FESADev/docs/linear-static-3d-euler-beam/physics-evaluation.md

Linear Static 3D Euler Beam Physics Evaluation Report

Metadata

• feature_id: linear-static-3d-euler-beam
• model_id: cantilever-beam-b33
• evaluated_head: d76d052456ec134a98bcd5aa3b3c18a6b0ad6ba4
• source_reference_verification_report: docs/reference-verifications/linear-static-3d-euler-beam-reference-verification.md
• source_reference_model: docs/reference-models/linear-static-3d-euler-beam-reference-models.md
• source_requirement: docs/requirements/linear-static-3d-euler-beam.md
• source_formulation: docs/formulations/3d-isoparametric-euler-beam-formulation.md
• source_numerical_review: docs/numerical-reviews/linear-static-3d-euler-beam-review.md
• source_io_definition: docs/io-definitions/linear-static-3d-euler-beam-io.md
• status: pass-for-release-agent
• owner_agent: physics-evaluation-agent
• date: 2026-08-09

This verdict means that the documented physical checks pass and the Release Agent may audit release readiness. It does not approve release readiness and does not re-evaluate the Step 26 reference tolerance decision.

Input Evidence

The reference-verification prerequisite has status pass-for-physics-evaluation. Its checked artifact identity was reproduced before the physics checks and again after the targeted CTest.

evidence	exact path or identity	status	notes
reference verification	docs/reference-verifications/linear-static-3d-euler-beam-reference-verification.md	pass-for-physics-evaluation	Required gate satisfied.
solver HDF5	.harness/build/reference/cantilever-beam-b33/results.h5	present and readable	25,336 bytes; post-acceptance-run SHA-256 13ECCF68262C14BBDE0F63667C0F10896ACD40EFEC56E8C9121C298333FD9B6D.
comparison evidence	.harness/build/reference/cantilever-beam-b33/comparison.json	present and passing	128,118 bytes; SHA-256 258347AEA791D981AEA9B2BCAD85DE5344D4859ECA3692DC5E7AA01A848F8E0D; passed=true, 176 rows, 16 metrics.
reference input	reference/cantilever beam/cantilever beam.inp	exact read-only artifact	SHA-256 E406EA9560321B791DB829E03BD24593B9875E0195D35B86BD931EDA122EF3; TYPE=B33.
reference displacement	reference/cantilever beam/cantilever beam displacements.csv	exact read-only artifact	SHA-256 7B3312FBC8848E81D9A0FD4FF2B56BC1954636A2C14B5C1CBB269CB9477D3C31.
reference reaction	reference/cantilever beam/cantilever beam reactions.csv	exact read-only artifact	SHA-256 BF30CDB0CD50106885DE14D63492737736C587426EBD787DE4F7EE6AA86DAA23.
reference elemental force	reference/cantilever beam/cantilever beam elemental forces.csv	exact read-only artifact	SHA-256 E5E77FEC0FA9482AE018DBF296E74D396335C7C711BD2E9AA2315247A34290BA.
solver CSV views	N/A	not used	No derived FESA CSV was generated or used.
stress reference CSV	N/A by approved contract	not applicable	S11 is evaluated from HDF5 schema, formulation, and analytical/unit evidence only.
targeted physics tests	.harness/build, MSVC x64 Debug	pass	Exact Step 27 CTest passed 17/17: EulerBeam3D 10, ResultRecovery 6, B33ReferenceComparison 1.

Read-only HDF5 inspection confirmed schema 0, solver 0.1.0, feature identity, Step-1 frame 0, formulation B33-3D-Euler-Bernoulli, source content identity fnv1a64:04543464cc970405, and coordinate convention global-cartesian; beam-local=(t,n1,t-cross-n1). The file contains 11 nodes at (x,y,z)=(0..10,0,0) m and 10 consecutive one-metre elements. Every element has identity local axes, so local (x,y,z) equals global (X,Y,Z) for this model.

The documented physical model is a 10 m cantilever with node 1 fixed in all six DOFs and a free-end global/local FZ=-1.0e6 N at node 11. The section and material are SI: E=2.1e11 Pa, Iy=I11=0.0833333 m^4, and the only expected deformation mode is local-z translation with bending about local y.

