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

Linear Static 3D Euler Beam Requirements

Metadata

• feature_id: linear-static-3d-euler-beam
• title: Linear Static 3D Euler Beam
• status: approved
• owner_agent: requirement-agent
• date: 2026-08-09
• approved_design: docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md
• approval_basis: design status: approved, user approval on 2026-08-08, and amendment on 2026-08-09
• source_formulation: docs/formulations/3d-isoparametric-euler-beam-formulation.md
• reference_baseline: reference/cantilever beam/ at source commit 2b34d0b

Purpose

이 baseline은 승인된 Abaqus .inp subset을 입력으로 받아 2절점 3차원 Euler–Bernoulli beam의 단일 선형 정적 step을 해석하고, 검증 가능한 변위, 반력, 요소 결과와 축응력을 authoritative results.h5에 기록하는 FESA V0 기능을 정의한다. 이 문서는 승인 설계를 검증 가능한 shall 요구조건으로 전사하며 Abaqus full compatibility, 새로운 수학 계약 또는 새로운 구현 정책을 추가하지 않는다.

In Scope

• 입력 파일당 하나의 *STEP, *STATIC 선형 정적 해석
• small displacement, small rotation, 균질 선형 등방 탄성
• 2절점 직선 prismatic 3D Euler–Bernoulli beam과 Abaqus TYPE=B33
• 절점당 전역 자유도 [UX, UY, UZ, URX, URY, URZ]
• 축 변형, 두 방향 굽힘, Saint-Venant 비틀림
• nodal concentrated load와 zero/nonzero prescribed displacement
• formulation 검증용 constant local line-load equivalent nodal vector kernel
• identity *PART/*ASSEMBLY/*INSTANCE wrapper와 stable source identity
• deterministic COO-to-CSR assembly, element-local oneTBB 계산, MKL PARDISO factorization/substitution
• HDF5 displacement, reaction, equilibrium end action, section resultant, generalized strain/resultant, axial S11
• 승인된 reference/cantilever beam/ legacy B33 bundle의 displacement, reaction, section resultant comparison

Out Of Scope

• Abaqus full compatibility와 Abaqus TYPE=B31 Timoshenko beam
• 다중 analysis step과 step 간 load/BC propagation
• instance translation/rotation, nested assembly, dependent/independent mesh semantics
• I12 != 0, taper, offset, release, curved beam, warping
• Abaqus *DLOAD 입력과 Domain distributed-load object
• 기하·재료비선형, dynamics, contact, thermal effects
• transverse shear stress와 torsional shear stress recovery
• beam stress에 대한 Abaqus reference comparison
• Abaqus, Nastran 또는 다른 reference solver 실행과 reference artifact 생성·수정·복원

Analysis Definition

• analysis_type: single-step linear static
• kinematics: small displacement and small rotation
• element: two-node straight prismatic 3D Euler–Bernoulli beam, Abaqus TYPE=B33
• nodal_dofs: global [UX, UY, UZ, URX, URY, URZ]
• deformation_modes: axial, local-y/local-z bending, Saint-Venant torsion
• material_model: homogeneous isotropic linear elasticity from E and nu
• boundary_conditions: DOF 1 through 6, including nonzero prescribed displacement
• loads: nodal concentrated load; formulation-only constant local line-load kernel
• local_coordinate_system: t -> local x, Abaqus first section axis n1 -> local y, t x n1 -> local z, right-handed
• units: input uses a user-consistent unit system; the approved cantilever reference bundle is SI
• authoritative_output: HDF5 results.h5

