FESADev/docs/linear-static-mitc4-shell/physics-evaluation.md

Linear Static MITC4 Shell Physics Evaluation Report

Metadata

• feature_id: linear-static-mitc4-shell
• model_id: shell-s4
• evaluated_head: 820ba30c717b3d0e113775608e20dfd5fbc05d53
• source_build_test_report: docs/linear-static-mitc4-shell/build-test.md
• source_reference_verification_report: docs/linear-static-mitc4-shell/reference-comparison.md
• source_reference_model: docs/linear-static-mitc4-shell/reference-model.md
• source_requirement: docs/linear-static-mitc4-shell/requirements.md
• source_formulation: docs/linear-static-mitc4-shell/formulation.md
• source_numerical_review: docs/linear-static-mitc4-shell/numerical-review.md
• source_io_definition: docs/linear-static-mitc4-shell/io.md
• status: pass-for-release-agent
• owner_agent: physics-evaluation-agent
• date: 2026-08-13

This verdict means that the documented physical checks pass and the Release Agent may audit release readiness. It does not approve release readiness, re-approve the reference comparison, or change its tolerance decision.

Input Evidence

The prerequisite reference-verification report has status pass-for-physics-evaluation. The existing S4 reference-test route was rebuilt and executed to regenerate fresh FESA evidence. Abaqus and other reference solvers were not executed.

evidence	exact path or identity	status	notes
build/test report	docs/linear-static-mitc4-shell/build-test.md	pass-for-reference-verification	Clean MSVC x64 Debug build, focused 87/87, lifecycle 10/10, reference 8/8, and full 144/144 CTest passed.
reference verification	docs/linear-static-mitc4-shell/reference-comparison.md	pass-for-physics-evaluation	Required prerequisite satisfied; 147/147 blocking U rows passed and no UR warning was emitted.
solver HDF5	.harness/build/reference/mitc4-shell-s4-comparison/results.h5	present and readable	Freshly generated, 95,024 bytes; observed raw SHA-256 E102D80E82BA133EBDF1C5532F3A0A4FE9984AB6CC36D00264399F7308D9230F (inventory only).
comparison ledger	.harness/build/reference/mitc4-shell-s4-comparison/comparison.json	present and passing	94,349 bytes; SHA-256 8E8DEA51B6F7C663BACC41FDA6103A4596DB26E02F1EAD6069D458F51E0102E6; passed=true.
declared S4 input	reference/shell/shell.inp	present, unchanged, read-only	SHA-256 4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF.
declared displacement CSV	reference/shell/shell displacements.csv	present, unchanged, read-only	SHA-256 C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B.
optional Abaqus reaction/stress CSVs	reference/shell/shell reactions.csv, reference/shell/shell stresses.csv	not used as equality gates	Their presence did not expand the approved U-only blocking boundary.
solver CSV views	N/A	not generated	HDF5 was inspected directly.
fresh S4 route	.harness/build, MSVC x64 Debug	pass	Mitc4S4Reference.* passed 2/2.

The HDF5 contains 49 nodes, 36 source-S4 elements, internal formulation FESA-MITC4, and the required full 2 x 2 x 2 result inventory. All inspected numeric model and result values were finite. The diagnostics dataset contains four approved warning rows for ignored PREPRINT, RESTART, and OUTPUT keywords and no error diagnostic.

Raw HDF5 bytes are not a physics decision identity and may change across valid regenerations. The projected values and deterministic comparison ledger are the relevant evidence.

Documented model expectation

The reference input is a flat 10 x 10, thickness 0.5, homogeneous isotropic square plate with E=2.1e11 and nu=0.3. Its 24 perimeter nodes are fully clamped in all six global DOFs, and center node 2 at the global origin carries one F3=-100000 concentrated force. The geometry, boundary, material, and load are symmetric about both global x=0 and y=0 planes.

The documented physical expectations are therefore:

• total constrained reaction force opposes the applied -Z force;
• total force and moment about the global origin balance within the approved normalized 1e-10 limit;
• perimeter displacements are zero and the interior deflects in -Z, with the largest magnitude at the center;
• the displacement and rotation field obeys the polar/axial-vector reflection parity about both symmetry planes;
• a linear, flat transverse plate response has no membrane strain/resultant or middle-surface in-plane stress, while bottom and top in-plane stresses reverse;
• stored physical strain energy is finite, strictly positive, and consistent with the recovered generalized fields and 0.5 F^T d;
• free residual, finite results, rank/rigid-mode evidence, and the approved one-case coverage show no rigid-body or unsupported-mode symptom.

