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WP10 WEDGE6 Modal Qualification Evidence

WP10-FINAL is PASS within the declared bounded scope. The gate remains PASS_WITH_LIMITATIONS because the qualification is limited to the tested consistent-mass WEDGE6 modal route and does not make a general dynamics claim. The active Owner decision is OWNER_APPROVED_BOUNDED.

Scope and policy

The tested route is the common modal assembler with a six-node, 18-DOF WEDGE6, homogeneous isotropic small-strain elasticity, positive density and the consistent translational mass matrix M = rho * integral(N^T N det(J)) tensor I3. Production integration is TRI3_X_GAUSS2 (6 points). DUFFY_GAUSS5_X_GAUSS4 (100 points) is a verification reference only. No lumped-mass or reduced-integration route is qualified.

The final policy was fixed in the declarative catalog before replay: mass symmetry relative error <= 1e-14, rigid-translation mass conservation absolute error <= 1e-10 in the declared model units, modal eigenpair residual <= 1e-7, mass orthogonality error <= 1e-12, and finite positive requested frequencies. Same-mesh external frequency comparison uses relative tolerance 1e-2, MAC uses >= 0.99, and a relative frequency gap <= 1e-5 uses subspace MAC. The refinement criterion is <= 1e-2 between the final levels for the first three modes. These tolerances are approved only for this bounded scope; post-result retuning is forbidden and monotonicity is not required.

Evidence summary

The catalog contains 16 cases: 15 PASS, one controlled EXPECTED_FAILURE_PASS for zero density, and no unexpected failure.

Check Result
Mass symmetry relative error 0.0; PASS
Mass positivity minimum eigenvalue 324.9999999999996; PASS
Total mass expected 23399.999999999993; maximum translation error 7.28e-12; PASS
Production/reference mass relative difference 3.32e-16; PASS
Density and geometry scaling PASS; geometry ratio 7.9999999999999964
Single-element modal solve six finite positive frequencies; residual 1.08e-13; PASS
Three-element modal solve residual 6.31e-13; mass orthogonality 5.14e-16; PASS
Distorted valid prism finite modal solve; residual 4.30e-13; PASS
Deterministic replay frequencies and mode vectors identical; PASS
Zero-density input fail-closed expected failure; PASS

The final replay used 4, 8, 16 and 32 prism segments. The first three final adjacent relative changes were 0.779170%, 0.125485% and 0.030112%, all within the 1% rule. Modes four to six remain diagnostic because their fourth final adjacent change is 1.075439%. The maximum normalized eigenpair residual was 2.3993260594985674e-11, all requested frequencies were finite and positive, and deterministic replay passed.

Segments Mode 1 (Hz) Mode 2 (Hz) Mode 3 (Hz)
4 81.556398 151.870479 269.886494
8 73.511829 148.992958 268.591238
16 71.335789 148.253799 268.267970
32 70.779961 148.067764 268.187189

Refinement status is PASS_QUALIFIED for the first-three-mode observable; higher modes are not silently counted as converged.

Code_Aster correlation

The reproducible headless reference is Code_Aster 18.1.0/PENTA6 in the pinned image simvia/code_aster@sha256:4629a21a109309bb97fbdc27d750445cc869e151e2e2ed6290f69539614e4435. Four same-mesh cases were executed: axial single prism, bending multi-prism, distorted valid prism and multi-WEDGE mesh. They use the same geometry, node order, material, fixed condition, mass convention and six-mode request. The maximum frequency relative error was 1.927e-13, the minimum MAC was 0.9999999999999991, and all 24/24 mode pairs passed the predeclared frequency and MAC rules. The deck extracts physical DX, DY and DZ components and excludes Lagrange multiplier components before comparison. This is bounded cross-solver evidence, not universal modal validation.

The canonical deck and compact result are recorded at:

  • qualification/0_2_7/external_oracles/wedge6/decks/code_aster/WP10-A-penta6-modal.comm
  • qualification/0_2_7/external_oracles/wedge6/decks/code_aster/WP10-A-penta6-modal.mail
  • qualification/0_2_7/external_oracles/wedge6/results/wp10_code_aster_modal.json

Limitations and next gate

  • WEDGE6 modal maturity is QUALIFIED_BOUNDED only for the scope declared above; the gate remains PASS_WITH_LIMITATIONS.
  • Modes four to six are externally matched but remain diagnostic for mesh convergence.
  • No lumped-mass route is qualified.
  • No qualification transfers to Newmark, harmonic, nonlinear, J2, TL, contact or general dynamic routes.
  • Newmark, harmonic, nonlinear, J2, TL and contact WEDGE6 routes are outside WP10.
  • Full regression was not run under the WP10 T0/T1/T2 targeted policy; no existing-element numerical formulation was changed.

Machine-readable records are the source for the final case-level evidence: qualification/0_2_7/vnv_v2/wp10_final_cases.json, qualification/0_2_7/vnv_v2/wp10_final_evidence.json and qualification/0_2_7/wp10_final_state.json. The original 16-case records qualification/0_2_7/vnv_v2/wp10_cases.json and qualification/0_2_7/vnv_v2/wp10_evidence.json remain preserved as historical evidence and are not used to dilute the final policy.