Input Requirements

• FESA-REQ-LS3DEB-001 — The FESA solver shall accept exactly one *STEP containing *STATIC per input file and shall reject a second analysis step with a structured unsupported diagnostic.
• FESA-REQ-LS3DEB-002 — The FESA solver shall analyze only straight, prismatic, two-node 3D Euler–Bernoulli beams under small-displacement, small-rotation, linear-static assumptions.
• FESA-REQ-LS3DEB-003 — The FESA solver shall assign each beam node the six global DOFs [UX, UY, UZ, URX, URY, URZ] in that order.
• FESA-REQ-LS3DEB-004 — The FESA solver shall support axial deformation, bending about both local section axes, Saint-Venant torsion, and homogeneous isotropic linear elasticity.
• FESA-REQ-LS3DEB-005 — The FESA solver shall map only *ELEMENT, TYPE=B33 to the V0 Euler–Bernoulli beam formulation.
• FESA-REQ-LS3DEB-006 — The FESA solver shall reject *ELEMENT, TYPE=B31 with unsupported-element-formulation and shall not reinterpret B31 as B33.
• FESA-REQ-LS3DEB-007 — The FESA solver shall support nodal *CLOAD and *BOUNDARY data for DOFs 1 through 6, including nonzero prescribed displacement.
• FESA-REQ-LS3DEB-008 — The element verification contract shall include a constant local line-load equivalent nodal vector kernel, while the V0 parser and CLI shall not support *DLOAD or create a Domain distributed-load object.
• FESA-REQ-LS3DEB-009 — The parser shall support exactly *HEADING; *PART, *END PART; *NODE; *ELEMENT, TYPE=B33; *NSET, *ELSET, including GENERATE; *MATERIAL, *ELASTIC; *BEAM GENERAL SECTION, SECTION=GENERAL; *SECTION POINTS; *ASSEMBLY, *END ASSEMBLY; *INSTANCE, *END INSTANCE; *BOUNDARY; *CLOAD; *STEP, *STATIC, and *END STEP as model/procedure keywords.
• FESA-REQ-LS3DEB-010 — The parser shall interpret keyword and parameter names case-insensitively, recognize ** comment lines, and preserve source label text for external identity.
• FESA-REQ-LS3DEB-011 — The parser shall accept *BOUNDARY rows only as target, first_dof, last_dof[, value], default an omitted value to zero, and accept *CLOAD rows only as target, dof, magnitude; targets shall resolve by source node label or node set, including assembly-level sets with INSTANCE.
• FESA-REQ-LS3DEB-012 — The semantic mapping shall read general-section data as A, I11, I12, I22, J, require I12=0, map Iy=I11 and Iz=I22, and construct local axes as n1 -> y and t x n1 -> z.
• FESA-REQ-LS3DEB-013 — A general beam section shall reference a material whose isotropic *ELASTIC data provides exactly E, nu; the solver shall compute G=E/(2(1+nu)) and require positive E, G, A, Iy, Iz, and J.
• FESA-REQ-LS3DEB-014 — Before element calculation, the solver shall require L > 1e-12 * max(1, norm(X1), norm(X2)) and norm(a_perp) > 1e-12 * max(1, norm(a)); zero/near-zero length, a zero guide vector, and a tangent-parallel guide vector shall produce structured model-validation diagnostics.
• FESA-REQ-LS3DEB-015 — *PART/*ASSEMBLY/*INSTANCE mapping shall preserve SourceEntityId { instance_name, source_label } for nodes, elements, and sets and shall map it deterministically to a separate stable Domain internal index.
• FESA-REQ-LS3DEB-016 — The semantic model shall allow multiple identity instances of the same part without merging their source identities.
• FESA-REQ-LS3DEB-017 — An instance containing translation or rotation data shall be rejected with unsupported-instance-transform.
• FESA-REQ-LS3DEB-018 — Nested assembly and dependent/independent mesh semantics shall be rejected as unsupported rather than silently approximated.
• FESA-REQ-LS3DEB-019 — The parser shall issue structured warnings and no-op the exact allowlist *PREPRINT, *RESTART, *TRANSVERSE SHEAR STIFFNESS, *OUTPUT, FIELD, *OUTPUT, HISTORY, *NODE OUTPUT, *ELEMENT OUTPUT, *CONTACT OUTPUT, and unsupported variable data belonging to those output requests.
• FESA-REQ-LS3DEB-020 — Unsupported model-affecting keywords outside the no-op allowlist shall be errors, and accepted Abaqus output requests shall not change or suppress FESA's mandatory HDF5 results.