Physics Checks

All normalized physics criteria below come from the approved 1e-10 residual/equilibrium, 1e-12 matrix/transform/end-sign, or 1e-9 analytical contracts. They are independent checks of physical meaning, not a second application of the Abaqus row tolerance.

1. global equilibrium

In global Cartesian coordinates, force equilibrium is

r_F = sum(F_applied) + sum(R),

with criterion

||r_F|| / max(||sum(F_applied)||, ||sum(R)||) <= 1e-10.

The comparison physics evidence records sum(F_applied)=[0,0,-1000000] N and sum(R)=[0,0,999999.9999998808] N. Therefore r_F=[0,0,-1.1920928955078125e-7] N, its norm is 1.1920928955078125e-7 N, and the normalized value is 1.1920928955078125e-13. Verdict: pass.

Moment equilibrium about the global origin is

r_M = sum(M_applied) + sum(X cross F_applied) + sum(M_reaction) + sum(X cross R_force).

The free-end force gives [0,1.0e7,0] N*m; the complete HDF5 reaction field gives [0,-9999999.999997258,0] N*m. Thus r_M=[0,2.7418136596679688e-6,0] N*m, with normalized norm 2.7418136596679688e-13 against 1.0e7 N*m. Verdict: pass.

2. reaction consistency and true free residual

The constrained reaction contract is R_c=(K*d-F)_c. At fixed node 1 the observed global row is [RF1,RF2,RF3,RM1,RM2,RM3] = [0,0,1000000.0000008196,0,-10000000.000005051,0] in [N,N,N,N*m,N*m,N*m]. It opposes the applied -Z force and balances its positive origin moment. Differences from the physical closed-form reactions are 8.195638656616211e-7 N and 5.0514936447143555e-6 N*m, normalized to 8.195638656616211e-13 and 5.0514936447143555e-13. Verdict: pass.

The reaction dataset intentionally preserves free residuals. The implementation uses

rho_f = ||(K*d-F)_f||_2 / max(||K*d||_f, ||F||_f)

with no artificial unit floor. The serialized true free residual norm is 9.356339321107032e-7 N-equivalent; the physical free scale is 1.0e6 N, so rho_f=9.356339321107032e-13 <= 1e-10. The largest observed free force-residual component is 5.9604644775390625e-7 N, and the largest free moment-residual component is 2.0861625671386719e-7 N*m. Verdict: pass.

3. displacement direction and rotation sign

For free-end local Pz=-1.0e6 N, the documented Euler-Bernoulli solution is

w(L)=Pz*L^3/(3*E*Iy), theta_y(L)=-Pz*L^2/(2*E*Iy).

The expected values are -0.0190476266666697 m and +0.00285714400000046 rad. HDF5 gives tip UZ=-0.019047626666677083 m and URY=+0.0028571440000013902 rad, with relative errors 3.87e-13 and 3.27e-13, below the analytical 1e-9 criterion. All non-root UZ values are negative and monotonically increase in magnitude toward the loaded tip; all non-root URY values are positive, as required by theta_y=-dw/dx. Verdict: pass.

4. expected zero and uncoupled symmetry

The fixed-root displacement row is exactly zero in all six components. Across all nodes, UX, UY, URX, and URZ are exactly zero. The only nonzero kinematic components are UZ and URY, and the only physical constrained reactions are RF3 and RM2. In the element recovery, epsilon0, kappa_x, and kappa_z, and the corresponding N, T, and Mz, are exactly zero. This is the documented uncoupled local-z bending symmetry, with no axial, torsional, or cross-plane leakage. Verdict: pass.

5. element force, adjacent endpoints, and boundary balance

The HDF5 end_force_local rows are outward endpoint actions in [FX,FY,FZ,MX,MY,MZ]; section_resultant rows are positive-local-x section cuts in [N,T,My,Mz]. With no distributed load,

F_X=n*N, M_X=n*T, M_Y=n*My, M_Z=n*Mz, F_Y=-n*dMz/dx, and F_Z=n*dMy/dx, where n=-1 at xi=-1 and n=+1 at xi=+1.

