pystran/tutorials/05_hinge_frame_tut.py at main · PetrKryslUCSD/pystran · GitHub

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"""
pystran - Python package for structural analysis with trusses and beams

(C) 2025, Petr Krysl, pkrysl@ucsd.edu

# Example of a frame with a hinge

## Problem description:

Portal frame with a hinge at the top of the left column. The frame is loaded
with a sideways force.

Displacements and internal forces are provided in the book, and we can check our
solution against these reference values.

## References

This example is completely solved in the book Matrix Analysis of Structures by
Robert E. Sennett, ISBN 978-1577661436. Example 7.4.
"""

from numpy.linalg import norm
import context
from pystran import model
from pystran import section
from pystran import freedoms
from pystran import plots

# US customary units, inches, pounds, seconds are assumed.

# The book gives the product of the modulus of elasticity and the moment of
# inertia as 2.9e6.
E = 29e6
I = 100.0
A = 10.0  # cross-sectional area does not influence the results
L = 10 * 12  # span in inches

m = model.create(2)

# First we create the four joints given in the textbook.
model.add_joint(m, 1, [0.0, 0.0])
model.add_joint(m, 2, [0, L])
model.add_joint(m, 3, [L, L])
model.add_joint(m, 4, [L, 0.0])

# There needs to be a hinge (not transferring bending moments, but ensuring
# continuity of displacements) at the joint 2. We add another joint, 5, at the
# same location, and we link the degrees of freedom that needs to be the same.
model.add_joint(m, 5, [0, L])

# We supply the list of joints that need to be linked (2 and 5), and the
# degrees of freedom that are to be the same.
model.add_dof_links(m, [2, 5], freedoms.U1)
model.add_dof_links(m, [2, 5], freedoms.U2)

# Now we apply the supports -- both bottom joints are simply supported
# (pinned).
model.add_support(m["joints"][1], freedoms.TRANSLATION_DOFS)
model.add_support(m["joints"][4], freedoms.TRANSLATION_DOFS)


# Define the beam members.
s1 = section.beam_2d_section("s1", E, A, I)
model.add_beam_member(m, 1, [1, 2], s1)
model.add_beam_member(m, 2, [5, 3], s1)
model.add_beam_member(m, 3, [4, 3], s1)

# Sideload is applied at joint 2.
model.add_load(m["joints"][2], freedoms.U1, 1000.0)

# The discrete model can now be reviewed. Note the orientations of the local
# coordinate systems.
plots.setup(m)
plots.plot_members(m)
plots.plot_member_ids(m)
plots.plot_joint_ids(m)
plots.plot_member_orientation(m, 10.0)
plots.show(m)

# Solve the discrete model.
model.number_dofs(m)
model.solve_statics(m)

# First check of the solution is the plot of the deformation.
plots.setup(m)
plots.plot_members(m)
ax = plots.plot_deformations(m, 100.0)
ax.set_title("Deformations (x100)")
plots.show(m)

# The displacements at the movable joints are printed out.
for jid in [2, 3]:
    j = m["joints"][jid]
    print(jid, j["displacements"])

# The displacements at the hinge joints are compared to each other: the
# translations should be identical.
d2 = m["joints"][2]["displacements"]
d5 = m["joints"][5]["displacements"]
if norm(d2[0:2] - d5[0:2]) > 1e-3:
    raise ValueError("Incorrect displacement")

# The displacements at the hinge are compared to the reference values from the
# textbook.
if abs(d2[0] - 0.3985) / 0.3985 > 1e-3:
    raise ValueError("Incorrect displacement")
if abs(d2[1] - 0.00041) / 0.00041 > 1e-2:
    raise ValueError("Incorrect displacement")

# The obligatory diagrams of bending moments and shear forces follow.
plots.setup(m)
plots.plot_members(m)
ax = plots.plot_bending_moments(m)
ax.set_title("Moments")
plots.show(m)

plots.setup(m)
plots.plot_members(m)
ax = plots.plot_shear_forces(m)
ax.set_title("Shear forces")
plots.show(m)