Architecture and Execution Requirements

• FESA-REQ-LS3DEB-021 — Domain shall own the complete parsed model and remain effectively immutable after mapping; AnalysisModel shall expose references or IDs for the single active step without copying Domain objects.
• FESA-REQ-LS3DEB-022 — DofManager alone shall own node DOF definitions, full/free equation numbering, constrained/free mappings, element scatter maps, sparse patterns, and full/reduced vector reconstruction; Node and Element shall not store equation IDs.
• FESA-REQ-LS3DEB-023 — V0 AnalysisState shall own full displacement, external/internal force, residual, constrained reaction, step/frame identity, and element recovery rows and shall not allocate velocity, acceleration, temperature, iteration history, or nonlinear element state.
• FESA-REQ-LS3DEB-024 — Element-local stiffness work shall use the ParallelFor/oneTBB boundary, and global assembly shall deterministically reduce element contributions in stable element order from COO triplets into a 0-based CSR matrix.
• FESA-REQ-LS3DEB-025 — MKL, TBB, and HDF5 API/types shall remain behind the LinearSolver, ParallelFor, dense/sparse math, and ResultsWriter adapter boundaries; Vector shall use contiguous doubles, Matrix row-major contiguous doubles, and SparseMatrix a separate 0-based CSR representation.
• FESA-REQ-LS3DEB-026 — The linear-static lifecycle shall assemble and partition stiffness, call Kff factorization, and only then assemble the full load vector, form the effective RHS, and perform substitution; factorization and substitution shall remain observably separate.
• FESA-REQ-LS3DEB-027 — For prescribed displacement dc, the solver shall form rhs=Ff-Kfc*dc, reconstruct the full displacement after substitution, and recover constrained reaction from K*d-F, equivalently Rc=Kcf*df+Kcc*dc-Fc, rather than a separate end-force sum.

Output Requirements

• FESA-REQ-LS3DEB-028 — The sole authoritative solver output shall be HDF5 results.h5; the writer shall complete a temporary file before replacing the final path and shall leave no incomplete final file after a writer failure.
• FESA-REQ-LS3DEB-029 — HDF5 schema v0 shall contain /metadata, /model/nodes, /model/elements, /steps/<step-name>/frames/0/nodal/displacement, /steps/<step-name>/frames/0/nodal/reaction, /steps/<step-name>/frames/0/element/end_force_local, /steps/<step-name>/frames/0/element/section_resultant, /steps/<step-name>/frames/0/element/generalized_strain, /steps/<step-name>/frames/0/element/stress_s11, and /diagnostics.
• FESA-REQ-LS3DEB-030 — HDF5 metadata/model identity shall record schema version, solver version, source input identity, unit-system label, coordinate convention, element formulation, stable internal IDs, and instance/source-label mappings; ordinary input shall use user-consistent-unspecified, while the approved cantilever comparison shall apply its external SI contract without inferring SI from .inp alone.
• FESA-REQ-LS3DEB-031 — Output shall include every node's global displacement/reaction in [UX, UY, UZ, URX, URY, URZ], local endpoint equilibrium end actions in [FX,FY,FZ,MX,MY,MZ], endpoint section resultants in [N,T,My,Mz], and generalized strain/resultant values at the two Gauss points, independent of Abaqus output requests.
• FESA-REQ-LS3DEB-032 — The solver shall output axial S11 at both Gauss points and each input section point, or at centroid (0,0) with source=fesa-default when section points are absent; transverse/torsional shear stress shall not be recovered, and Abaqus beam-stress reference comparison shall remain explicit N/A while analytical/unit and HDF5 schema tests remain mandatory.
• FESA-REQ-LS3DEB-033 — The CLI shall support fesa.exe <model.inp> --output <results.h5>, default output to the current directory's results.h5, use exit codes 0=success, 2=usage, 3=input, 4=model, 5=solver, 6=HDF5, and emit severity, code, file, line, keyword, entity_identity, and message diagnostics to stderr in deterministic order.