Physics Checks

check	documented expectation	observed evidence	verdict	classification
global equilibrium	Applied plus constrained reaction force/moment about origin; normalized metrics <=1e-10	force residual [0,0,-1.12049747258425e-9]; moment residual [6.45741238258779e-10,-2.63753463514149e-10,0]; normalized force/moment 1.12049747258425e-14 / 2.35981341581908e-15	pass	N/A
reaction consistency	Perimeter-only reactions from full residual oppose F3=-100000; constrained motion is zero	summed constrained force [0,0,99999.9999999989]; constrained displacement exactly zero	pass	N/A
displacement direction	Interior bends in -Z; center is maximum; no in-plane or drilling leakage	center U3=-2.35504417650849e-5; all 25 free-node U3 values nonpositive; U1/U2/UR3 exactly zero	pass	N/A
symmetry	Correct polar/axial reflection parity about x=0 and y=0	max absolute reflection mismatch 4.27126230127111e-20 / 2.29087480670778e-20	pass	N/A
element force balance	No documented direct element-end-action output exists for shell GP resultants	Global assembled residual/equilibrium passed; direct element-end-action balance is skipped rather than inferred from mismatched locations	skipped	N/A
recovered resultant consistency	N=A*epsilon0, M=D*kappa, Q=As*gamma0 at each of 144 GP rows	absolute L2 residual 9.9301874551584e-12; normalized L2 5.56240926027087e-17	pass	N/A
stress/location/sign sanity	Local [S11,S22,S12] at bottom/middle/top; middle zero and faces reverse for this linear flat bending field	absolute L2 constitutive residual 1.29488994752188e-9; normalized 3.05323934859307e-16; middle stress exactly zero; face reversal exact	pass	N/A
rigid body/nonfinite	Complete constraints, finite solution, acceptable residual, no abnormal uncontrolled mode	zero nonfinite values; FREE_RESIDUAL_NORMALIZED=1.07747756058988e-14; rank/rigid-mode tests passed upstream	pass	N/A
physical energy	Positive and consistent physical-only energy; no drilling-energy gate	1.17752208825422; independently recovered value identical to relative 1.88569375589575e-16; 0.5F^Td=1.17752208825424	pass	N/A
model coverage	Approved sole S4 case plus declared invariant/patch/common-path portfolio	S4 case covers end-to-end symmetric plate response; focused build/test portfolio passed; expanded models are explicitly nonblocking	pass	N/A

1. Global force and moment equilibrium

The reaction dataset is the assembled full residual K*d-F. Applying the constraint mask gives

sum constrained RF = [0, 0, 99999.9999999989]
sum applied F       = [0, 0, -100000]
force residual      = [0, 0, -1.12049747258425e-9]

The load acts at the global origin and therefore contributes no origin moment. The constrained force and moment rows give

moment residual = [ 6.45741238258779e-10,
                   -2.63753463514149e-10,
                    0 ]

These independently reconstructed values match the stored HDF5 equilibrium vector exactly. The serialized normalized metrics are:

metric	value	threshold	result
FREE_RESIDUAL_NORMALIZED	1.07747756058988e-14	1.0e-10	pass
FORCE_BALANCE_NORMALIZED	1.12049747258425e-14	1.0e-10	pass
MOMENT_BALANCE_NORMALIZED	2.35981341581908e-15	1.0e-10	pass

2. Reaction consistency and constrained/free meaning

The 24 perimeter nodes provide 144 constrained DOFs; the remaining 150 DOFs are free. The HDF5 constraint mask agrees with the input set exactly, all prescribed values are zero, and the maximum constrained displacement is exactly zero.

The total positive RF3=99999.9999999989 opposes the center F3=-100000. The nearly zero total RF1/RF2 and origin RM1/RM2/RM3 are required by the centered load and double symmetry. The largest raw free residual component is 7.62156560085714e-10; because translational and rotational entries have different dimensions, the decision uses the documented normalized metric rather than this raw maximum. The normalized free residual passes by more than three orders of magnitude.

