", + "els_opt_2d, nodes_opt_2d, UC_2d, E_nodes_2d, S_nodes_2d = ESO_stress(\n", + " nodes=nodes_2d,\n", + " els=els_2d,\n", + " mats=mats_2d,\n", + " loads=loads_2d,\n", + " idx_BC=idx_BC_2d,\n", + " niter=200,\n", + " RR=0.001, # Initial removal ratio for 2D\n", + " ER=0.01, # Removal ratio increment for 2D\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True,\n", + " dim_problem=2,\n", + " nnodes=4 # 4-node quadrilateral\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes:\n", + "- The plotting functionality (with `plot=True`) will use **solidspy**'s plotting utilities under the hood.\n", + "- If you are running this in a non-interactive environment, you may need to change or remove `%matplotlib widget`.\n", + "- If you want to disable plotting, simply set `plot=False` in the call to `ESO_stress`.\n", + "\n", + "### References:\n", + "- **Evolutionary Structural Optimization** [Xie and Steven, 1993].\n", + "- [**SolidSpy** GitHub](https://github.com/AppliedMechanics-EAFIT/SolidSpy).\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + }, + "name": "example_eso" + }, + "nbformat": 4, + "nbformat_minor": 5 +} + diff --git a/examples/simp.ipynb b/examples/simp.ipynb new file mode 100644 index 0000000..e31bce8 --- /dev/null +++ b/examples/simp.ipynb @@ -0,0 +1,175 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# **Structural Optimization using the SIMP Method**\n", + "\n", + "This notebook provides examples on how to use the `SIMP` function from the `solidspy_opt.optimize` module for:\n", + "1. A 3D cubic structure.\n", + "2. A 2D square/rectangular structure.\n", + "\n", + "We will also use the helper functions `structure_3d` and `structures` from the `solidspy_opt.utils` module to create the respective meshes and boundary/loads arrays.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "imports" + ] + }, + "outputs": [], + "source": [ + "%matplotlib widget\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Import the SIMP solver and utility functions from your package\n", + "from solidspy_opt.optimize import SIMP\n", + "from solidspy_opt.utils import structure_3d, structures\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1: 3D Structure\n", + "In this example, we create a 3D 10×10×10 cubic mesh with some loads applied on its top face. We then run the SIMP optimization for up to 200 iterations, with a target volume fraction (`volfrac`) of 0.5 and a penalization factor (`penal=3`).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "3D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions on the top face\n", + "load_directions_3d = np.array([\n", + " [0, 1, 0], # Load in the Y direction\n", + " [1, 0, 0], # Load in the X direction\n", + " [0, 0, -1] # Load in the negative Z direction\n", + "])\n", + "load_positions_3d = np.array([\n", + " [5, 5, 9], # Position near the center of the top face\n", + " [1, 1, 9], # Position near one corner of the top face\n", + " [8, 8, 9] # Position near another corner of the top face\n", + "])\n", + "\n", + "# Generate the nodes, materials, elements, loads, and boundary indices\n", + "nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d(\n", + " L=10, # length in X\n", + " H=10, # length in Y\n", + " W=10, # length in Z\n", + " E=206.8e9, # Young's modulus\n", + " v=0.28, # Poisson's ratio\n", + " nx=10, # number of divisions in X\n", + " ny=10, # number of divisions in Y\n", + " nz=10, # number of divisions in Z\n", + " dirs=load_directions_3d,\n", + " positions=load_positions_3d\n", + ")\n", + "\n", + "# Run the SIMP optimization\n", + "rho_3d, nodes_opt_3d, UC_3d, E_nodes_3d, S_nodes_3d = SIMP(\n", + " nodes=nodes_3d,\n", + " els=els_3d,\n", + " mats=mats_3d,\n", + " loads=loads_3d,\n", + " idx_BC=idx_BC_3d,\n", + " niter=200, # Maximum number of iterations\n", + " penal=3, # Penalization factor\n", + " volfrac=0.5, # Target volume fraction\n", + " plot=True, # Whether to plot the 3D structure\n", + " dim_problem=3,\n", + " nnodes=8 # 8-node hexahedron elements\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2: 2D Structure\n", + "In this example, we generate a 2D 60×60 square mesh, with a single load applied in the negative Y direction near the top of the structure. We run the SIMP optimization for up to 200 iterations, again using a `volfrac` of 0.5.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "2D-example" + ] + }, + "outputs": [], + "source": [ + "# Define the load directions and positions for the 2D example\n", + "load_directions_2d = np.array([[0, -1]])\n", + "load_positions_2d = np.array([[15, 1]]) # near the middle of the top edge\n", + "\n", + "# Generate the 2D structure\n", + "nodes_2d, mats_2d, els_2d, loads_2d, idx_BC_2d = structures(\n", + " L=60, # length in X\n", + " H=60, # length in Y\n", + " nx=60, # number of divisions in X\n", + " ny=60, # number of divisions in Y\n", + " dirs=load_directions_2d,\n", + " positions=load_positions_2d,\n", + " n=1 # Single load\n", + ")\n", + "\n", + "# Run the SIMP optimization in 2D\n", + "rho_2d, nodes_opt_2d, UC_2d, E_nodes_2d, S_nodes_2d = SIMP(\n", + " nodes=nodes_2d,\n", + " els=els_2d,\n", + " mats=mats_2d,\n", + " loads=loads_2d,\n", + " idx_BC=idx_BC_2d,\n", + " niter=200, # Maximum number of iterations\n", + " penal=3, # Penalization factor\n", + " volfrac=0.5, # Target volume fraction\n", + " dimensions=[60, 60], # Grid dimensions for 2D problems\n", + " plot=True, # Enable plotting to visualize the final density distribution\n", + " dim_problem=2,\n", + " nnodes=4 # 4-node quadrilateral elements\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes:\n", + "- The plotting functionality (with `plot=True`) will use **SolidSpy**'s plotting utilities under the hood.\n", + "- For 2D problems, be sure to pass `dimensions=[nx, ny]` into the SIMP function so that the density distribution can be properly reshaped and plotted.\n", + "- If you are running this in a non-interactive environment, you may need to change or remove `%matplotlib widget`.\n", + "- If you want to disable plotting, simply set `plot=False` in the call to `SIMP`.\n", + "\n", + "### References:\n", + "- **SIMP** (Solid Isotropic Material with Penalization) [Bendsøe and Sigmund, 1999].\n", + "- [**SolidSpy** GitHub](https://github.com/AppliedMechanics-EAFIT/SolidSpy).\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python" + }, + "name": "example_simp" + }, + "nbformat": 4, + "nbformat_minor": 5 +} + diff --git a/paper/paper.bib b/paper/paper.bib index 1d1e6d6..ca4bf35 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -5,15 +5,24 @@ @book{bathe publisher={Klaus-Jurgen Bathe} } -@article{gmsh, - title={Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities}, - author={Geuzaine, Christophe and Remacle, Jean-Fran{\c{c}}ois}, - journal={International journal for numerical methods in engineering}, - volume={79}, - number={11}, - pages={1309--1331}, - year={2009}, - publisher={Wiley Online Library} +@book{huang, + place={Chichester, West Sussex, U.K.}, + title={Evolutionary topology optimization of Continuum Structures: Methods and Applications}, + publisher={Wiley}, + author={Huang, X. and Xie, Y. M.}, + year={2010} +} + +@book{peter, + title = {An Introduction to Structural Optimization}, + author = {Peter W. Christensen, A. Klarbring}, + publisher = {Springer}, + isbn = {1402086652,9781402086656}, + year = {2009}, + series = {Solid Mechanics and Its Applications}, + edition = {}, + volume = {}, + url = {https://link.springer.com/book/10.1007/978-1-4020-8666-3} } @Misc{scipy, @@ -24,6 +33,20 @@ @Misc{scipy note = {[Online; accessed June 12, 2018]} } +@software{solidspy, + title = {SolidsPy: 2D/3D-Finite Element Analysis with Python}, + version = {2.0.0}, + author = {Guarín-Zapata, Nicolás and Gómez, Juan}, + year = 2020, + keywords = {Python, Finite elements, Scientific computing, Computational mechanics}, + abstract = {SolidsPy is a simple finite element analysis code for + 2D/3D elasticity problems. The code uses as input simple-to-create text + files defining a model in terms of nodal, element, material and + load data.}, + url = {https://github.com/AppliedMechanics-EAFIT/SolidsPy}, + doi = {http://doi.org/10.5281/zenodo.4029270} +} + @Misc{meshio, author = {Nico Schlömer et al.}, title = {{meshio v1.11.7. Zenodo. http://doi.org/10.5281/zenodo.1173116}}, diff --git a/pyproject.toml b/pyproject.toml index 927b5d7..3d67d7d 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -28,7 +28,7 @@ dependencies = [ "easygui", "meshio==5.3.5", "tensorflow", - "solidspy" + # "solidspy" # PyPi test package ] [project.optional-dependencies] @@ -38,8 +38,8 @@ dev = [ "pytest-cov", "black", "flake8", - "solidspy", - "numpy" + "numpy", + # "solidspy" ] [project.urls] diff --git a/src/solidspy_opt/optimize.py b/src/solidspy_opt/optimize.py index 2abaf73..4a3a242 100644 --- a/src/solidspy_opt/optimize.py +++ b/src/solidspy_opt/optimize.py @@ -1,5 +1,3 @@ -# %% -%matplotlib widget import matplotlib.pyplot as plt from matplotlib import colors import numpy as np @@ -7,9 +5,9 @@ from typing import List, Tuple, AnyStr from scipy.sparse.linalg import spsolve -from utils.structures import * -from utils.solver import * -from utils.volumes import * +from solidspy_opt.utils.structures import * +from solidspy_opt.utils.solver import * +from solidspy_opt.utils.volumes import * import solidspy.assemutil as ass import solidspy.postprocesor as pos @@ -124,7 +122,7 @@ def ESO_stress( elsI = np.copy(els) # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -149,7 +147,7 @@ def ESO_stress( ELS = els # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -293,7 +291,7 @@ def ESO_stiff( elsI= np.copy(els) # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -318,7 +316,7 @@ def ESO_stiff( ELS = els # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -464,7 +462,7 @@ def BESO( elsI = np.copy(els) # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -475,7 +473,6 @@ def BESO( r_min = np.linalg.norm(nodes[0,1:-dim_problem] - nodes[1,1:-dim_problem]) * 1 # Radius for the sensitivity filter adj_nodes = adjacency_nodes(nodes, els, nnodes) # Adjacency nodes - # centers = center_els(nodes, els) # Centers of elements centers = calculate_element_centers(nodes, els, dim_problem, nnodes) V = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) @@ -503,7 +500,7 @@ def BESO( ELS = els_del # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els_del, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els_del, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els_del, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -669,7 +666,7 @@ def SIMP( elsI = np.copy(els) # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) @@ -707,7 +704,7 @@ def SIMP( mats[:,2] = Emin+rho**penal*(Emax-Emin) # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) + assem_op, IBC, neq = ass.node2dof(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) # stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) stiff_mat = sparse_assem(els, nodes, mats, neq, assem_op, dim_problem, uel=uel_func) rhs_vec = ass.loadasem(loads, IBC, neq) diff --git a/src/solidspy_opt/square.msh b/src/solidspy_opt/square.msh deleted file mode 100644 index d13f6fb..0000000 --- a/src/solidspy_opt/square.msh +++ 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-np.seterr(divide='ignore', invalid='ignore') - -def ESO_stress( - nodes: NDArray[np.float64], - els: NDArray[np.int_], - mats: NDArray[np.float64], - loads: NDArray[np.float64], - idx_BC: NDArray[np.float64], - niter: int, - RR: float, - ER: float, - volfrac: float, - plot: bool = False, - dim_problem: int = 2, - nnodes: int = 4 -) -> None: - """ - Performs Evolutionary Structural Optimization (ESO) based on stress for a 3D structure. - - Parameters - ---------- - nodes : ndarray - Array of node coordinates and boundary conditions with the format - [node number, x, y, z, BC], where BC indicates boundary conditions. - els : ndarray - Array of elements with the format [element number, material, node 1, node 2, ...]. - mats : ndarray - Array of material properties with the format [E, nu, rho], where: - - E is the Young's modulus, - - nu is the Poisson's ratio, - - rho is the density. - loads : ndarray - Array of elements with the format [node number, X load magnitud, Y load magnitud, Z load magnitud]. - idx_BC : ndarray - Array of node indices with boundary conditions applied. - niter : int - Number of iterations for the ESO process. - RR : float - Initial relative stress threshold for removing elements. - ER : float - Increment of the relative stress threshold (RR) for each iteration. - volfrac : float - Target volume fraction for the optimized structure, expressed as a fraction of the initial volume. - plot : bool, optional - If True, plot the initial and optimized meshes. Defaults to False. - dim_problem : int, optional - Dimension of the problem (2 for 2D, 3 for 3D). Default is 2. - nnodes : int, optional - Number of nodes per element. For 2D problems it can be 3 or 4 and for 3D problems 4 or 8. Default is 4. - - Returns - ------- - ELS : ndarray - Array of the optimized elements after the ESO process. - nodes : ndarray - Array of the optimized nodes after the ESO process. - UC : ndarray - Array with the displacements. - E_nodes : ndarray - Strains evaluated at the nodes. - S_nodes : ndarray - Stresses evaluated at the nodes. - - Notes - ----- - - This function performs structural optimization by iteratively removing elements with low relative stress. - - The relative stress threshold (RR) increases in each iteration to progressively refine the structure. - - The optimization stops either after reaching the specified number of iterations or if the target volume fraction is achieved. - - Process - ------- - 1. Assemble the global stiffness matrix and load vector. - 2. Solve the linear system to compute nodal displacements. - 3. Calculate element stresses and strains. - 4. Compute the von Mises stress for each element and identify elements to remove. - 5. Update the structure by removing selected elements and their associated nodes. - 6. Repeat until the specified number of iterations or target volume fraction is reached. - - Visualization - ------------- - If `plot` is True, the function will generate: - - A plot of the initial and optimized structures showing displacements, strains, and stresses. - - A filled contour plot of the final optimized mesh. - - Example - ------- - >>> optimized_els, optimized_nodes = ESO_stress( - ... nodes, els, mats, idx_BC, niter=10, RR=0.8, ER=0.05, volfrac=0.5, plot=True - ... ) - """ - assert dim_problem in [2, 3], "dim_problem must be either 2 (for 2D) or 3 (for 3D)" - assert nnodes in [3, 4, 8], "nnodes must be either 3, 4 (for 2D) or 4, 8 (for 3D)" - - uel_func = None - if dim_problem == 2: - if nnodes == 3: - uel_func = uel.elast_tri3 - else: - uel_func = uel.elast_quad4 - elif dim_problem == 3: - if nnodes == 4: - uel_func = uel.elast_tet4 - else: - uel_func = uel.elast_hex8 - - elsI = np.copy(els) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UCI = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodesI, S_nodesI = pos.strain_nodes_3d(nodes, els, mats[:,:2], UCI) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UCI) - - Vi = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - V_opt = Vi * volfrac - - ELS = None - for _ in range(niter): - print("Number of elements: {}".format(els.shape[0])) - - # Check equilibrium - Vi = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - if not np.allclose(stiff_mat.dot(disp)/stiff_mat.max(), rhs_vec/stiff_mat.max()) or Vi < V_opt: - break - - # Storage the solution - ELS = els - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UC = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodes, S_nodes = pos.strain_nodes_3d(nodes, els, mats[:,:2], UC) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UC) - E_els, S_els = strain_els(els, E_nodes, S_nodes) # Calculate strains and stresses in elements - - vons = np.sqrt(S_els[:,0]**2 - (S_els[:,0]*S_els[:,1]) + S_els[:,1]**2 + 3*S_els[:,2]**2) - - # Remove/add elements - RR_el = vons/vons.max() # Relative stress - mask_del = RR_el < RR # Mask for elements to be deleted - mask_els = protect_elsESO(els, loads, idx_BC, nnodes) # Mask of elements to do not remove - mask_del *= mask_els - els = np.delete(els, mask_del, 0) # Delete elements - del_nodeESO(nodes, els, nnodes, dim_problem) # Remove nodes - - RR += ER - - if plot and dim_problem == 2: - pos.fields_plot(elsI, nodes, UCI, E_nodes=E_nodesI, S_nodes=S_nodesI) # Plot initial mesh - pos.fields_plot(ELS, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # Plot optimized mesh - - fill_plot = np.ones(E_nodes.shape[0]) - plt.figure() - tri = pos.mesh2tri(nodes, ELS) - plt.tricontourf(tri, fill_plot, cmap='binary') - plt.axis("image"); - elif plot and dim_problem == 3: - pos.fields_plot_3d(nodes, ELS, loads, idx_BC, S_nodes, E_nodes, nnodes=8, data_type='stress', show_BC=True, show_loads=True, arrow_scale=2.0, arrow_color="blue", cmap="viridis", show_axes=True, show_bounds=True, show_edges=False) - - return ELS, nodes, UC, E_nodes, S_nodes - -# %% -# load_directions = np.array([[0, 1, 0]]) -# load_positions = np.array([[0, 0, 1]]) -load_directions = np.array([[0, 1, 0], [1, 0, 0], [0, 0, -1]]) -load_positions = np.array([[5, 5, 9], [1, 1, 9], [8, 8, 9]]) - -# Call the function -nodes, mats, els, loads, idx_BC = structure_3d( - L=10, - H=10, - W=10, - E=206.8e9, - v=0.28, - nx=10, - ny=10, - nz=10, - dirs=load_directions, - positions=load_positions -) - -els, nodes, UC, E_nodes, S_nodes = ESO_stress( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - RR=0.005, - ER=0.05, - volfrac=0.5, - plot=True, - dim_problem=3, - nnodes=8) - -# %% -nodes, mats, els, loads, idx_BC = structures( - L=60, - H=60, - nx=60, - ny=60, - dirs=np.array([[0, -1]]), - positions=np.array([[15, 1]]), - n=1) - -els, nodes, UC = ESO_stress( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - RR=0.001, - ER=0.01, - volfrac=0.5, - plot=True, - dim_problem=2, - nnodes=4) \ No newline at end of file diff --git a/src/solidspy_opt/test_opt2.py b/src/solidspy_opt/test_opt2.py deleted file mode 100644 index 866c595..0000000 --- a/src/solidspy_opt/test_opt2.py +++ /dev/null @@ -1,242 +0,0 @@ -# %% -%matplotlib widget -import matplotlib.pyplot as plt -from matplotlib import colors -import numpy as np -from numpy.typing import NDArray -from typing import List, Tuple, AnyStr -from scipy.sparse.linalg import spsolve - -from utils.structures import * -from utils.solver import * -from utils.volumes import * - -import solidspy.assemutil as ass -import solidspy.postprocesor as pos -import solidspy.uelutil as uel -np.seterr(divide='ignore', invalid='ignore') - -def ESO_stiff( - nodes: NDArray[np.float64], - els: NDArray[np.int_], - mats: NDArray[np.float64], - loads: NDArray[np.float64], - idx_BC: NDArray[np.float64], - niter: int, - RR: float, - ER: float, - volfrac: float, - plot: bool = False, - dim_problem: int = 2, - nnodes: int = 4 -) -> None: - """ - Performs Evolutionary Structural Optimization (ESO) based on stiff for a structure. - - Parameters - ---------- - nodes : ndarray - Array of node coordinates and boundary conditions with the format - [node number, x, y, z, BC], where BC indicates boundary conditions. - els : ndarray - Array of elements with the format [element number, material, node 1, node 2, ...]