Validation objective

These cases verify that Indux Mechanical solves its governing equations correctly by comparing the numerical results with published closed-form solutions. Because no experimental uncertainty is involved, they isolate the numerical formulation and implementation. Mesh refinement is also checked where appropriate to confirm that the error decreases at the theoretically expected rate.

Validation matrix

The suite contains eight cases across four physics areas: four structural, two heat-transfer, one thermal-stress, and one coupled thermo-mechanical problem.

• Tools: Gmsh 4.12.2 for mesh generation, SU2 mesh format, Indux Mechanical built with MSVC/VS2022, and MKL PARDISO/FGMRES linear solvers
• Acceptance criteria: relative error $|\varepsilon| < 1\%$ for smooth, nonsingular quantities and an observed mesh-convergence order $p_{obs}\approx2$
• Quantity-selection rule: isolated maxima at boundary-condition corners, constrained edges, and mesh-star centers are not used as primary evidence; interior values, averages, and profiles are preferred
• Overall result: 8/8 PASS

Detailed equations, boundary conditions, acceptance quantities, and results are documented separately.

1. Tension Bar — uniaxial tension
2. Lamé Cylinder — internally pressurized thick cylinder
3. Plate with Hole — elastic stress concentration
4. Rotating Disk — centrifugal loading
5. Fin Convection — convective heat transfer
6. 1D Heat Conduction — steady conduction
7. Thermal Stress Bar — restrained thermal expansion
8. Coupled Thermal Stress — one-way thermal-to-structural coupling

Results summary

All eight cases satisfy the acceptance criteria for their designated primary quantities. Comparisons with experimental measurements are planned as a separate validation stage; these closed-form cases specifically address code and solution verification.