continuum-fea

Continuum FEA — gmsh + CalculiX (tier 3)

This is the heavy tier of the FEA ladder, used ONLY for continuum parts that a beam or closed-form check can't represent:

tier 1  analytic checks in audit.py     (Euler buckling, beam bending, slam)  <- first
tier 2  in-house numpy space-frame FEA  (frames / trusses)
tier 3  THIS: gmsh + CalculiX (ccx)     (brackets, panels, shells, lugs)      <- last

The solver is settled: CalculiX (ccx) + gmsh. It is the OpenFOAM-of-FEA for this stack — a turnkey, Abaqus-style text-deck CLI solver (not a write-your-own-weak-forms framework), runs headless, and is already installed (/Applications/FreeCAD.app/Contents/Resources/bin/ccx, v2.23, arm64). This was confirmed by a sourced multi-methodology sweep (2026-06-13): ccx is the robust pick across weighting schemes; Code_Aster / Elmer are escalation options only if coupled multiphysics or advanced contact becomes load-bearing, and both have a real macOS-install cost (Code_Aster has no turnkey Apple-Silicon path; Elmer is Rosetta-source-build only).

The discipline (this is the whole point)

A continuum solve that "ran clean" is not one that is correct — linear tets lock, units slip, and a clamped BC invents a stress singularity, all silently. So, exactly like CFD (c* / choked-mdot anchor + grid study):

1. Validate tier 3 against the tier below FIRST. Before you trust a result on the real part, solve a case with a closed-form answer and GATE on matching it: a cantilever whose tip deflection is F·L³/3EI, or — the canonical project anchor — a *BUCKLE step whose first eigenvalue must reproduce the audit's analytic Euler P_cr within a few percent. The scaffold ships fea_continuum.py, which does exactly this and exits 1 if the anchor misses.
2. Then a mesh-convergence study. Refine until the validated quantity stops moving (<~2-3%). One mesh is never a result. log() the sequence.
3. Anchor the peak stress honestly. A fully-clamped face has a stress singularity at its edge — peak von Mises will overshoot the nominal and will NOT converge there. Gate on a clean quantity (deflection, a *BUCKLE eigenvalue, or stress sampled away from the singularity); treat the raw peak as informational and say so.