. - mats : ndarray - Array of material properties with the format [E, nu, rho], where: - - E is the Young's modulus, - - nu is the Poisson's ratio, - - rho is the density. - loads : ndarray - Array of elements with the format [node number, X load magnitud, Y load magnitud, Z load magnitud]. - idx_BC : ndarray - Array of node indices with boundary conditions applied. - niter : int - Number of iterations for the ESO process. - RR : float - Initial relative stress threshold for removing elements. - ER : float - Increment of the relative stress threshold (RR) for each iteration. - volfrac : float - Target volume fraction for the optimized structure, expressed as a fraction of the initial volume. - plot : bool, optional - If True, plot the initial and optimized meshes. Defaults to False. - dim_problem : int, optional - Dimension of the problem (2 for 2D, 3 for 3D). Default is 2. - nnodes : int, optional - Number of nodes per element. For 2D problems it can be 3 or 4 and for 3D problems 4 or 8. Default is 4. - - Returns - ------- - ELS : ndarray - Array of the optimized elements after the ESO process. - nodes : ndarray - Array of the optimized nodes after the ESO process. - UC : ndarray - Array with the displacements. - E_nodes : ndarray - Strains evaluated at the nodes. - S_nodes : ndarray - Stresses evaluated at the nodes. - - Notes - ----- - - This function performs structural optimization by iteratively removing elements with low relative stress. - - The relative stress threshold (RR) increases in each iteration to progressively refine the structure. - - The optimization stops either after reaching the specified number of iterations or if the target volume fraction is achieved. - - Process - ------- - 1. Assemble the global stiffness matrix and load vector. - 2. Solve the linear system to compute nodal displacements. - 3. Calculate element stresses and strains. - 4. Compute the von Mises stress for each element and identify elements to remove. - 5. Update the structure by removing selected elements and their associated nodes. - 6. Repeat until the specified number of iterations or target volume fraction is reached. - - Visualization - ------------- - If `plot` is True, the function will generate: - - A plot of the initial and optimized structures showing displacements, strains, and stresses. - - A filled contour plot of the final optimized mesh. - - Example - ------- - >>> optimized_els, optimized_nodes = ESO_stiff( - ... nodes, els, mats, idx_BC, niter=10, RR=0.8, ER=0.05, volfrac=0.5, plot=True - ... ) - """ - assert dim_problem in [2, 3], "dim_problem must be either 2 (for 2D) or 3 (for 3D)" - assert nnodes in [3, 4, 8], "nnodes must be either 3, 4 (for 2D) or 4, 8 (for 3D)" - - uel_func = None - if dim_problem == 2: - if nnodes == 3: - uel_func = uel.elast_tri3 - else: - uel_func = uel.elast_quad4 - elif dim_problem == 3: - if nnodes == 4: - uel_func = uel.elast_tet4 - else: - uel_func = uel.elast_hex8 - - elsI= np.copy(els) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UCI = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodesI, S_nodesI = pos.strain_nodes_3d(nodes, els, mats[:,:2], UCI) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UCI) - - Vi = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - V_opt = Vi * volfrac - - ELS = None - for _ in range(niter): - print("Number of elements: {}".format(els.shape[0])) - - # Check equilibrium - Vi = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - if not np.allclose(stiff_mat.dot(disp)/stiff_mat.max(), rhs_vec/stiff_mat.max()) or Vi < V_opt: - break - - # Storage the solution - ELS = els - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UC = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodes, S_nodes = pos.strain_nodes_3d(nodes, els, mats[:,:2], UC) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UC) - - # Compute Sensitivity number - sensi_number = sensitivity_elsESO(nodes, mats, els, UC, uel_func, dim_problem, nnodes) # Sensitivity number - - mask_del = sensi_number < RR # Mask of elements to be removed - mask_els = protect_elsESO(els, loads, idx_BC, nnodes) # Mask of elements to do not remove - mask_del *= mask_els # Mask of elements to be removed and not protected - - # Remove/add elements - els = np.delete(els, mask_del, 0) # Remove elements - del_nodeESO(nodes, els, nnodes, dim_problem) # Remove nodes - - RR += ER - - if plot and dim_problem == 2: - pos.fields_plot(elsI, nodes, UCI, E_nodes=E_nodesI, S_nodes=S_nodesI) # Plot initial mesh - pos.fields_plot(ELS, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # Plot optimized mesh - - fill_plot = np.ones(E_nodes.shape[0]) - plt.figure() - tri = pos.mesh2tri(nodes, ELS) - plt.tricontourf(tri, fill_plot, cmap='binary') - plt.axis("image"); - elif plot and dim_problem == 3: - pos.fields_plot_3d(nodes, ELS, loads, idx_BC, S_nodes, E_nodes, nnodes=8, data_type='stress', show_BC=True, show_loads=True, arrow_scale=2.0, arrow_color="blue", cmap="viridis", show_axes=True, show_bounds=True, show_edges=False) - - return ELS, nodes, UC, E_nodes, S_nodes - -# %% -# load_directions = np.array([[0, 1, 0]]) -# load_positions = np.array([[0, 0, 1]]) -load_directions = np.array([[0, 1, 0], [1, 0, 0], [0, 0, -1]]) -load_positions = np.array([[5, 5, 9], [1, 1, 9], [8, 8, 9]]) - -# Call the function -nodes, mats, els, loads, idx_BC = structure_3d( - L=10, - H=10, - W=10, - E=206.8e9, - v=0.28, - nx=10, - ny=10, - nz=10, - dirs=load_directions, - positions=load_positions -) - -els, nodes, UC, E_nodes, S_nodes = ESO_stiff( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - RR=0.0001, - ER=0.001, - volfrac=0.5, - plot=True, - dim_problem=3, - nnodes=8) - -# %% -nodes, mats, els, loads, idx_BC = structures( - L=60, - H=60, - nx=60, - ny=60, - dirs=np.array([[0, -1]]), - positions=np.array([[15, 1]]), - n=1) - -els, nodes, UC, E_nodes, S_nodes = ESO_stiff( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - RR=0.0001, - ER=0.001, - volfrac=0.5, - plot=True, - dim_problem=2, - nnodes=4) \ No newline at end of file diff --git a/src/solidspy_opt/test_opt3.py b/src/solidspy_opt/test_opt3.py deleted file mode 100644 index 6628b88..0000000 --- a/src/solidspy_opt/test_opt3.py +++ /dev/null @@ -1,287 +0,0 @@ -# %% -%matplotlib widget -import matplotlib.pyplot as plt -from matplotlib import colors -import numpy as np -from numpy.typing import NDArray -from typing import List, Tuple, AnyStr -from scipy.sparse.linalg import spsolve - -from utils.structures import * -from utils.solver import * -from utils.volumes import * - -import solidspy.assemutil as ass -import solidspy.postprocesor as pos -import solidspy.uelutil as uel -np.seterr(divide='ignore', invalid='ignore') - -def BESO( - nodes: NDArray[np.float64], - els: NDArray[np.int_], - mats: NDArray[np.float64], - loads: NDArray[np.float64], - idx_BC: NDArray[np.float64], - niter: int, - t: float, - ER: float, - volfrac: float, - plot: bool = False, - dim_problem: int = 2, - nnodes: int = 4 -) -> None: - """ - Performs Bi-directional Evolutionary Structural Optimization (BESO) for a 3D structure. - - Parameters - ---------- - nodes : ndarray - Array of node coordinates and boundary conditions with the format - [node number, x, y, z, BC], where BC indicates boundary conditions. - els : ndarray - Array of elements with the format [element number, material, node 1, node 2, ...]. - mats : ndarray - Array of material properties with the format [E, nu, rho], where: - - E is the Young's modulus, - - nu is the Poisson's ratio, - - rho is the density. - loads : ndarray - Array of elements with the format [node number, X load magnitud, Y load magnitud, Z load magnitud]. - idx_BC : ndarray - Array of node indices with boundary conditions applied. - niter : int - Number of iterations for the BESO process. - t : float - Target stress ratio for adding or removing elements. - ER : float - Increment of the stress ratio (t) for each iteration. - volfrac : float - Target volume fraction for the optimized structure, expressed as a fraction of the initial volume. - plot : bool, optional - If True, plot the initial and optimized meshes. Defaults to False. - dim_problem : int, optional - Dimension of the problem (2 for 2D, 3 for 3D). Default is 2. - nnodes : int, optional - Number of nodes per element. For 2D problems it can be 3 or 4 and for 3D problems 4 or 8. Default is 4. - - Returns - ------- - ELS : ndarray - Array of the optimized elements after the BESO process. - nodes : ndarray - Array of the optimized nodes after the BESO process. - UC : ndarray - Array with the displacements. - E_nodes : ndarray - Strains evaluated at the nodes. - S_nodes : ndarray - Stresses evaluated at the nodes. - - Notes - ----- - - This function performs structural optimization by iteratively adding or removing elements based on stress ratios. - - The stress ratio (t) adjusts in each iteration to refine the structure, achieving a balance between material addition and removal. - - The optimization stops either after reaching the specified number of iterations or if the target volume fraction is achieved. - - Process - ------- - 1. Assemble the global stiffness matrix and load vector. - 2. Solve the linear system to compute nodal displacements. - 3. Calculate element stresses and strains. - 4. Compute the von Mises stress for each element and identify elements to add or remove. - 5. Update the structure by modifying the elements and their associated nodes. - 6. Repeat until the specified number of iterations or target volume fraction is reached. - - Visualization - ------------- - If `plot` is True, the function will generate: - - A plot of the initial and optimized structures showing displacements, strains, and stresses. - - A filled contour plot of the final optimized mesh. - - Example - ------- - >>> optimized_els, optimized_nodes = BESO( - ... nodes, els, mats, idx_BC, niter=10, t=0.8, ER=0.05, volfrac=0.5, plot=True - ... ) - - """ - assert