3. Displacement direction and deformation mode

Center node 2 has

[U1,U2,U3,UR1,UR2,UR3]
= [0, 0, -2.35504417650849e-5, 0, 0, 0]

Every free-node U3 is nonpositive, the center is the maximum-magnitude translation, and every clamped boundary displacement is zero. Across the complete model, maximum absolute U1, U2, and UR3 are exactly zero. Maximum absolute UR1 and UR2 are 7.55060026636931e-6 and 7.55060026636933e-6, respectively. This is the expected symmetric plate-bending mode under a negative transverse center load, with no in-plane or drilling deformation leakage.

4. Reflection symmetry and expected zeros

For reflection through x=0, polar displacement components transform as [-U1,+U2,+U3], while the axial rotation vector transforms as [+UR1,-UR2,-UR3]. Reflection through y=0 similarly uses [+U1,-U2,+U3,-UR1,+UR2,-UR3].

All 294 scalar nodal component comparisons per reflection were paired by source coordinates. The maximum absolute mismatch was 4.27126230127111e-20 for the x reflection and 2.29087480670778e-20 for the y reflection. The equality evidence is numerical roundoff, not a new acceptance tolerance.

5. Shell generalized resultants and physical work signs

At every one of 36 elements times four midsurface Gauss locations, an independent constitutive reconstruction applied the documented centered-section identities:

N = A * epsilon0
M = D * kappa
Q = As * gamma0

The complete 1,152-component resultant comparison has absolute L2 residual 9.9301874551584e-12 and normalized L2 residual 5.56240926027087e-17. All membrane strains and N resultants are exactly zero, as required for this linear flat plate bending response.

The generalized work density generalized_strain dot section_resultant is strictly positive at all 144 locations: minimum 4.46321446508071e-4, maximum 1.27059464107458e-1, negative count 0. This supports the physical sign and component-order interpretation.

The shell contract does not expose element-end nodal actions and explicitly forbids averaging mismatched result locations. Consequently a separate GP-to-element-end force-balance assertion is not documented and is marked skipped; the assembled global residual and equilibrium checks provide the required force-balance evidence.

6. Stress component, location, and sign sanity

HDF5 stores local in-plane [S11,S22,S12] directly at each GP and ordered section positions BOTTOM(-1), MIDDLE(0), TOP(+1). Independent reconstruction used Cps*(epsilon0+z*kappa) at all 432 section locations. The absolute L2 residual is 1.29488994752188e-9, or normalized 3.05323934859307e-16, against a maximum absolute stored stress of 313250.779137971.

All middle-surface in-plane stresses are exactly zero. For every component and GP, bottom and top stresses are equal in magnitude and opposite in sign. This is the documented curvature/stress-location convention for a centered homogeneous section. No S33, S13, S23, nodal stress, or Abaqus stress equality was inferred.

7. Physical energy, residual, and rigid-body symptoms

The stored PHYSICAL_STRAIN_ENERGY is finite and positive:

HDF5 physical energy              = 1.17752208825422
independent GP generalized energy = 1.17752208825422
0.5 * F^T * d                     = 1.17752208825424

The HDF5-versus-recovered normalized difference is 1.88569375589575e-16; the final fresh HDF5-versus-external-work normalized difference is 9.14561471609432e-15. The HDF5 value excludes numerical drilling stabilization, as required. No drilling-energy ratio, calibration, or warning criterion was introduced.

The solution is finite, the full perimeter support is enforced, the expected deformation mode is smooth and symmetric, all three normalized verification metrics pass 1e-10, and the build/test evidence passes six-rigid-mode, stabilized-rank, non-rigid positive-energy, and pure-drill separation tests. No rigid-body, singular, nonfinite, or abnormal-mode symptom is present.

8. Approved model coverage

The sole approved reference model provides end-to-end evidence for the full-integration S4 -> FESA-MITC4 path, a nonzero transverse bending response, fully constrained reaction recovery, global force/moment balance, two-axis symmetry, physical energy, and shell result recovery.

The prerequisite focused 87/87 build/test portfolio supplies the documented complementary element evidence: membrane, bending, transverse-shear and twist patch fields; six physical rigid modes; expected physical/stabilized rank; frame and energy invariance; fixed numerical drilling and physical-recovery separation; and S4/S4R common-kernel/source-metadata behavior. The reference verification supplies the approved external displacement comparison.

This is the complete approved coverage for the feature. Pinched-cylinder, hemisphere, Scordelis-Lo, locking/convergence sequences, drilling calibration, expanded distorted/curved portfolios, and NR-O01 through NR-O04 are explicitly nonblocking or out of scope and were not invented as new physics gates.

