FESADev/docs/nonlinear-static-newton-raphson/translation-displacement-comparison.md

Translation Displacement Comparison Report

1. Metadata and scope

• feature_id: nonlinear-static-newton-raphson
• report_id: TRANSLATION-REPORT-001
• date: 2026-08-26
• owner_agent: implementation-agent (bounded diagnostic dispatch)
• dispatch coordination SHA-256: D7CE6264EE3FD20FB6CD74CF1FC28E05EEEEFA67B25AF737D2DF989059A72D6F
• status: translation-diagnostic-pass-not-a-gate
• tolerance source: docs/TOLERANCE.md

This focused report recomputes only global translational displacement components U1/U2/U3 for the existing coarse reference/shellNL case and the added fine reference/shellNL-meshfine case. It is diagnostic evidence for the observed mesh sensitivity; it does not create or replace the canonical Stage 6 reference-comparison.md. In particular, it is not Step 12 implementation evidence and does not change any workflow gate.

The two meshes are compared separately to their own read-only Abaqus CSV artifacts. No coarse-to-fine node interpolation, row pairing, averaging, or direct FESA-to-FESA error was used.

2. Artifact inventory and accepted-frame identity

All paths below are relative to the feature worktree. SHA-256 and byte counts were recomputed before comparison.

mesh	artifact	path	bytes	SHA-256
coarse	input	reference/shellNL/shellNL.inp	4,778	4BF3ECB0F7F1E8462C573E993DBC97AC5D920C91CF6F23AD4C6891D77FFBADA2
coarse	translation CSV	reference/shellNL/shellNL displacements.csv	7,542	4E0F99CA9372B1ADF7FAF102F43BC0B887DC743FDEDA378E4342D2CF8E0C0786
coarse	FESA HDF5	.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL/shellnl-s4-final-441600152250700-0/shellNL_results.h5	934,602	9744814BEBF33486F526F821EDC7D96F072F34E988D70A00AC7AA063570FFA40
fine	input	reference/shellNL-meshfine/shellNL-meshfine.inp	56,516	40DF1CE77311C8D799564A21A60F3BDEBB8148D52CAE22B7292FDFAD32018220
fine	translation CSV	reference/shellNL-meshfine/shellNL-meshfine displacements.csv	111,184	740819FF8AED0E279961581F7CDBFA12784CFBA3A488C35A652E80103F64433F
fine	FESA HDF5	.harness/build-ninja-msvc-debug/reference/meshfine-diagnostic/run-1787669003801/shellNL-meshfine_results.h5	10,547,651	81A3C431E2977D2482D212877C3C306FFBB19CD1F0C47FBF1C936AE06CC93ACA

For both HDF5 artifacts, /steps/Step-1/accepted_frames has ten accepted rows. The unique row satisfying is_factor_one=1 and load_factor=1.0 is frame_index=9, increment_index=10, and iteration_count=2. Translation values were projected only from /steps/Step-1/frames/9/nodal/displacement, columns [UX, UY, UZ]:

mesh	HDF5 node rows	displacement shape	CSV wide rows	exact CSV Frame
coarse	49	[49, 6]	49	Increment 10: Step Time = 1.000
fine	729	[729, 6]	729	Increment 10: Step Time = 1.000

3. Source identity and prechecks

The comparison key is

(accepted_state=factor-one, canonical_instance_name, source_node_label, component)

canonical_instance_name is matched case-insensitively; the CSV/HDF5 source spelling itself is not rewritten. CSV columns were selected after trimming only surrounding header whitespace. The U-U1/U-U2/U-U3 columns map respectively to HDF5 UX/UY/UZ. Row order is not part of the identity and was not used for matching.

mesh	component rows	duplicate CSV wide/component/HDF5 keys	nonfinite CSV/HDF5 values	missing HDF5 keys	extra HDF5 keys	precheck
coarse	147	0 / 0 / 0	0 / 0	0	0	pass
fine	2,187	0 / 0 / 0	0 / 0	0	0	pass

Each CSV contains only the exact factor-one Frame value shown above. Thus the row prechecks required before numerical tolerance evaluation pass for the translation projection in each mesh.

4. Applied tolerance policy

U1/U2/U3 remain one global-length, blocking translation family within each case. The component rows in Section 6 are diagnostics only: they use the same case-family scale and near-zero band below and do not introduce a component scale, component-specific tolerance, or a new approved family.

For the reference values r_i and FESA values f_i, docs/TOLERANCE.md is applied exactly:

[ S=\max_i|r_i|,\qquad B=0.01S,\qquad e_i=|f_i-r_i|. ]

• If |r_i| <= B, the row passes iff e_i <= B.
• Otherwise, the row passes iff e_i / |r_i| <= 0.05.
• The whole family also requires RMS(e_i) / S <= 0.01.
• There is no independent absolute-error gate, max(1,S) floor, zero clamp, row omission, or averaging. A zero-scale family would require exact FESA zero; neither translation family has zero reference scale.

5. Translation-family results

mesh	rows	S	B=0.01S	near-zero / significant rows	row failures	max absolute error	max significant-row relative error	RMS error	L2(error)	relative RMS	verdict
coarse	147	2.3740820300000001e-05	2.3740820300000003e-07	122 / 25	0	1.9037855439354404e-07	8.5711169439298945e-03	2.4530813178127803e-08	2.9742030342848264e-07	1.0332757195473908e-03	pass
fine	2,187	2.5795705400000001e-05	2.5795705400000002e-07	1,626 / 561	0	1.6193812501096337e-07	6.2777164841928829e-03	5.8615647876386634e-09	2.7411825664926473e-07	2.2723025777921402e-04	pass

Both sets have zero row failures and relative RMS values below the common 0.01 threshold. This is a translation-only diagnostic pass; it is not a full external-reference verdict for the nonlinear-static feature.