Verification Requirements

• FESA-REQ-LS3DEB-034 — Every production C++ behavior shall be developed in one step as GoogleTest RED -> GREEN -> VERIFY, with a related C++ test file, focused CTest evidence, full MSVC x64 Debug build/CTest evidence, at least one discovered test, and no new warning under the FESA target's /W4 /WX policy.
• FESA-REQ-LS3DEB-035 — Numerical tests shall satisfy normalized 1e-12 for stiffness symmetry and two-point-Gauss/closed-form agreement, normalized 1e-10 for rigid-mode and linear-system residual, and relative 1e-9 for analytical solutions, while checking six rigid modes, rank 6, positive deformation energy, transformation orthogonality/energy invariance, prescribed-displacement recovery, and axial/torsion/two-plane bending benchmarks.

Verification Quantities

• nodal_displacement: required, global six components, HDF5-to-Abaqus CSV comparison
• reaction: required, global six components plus global force/moment equilibrium
• equilibrium_end_action: required, local endpoint six components; unit/analytical and physics tests
• section_resultant: required, endpoint [N,T,My,Mz], node-station-normalized reference comparison
• generalized_strain_and_resultant: required at two Gauss points; formulation and schema tests
• stress: axial S11 required; Abaqus reference comparison N/A
• residual: required, free-DOF and normalized global equilibrium checks
• energy_and_modes: required for symmetry, rank, rigid modes, and transform invariance

Tolerance Policy

• FESA-REQ-LS3DEB-036 — The approved B33 reference comparison shall group rows by the same model, step/frame, quantity, and component, compute reference_scale only from read-only Abaqus values, and apply absolute_floor + 1e-6 * reference_scale to every matched row.
• FESA-REQ-LS3DEB-037 — For the approved SI bundle, displacement and rotation shall use absolute_floor=1e-9, force and moment shall use absolute_floor=1e-3, and a zero component scale shall use the applicable absolute floor alone.
• FESA-REQ-LS3DEB-038 — Reference values shall not be zero-clamped and rows shall not be dropped; missing, extra, duplicate, nonfinite, schema-mismatched, or identity-mismatched rows shall fail before tolerance evaluation.
• FESA-REQ-LS3DEB-039 — The verification report shall record every row decision and maximum absolute error, component-scale normalized error, RMS error, norm error, and worst row/component for each compared quantity.

Reference Artifact Requirements

The approved logical model is cantilever-beam-b33, schema is abaqus-cae-report-csv-v0, source commit is 2b34d0b, generator is Abaqus/CAE Learning Edition 2024, and the coordinate/output contract is global Cartesian nodal output plus beam-local section-force output at Step-1, increment 1, step time 1.0.

• FESA-REQ-LS3DEB-040 — The V0 reference baseline shall use the exact read-only files reference/cantilever beam/cantilever beam.inp, reference/cantilever beam/cantilever beam displacements.csv, reference/cantilever beam/cantilever beam reactions.csv, and reference/cantilever beam/cantilever beam elemental forces.csv without rename, rewrite, correction, or restoration; absent metadata.json is allowed by project-wide policy and README.md is N/A for this approved legacy bundle.
• FESA-REQ-LS3DEB-041 — Before comparison, artifact validation shall confirm all four files, TYPE=B33, expected CAE report headers, unique row keys, and finite values; failure shall be classified as needs-reference-artifacts or schema-mismatch and comparison shall not start.
• FESA-REQ-LS3DEB-042 — Reference verification shall compare displacement by source-node identity (U1/U2/U3/UR1/UR2/UR3), reaction by source-node identity (RF1/RF2/RF3/RM1/RM2/RM3), and node-station-normalized section resultant by SF1->N, SM1->My, SM2->Mz, SM3->T; adjacent interior endpoints shall first agree within approved tolerance and shall not be averaged to hide a mismatch.
• FESA-REQ-LS3DEB-043 — Reference comparison shall run only after build/test passes; physics sanity shall run only after reference comparison passes and shall check global force/moment equilibrium, reaction sign, displacement direction, symmetry, element section-force consistency, and normalized residual; release readiness shall require all prior gate evidence and known limitations.
• FESA-REQ-LS3DEB-044 — FESA agents and Harness shall not execute Abaqus, Nastran, or another reference solver and shall not create, modify, rename, or restore reference artifacts; release documentation shall not claim support for any Out Of Scope behavior.