dim_problem in [2, 3], "dim_problem must be either 2 (for 2D) or 3 (for 3D)" - assert nnodes in [3, 4, 8], "nnodes must be either 3, 4 (for 2D) or 4, 8 (for 3D)" - - uel_func = None - if dim_problem == 2: - if nnodes == 3: - uel_func = uel.elast_tri3 - else: - uel_func = uel.elast_quad4 - elif dim_problem == 3: - if nnodes == 4: - uel_func = uel.elast_tet4 - else: - uel_func = uel.elast_hex8 - - elsI = np.copy(els) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UCI = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodesI, S_nodesI = pos.strain_nodes_3d(nodes, els, mats[:,:2], UCI) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UCI) - - r_min = np.linalg.norm(nodes[0,1:-dim_problem] - nodes[1,1:-dim_problem]) * 1 # Radius for the sensitivity filter - adj_nodes = adjacency_nodes(nodes, els, nnodes) # Adjacency nodes - # centers = center_els(nodes, els) # Centers of elements - centers = calculate_element_centers(nodes, els, dim_problem, nnodes) - - V = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - V_opt = V * volfrac - - # Initialize variables. - ELS = None - mask = np.ones(els.shape[0], dtype=bool) # Mask of elements to be removed - sensi_I = None - C_h = np.zeros(niter) # History of compliance - error = 1000 - - for i in range(niter): - # Calculate the optimal design array elements - els_del = els[mask].copy() # Elements to be removed - - print("Number of elements: {}".format(els_del.shape[0])) - - # Check equilibrium - Vi = calculate_mesh_volume(nodes, els_del) if dim_problem==3 else calculate_mesh_area(nodes, els_del) - if not np.allclose(stiff_mat.dot(disp)/stiff_mat.max(), rhs_vec/stiff_mat.max()) or Vi < V_opt: - break - - # Storage the solution - ELS = els_del - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els_del, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els_del, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UC = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodes, S_nodes = pos.strain_nodes_3d(nodes, els_del, mats[:,:2], UC) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UC) - - # Sensitivity filter - sensi_e = sensitivity_elsBESO(nodes, mats, els, mask, UC, uel_func, nnodes, dim_problem) # Calculate the sensitivity of the elements - sensi_nodes = sensitivity_nodes(nodes, adj_nodes, centers, sensi_e, dim_problem) # Calculate the sensitivity of the nodes - sensi_number = sensitivity_filter(nodes, centers, sensi_nodes, r_min, dim_problem) # Perform the sensitivity filter - - # Average the sensitivity numbers to the historical information - if i > 0: - sensi_number = (sensi_number + sensi_I)/2 # Average the sensitivity numbers to the historical information - sensi_number = sensi_number/sensi_number.max() # Normalize the sensitivity numbers - - # Check if the optimal volume is reached and calculate the next volume - V_r = False - if Vi <= V_opt: - els_k = els_del.shape[0] - V_r = True - break - else: - V_k = Vi * (1 + ER) if Vi < V_opt else Vi * (1 - ER) - - # Remove/add threshold - sensi_sort = np.sort(sensi_number)[::-1] # Sort the sensitivity numbers - els_k = els_del.shape[0]*V_k/Vi # Number of elements to be removed - alpha_del = sensi_sort[int(els_k)] # Threshold for removing elements - - # Remove/add elements - mask = sensi_number > alpha_del # Mask of elements to be removed - mask_els = protect_els(els[np.invert(mask)], els.shape[0], loads, idx_BC, nnodes) # Mask of elements to be protected - mask = np.bitwise_or(mask, mask_els) - del_node(nodes, els[mask], loads, idx_BC, dim_problem, nnodes) # Delete nodes - - # Calculate the strain energy and storage it - C = 0.5*rhs_vec.T@disp - C_h[i] = C - if i > 10: error = C_h[i-5:].sum() - C_h[i-10:-5].sum()/C_h[i-5:].sum() - - # Check for convergence - if error <= t and V_r == True: - print("convergence") - break - - # Save the sensitvity number for the next iteration - sensi_I = sensi_number.copy() - - if plot and dim_problem == 2: - pos.fields_plot(elsI, nodes, UCI, E_nodes=E_nodesI, S_nodes=S_nodesI) # Plot initial mesh - pos.fields_plot(ELS, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # Plot optimized mesh - - fill_plot = np.ones(E_nodes.shape[0]) - plt.figure() - tri = pos.mesh2tri(nodes, ELS) - plt.tricontourf(tri, fill_plot, cmap='binary') - plt.axis("image"); - elif plot and dim_problem == 3: - pos.fields_plot_3d(nodes, ELS, loads, idx_BC, S_nodes, E_nodes, nnodes=8, data_type='stress', show_BC=True, show_loads=True, arrow_scale=2.0, arrow_color="blue", cmap="viridis", show_axes=True, show_bounds=True, show_edges=False) - - return ELS, nodes, UC, E_nodes, S_nodes - -# %% -# load_directions = np.array([[0, 1, 0]]) -# load_positions = np.array([[0, 0, 1]]) -load_directions = np.array([[0, 1, 0], [1, 0, 0], [0, 0, -1]]) -load_positions = np.array([[5, 5, 9], [1, 1, 9], [8, 8, 9]]) - -# Call the function -nodes, mats, els, loads, idx_BC = structure_3d( - L=10, - H=10, - W=10, - E=206.8e9, - v=0.28, - nx=10, - ny=10, - nz=10, - dirs=load_directions, - positions=load_positions -) - -els, nodes, UC, E_nodes, S_nodes = BESO( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - t=0.0001, - ER=0.005, - volfrac=0.5, - plot=True, - dim_problem=3, - nnodes=8) - -# %% -nodes, mats, els, loads, idx_BC = structures( - L=60, - H=60, - nx=60, - ny=60, - dirs=np.array([[0, -1]]), - positions=np.array([[15, 1]]), - n=1) - -els, nodes, UC, E_nodes, S_nodes = BESO( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - t=0.0001, - ER=0.005, - volfrac=0.5, - plot=True, - dim_problem=2, - nnodes=4) \ No newline at end of file diff --git a/src/solidspy_opt/test_opt4.py b/src/solidspy_opt/test_opt4.py deleted file mode 100644 index 655397b..0000000 --- a/src/solidspy_opt/test_opt4.py +++ /dev/null @@ -1,254 +0,0 @@ -# %% -%matplotlib widget -import matplotlib.pyplot as plt -from matplotlib import colors -import numpy as np -from numpy.typing import NDArray -from typing import List, Tuple, AnyStr -from scipy.sparse.linalg import spsolve - -from utils.structures import * -from utils.solver import * -from utils.volumes import * - -import solidspy.assemutil as ass -import solidspy.postprocesor as pos -import solidspy.uelutil as uel -np.seterr(divide='ignore', invalid='ignore') - -def SIMP( - nodes: NDArray[np.float64], - els: NDArray[np.int_], - mats: NDArray[np.float64], - loads: NDArray[np.float64], - idx_BC: NDArray[np.float64], - niter: int, - penal: float, - volfrac: float, - dimensions: List[int]=None, - plot: bool = False, - dim_problem: int = 2, - nnodes: int = 4 -) -> None: - """ - Performs Structural Optimization using the Solid Isotropic Material with Penalization (SIMP) method for a 3D structure. - - Parameters - ---------- - nodes : ndarray - Array of node coordinates and boundary conditions with the format - [node number, x, y, z, BC], where BC indicates boundary conditions. - els : ndarray - Array of elements with the format [element number, material, node 1, node 2, ...]. - mats : ndarray - Array of material properties with the format [E, nu, rho], where: - - E is the Young's modulus, - - nu is the Poisson's ratio, - - rho is the density. - loads : ndarray - Array of elements with the format [node number, X load magnitud, Y load magnitud, Z load magnitud]. - idx_BC : ndarray - Array of boundary conditions. - niter : int - Number of iterations for the SIMP process. - penal : float - Penalization factor used to enforce material stiffness in intermediate densities. - volfrac : float - Target volume fraction for - dimensions : list - List of dimensions of the problem. Only need it for 2D problems. [nx, ny]. - nnodes : int, optional - Number of nodes per element. For 2D problems it can be 3 or 4 and for 3D problems 4 or 8. Default is 4. - - Returns - ------- - ELS : ndarray - Array of the optimized elements after the SIMP process. - nodes : ndarray - Array of the optimized nodes after the SIMP process. - - Notes - ----- - - The SIMP method iteratively updates element densities to optimize the material distribution. - - Element stiffness is penalized for intermediate densities to encourage a binary (solid or void) material distribution. - - The optimization stops after reaching the specified number of iterations or if the target volume fraction is achieved. - - Process - ------- - 1. Initialize element densities to satisfy the target volume fraction. - 2. Assemble the global stiffness matrix and load vector. - 3. Solve the linear system to compute nodal displacements. - 4. Compute element stiffnesses and objective function (e.g., compliance). - 5. Update element densities using the Optimality Criteria method. - 6. Repeat until the specified number of iterations or target volume fraction is reached. - - Visualization - ------------- - If `plot` is True, the function will generate: - - A plot of the initial and optimized structures showing displacements, strains, and stresses. - - A filled contour plot of the final optimized mesh. - - Example - ------- - >>> optimized_els, optimized_nodes = SIMP( - ... nodes, els, mats, niter=50, penal=3.0, volfrac=0.5, plot=True - ... ) - - """ - assert dim_problem in [2, 3], "dim_problem must be either 2 (for 2D) or 3 (for 3D)" - assert nnodes in [3, 4, 8], "nnodes must be either 3, 4 (for 2D) or 4, 8 (for 3D)" - - uel_func = None - if dim_problem == 2: - assert dimensions is not None, "For 2D problems, the dimensions parameter cannot be None" - if nnodes == 3: - uel_func = uel.elast_tri3 - else: - uel_func = uel.elast_quad4 - elif dim_problem == 3: - if nnodes == 4: - uel_func = uel.elast_tet4 - else: - uel_func = uel.elast_hex8 - - elsI = np.copy(els) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UCI = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodesI, S_nodesI = pos.strain_nodes_3d(nodes, els, mats[:,:2], UCI) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UCI) - - # Initialize