3D beam distributed load : SOFA vs FF cross-validation

[Fimache]

Summary

Extends the 2D distributed-load cross-validation (cantilever beam, no analytical
solution) to 3D with a tetrahedral mesh. The load is applied as a surface traction
(Neumann) on the Top face, equivalent to the FreeFEM term int2d(Th,4)(-Q*vy).
No plane-strain/plane-stress distinction is needed here since the full 3D volume
is modeled directly.

Files

• beam3dtet.py — Gmsh tetrahedral mesh generator for the 3D beam (box geometry,
  physical tags: 1=Fixed, 2=Bottom, 3=Right, 4=Top, 5=Front, 6=Back, 7=Beam volume)
• freefem_beam3d_distributed.edp — full 3D bilinear form (int3d, all cross-shear
  terms), Neumann load via int2d(Th,4), mesh loaded with gmshload3
• comparaison_script3d.py — SOFA vs FreeFEM comparison, coordinate-based node
  matching, separate RMS on ux/uy/uz, parity plots
• params_beam3d_distributed.json — physical parameters (same as the 2D case)

Bug fixed: non-conforming mesh

setTransfiniteVolume() was used together with triangulated (non-recombined)
boundary surfaces. Transfinite volume meshing picks its own internal diagonal
split, independent of the diagonals already chosen by the transfinite surface
mesh — the two are not guaranteed to agree, which produced boundary triangles
not matching any tetrahedron face (Border element not in mesh in FreeFEM).

Fix: removed setTransfiniteVolume(). Surfaces stay transfinite (controlled,
structured boundary mesh); the volume is filled by the standard (Delaunay)
3D algorithm, which is constrained to respect the already-fixed boundary mesh
exactly. Conformity confirmed via check_mesh_conformity.py at multiple
resolutions (all 6 tagged faces OK).

[th-skam]

works