Requirement Verification Matrix

id	statement	category	rationale	source	priority	verification_method	acceptance_criteria	tolerance	downstream_agents	status
FESA-REQ-LS3DEB-001	The FESA solver shall accept exactly one *STEP containing *STATIC per input file and shall reject a second analysis step with a structured unsupported diagnostic.	analysis	Preserve the approved V0 single-step boundary.	Approved design §§2, 6.1; PRD FESA-PRD-011	must	Parser/semantic unit test; CLI integration test	One static step runs; a second step fails with a structured unsupported diagnostic.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-002	The FESA solver shall analyze only straight, prismatic, two-node 3D Euler–Bernoulli beams under small-displacement, small-rotation, linear-static assumptions.	analysis	Bound the formulation and validation domain.	Approved design §2; formulation §2	must	Model validation test; formulation review	Accepted models satisfy every listed assumption and excluded procedures are not represented as supported.	N/A	research-agent; formulation-agent; numerical-review-agent	approved
FESA-REQ-LS3DEB-003	The FESA solver shall assign each beam node the six global DOFs [UX, UY, UZ, URX, URY, URZ] in that order.	analysis	Keep assembly and result components deterministic.	Approved design §§2, 4.3	must	DofManager unit test; HDF5 schema test	DOF mapping and nodal result columns use the exact approved order.	Exact ordering	formulation-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-004	The FESA solver shall support axial deformation, bending about both local section axes, Saint-Venant torsion, and homogeneous isotropic linear elasticity.	analysis	Define the complete V0 beam physics.	Approved design §2; formulation §§2, 10	must	Element unit tests; analytical benchmarks	Axial, torsion, local-y bending, and local-z bending cases recover the approved analytical quantities.	Relative 1e-9 analytical	research-agent; formulation-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-005	The FESA solver shall map only *ELEMENT, TYPE=B33 to the V0 Euler–Bernoulli beam formulation.	input	Preserve Abaqus element-family meaning.	Approved design §6.3; PRD FESA-PRD-011	must	Parser/semantic unit test	B33 creates the approved beam semantic object and reaches model validation.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-006	The FESA solver shall reject *ELEMENT, TYPE=B31 with unsupported-element-formulation and shall not reinterpret B31 as B33.	input	B31 includes transverse shear deformation.	Approved design §§2.2, 6.3; ADR-013	must	Parser diagnostic test	B31 fails with the exact approved diagnostic code and creates no Euler beam.	Exact diagnostic code	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-007	The FESA solver shall support nodal *CLOAD and *BOUNDARY data for DOFs 1 through 6, including nonzero prescribed displacement.	input	Exercise constrained partition and RHS correction.	Approved design §§2.1, 6.1, 7	must	Parser test; constraint/load integration test	DOFs 1..6 map correctly and nonzero dc contributes to effective RHS and reaction.	Residual normalized 1e-10	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-008	The element verification contract shall include a constant local line-load equivalent nodal vector kernel, while the V0 parser and CLI shall not support *DLOAD or create a Domain distributed-load object.	scope	Verify the formulation without widening CLI input.	Approved design §§2.1, 2.2, 4.5	must	Element unit test; parser negative test	The closed-form equivalent vector passes and *DLOAD is rejected without a Domain distributed-load object.	Normalized 1e-12 kernel comparison	formulation-agent; io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-009	The parser shall support exactly *HEADING; *PART, *END PART; *NODE; *ELEMENT, TYPE=B33; *NSET, *ELSET, including GENERATE; *MATERIAL, *ELASTIC; *BEAM GENERAL SECTION, SECTION=GENERAL; *SECTION POINTS; *ASSEMBLY, *END ASSEMBLY; *INSTANCE, *END INSTANCE; *BOUNDARY; *CLOAD; *STEP, *STATIC, and *END STEP as model/procedure keywords.	input	Avoid a full-compatibility claim.	Approved design §6.1; ADR-003	must	Keyword inventory review; parser tests	Every listed keyword has positive coverage and no unlisted keyword is documented as supported.	