variables - Emin=1e-9 # Minimum young modulus of the material - Emax=1.0 # Maximum young modulus of the material - - # Initialize the design variables - change = 10 # Change in the design variable - g = 0 # Constraint - nels = els.shape[0] # Number of elements - rho = 0.5 * np.ones(nels, dtype=float) # Initialize the density - sensi_rho = np.ones(nels) # Initialize the sensitivity - rho_old = rho.copy() # Initialize the density history - d_c = np.ones(nels) # Initialize the design change - - r_min = np.linalg.norm(nodes[0,1:-dim_problem] - nodes[1,1:-dim_problem]) * 4 # Radius for the sensitivity filter - centers = calculate_element_centers(nodes, els, dim_problem, nnodes) - - iter = 0 - for _ in range(niter): - iter += 1 - - # Check convergence - if change < 0.01: - print('Convergence reached') - break - - # Change density - mats[:,2] = Emin+rho**penal*(Emax-Emin) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - # stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - stiff_mat = sparse_assem(els, nodes, mats, neq, assem_op, dim_problem, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UC = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodes, S_nodes = pos.strain_nodes_3d(nodes, els, mats[:,:2], UC) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UC) - - compliance = rhs_vec.T.dot(disp) - - # Sensitivity analysis - # sensi_rho[:] = (np.dot(UC[els[:,-nnodes:]].reshape(els.shape[0],nnodes*dim_problem),kloc) * UC[els[:,-4:]].reshape(els.shape[0],nnodes*dim_problem) ).sum(1) - sensi_rho = sensitivity_elsSIMP(nodes, mats, els, UC, uel_func, nnodes, dim_problem) - d_c[:] = (-penal*rho**(penal-1)*(Emax-Emin))*sensi_rho - d_c[:] = density_filter(centers, r_min, rho, d_c) - - # Optimality criteria - rho_old[:] = rho - rho[:], g = optimality_criteria(nels, rho, d_c, g) - - # Compute the change - change = np.linalg.norm(rho.reshape(nels,1)-rho_old.reshape(nels,1),np.inf) - print(change) - - # Check equilibrium - if not np.allclose(stiff_mat.dot(disp)/stiff_mat.max(), rhs_vec/stiff_mat.max()): - break - - if plot and dim_problem == 2: - pos.fields_plot(elsI, nodes, UCI, E_nodes=E_nodesI, S_nodes=S_nodesI) # Plot initial mesh - pos.fields_plot(els, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # Plot optimized mesh - - plt.ion() - fig,ax = plt.subplots() - ax.imshow(-rho.reshape(dimensions[0], dimensions[1]), cmap='gray', interpolation='none',norm=colors.Normalize(vmin=-1,vmax=0)) - ax.set_title('Predicted') - fig.show() - elif plot and dim_problem == 3: - pos.fields_plot_3d(nodes, els, loads, idx_BC, S_nodes, E_nodes, rho=rho, nnodes=8, data_type='stress', show_BC=True, show_loads=True, arrow_scale=2.0, arrow_color="blue", cmap="viridis", show_axes=True, show_bounds=True, show_edges=False) - - return rho, nodes, UC, E_nodes, S_nodes - -# %% -# load_directions = np.array([[0, 1, 0]]) -# load_positions = np.array([[0, 0, 1]]) -load_directions = np.array([[0, 1, 0], [1, 0, 0], [0, 0, -1]]) -load_positions = np.array([[5, 5, 9], [1, 1, 9], [8, 8, 9]]) - -# Call the function -nodes, mats, els, loads, idx_BC = structure_3d( - L=10, - H=10, - W=10, - E=206.8e9, - v=0.28, - nx=10, - ny=10, - nz=10, - dirs=load_directions, - positions=load_positions -) - -rho, nodes, UC, E_nodes, S_nodes = SIMP( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - penal=3, - volfrac=0.5, - plot=True, - dim_problem=3, - nnodes=8) - -# %% -nodes, mats, els, loads, idx_BC = structures( - L=60, - H=60, - nx=60, - ny=60, - dirs=np.array([[0, -1]]), - positions=np.array([[15, 1]]), - n=1) - -rho, nodes, UC, E_nodes, S_nodes = SIMP( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - penal=3, - volfrac=0.5, - dimensions=[60, 60], - plot=True, - dim_problem=2, - nnodes=4) \ No newline at end of file diff --git a/src/solidspy_opt/testtest.py b/src/solidspy_opt/testtest.py deleted file mode 100644 index f90cee6..0000000 --- a/src/solidspy_opt/testtest.py +++ /dev/null @@ -1,287 +0,0 @@ -# %% -%matplotlib widget -import matplotlib.pyplot as plt -from matplotlib import colors -import numpy as np -from numpy.typing import NDArray -from typing import List, Tuple, AnyStr -from scipy.sparse.linalg import spsolve - -from utils.structures import * -from utils.solver import * -from utils.volumes import * - -import solidspy.assemutil as ass -import solidspy.postprocesor as pos -import solidspy.uelutil as uel -np.seterr(divide='ignore', invalid='ignore') - -def BESO( - nodes: NDArray[np.float64], - els: NDArray[np.int_], - mats: NDArray[np.float64], - loads: NDArray[np.float64], - idx_BC: NDArray[np.float64], - niter: int, - t: float, - ER: float, - volfrac: float, - plot: bool = False, - dim_problem: int = 2, - nnodes: int = 4 -) -> None: - """ - Performs Bi-directional Evolutionary Structural Optimization (BESO) for a 3D structure. - - Parameters - ---------- - nodes : ndarray - Array of node coordinates and boundary conditions with the format - [node number, x, y, z, BC], where BC indicates boundary conditions. - els : ndarray - Array of elements with the format [element number, material, node 1, node 2, ...]. - mats : ndarray - Array of material properties with the format [E, nu, rho], where: - - E is the Young's modulus, - - nu is the Poisson's ratio, - - rho is the density. - loads : ndarray - Array of elements with the format [node number, X load magnitud, Y load magnitud, Z load magnitud]. - idx_BC : ndarray - Array of node indices with boundary conditions applied. - niter : int - Number of iterations for the BESO process. - t : float - Target stress ratio for adding or removing elements. - ER : float - Increment of the stress ratio (t) for each iteration. - volfrac : float - Target volume fraction for the optimized structure, expressed as a fraction of the initial volume. - plot : bool, optional - If True, plot the initial and optimized meshes. Defaults to False. - dim_problem : int, optional - Dimension of the problem (2 for 2D, 3 for 3D). Default is 2. - nnodes : int, optional - Number of nodes per element. For 2D problems it can be 3 or 4 and for 3D problems 4 or 8. Default is 4. - - Returns - ------- - ELS : ndarray - Array of the optimized elements after the BESO process. - nodes : ndarray - Array of the optimized nodes after the BESO process. - UC : ndarray - Array with the displacements. - E_nodes : ndarray - Strains evaluated at the nodes. - S_nodes : ndarray - Stresses evaluated at the nodes. - - Notes - ----- - - This function performs structural optimization by iteratively adding or removing elements based on stress ratios. - - The stress ratio (t) adjusts in each iteration to refine the structure, achieving a balance between material addition and removal. - - The optimization stops either after reaching the specified number of iterations or if the target volume fraction is achieved. - - Process - ------- - 1. Assemble the global stiffness matrix and load vector. - 2. Solve the linear system to compute nodal displacements. - 3. Calculate element stresses and strains. - 4. Compute the von Mises stress for each element and identify elements to add or remove. - 5. Update the structure by modifying the elements and their associated nodes. - 6. Repeat until the specified number of iterations or target volume fraction is reached. - - Visualization - ------------- - If `plot` is True, the function will generate: - - A plot of the initial and optimized structures showing displacements, strains, and stresses. - - A filled contour plot of the final optimized mesh. - - Example - ------- - >>> optimized_els, optimized_nodes = BESO( - ... nodes, els, mats, idx_BC, niter=10, t=0.8, ER=0.05, volfrac=0.5, plot=True - ... ) - - """ - assert dim_problem in [2, 3], "dim_problem must be either 2 (for 2D) or 3 (for 3D)" - assert nnodes in [3, 4, 8], "nnodes must be either 3, 4 (for 2D) or 4, 8 (for 3D)" - - uel_func = None - if dim_problem == 2: - if nnodes == 3: - uel_func = uel.elast_tri3 - else: - uel_func = uel.elast_quad4 - elif dim_problem == 3: - if nnodes == 4: - uel_func = uel.elast_tet4 - else: - uel_func = uel.elast_hex8 - - elsI = np.copy(els) - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UCI = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodesI, S_nodesI = pos.strain_nodes_3d(nodes, els, mats[:,:2], UCI) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UCI) - - r_min = np.linalg.norm(nodes[0,1:-dim_problem] - nodes[1,1:-dim_problem]) * 1 # Radius for the sensitivity filter - adj_nodes = adjacency_nodes(nodes, els, nnodes) # Adjacency nodes - # centers = center_els(nodes, els) # Centers of elements - centers = calculate_element_centers(nodes, els, dim_problem, nnodes) - - V = calculate_mesh_volume(nodes, els) if dim_problem==3 else calculate_mesh_area(nodes, els) - V_opt = V * volfrac - - # Initialize variables. - ELS = None - mask = np.ones(els.shape[0], dtype=bool) # Mask of elements to be removed - sensi_I = None - C_h = np.zeros(niter) # History of compliance - error = 1000 - - for i in range(niter): - # Calculate the optimal design array elements - els_del = els[mask].copy() # Elements to be removed - - print("Number of elements: {}".format(els_del.shape[0])) - - # Check equilibrium - Vi = calculate_mesh_volume(nodes, els_del) if dim_problem==3 else calculate_mesh_area(nodes, els_del) - if not np.allclose(stiff_mat.dot(disp)/stiff_mat.max(), rhs_vec/stiff_mat.max()) or Vi < V_opt: - break - - # Storage the solution - ELS = els_del - - # System assembly - assem_op, IBC, neq = ass.DME(nodes[:, -dim_problem:], els_del, ndof_el_max=nnodes*dim_problem) - stiff_mat, _ = ass.assembler(els_del, mats, nodes[:, :-dim_problem], neq, assem_op, uel=uel_func) - rhs_vec = ass.loadasem(loads, IBC, neq) - - # System solution - disp = spsolve(stiff_mat, rhs_vec) - UC = pos.complete_disp(IBC, nodes, disp, ndof_node=dim_problem) - E_nodes, S_nodes = pos.strain_nodes_3d(nodes, els_del, mats[:,:2], UC) if dim_problem==3 else pos.strain_nodes(nodes, els, mats[:,:2], UC) - - # Sensitivity filter - sensi_e = sensitivity_elsBESO(nodes, mats, els, mask, UC, uel_func, nnodes, dim_problem) # Calculate the sensitivity of the elements - sensi_nodes = sensitivity_nodes(nodes, adj_nodes, centers, sensi_e, dim_problem) # Calculate the sensitivity of the nodes - sensi_number = sensitivity_filter(nodes, centers, sensi_nodes, r_min, dim_problem) # Perform the sensitivity filter - - # Average the sensitivity numbers to the historical information - if i > 0: - sensi_number = (sensi_number + sensi_I)/2 # Average the sensitivity numbers to the historical information - sensi_number = sensi_number/sensi_number.max() # Normalize the sensitivity numbers - - # Check if the optimal volume is reached and calculate the next volume - V_r = False - if Vi <= V_opt: - els_k = els_del.shape[0] - V_r = True - break - else: - V_k = Vi * (1 + ER) if Vi < V_opt else Vi * (1 - ER) - - # Remove/add threshold - sensi_sort = np.sort(sensi_number)[::-1] # Sort the sensitivity numbers - els_k = els_del.shape[0]*V_k/Vi # Number of elements to be removed - alpha_del = sensi_sort[int(els_k)] # Threshold for removing elements - - # Remove/add elements - mask = sensi_number > alpha_del # Mask of elements to be removed - mask_els = protect_els(els[np.invert(mask)], els.shape[0], loads, idx_BC, nnodes) # Mask of elements to be protected - mask = np.bitwise_or(mask, mask_els) - del_node(nodes, els[mask], loads, idx_BC, dim_problem, nnodes) # Delete nodes - - # Calculate the strain energy and storage it - C = 0.5*rhs_vec.T@disp - C_h[i] = C - if i > 10: error = C_h[i-5:].sum() - C_h[i-10:-5].sum()/C_h[i-5:].sum() - - # Check for convergence - if error <= t and V_r == True: - print("convergence") - break - - # Save the sensitvity number for the next iteration - sensi_I = sensi_number.copy() - - if plot and dim_problem == 2: - pos.fields_plot(elsI, nodes, UCI, E_nodes=E_nodesI, S_nodes=S_nodesI) # Plot initial mesh - pos.fields_plot(ELS, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # Plot optimized mesh - - fill_plot = np.ones(E_nodes.shape[0]) - plt.figure() - tri = pos.mesh2tri(nodes, ELS) - plt.tricontourf(tri, fill_plot, cmap='binary') - plt.axis("image"); - elif plot and dim_problem == 3: - pos.fields_plot_3d(nodes, ELS, loads, idx_BC, S_nodes, E_nodes, nnodes=8, data_type='stress', show_BC=True, show_loads=True, arrow_scale=2.0, arrow_color="blue", cmap="viridis", show_axes=True, show_bounds=True, show_edges=False) - - return ELS, nodes, UC, E_nodes, S_nodes - -# %% -# load_directions = np.array([[0, 1, 0]]) -# load_positions = np.array([[0, 0, 1]]) -load_directions = np.array([[0, 1, 0], [1, 0, 0], [0, 0, -1]]) -load_positions = np.array([[5, 5, 9], [1, 1, 9], [8, 8, 9]]) - -# Call the function -nodes, mats, els, loads, idx_BC = structure_3d( - L=10, - H=10, - W=10, - E=206.8e9, - v=0.28, - nx=10, - ny=10, - nz=10, - dirs=load_directions, - positions=load_positions -) - -els, nodes, UC, E_nodes, S_nodes = BESO( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - t=0.005, - ER=0.005, - volfrac=0.5, - plot=True, - dim_problem=3, - nnodes=8) - -# %% -nodes, mats, els, loads, idx_BC = structures( - L=60, - H=60, - nx=60, - ny=60, - dirs=np.array([[0, -1]]), - positions=np.array([[15, 1]]), - n=1) - -els, nodes, UC, E_nodes, S_nodes = BESO( - nodes=nodes, - els=els, - mats=mats, - loads=loads, - idx_BC=idx_BC, - niter=200, - t=0.0001, - ER=0.005, - volfrac=0.5, - plot=False, - dim_problem=2, - nnodes=4) \ No newline at end of file diff --git a/src/solidspy_opt/utils/__init__.py b/src/solidspy_opt/utils/__init__.py index 4ce19f7..c86ae9a 100644 --- a/src/solidspy_opt/utils/__init__.py +++ b/src/solidspy_opt/utils/__init__.py @@ -1,2 +1,3 @@ -from utils.structures import structures -from utils.solver import protect_els, del_node, volume, sensitivity_elsBESO, adjacency_nodes, center_els, sensitivity_nodes, sensitivity_filter, sensitivity_elsESO, strain_els, protect_elsESO, del_nodeESO, sparse_assem, optimality_criteria, density_filter, center_els \ No newline at end of file +from solidspy_opt.utils.structures import * +from solidspy_opt.utils.solver import * +from solidspy_opt.utils.volumes import * \ No newline at end of file diff --git a/src/solidspy_opt/utils/solver.py b/src/solidspy_opt/utils/solver.py index 55a1e5b..025b130 100644 --- a/src/solidspy_opt/utils/solver.py +++ b/src/solidspy_opt/utils/solver.py @@ -6,7 +6,6 @@ import solidspy.uelutil as uel import solidspy.assemutil as ass - def protect_els( els: NDArray[np.float64], nels: int, @@ -726,8 +725,7 @@ def calculate_element_centers( for el in els: el_num = int(el[0]) - node_indices = el[2 : 2 + nnodes].astype(int) - node_coords = nodes[node_indices, 1 : 1 + dim_problem] + node_coords = nodes[el[-nnodes:], 1:-dim_problem] if dim_problem == 2: # Triangles or quads diff --git a/src/solidspy_opt/utils/structures.py b/src/solidspy_opt/utils/structures.py index c2a855d..b2255f2 100644 --- a/src/solidspy_opt/utils/structures.py +++ b/src/solidspy_opt/utils/structures.py @@ -1,18 +1,28 @@ import numpy as np import solidspy.preprocesor as pre +from typing import Tuple +from numpy.typing import NDArray -def structures(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), positions=np.array([]), n=1): +def structures( + L: float = 10, + H: float = 10, + E: float = 206.8e9, + v: float = 0.28, + nx: int = 20, + ny: int = 20, + dirs: np.ndarray = np.array([]), + positions: np.ndarray = np.array([]), + n: int = 1 +): """ - This function selects the appropriate structure function to call based on the value of n. + This function selects the appropriate structure function to call based on n. Parameters ---------- L : float, optional - structure's length, by default 10 + Structure's length, by default 10 H : float, optional - structure's height, by default 10 - F : float, optional - Vertical force, by default -1000000 + Structure's height, by default 10 E : float, optional Young's modulus, by default 206.8e9 v : float, optional @@ -21,31 +31,54 @@ def structures(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), p Number of elements in the x direction, by default 20 ny : int, optional Number of elements in the y direction, by default 20 + dirs : np.ndarray, optional + Directions of the loads, default np.array([]) + positions : np.ndarray, optional + Positions of the loads, default np.array([]) n : int, optional Selector for the structure function to call, by default 1 Returns ------- - ndarray - Nodes array returned by the selected structure function + nodes, mats, els, loads, idx_BC + The outputs returned by the selected structure function. """ - match n: - case 1: - return structure_1(L, H, E, v, nx, ny, dirs, positions) - case 2: - return structure_2(L, H, E, v, nx, ny, dirs, positions) + structure_map = { + 1: structure_1, + 2: structure_2, + # If you had more, you could add them here, + # 3: structure_3, etc. + } + if n not in structure_map: + raise ValueError( + f"Invalid structure ID: {n}. " + f"Available structures are: {list(structure_map.keys())}" + ) -def structure_1(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), positions=np.array([])): + # Call the function corresponding to 'n' + return structure_map[n](L, H, E, v, nx, ny, dirs, positions) + + +def structure_1( + L: float = 10.0, + H: float = 10.0, + E: float = 206.8e9, + v: float = 0.28, + nx: int = 20, + ny: int = 20, + dirs: NDArray[np.float64] = np.array([]), + positions: NDArray[np.float64] = np.array([]) +) -> Tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.int_], NDArray[np.int_], NDArray[np.float64]]: """ - Make the mesh for a cuadrilateral model with cantilever structure's constrains. + Make the mesh for a quadrilateral model with cantilever constraints. Parameters ---------- L : float, optional - Length of the structure, by default 10 + Length of the structure (in the x-direction), by default 10.0 H : float, optional - Height of the structure, by default 10 + Height of the structure (in the y-direction), by default 10.0 E : float, optional Young's modulus, by default 206.8e9 v : float, optional @@ -54,51 +87,73 @@ def structure_1(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), Number of elements in the x direction, by default 20 ny : int, optional Number of elements in the y direction, by default 20 - dirs : ndarray, optional - An array with the directions of the loads, by default empty array. [[0,1],[1,0],[0,-1]] - positions : ndarray, optional - An array with the positions of the loads, by default empty array. [[61,30], [1,30], [30, 1]] + dirs : NDArray[np.float64], optional + Array with the directions of the loads, shape (n_loads, 2). + Example: [[0,1],[1,0],[0,-1]] + By default an empty array. + positions : NDArray[np.float64], optional + Array with the positions of the loads, shape (n_loads, 2). + Example: [[61,30], [1,30], [30, 1]] + By default an empty array. Returns ------- - nodes : ndarray - Array of nodes - mats : ndarray - Array of material properties - els : ndarray - Array of elements - loads : ndarray - Array of loads + nodes : NDArray[np.float64] + Node array with shape ((nx+1)*(ny+1), 5). Columns: + [node_id, x, y, BC_x, BC_y]. + mats : NDArray[np.float64] + Material properties array with shape (number_of_elements, 3). + Each row: [E, v, placeholder]. + els : NDArray[np.int_] + Element connectivity array from `pre.rect_grid`, shape (number_of_elements, ?). + loads : NDArray[np.int_] + Load array with shape (dirs.shape[0], 3), columns: + [node_id, load_dir_x, load_dir_y]. + idx_BC : NDArray[np.float64] + Indices of nodes with boundary conditions (where x == -L/2). """ x, y, els = pre.rect_grid(L, H, nx, ny) mats = np.zeros((els.shape[0], 3)) - mats[:] = [E,v,1] - nodes = np.zeros(((nx + 1)*(ny + 1), 5)) - nodes[:, 0] = range((nx + 1)*(ny + 1)) + mats[:] = [E, v, 1] + nodes = np.zeros(((nx + 1) * (ny + 1), 5)) + nodes[:, 0] = range((nx + 1) * (ny + 1)) nodes[:, 1] = x nodes[:, 2] = y - mask = (x==-L/2) - nodes[mask, 3:] = -1 - loads = np.zeros((dirs.shape[0], 3), dtype=int) - node_index = nx*positions[:,0]+(positions[:,0]-positions[:,1]) + # Constrain nodes on left face (x == -L/2) + mask = (x == -L / 2) + nodes[mask, 3:] = -1 # BC flags in last two columns + # Prepare loads + loads = np.zeros((dirs.shape[0], 3), dtype=int) + node_index = nx * positions[:, 0] + (positions[:, 0] - positions[:, 1]) loads[:, 0] = node_index - loads[:, 1] = dirs[:,0] - loads[:, 2] = dirs[:,1] + loads[:, 1] = dirs[:, 0] + loads[:, 2] = dirs[:, 1] + idx_BC = nodes[mask, 0] return nodes, mats, els, loads, idx_BC -def structure_2(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), positions=np.array([])): + +def structure_2( + L: float = 10.0, + H: float = 10.0, + E: float = 206.8e9, + v: float = 0.28, + nx: int = 20, + ny: int = 20, + dirs: NDArray[np.float64] = np.array([]), + positions: NDArray[np.float64] = np.array([]) +) -> Tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.int_], NDArray[np.int_], NDArray[np.float64]]: """ - Make the mesh for a cuadrilateral model with simply supported structure's constrains. + Make the mesh for a quadrilateral model with simply supported constraints. Parameters ---------- L : float, optional - Length of the structure, by default 10 + Length of the structure (in the x-direction), by default 10.0 H : float, optional - Height of the structure, by default 10 + Height of the structure (in the y-direction), by default 10.0 E : float, optional Young's modulus, by default 206.8e9 v : float, optional @@ -107,55 +162,80 @@ def structure_2(L=10, H=10, E=206.8e9, v=0.28, nx=20, ny=20, dirs=np.array([]), Number of elements in the x direction, by default 20 ny : int, optional Number of elements in the y direction, by default 20 - dirs : ndarray, optional - An array with the directions of the loads, by default empty array. [[0,1],[1,0],[0,-1]] - positions : ndarray, optional - An array with the positions of the loads, by default empty array. [[61,30], [1,30], [30, 1]] + dirs : NDArray[np.float64], optional + Array with the directions of the loads, shape (n_loads, 2). + Example: [[0,1],[1,0],[0,-1]] + By default an empty array. + positions : NDArray[np.float64], optional + Array with the positions of the loads, shape (n_loads, 2). + Example: [[61,30], [1,30], [30, 1]] + By default an empty array. Returns ------- - nodes : ndarray - Array of nodes - mats : ndarray - Array of material properties - els : ndarray - Array of elements - loads : ndarray - Array of loads + nodes : NDArray[np.float64] + Node array with shape ((nx+1)*(ny+1), 5). Columns: + [node_id, x, y, BC_x, BC_y]. + mats : NDArray[np.float64] + Material properties array with shape (number_of_elements, 3). + Each row: [E, v, placeholder]. + els : NDArray[np.int_] + Element connectivity array from `pre.rect_grid`, shape (number_of_elements, ?). + loads : NDArray[np.int_] + Load array with shape (dirs.shape[0], 3), columns: + [node_id, load_dir_x, load_dir_y]. + idx_BC : NDArray[np.float64] + Indices of nodes with boundary conditions on two regions: + (x == L/2) & (y > H/4) or (x == L/2) & (y < -H/4). """ x, y, els = pre.rect_grid(L, H, nx, ny) mats = np.zeros((els.shape[0], 3)) - mats[:] = [E,v,1] - nodes = np.zeros(((nx + 1)*(ny + 1), 5)) - nodes[:, 0] = range((nx + 1)*(ny + 1)) + mats[:] = [E, v, 1] + nodes = np.zeros(((nx + 1) * (ny + 1), 5)) + nodes[:, 0] = range((nx + 1) * (ny + 1)) nodes[:, 1] = x nodes[:, 2] = y - mask_1 = (x == L/2) & (y > H/4) - mask_2 = (x == L/2) & (y < -H/4) + + # Constrain nodes on right face (x == L/2) but only above y>H/4 or below y<-H/4 + mask_1 = (x == L / 2) & (y > H / 4) + mask_2 = (x == L / 2) & (y < -H / 4) mask = np.bitwise_or(mask_1, mask_2) nodes[mask, 3:] = -1 + # Prepare loads loads = np.zeros((dirs.shape[0], 3), dtype=int) - node_index = nx*positions[:,0]+(positions[:,0]-positions[:,1]) - + node_index = nx * positions[:, 0] + (positions[:, 0] - positions[:, 1]) loads[:, 0] = node_index - loads[:, 1] = dirs[:,0] - loads[:, 2] = dirs[:,1] + loads[:, 1] = dirs[:, 0] + loads[:, 2] = dirs[:, 1] + idx_BC = nodes[mask, 0] return nodes, mats, els, loads, idx_BC -def structure_3d(L=10, H=10, W=10, E=206.8e9, v=0.28, nx=10, ny=10, nz=10, dirs=np.array([]), positions=np.array([])): + +def structure_3d( + L: float = 10.0, + H: float = 10.0, + W: float = 10.0, + E: float = 206.8e9, + v: float = 0.28, + nx: int = 10, + ny: int = 10, + nz: int = 10, + dirs: NDArray[np.float64] = np.array([]), + positions: NDArray[np.float64] = np.array([]) +) -> Tuple[NDArray[np.float64], NDArray[np.float64], NDArray[np.int_], NDArray[np.float64], NDArray[np.int_]]: """ - Make the mesh for a cubic model with cantilever structure constraints. + Make the mesh for a cubic model with cantilever constraints in 3D. Parameters ---------- L : float, optional - Length of the structure (x-direction), by default 10 + Length of the structure (x-direction), by default 10.0 H : float, optional - Height of the structure (y-direction), by default 10 + Height of the structure (y-direction), by default 10.0 W : float, optional - Width of the structure (z-direction), by default 10 + Width of the structure (z-direction), by default 10.0 E : float, optional Young's modulus, by default 206.8e9 v : float, optional @@ -166,38 +246,46 @@ def structure_3d(L=10, H=10, W=10, E=206.8e9, v=0.28, nx=10, ny=10, nz=10, dirs= Number of elements in the y direction, by default 10 nz : int, optional Number of elements in the z direction, by default 10 - dirs : ndarray, optional - An array with the directions of the loads, by default empty array. [[0,1,0],[1,0,0],[0,0,-1]] - positions : ndarray, optional - An array with the positions of the loads, by default empty array. [[5,5,9], [1,1,9], [8, 8, 9]] + dirs : NDArray[np.float64], optional + Array of load directions, shape (n_loads, 3). + Example: [[0,1,0],[1,0,0],[0,0,-1]] + By default an empty array. + positions : NDArray[np.float64], optional + Array of load positions (in grid indexing), shape (n_loads, 3). + Example: [[5,5,9], [1,1,9], [8,8,9]] + By default an empty array. Returns ------- - nodes : ndarray - Array of nodes - mats : ndarray - Array of material properties - els : ndarray - Array of elements - loads : ndarray - Array of loads - idx_BC : ndarray - Indices of nodes on the constrained face + nodes : NDArray[np.float64] + Node array of shape ((nx+1)*(ny+1)*(nz+1), 7). + Columns: [node_id, x, y, z, BC_x, BC_y, BC_z]. + mats : NDArray[np.float64] + Material properties array of shape (number_of_elements, 3). + Each row: [E, v, placeholder]. + els : NDArray[np.int_] + Element connectivity array of shape (nx*ny*nz, 11). + For example: [element_id, material_id, 0, n0, n2, n3, n1, n4, n6, n7, n5]. + loads : NDArray[np.float64] + Loads array of shape (dirs.shape[0], 4). + Columns: [node_id, Fx, Fy, Fz]. + idx_BC : NDArray[np.int_] + Indices of nodes on the constrained face (z = 0). """ # Generate 3D grid of nodes - x = np.linspace(-L/2, L/2, nx + 1) - y = np.linspace(-H/2, H/2, ny + 1) + x = np.linspace(-L / 2, L / 2, nx + 1) + y = np.linspace(-H / 2, H / 2, ny + 1) z = np.linspace(0, W, nz + 1) xv, yv, zv = np.meshgrid(x, y, z, indexing='ij') - - nodes = np.zeros(((nx + 1) * (ny + 1) * (nz + 1), 7)) # Added columns for BCs in X, Y, Z - nodes[:, 0] = np.arange(nodes.shape[0]) # Node IDs + + nodes = np.zeros(((nx + 1) * (ny + 1) * (nz + 1), 7)) + nodes[:, 0] = np.arange(nodes.shape[0]) # Node IDs nodes[:, 1] = xv.ravel() nodes[:, 2] = yv.ravel() nodes[:, 3] = zv.ravel() - # Create elements (hexahedral) - els = [] + # Build hexahedral elements + els_list = [] count = 0 for i in range(nx): for j in range(ny): @@ -210,34 +298,43 @@ def structure_3d(L=10, H=10, W=10, E=206.8e9, v=0.28, nx=10, ny=10, nz=10, dirs= n5 = n4 + 1 n6 = n4 + (nz + 1) n7 = n6 + 1 - els.append([count, 9, 0, n0, n2, n3, n1, n4, n6, n7, n5]) + # [element_id, material_id, 0, node0, node2, node3, node1, node4, node6, node7, node5] + els_list.append([count, 9, 0, n0, n2, n3, n1, n4, n6, n7, n5]) count += 1 - els = np.array(els, dtype=int) + els = np.array(els_list, dtype=int) - # Assign material properties to elements + # Assign material properties mats = np.zeros((els.shape[0], 3)) - mats[:, 0] = E # Young's modulus - mats[:, 1] = v # Poisson's ratio - mats[:, 2] = 1 # Placeholder property - - # Apply constraints on one face (z = 0) - mask_z0 = nodes[:, 3] == 0 # Nodes where z = 0 - nodes[mask_z0, 4] = -1 # BC in X direction - nodes[mask_z0, 5] = -1 # BC in Y direction - nodes[mask_z0, 6] = -1 # BC in Z direction + mats[:, 0] = E + mats[:, 1] = v + mats[:, 2] = 1 + # Apply constraints on face z = 0 + mask_z0 = (nodes[:, 3] == 0.0) + nodes[mask_z0, 4] = -1 # BC_x + nodes[mask_z0, 5] = -1 # BC_y + nodes[mask_z0, 6] = -1 # BC_z idx_BC = nodes[mask_z0, 0].astype(int) - # Define loads on the opposite face (z = W) + # Define loads on face z = W loads = np.zeros((dirs.shape[0], 4)) - mask_load = nodes[:, 3] == W # Nodes where z = W + mask_load = (nodes[:, 3] == W) node_indices = np.where(mask_load)[0] - node_indices_selected = node_indices[positions[:, 0] * (ny + 1) + positions[:, 1]] - - loads[:, 0] = node_indices_selected # Node indices for loads - loads[:, 1] = dirs[:, 0] # X-direction load - loads[:, 2] = dirs[:, 1] # Y-direction load - loads[:, 3] = dirs[:, 2] # Z-direction load - return nodes, mats, els, loads, idx_BC + # The user supplies positions in a "grid" sense: [x_index, y_index, z_index]. + # We slice