Observed section My is positive and decreases linearly from 10000000.000005048 N*m at the root to 2.4286118949223834e-7 N*m at the free end. The maximum positive-face My mismatch between adjacent unloaded endpoints is 2.73110345005989e-7 N*m, normalized to 2.73110345005989e-14 against the model moment scale. The comparison ledger independently records endpoint_consistency_passed=true without averaging.

Adjacent outward actions cancel. The maximum interior FZ_right+FZ_left magnitude is 5.364418029785156e-7 N (5.364418029785156e-13 normalized); the maximum interior MY_right+MY_left magnitude is 2.682209014892578e-7 N*m (2.682209014892578e-14 normalized). Both satisfy the documented end-sign/residual criteria.

At the root, the first element action is exactly the constrained reaction evidence: FZ=+1000000.0000008196 N, MY=-10000000.000005051 N*m. At the free boundary, the last element has FZ=-999999.9999998808 N and MY=-5.9604644775390625e-8 N*m, balancing the applied end force and the zero applied end moment to normalized residual scale. Verdict: pass.

6. local/global mapping and section-force signs

Every stored local-axis matrix is the identity. Therefore the global -Z load is local Pz=-1.0e6 N, UZ=w<0, URY=theta_y>0, and the positive-face section resultant is My=-Pz*(L-x)>0. The observed outward signs are FZ>0, MY<0 at left endpoints and FZ<0, MY>0 at right endpoints, except for the physically zero free-end moment residue. These values satisfy the documented theta_y=-w', My=-E*Iy*w'', outward-normal, and positive-face-section-cut conventions. Verdict: pass.

7. stress location, unit, and sign sanity

The stress contract is

S11(xi,y,z)=E*(epsilon0 + z*kappa_y - y*kappa_z),

where x1=y, x2=z, the coordinate system is beam local, the unit is force/length^2, and the location is a section point at each of two Gauss points. The reference input has no section points, so HDF5 correctly contains 20 ordered fesa-default centroid rows (x1,x2)=(0,0), one at each Gauss point of ten elements. This model has pure bending with epsilon0=0; consequently all 20 observed centroid S11 values are exactly 0 Pa.

Nonzero location/sign evidence comes only from the approved analytical/unit portfolio, not from an Abaqus stress comparison. EulerBeam3D.RecoversSectionPointAndDefaultCentroidS11 passed with epsilon0=0.01, kappa_y=0.02 1/m, kappa_z=-0.03 1/m, E=2.1e11 Pa: the formula gives 1.575e9 Pa at (y,z)=(0.25,-0.5), 8.4e8 Pa at (-0.4,0.3), and 2.1e9 Pa at the default centroid. The test enforces the formula at both Gauss points with normalized 1e-12 evidence. Abaqus beam stress comparison remains explicitly N/A. Verdict: pass.

8. nonfinite, rigid-body, abnormal-magnitude, and energy symptoms

All mandatory numeric HDF5 rows inspected here are finite; comparison.json also records no nonfinite row among the 176 compared rows and the 20 stress rows are finite. The fixed root is exactly zero, factorization/solution completed, the normalized free residual is 9.36e-13, and the displacement field is smooth, so there is no rigid-body-mode symptom.

For this one-load linear case, the recoverable strain energy is U=0.5*F^T*d=9523.81333333854 N*m, which is finite and positive. The ratios |UZ_tip|/L=0.00190476266666771 and |URY_tip|=0.00285714400000139 rad agree with the analytical solution and show no abnormal magnitude relative to the documented small-displacement/rotation model. The targeted rank/energy test also passed the six-rigid-mode, rank-six, and positive deformation-energy checks. Verdict: pass.