Exact keyword inventory	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-010	The parser shall interpret keyword and parameter names case-insensitively, recognize ** comment lines, and preserve source label text for external identity.	input	Match approved syntax and identity behavior.	Approved design §6.1	must	Lexer/parser unit tests	Case variants parse equally, comments are ignored, and original label text survives mapping.	Exact source-label identity	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-011	The parser shall accept *BOUNDARY rows only as target, first_dof, last_dof[, value], default an omitted value to zero, and accept *CLOAD rows only as target, dof, magnitude; targets shall resolve by source node label or node set, including assembly-level sets with INSTANCE.	input	Prevent ambiguous semantic mapping.	Approved design §6.1	must	Parser positive/negative tests	Only approved row arities and DOFs 1..6 pass, and all approved target forms resolve deterministically.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-012	The semantic mapping shall read general-section data as A, I11, I12, I22, J, require I12=0, map Iy=I11 and Iz=I22, and construct local axes as n1 -> y and t x n1 -> z.	input	Preserve stiffness directions and signs.	Approved design §6.2; PRD FESA-PRD-019	must	Section-mapping test; rotated-element test	Every property and right-handed local-axis mapping matches the approved contract.	Exact mapping; transform normalized 1e-12	formulation-agent; io-definition-agent; numerical-review-agent	approved
FESA-REQ-LS3DEB-013	A general beam section shall reference a material whose isotropic *ELASTIC data provides exactly E, nu; the solver shall compute G=E/(2(1+nu)) and require positive E, G, A, Iy, Iz, and J.	input	Prevent nonphysical or indefinite stiffness.	Approved design §6.2; formulation §10	must	Semantic/model validation tests	Complete valid data passes; malformed elasticity data or any nonpositive required property fails.	Input-consistent units; normalized 1e-12 for computed G	formulation-agent; io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-014	Before element calculation, the solver shall require L > 1e-12 * max(1, norm(X1), norm(X2)) and norm(a_perp) > 1e-12 * max(1, norm(a)); zero/near-zero length, a zero guide vector, and a tangent-parallel guide vector shall produce structured model-validation diagnostics.	input	Prevent singular geometry and undefined local axes.	Approved design §6.2; formulation §§3.1, 19	must	Geometry validation tests	Values at or below either approved threshold fail and valid values produce a right-handed orthonormal frame.	Both thresholds use coefficient 1e-12	numerical-review-agent; io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-015	*PART/*ASSEMBLY/*INSTANCE mapping shall preserve SourceEntityId { instance_name, source_label } for nodes, elements, and sets and shall map it deterministically to a separate stable Domain internal index.	model	Make row mapping and diagnostics traceable.	Approved design §§4.1, 6.4	must	Semantic mapping and determinism tests	Instance/source labels round-trip and map to stable unique internal IDs.	Exact identity	io-definition-agent; reference-model-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-016	The semantic model shall allow multiple identity instances of the same part without merging their source identities.	model	Support approved wrapper reuse without transforms.	Approved design §§2.1, 6.4; ADR-013	must	Multi-instance semantic integration test	Nodes, elements, and sets for each identity instance remain distinct and deterministic.	Exact identity	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-017	An instance containing translation or rotation data shall be rejected with unsupported-instance-transform.	model	V0 has no transform semantics.	Approved design §§2.2, 6.4	must	Parser/semantic negative tests	Any translation or rotation data fails with the exact approved diagnostic code.	Exact diagnostic code	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-018	Nested assembly and dependent/independent mesh semantics shall be rejected as unsupported rather than silently approximated.	model	Prevent silent topology changes.	Approved design §§2.2, 6.4	must	Semantic negative tests	Each excluded construct produces a structured unsupported diagnostic and no Domain model.