out the correct nodes from node_indices. Implementation is up to the user. + # Example: node_indices_selected = ... + # For demonstration, the code uses the provided positions as if + # positions[:,0] is x_index, positions[:,1] is y_index, + # and we assume z_index = positions[:,2] (already at z=W). + # This line is a placeholder; adjust indexing logic as needed. + node_indices_selected = node_indices[ + positions[:, 0] * (ny + 1) + positions[:, 1] + ] + + loads[:, 0] = node_indices_selected + loads[:, 1] = dirs[:, 0] # Fx + loads[:, 2] = dirs[:, 1] # Fy + loads[:, 3] = dirs[:, 2] # Fz + return nodes, mats, els, loads, idx_BC \ No newline at end of file diff --git a/tests/test_optimize.py b/tests/test_optimize.py index a8b19f4..1982384 100755 --- a/tests/test_optimize.py +++ b/tests/test_optimize.py @@ -1,102 +1,274 @@ -# -*- coding: utf-8 -*- -""" -Test cases for functions on ``assemutil`` module - -""" -import numpy as np -import solidspy_opt import unittest +import numpy as np + +# Import your package and relevant functions +from solidspy_opt.optimize import ESO_stress, ESO_stiff, BESO, SIMP +from solidspy_opt.utils.structures import structure_3d, structures + +class TestSolidspyOpt(unittest.TestCase): -import solidspy_opt.optimize - -class TestSolidsPyOpt(unittest.TestCase): - def setUp(self): - # Common parameters for the tests - self.length = 60 - self.height = 60 - self.nx = 60 - self.ny = 60 - self.dirs = np.array([[0, -1]]) - self.positions = np.array([[15, 1]]) - self.niter = 50 # Reduced for testing efficiency - self.penal = 3 - self.volfrac = 0.5 - self.RR = 0.005 - self.ER = 0.05 - self.t = 1e-3 - - def test_SIMP(self): - """Test SIMP functionality.""" - rho = solidspy_opt.optimize.SIMP( - self.length, - self.height, - self.nx, - self.ny, - self.dirs, - self.positions, - self.niter, - self.penal, - plot=False + def test_eso_stress_2D(self): + """ + Test ESO_stress in 2D with a small mesh. + """ + # Create a tiny 2D structure + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) # single downward load + positions = np.array([[4, 1]]) # near top-right corner + nodes, mats, els, loads, idx_BC = structures(L=L, H=H, nx=nx, ny=ny, dirs=dirs, positions=positions, n=1) + + # Run a short ESO_stress optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stress( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, # minimal iterations for quick test + RR=0.1, + ER=0.1, + volfrac=0.5, + plot=False, # disable plotting for tests + dim_problem=2, + nnodes=4 ) - self.assertIsInstance(rho, np.ndarray, "SIMP should return a numpy array.") - self.assertEqual(rho.size, self.nx * self.ny, "Density array size should match the number of elements.") - - def test_ESO_stress(self): - """Test ESO based on stress.""" - els, nodes = solidspy_opt.optimize.ESO_stress( - self.length, - self.height, - self.nx, - self.ny, - self.dirs, - self.positions, - self.niter, - self.RR, - self.ER, - self.volfrac, - plot=False + + # Basic checks + self.assertIsNotNone(ELS_opt, "Returned elements array is None.") + self.assertGreater(ELS_opt.shape[0], 0, "No elements remain after optimization.") + self.assertIsNotNone(nodes_opt, "Returned nodes array is None.") + self.assertIsNotNone(UC, "No displacement array returned.") + + def test_eso_stress_3D(self): + """ + Test ESO_stress in 3D with a small mesh. + """ + # Create a tiny 3D structure + L = H = W = 8 + nx = ny = nz = 8 + dirs = np.array([[0, 0, -1]]) # single downward load + positions = np.array([[1, 1, 9]]) # near top corner + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L, H, W, 2.0e5, 0.3, nx, ny, nz, dirs, positions ) - self.assertIsInstance(els, np.ndarray, "ESO_stress should return an array of elements.") - self.assertIsInstance(nodes, np.ndarray, "ESO_stress should return an array of nodes.") - self.assertTrue(els.size > 0, "The element array should not be empty.") - - def test_ESO_stiff(self): - """Test ESO based on stiffness.""" - els, nodes = solidspy_opt.optimize.ESO_stiff( - self.length, - self.height, - self.nx, - self.ny, - self.dirs, - self.positions, - self.niter, - self.RR, - self.ER, - self.volfrac, - plot=False + + # Run a short ESO_stress optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stress( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=2, + RR=0.1, + ER=0.1, + volfrac=0.5, + plot=False, + dim_problem=3, + nnodes=8 ) - self.assertIsInstance(els, np.ndarray, "ESO_stiff should return an array of elements.") - self.assertIsInstance(nodes, np.ndarray, "ESO_stiff should return an array of nodes.") - self.assertTrue(els.size > 0, "The element array should not be empty.") - - def test_BESO(self): - """Test Bi-directional ESO.""" - els, nodes = solidspy_opt.optimize.BESO( - self.length, - self.height, - self.nx, - self.ny, - self.dirs, - self.positions, - self.niter, - self.t, - self.ER, - self.volfrac, - plot=False + + # Basic checks + self.assertIsNotNone(ELS_opt, "Returned 3D elements array is None.") + self.assertGreater(ELS_opt.shape[0], 0, "No 3D elements remain after optimization.") + self.assertIsNotNone(nodes_opt, "Returned 3D nodes array is None.") + self.assertIsNotNone(UC, "No 3D displacement array returned.") + + def test_eso_stiff_2D(self): + """ + Test ESO_stiff in 2D with a small mesh. + """ + # Create a tiny 2D structure + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) # single downward load + positions = np.array([[4, 1]]) # near top-right corner + nodes, mats, els, loads, idx_BC = structures(L=L, H=H, nx=nx, ny=ny, dirs=dirs, positions=positions, n=1) + + # Run a short ESO_stiff optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stiff( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, + RR=0.1, + ER=0.1, + volfrac=0.5, + plot=False, + dim_problem=2, + nnodes=4 + ) + + # Basic checks + self.assertIsNotNone(ELS_opt) + self.assertGreater(ELS_opt.shape[0], 0) + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + + def test_eso_stiff_3D(self): + """ + Test ESO_stiff in 3D with a small mesh. + """ + # Create a tiny 3D structure + L = H = W = 8 + nx = ny = nz = 8 + dirs = np.array([[0, 0, -1]]) # single downward load + positions = np.array([[1, 1, 9]]) # near top corner + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L, H, W, 2.0e5, 0.3, nx, ny, nz, dirs, positions ) - self.assertIsInstance(els, np.ndarray, "BESO should return an array of elements.") - self.assertIsInstance(nodes, np.ndarray, "BESO should return an array of nodes.") - self.assertTrue(els.size > 0, "The element array should not be empty.") + + # Run a short ESO_stiff optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = ESO_stiff( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=2, + RR=0.1, + ER=0.1, + volfrac=0.5, + plot=False, + dim_problem=3, + nnodes=8 + ) + + self.assertIsNotNone(ELS_opt) + self.assertGreater(ELS_opt.shape[0], 0) + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + + def test_beso_2D(self): + """ + Test BESO in 2D with a small mesh. + """ + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) # single downward load + positions = np.array([[4, 1]]) # near top-right corner + nodes, mats, els, loads, idx_BC = structures(L=L, H=H, nx=nx, ny=ny, dirs=dirs, positions=positions, n=1) + + # Run a short BESO optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = BESO( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, + t=0.0001, + ER=0.001, + volfrac=0.5, + plot=False, + dim_problem=2, + nnodes=4 + ) + + self.assertIsNotNone(ELS_opt) + self.assertGreater(ELS_opt.shape[0], 0) + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + + def test_beso_3D(self): + """ + Test BESO in 3D with a small mesh. + """ + L = H = W = 8 + nx = ny = nz = 8 + dirs = np.array([[0, 0, -1]]) # single downward load + positions = np.array([[1, 1, 9]]) # near top corner + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L, H, W, 2.0e5, 0.3, nx, ny, nz, dirs, positions + ) + + # Run a short BESO optimization + ELS_opt, nodes_opt, UC, E_nodes, S_nodes = BESO( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=2, + t=0.0001, + ER=0.001, + volfrac=0.5, + plot=False, + dim_problem=3, + nnodes=8 + ) + + self.assertIsNotNone(ELS_opt) + self.assertGreater(ELS_opt.shape[0], 0) + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + + def test_simp_2D(self): + """ + Test SIMP in 2D with a small mesh. + """ + L, H = 8, 8 + nx, ny = 8, 8 + dirs = np.array([[0, -1]]) # single downward load + positions = np.array([[4, 1]]) # near top-right corner + nodes, mats, els, loads, idx_BC = structures(L=L, H=H, nx=nx, ny=ny, dirs=dirs, positions=positions, n=1) + + # Run SIMP for a few iterations + rho, nodes_opt, UC, E_nodes, S_nodes = SIMP( + nodes=nodes, + els=els, + mats=mats, + loads=loads, + idx_BC=idx_BC, + niter=2, + penal=3, + volfrac=0.5, + dimensions=[nx, ny], + plot=False, + dim_problem=2, + nnodes=4 + ) + + self.assertIsNotNone(rho) + self.assertTrue(len(rho) > 0, "Density array is empty in SIMP 2D.") + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + + def test_simp_3D(self): + """ + Test SIMP in 3D with a small mesh. + """ + L = H = W = 8 + nx = ny = nz = 8 + dirs = np.array([[0, 1, 0]]) # single downward load + positions = np.array([[5, 5, 9]]) # near top corner + nodes_3d, mats_3d, els_3d, loads_3d, idx_BC_3d = structure_3d( + L, H, W, 2.0e5, 0.3, nx, ny, nz, dirs, positions + ) + + # Run SIMP for a few iterations + rho, nodes_opt, UC, E_nodes, S_nodes = SIMP( + nodes=nodes_3d, + els=els_3d, + mats=mats_3d, + loads=loads_3d, + idx_BC=idx_BC_3d, + niter=2, + penal=3, + volfrac=0.5, + plot=False, + dim_problem=3, + nnodes=8 + ) + + self.assertIsNotNone(rho) + self.assertTrue(len(rho) > 0, "Density array is empty in SIMP 3D.") + self.assertIsNotNone(nodes_opt) + self.assertIsNotNone(UC) + if __name__ == "__main__": unittest.main()