Fix 6x-too-flexible TenNodeTetrahedron (double-applied 1/6 Jacobian factor in shp3d)

[nmorabowen]

Summary

TenNodeTetrahedron::shp3d returns the Jacobian measure xsj used by every quadrature loop in the element (dvol = wg * xsj). The assembled determinant is divided by 6 —

double Jdet = (t1*(t5*t9-t6*t8) - t2*(t4*t9-t6*t7) + t3*(t4*t8-t5*t7))/6.0;
xsj = Jdet;   // <-- bug

— which makes Jdet the element volume, not the raw 3×3 determinant. But the Gauss weights already carry the natural-tet volume: wg[] = {1/24} over 4 points sums to 1/6. So the 1/6 factor was applied twice, and every integrated quantity (stiffness, consistent and lumped mass, body loads, stress resultants) came out 6× too small.

Fix

xsj = 6.0 * Jdet;

so that Σ wg·xsj = (1/6)·(6·Jdet) = V exactly. The shape-function derivatives are unaffected — they already normalize by 1/(6·Jdet).

Verification

Uniaxial patch test — a single-element column with prescribed axial strain ε:

	reaction
before	E·ε·A / 6
after	E·ε·A (exact)

The total volume accumulated in formInertiaTerms (volume += dvol) now matches the geometric tet volume.

Impact

Because K and M scaled down together, modal frequencies were essentially unchanged by the bug — which is why it could go unnoticed in eigen checks. The error shows up in absolute quantities: displacements under external loads 6× too large, reactions/element mass/self-weight 6× under-counted. Any model using TenNodeTetrahedron is affected, so this is worth flagging in release notes.

Authors: Nicolas Mora Bowen, Patricio Palacios, José A. Abell