Verification
WebCAE is checked against publicly documented benchmark suites used for finite-element verification. The catalog below separates named external references from work that is still in development; real results appear only after an actual solver run.
Methodology
MacNeal–Harder
A recognized element and shell benchmark suite covering patch behavior, mesh distortion, bending, twisting and locking sensitivity.
NAFEMS
The de-facto industry standard, with reference values across static, thermal, modal and buckling problems.
Element families
Each published result identifies whether it was solved with solid, shell or beam elements, so the catalog does not imply a solid-only solver.
Reference cases
| Case | Discipline | What it checks | Source | Tolerance | Element family | Status |
|---|---|---|---|---|---|---|
| Patch test | Static | Baseline element correctness on a coarse, irregular mesh | MacNeal–Harder benchmark suite | 5% | Solid element | PASS · 0% |
| NAFEMS LE1 | Static | Elliptical membrane — stress concentration | NAFEMS LE benchmark suite | 5% | Shell element | PASS · 3.62% |
| NAFEMS FV2 | Modal analysis | Natural frequencies of a flat plate | NAFEMS FV benchmark suite | 5% | Beam element | PASS · 1.2% |
| Cantilever beam (Euler-Bernoulli) | Static | Tip deflection of a slender cantilever under a distributed load | Classical analytical solution | 5% | Solid element | PASS · 1.03% |
| Cantilever beam (Timoshenko) | Static | Tip deflection of a stocky beam including shear deformation | Classical analytical solution | 5% | Solid element | PASS · 1.29% |
| NAFEMS LE10 | Static | Thick plate under pressure — bending stress | NAFEMS LE benchmark suite | 5% | Solid element | PASS · 0.67% |
| NAFEMS FV5 | Modal analysis | Deep simply supported beam — repeated eigenvalues, shear and rotary inertia | NAFEMS FV benchmark suite | 5% | Beam element | PASS · 3.49% |
| Thick cylinder prescribed normal expansion | Static | Prescribed non-zero displacement along surface normal (d ≠ 0): thick cylinder expanded radially by d = 50 μm on outer surface, verified against Lamé analytical elasticity. | Classical analytical solution | 5% | Solid element | PASS · 0.24% |
| Lamé thick cylinder in rigid casing | Static | Stress and radial displacement distribution in a thick-walled cylinder under internal pressure with outer surface constrained along its surface normal (rigid casing, ur(b) = 0). | Classical analytical solution | 5% | Solid element | PASS · 0.48% |
| MacNeal-Harder rectangular plate | Static (shells) | Rectangular plate/shell benchmark family with aspect ratios 1 and 5, in simply-supported and clamped variants, under either uniform pressure or a concentrated center load. Center-point deflection is compared against a normalized coefficient table, making this… show full textRectangular plate/shell benchmark family with aspect ratios 1 and 5, in simply-supported and clamped variants, under either uniform pressure or a concentrated center load. Center-point deflection is compared against a normalized coefficient table, making this a classical check against plate-bending locking and load-application errors. | MacNeal–Harder benchmark suite | 5% | Shell element | PASS · 0.83% |
| NAFEMS FV12 | Modal analysis | Free thin square plate with in-plane motion constrained — rigid-body mode filtering and repeated eigenvalues in shell elements. | NAFEMS FV benchmark suite | 5% | Shell element | PASS · 1.44% |
| NAFEMS FV13 | Modal analysis | Simply-supported thin square plate — out-of-plane bending modes with repeated eigenvalue pairs; the reference row is independently reproducible by the Navier closed-form solution. | NAFEMS FV benchmark suite | 5% | Shell element | PASS · 3.95% |
| NAFEMS FV15 | Modal analysis | Clamped thin rhombic (skew) plate — out-of-plane bending modes on a highly skewed planform; a stringent element-distortion check for plate bending. | NAFEMS FV benchmark suite | 5% | Shell element | PASS · 1.11% |
| NAFEMS FV16 | Modal analysis | Cantilevered thin square plate — shell modal and mass formulation test with a single fixed edge. | NAFEMS FV benchmark suite | 5% | Shell element | PASS · 0.66% |
| NAFEMS FV22 | Modal analysis | Clamped thick rhombic (skew) plate — Mindlin-regime bending modes (t/a = 0.1) on a highly skewed planform; checks transverse-shear behavior on distorted elements. | NAFEMS FV benchmark suite | 5% | Shell element | PASS · 2.98% |
| NAFEMS FV4 | Modal analysis | Cantilever beam with off-centre tip point masses — bending-torsion coupling and closely spaced eigenvalues. | NAFEMS FV benchmark suite | 5% | Beam element | PASS · 1.06% |
| NAFEMS FV52 | Modal analysis | Simply-supported solid square plate — normal modes of a solid (brick) plate model, first three modes are rigid-body/near-zero. | NAFEMS FV benchmark suite | 5% | Solid element | PASS · 4.22% |
| NAFEMS LE5 | Static | Z-section cantilever under torsion — axial (warping) stress check near the fixed end. | NAFEMS LE benchmark suite | 5% | Beam element | PASS · 4.66% |
| NAFEMS LE6 | Static (shells) | Skew plate under uniform normal pressure — principal stress check near a corner singularity. | NAFEMS LE benchmark suite | 5% | Shell element | PASS · 1.65% |
| NAFEMS LE7 | Static (shells) | Axisymmetric thin-walled cylinder/sphere pressure vessel — axial stress check on the outer surface. | NAFEMS LE benchmark suite | 5% | Solid element | PASS · 3.4% |
| NAFEMS LE8 | Static (shells) | Axisymmetric shell under internal pressure — hoop stress check away from the boundary. | NAFEMS LE benchmark suite | 5% | Solid element | PASS · 4.35% |
| NAFEMS T1 | Thermomechanical | Membrane with a circular hot spot — steady-state thermoelastic stress at the spot boundary; the target is independently reproducible by the circular-inclusion closed form sigma = E*alpha*dT/2. | NAFEMS thermal benchmark suite | 5% | Shell element | PASS · 0.65% |
| NAFEMS T4 | Heat transfer | Two-dimensional steady-state heat conduction with convective boundary conditions — temperature check at an edge point, solved as an exact 3D extrusion equivalent. | NAFEMS thermal benchmark suite | 5% | Solid element | PASS · 0.31% |
| Plate with hole (symmetry planes via normal constraints) | Static | Stress concentration factor (Kirsch problem) for a tensioned plate with a central hole, solved on a quarter-symmetry model using surface normal constraints (n·u = 0) vs full model. | Classical analytical solution | 5% | Solid element | PASS · 1.38% |
| Uniaxial tension, material sensitivity (aluminum) | Static | Same geometry and load as the steel uniaxial tension case, aluminum instead of steel (E = 70 GPa) — verifies that the elastic modulus is correctly propagated to displacement (elongation scales as 1/E) while stress stays independent of the material in this stat… show full textSame geometry and load as the steel uniaxial tension case, aluminum instead of steel (E = 70 GPa) — verifies that the elastic modulus is correctly propagated to displacement (elongation scales as 1/E) while stress stays independent of the material in this statically determinate loading. | Classical analytical solution | 5% | Solid element | PASS · 0.64% |
| Uniaxial tension (steel) | Static | Stress recovery (von Mises, principal stresses) for a prismatic steel bar under uniform axial tension, checked away from the fixed-end boundary layer. | Classical analytical solution | 5% | Solid element | PASS · <0.01% |
Only public benchmark references are listed here. PASS/FAIL means a real solver run compared with the published reference; "In development" means the public case is cataloged but has not been run yet.