compute_timo_boun

module opensg.core.solid

opensg.core.solid.compute_timo_boun(mat_param, boundary_submeshdata)

Compute boundary stiffness matrices for solid elements using EB and Timoshenko theories.

This function solves both Euler-Bernoulli (EB) and Timoshenko beam models on the boundary of solid meshes to compute effective stiffness matrices and fluctuating functions used for Dirichlet boundary constraints in 3D solid segment analysis.

Parameters:

• mat_param (list[dict]) – List of material parameter dictionaries for each material phase. Each dictionary should contain elastic properties (E, G, nu) for the material.

• boundary_submeshdata (dict) –

  Dictionary containing boundary mesh data with keys:

  • ’mesh’: Boundary mesh object (2D surface mesh)

  • ’subdomains’: Subdomain tags for different materials

  • ’frame’: Local orientation frame functions for the boundary

Returns:

tuple – Contains (D_eff, Deff_srt, V0, V1s):

• D_effnumpy.ndarray

  4x4 boundary Euler-Bernoulli stiffness matrix for solid cross-section

• Deff_srtnumpy.ndarray

  6x6 boundary Timoshenko stiffness matrix including shear effects

• V0numpy.ndarray

  Boundary fluctuating function solutions [ndofs_boundary, 4] for EB model

• V1snumpy.ndarray

  Boundary fluctuating function solutions [ndofs_boundary, 4] for Timoshenko model

Notes

This is the solid element version of the boundary computation, handling:

• 3D constitutive relationships for solid materials

• Surface integration over the boundary mesh

• Proper coupling between membrane and bending effects in solid sections