9. model coverage

The approved B33 bundle is one identity-axis local-z bending cantilever. It directly covers the end-to-end parser/solver/HDF5 path, global equilibrium, reaction sign, UZ/URY, My/FZ, endpoint continuity, and the centroid stress fallback. It does not by itself cover axial, torsion, local-y bending, rotated space, nonzero fiber stress, prescribed displacement, or the formulation-only line-load kernel. The targeted analytical/unit portfolio supplies the documented complementary coverage:

coverage	targeted passing evidence	criterion
axial, torsion, both bending planes	EulerBeam3D.AnalyticalAxialTorsionAndTwoPlaneBendingRecover and ResultRecovery.MatchesAxialTorsionAndTwoPlaneEndSigns	analytical relative 1e-9; signed recovery contract
rotated local/global mapping	EulerBeam3D.RotatedTransformPreservesWorkAndEnergy	transform/work/energy normalized 1e-12
constant local line-load kernel	EulerBeam3D.ConstantLineLoadMatchesAllSignedComponents	all 12 signed components normalized 1e-12; *DLOAD remains outside CLI scope
rigid modes, rank, and energy	EulerBeam3D.HasSixRigidModesRankSixAndPositiveDeformationEnergy	rigid residual 1e-10, rank six, positive deformation energy
prescribed displacement and residual	ResultRecovery.ComputesResidualReactionForNonzeroPrescription, ResultRecovery.EnforcesNormalizedFreeResidual	partition/reaction and normalized residual 1e-10
result identity and continuity	ResultRecovery.KeepsEndActionSectionAndGaussResultsDistinct, ResultRecovery.RequiresInteriorEndpointConsistencyWithoutAveraging	distinct locations and no-average consistency
S11 location/sign/default	EulerBeam3D.RecoversSectionPointAndDefaultCentroidS11, ResultRecovery.OrdersStressPointsAndDefaultCentroid	formula/schema normalized 1e-12

The exact acceptance command passed all 17 selected tests. The single reference model plus this analytical portfolio covers every documented physical expectation without attributing unsupported coverage to the legacy CSV bundle. Verdict: pass.

Failure Classification

• classification: N/A
• primary_failure: N/A
• evidence: all documented physics checks passed; no equilibrium, reaction, displacement, symmetry, element-force, stress-location, rigid-body, nonfinite, coverage, contract, or environment failure was found
• correction_handoff: N/A

Evaluation Verdict

• verdict: pass-for-release-agent
• reason: the exact reference gate and artifact identity are valid; force and origin-moment equilibrium, constrained reaction consistency, true free residual, deformation signs, expected zeros, element force balance, local/global and section-force signs, S11 schema/analytical sanity, finite/energy/mode checks, and complementary model coverage all satisfy their documented criteria
• release_approval: not granted by this report

Handoff Recommendation

target_agent	reason	required_input
Release Agent	All documented physical checks passed.	This report, the Step 26 reference-verification report, exact build-local HDF5/comparison identities, targeted CTest evidence, and the limitations below.

No-Change Assertion

• source_files_modified: false
• test_files_modified: false
• cmake_files_modified: false
• requirements_modified: false
• formulations_modified: false
• numerical_review_modified: false
• io_contract_modified: false
• reference_model_contract_modified: false
• reference_verification_report_modified: false
• reference_artifacts_modified: false
• tolerance_policies_modified: false
• Abaqus_or_other_reference_solver_executed: false
• owned_report_created: true
• phase_index_step27_modified: true
• notes: HDF5, comparison JSON, and legacy reference artifacts were inspected read-only; the only generated files were the ignored build-local evidence regenerated by the exact approved CTest.

Open Issues

• Non-blocking coverage limitation: the approved Abaqus bundle is one identity-axis local-z bending cantilever. Axial, torsion, local-y, rotated, prescribed-displacement, line-load, and nonzero stress checks rely on the approved analytical/unit portfolio; no broader Abaqus reference coverage is claimed.
• Non-blocking stress limitation: the B33 bundle has no section points, so its physical S11 evidence is the correct zero centroid result. Nonzero fiber location/sign evidence is analytical; Abaqus beam stress comparison remains N/A.
• Non-blocking output limitation: HDF5 has no strain-energy dataset by contract. The positive energy value in this report is calculated from 0.5*F^T*d and is supported by the rank/energy unit test.
• Known formulation limitations remain: Euler-Bernoulli deep-beam applicability, transverse and torsional shear stress, warping, I12!=0, B31/Timoshenko behavior, and CLI *DLOAD are outside V0.
• No open issue blocks Release Agent review.