Execution Evidence

order	exact command or read-only operation	exit code	result
1	cmake --build .harness/build --config Debug --target fesa_reference_tests	0	Existing S4 reference route rebuilt.
2	ctest --test-dir .harness/build -C Debug -R '^Mitc4S4Reference\.' --output-on-failure	0	Fresh S4 tests 2/2 passed; FESA HDF5 and ledger regenerated.
3	h5dump.exe -n .harness/build/reference/mitc4-shell-s4-comparison/results.h5 with HDF5/oneAPI runtime on PATH	0	Required HDF5 inventory inspected read-only.
4	h5dump.exe -y -w 0 -m '%.17g' -d <dataset> .harness/build/reference/mitc4-shell-s4-comparison/results.h5 for model nodes/elements/mask/prescribed values, nodal U/R, shell frames/strain/resultant/stress, energy/equilibrium/metrics/diagnostics	0	High-precision read-only numerical audit supplied all reported values.
5	PowerShell independent input/mask, reaction/equilibrium, reflection, constitutive recovery, stress-location, energy, finite, and diagnostics audit over the h5dump values	0	All documented physics assertions passed.
6	cmake --build .harness/build --config Debug --target fesa_unit_tests fesa_reference_tests, then `ctest --test-dir .harness/build -C Debug -R 'Mitc4Shell(Kernel	Patch	Drilling

Three intermediate audit-helper incidents were diagnostic-only and did not alter the product or verdict: a compound-record regular expression initially omitted the last node, a PowerShell array-expression initially bound subtraction to an array, and a final optional h5ls operand-order probe exited 1. The root causes were confirmed as audit-command/parser usage, while successful high-precision HDF5 inspection established 49/49 nodes and the complete evidence above. They are not solver, HDF5-schema, reference, or physics failures.

Failure Classification

• classification: N/A
• primary_failure: N/A
• evidence: all documented force/moment equilibrium, reaction, displacement, symmetry, recovery, stress-location, physical-energy, residual, finite-result, rigid-mode and approved coverage checks passed
• correction_handoff: N/A
• non_gating_incident: resolved read-only audit helper parsing/usage errors only

Evaluation Verdict

• verdict: pass-for-release-agent
• reason: the prerequisite reference status is valid and fresh FESA S4 evidence satisfies every documented physical expectation under its approved threshold; no implementation, formulation, I/O, model-coverage, nonfinite, rigid-body, or environment failure remains
• release_approval: not granted by this report
• reference_reapproval: not performed by this report

Handoff Recommendation

target_agent	reason	required_input
Release Agent	All documented MITC4 physics checks passed.	This report, the build/test and reference-verification reports, the fresh build-local HDF5/comparison evidence, and the nonblocking limitations below.

No-Change Assertion

• source_files_modified: false
• test_files_modified: false
• cmake_files_modified: false
• requirements_modified: false
• formulation_modified: false
• numerical_review_modified: false
• io_contract_modified: false
• reference_model_contract_modified: false
• build_test_report_modified: false
• reference_verification_report_modified: false
• phase_files_modified: false
• tolerance_policies_modified: false
• reference_artifacts_modified: false
• Abaqus_or_other_reference_solver_executed: false
• owned_report_created: true
• generated_build_local_evidence: true, ignored under .harness/build/
• pre_existing_untracked_build_test_report_preserved: true
• pre_existing_untracked_reference_verification_report_preserved: true

Open Issues

• Nonblocking coverage limitation: the approved external reference inventory is one flat, symmetric, fully clamped S4 plate. The approved analytical/unit portfolio supplies membrane, shear, twist, rigid-mode, rank, drilling-separation and S4R common-path evidence. No broader Abaqus or benchmark portfolio is claimed.
• Known original-MITC4 limitations remain: transverse-shear locking is mitigated by the tying field, but distorted-curved membrane locking and broader thin/thick mesh convergence are not characterized by this release gate.
• Source S4R maps to the same full-integration FESA kernel and is not compared to the optional Abaqus S4R artifacts. This is an approved boundary, not missing physics evidence.
• The fixed numerical drilling stiffness is not a physical stress/resultant/energy channel. No drilling calibration, coefficient sweep, energy-ratio gate, or director-parallel moment support is claimed.
• Geometrically nonlinear execution remains outside the current feature even though future-only residual/tangent equations are documented. No nonlinear release claim is made.
• No open issue blocks Release Agent review.