6. Component diagnostics under the unchanged family scale

The near-zero/significant counts and every row decision below use the Section 5 family band B, not a component-derived scale. A dash for maximum relative error means all rows of that component were near-zero and were therefore judged only by the approved absolute-band rule.

6.1 Coarse mesh

component	rows	near-zero / significant	row failures	max absolute error	max significant-row relative error	RMS error	L2(error)	worst row (node; fesa; reference; abs error)
U1	49	49 / 0	0	5.9371608358817413e-12	—	1.7563955953584068e-12	1.2294769167508847e-11	12; -8.7994083858817417e-12; -2.8622475500000000e-12; 5.9371608358817413e-12
U2	49	49 / 0	0	5.9379769034414602e-12	—	1.7566506185832881e-12	1.2296554330083018e-11	19; 8.7996068934414599e-12; 2.8616299900000001e-12; 5.9379769034414602e-12
U3	49	24 / 25	0	1.9037855439354404e-07	8.5711169439298945e-03	4.2488614702881049e-08	2.9742030292016737e-07	2; -2.3550441745606457e-05; -2.3740820300000001e-05; 1.9037855439354404e-07

6.2 Fine mesh

component	rows	near-zero / significant	row failures	max absolute error	max significant-row relative error	RMS error	L2(error)	worst row (node; fesa; reference; abs error)
U1	729	729 / 0	0	5.6550975712048108e-12	—	1.5513648050863109e-12	4.1886849737330394e-11	27; -1.1143569120481096e-13; 5.5436618799999999e-12; 5.6550975712048108e-12
U2	729	729 / 0	0	5.6547834814404039e-12	—	1.5512360377367428e-12	4.1883373018892053e-11	16; -1.1132282144040392e-13; 5.5434606599999999e-12; 5.6547834814404039e-12
U3	729	168 / 561	0	1.6193812501096337e-07	6.2777164841928829e-03	1.0152527787009038e-08	2.7411825024924402e-07	2; -2.5633767274989038e-05; -2.5795705400000001e-05; 1.6193812501096337e-07

7. Deterministically ordered largest absolute-error rows

Rows are listed by descending absolute error, then source node label and component for a deterministic display. part-1-1 below is the canonical case-insensitive instance identity.

mesh	rank	key (instance, node, component)	FESA	reference	absolute error	applied rule and metric
coarse	1	(part-1-1, 2, U3)	-2.3550441745606457e-05	-2.3740820300000001e-05	1.9037855439354404e-07	relative; 8.0190386005130586e-03
coarse	2	(part-1-1, 35, U3)	-1.2104431681576916e-05	-1.2190867900000000e-05	8.6436218423083233e-08	relative; 7.0902432158323394e-03
coarse	3	(part-1-1, 39, U3)	-1.2104431681576916e-05	-1.2190867900000000e-05	8.6436218423083233e-08	relative; 7.0902432158323394e-03
fine	1	(part-1-1, 2, U3)	-2.5633767274989038e-05	-2.5795705400000001e-05	1.6193812501096337e-07	relative; 6.2777164841928829e-03
fine	2	(part-1-1, 21, U3)	-2.3863834908375246e-05	-2.3782464300000001e-05	8.1370608375244783e-08	relative; 3.4214540322150206e-03
fine	3	(part-1-1, 69, U3)	-2.3863834908375246e-05	-2.3782464300000001e-05	8.1370608375244783e-08	relative; 3.4214540322150206e-03

8. Mesh trend interpretation

The fine-mesh translation relative RMS divided by the coarse-mesh translation relative RMS is

[ \frac{2.2723025777921402\times10^{-4}} {1.0332757195473908\times10^{-3}} =0.21991251074664606. ]

This is a 78.008748925335397% reduction in the separately measured reference-normalized translation RMS. It is consistent with the hypothesis that the coarse-case discrepancy is mesh-sensitive, and the fine case also passes the same row/RMS policy.

It is not an observed order of convergence, a proof of monotonic convergence, or a solution-accuracy claim outside these translation rows: the two models have different meshes and distinct external-reference outputs, and no common-mesh interpolation or mesh-size-rate study was performed.

9. Explicit exclusions and no-change assertion

This report deliberately excludes:

• all reaction quantities;
• UR1/UR2/UR3 rotations;
• all stress quantities, including the user-noted reference/shell element-label ordering change;
• Newton convergence lifecycle and iteration-log acceptance beyond identifying the accepted factor-one HDF5 frame;
• USER-DECISION-004 disposition;
• Step 11 and Step 12 status, Physics Evaluation, and Release readiness.

No source, test, CMake, comparator, tolerance policy, phase file, canonical reference-comparison report, declared input, or reference artifact was modified for this report. The report also does not create implementation-report.md, build-test.md, or reference-comparison.md.

10. Handoff

Within this narrow scope there is no artifact, identity, finite-value, or translation-tolerance blocker. The report is handed to the Coordinator as translation-only diagnostic evidence; gate ownership and all excluded work remain unchanged.