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replicate the beam-2d.edp scene as well
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‎examples/Freefem/sofa/beam-2d.scn‎

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<?xml version="1.0"?>
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<!--
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2D cantilever beam under gravity — SOFA equivalent of beam-2d.edp (FreeFEM)
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Two formulations shown side by side:
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In SOFA with the Vec1, Vec2, Vec3 templates. Depending on how these are set up,
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in order to generate a similar outcome as FreeFEM, we need to make some adjustments.
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Just like in many FE codes, we can solve 2D problems in 3D space. This is what using a Vec3
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template does. The 'd' in Vec3d is the 'double' type of C++.
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Depending on the template we choose, SOFA will do things differently:
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In the Node with name:
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1. beam_plane_stress (Vec2) y in [0, 2]
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Lame lambda = E*nu / ((1+nu)*(1-nu))
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DOFs: 2 per node (u_x, u_y). Displacement in the x and y directions.
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2. beam_plane_strain (Vec3) y in [3, 5]
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Lame lambda = E*nu / ((1+nu)*(1-2*nu)) !!! Notice the 1-2*nu contrary to the above
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DOFs: 3 per node (u_x, u_y, u_z)
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The FreeFEM file (beam-2d.edp) uses 3D Lame coefficients, so formulation 2 is the exact replicate.
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Formulation 1 shows the Vec2d approach. There will be a difference in the results between the
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two.
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Young's modulus: E=21.5
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Poisson's ratio: nu=0.29
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-->
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<!-- Gravity is applied at the root node -->
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<Node name="root" gravity="0 -0.05 0" dt="1">
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<Node name="plugins">
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<RequiredPlugin name="Elasticity"/>
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<RequiredPlugin name="Sofa.Component.Constraint.Projective"/>
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<RequiredPlugin name="Sofa.Component.Engine.Select"/>
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<RequiredPlugin name="Sofa.Component.LinearSolver.Direct"/>
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<RequiredPlugin name="Sofa.Component.Mass"/>
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<RequiredPlugin name="Sofa.Component.ODESolver.Backward"/>
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<RequiredPlugin name="Sofa.Component.StateContainer"/>
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<RequiredPlugin name="Sofa.Component.Topology.Container.Dynamic"/>
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<RequiredPlugin name="Sofa.Component.Topology.Container.Grid"/>
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<RequiredPlugin name="Sofa.Component.Visual"/>
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<RequiredPlugin name="Sofa.GL.Component.Rendering3D"/>
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</Node>
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<DefaultAnimationLoop/>
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<VisualStyle displayFlags="showBehaviorModels showForceFields showWireframe"/>
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<!-- All template='' cases here are Vec2d-->
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<Node name="beam_plane_stress">
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<NewtonRaphsonSolver name="newtonSolver"
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printLog="true"
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warnWhenLineSearchFails="true"
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maxNbIterationsNewton="1"
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maxNbIterationsLineSearch="1"
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lineSearchCoefficient="1"
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relativeSuccessiveStoppingThreshold="0"
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absoluteResidualStoppingThreshold="1e-7"
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absoluteEstimateDifferenceThreshold="1e-12"
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relativeInitialStoppingThreshold="1e-12"
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relativeEstimateDifferenceThreshold="0"
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/>
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<SparseLDLSolver name="linearSolver" template="CompressedRowSparseMatrixd"/>
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<StaticSolver name="staticSolver" newtonSolver="@newtonSolver" linearSolver="@linearSolver"/>
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<RegularGridTopology name="grid" min="0 0 0" max="10 2 0" n="41 11 1"/>
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<MechanicalObject template="Vec2d" name="dofs"/>
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<Node name="triangles">
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<TriangleSetTopologyContainer name="topology" src="@../grid"/>
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<MeshMatrixMass template="Vec2d,Vec2d" totalMass="20" topology="@topology"/>
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<LinearSmallStrainFEMForceField name="FEM" template="Vec2d"
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youngModulus="21.5" poissonRatio="0.29"
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topology="@topology"
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/>
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</Node>
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<BoxROI name="fixed_roi" template="Vec2d"
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box="-0.01 -0.01 -0.01 0.01 2.01 0.01" drawBoxes="true"/>
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<FixedProjectiveConstraint template="Vec2d" indices="@fixed_roi.indices"/>
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</Node>
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<!-- All template='' cases here are Vec3d-->
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<Node name="beam_plane_strain">
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<NewtonRaphsonSolver name="newtonSolver"
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printLog="true"
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warnWhenLineSearchFails="true"
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maxNbIterationsNewton="1"
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maxNbIterationsLineSearch="1"
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lineSearchCoefficient="1"
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relativeSuccessiveStoppingThreshold="0"
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absoluteResidualStoppingThreshold="1e-7"
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absoluteEstimateDifferenceThreshold="1e-12"
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relativeInitialStoppingThreshold="1e-12"
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relativeEstimateDifferenceThreshold="0"
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/>
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<SparseLDLSolver name="linearSolver" template="CompressedRowSparseMatrixd"/>
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<StaticSolver name="staticSolver" newtonSolver="@newtonSolver" linearSolver="@linearSolver"/>
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<RegularGridTopology name="grid" min="0 3 0" max="10 5 0" n="41 11 1"/>
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<MechanicalObject template="Vec3d" name="dofs"/>
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<Node name="triangles">
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<TriangleSetTopologyContainer name="topology" src="@../grid"/>
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<TriangleSetTopologyModifier/>
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<TriangleSetGeometryAlgorithms template="Vec3d" drawTriangles="true"/>
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<MeshMatrixMass totalMass="20" topology="@topology"/>
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<LinearSmallStrainFEMForceField name="FEM"
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youngModulus="21.5" poissonRatio="0.29"
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topology="@topology"
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mstate="@../dofs"/>
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</Node>
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<!-- Clamp left edge: x=0, y in [3,5].
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FixedProjectiveConstraint fixes all 3 DOFs (u_x, u_y, u_z)
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of the left-edge nodes, which is all that is needed. -->
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<BoxROI name="fixed_roi" template="Vec3d"
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box="-0.01 2.99 -1.0 0.01 5.01 1.0" drawBoxes="true"/>
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<FixedProjectiveConstraint template="Vec3d" indices="@fixed_roi.indices"/>
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</Node>
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</Node>

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