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-019	The parser shall issue structured warnings and no-op the exact allowlist *PREPRINT, *RESTART, *TRANSVERSE SHEAR STIFFNESS, *OUTPUT, FIELD, *OUTPUT, HISTORY, *NODE OUTPUT, *ELEMENT OUTPUT, *CONTACT OUTPUT, and unsupported variable data belonging to those output requests.	input	Accept the legacy input without changing analysis meaning.	Approved design §6.5; PRD FESA-PRD-013	must	Parser diagnostic test	Every allowlisted keyword/data form yields deterministic warnings, no semantic effect, and no error.	Exact allowlist	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-020	Unsupported model-affecting keywords outside the no-op allowlist shall be errors, and accepted Abaqus output requests shall not change or suppress FESA's mandatory HDF5 results.	input/output	Keep the supported subset explicit.	Approved design §6.5; ADR-003	must	Parser negative test; HDF5 integration test	An unlisted model keyword fails and mandatory datasets exist with or without allowed output requests.	Exact dataset inventory	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-021	Domain shall own the complete parsed model and remain effectively immutable after mapping; AnalysisModel shall expose references or IDs for the single active step without copying Domain objects.	architecture	Preserve approved ownership and activation boundaries.	Approved design §§4.1, 4.2; ADR-004	must	Unit test; architecture review	Active-step view construction neither copies nor mutates Domain objects.	N/A	implementation-planning-agent	approved
FESA-REQ-LS3DEB-022	DofManager alone shall own node DOF definitions, full/free equation numbering, constrained/free mappings, element scatter maps, sparse patterns, and full/reduced vector reconstruction; Node and Element shall not store equation IDs.	architecture	Prevent distributed numbering state.	Approved design §4.3; ADR-004	must	DofManager tests; dependency/code review	All maps reconstruct correctly and no Node or Element stores equation IDs.	Exact mapping	implementation-planning-agent	approved
FESA-REQ-LS3DEB-023	V0 AnalysisState shall own full displacement, external/internal force, residual, constrained reaction, step/frame identity, and element recovery rows and shall not allocate velocity, acceleration, temperature, iteration history, or nonlinear element state.	architecture	Keep V0 state minimal and traceable.	Approved design §4.4; PRD FESA-PRD-005	must	State unit/integration tests	All required state is connected to output and every excluded state remains unallocated.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-024	Element-local stiffness work shall use the ParallelFor/oneTBB boundary, and global assembly shall deterministically reduce element contributions in stable element order from COO triplets into a 0-based CSR matrix.	architecture	Ensure repeatable sparse assembly and reference rows.	Approved design §§2.1, 7; ADR-008, ADR-009	must	Repeated assembly tests; CSR structure tests	Repeated and thread-count-varied runs produce identical CSR ordering and numerically identical values.	Stable ordering; normalized numeric 1e-12	numerical-review-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-025	MKL, TBB, and HDF5 API/types shall remain behind the LinearSolver, ParallelFor, dense/sparse math, and ResultsWriter adapter boundaries; Vector shall use contiguous doubles, Matrix row-major contiguous doubles, and SparseMatrix a separate 0-based CSR representation.	architecture	Isolate external backends from solver core.	Approved design §5; ADR-006	must	Dependency review; math/backend unit tests	No public core API exposes backend types and every storage layout matches the approved contract.	N/A	implementation-planning-agent	approved
FESA-REQ-LS3DEB-026	The linear-static lifecycle shall assemble and partition stiffness, call Kff factorization, and only then assemble the full load vector, form the effective RHS, and perform substitution; factorization and substitution shall remain observably separate.	execution	Preserve reusable factorization and failure classification.	Approved design §§1, 7; ADR-007	must	Orchestration test; solver-adapter test	The event trace is stiffness, partition, factorize, load, RHS, solve and no opaque solve hides factorization.	Exact event order	implementation-planning-agent; build-test-executor-agent	approved
FESA-REQ-LS3DEB-027	For prescribed displacement dc, the solver shall form rhs=Ff-Kfc*dc, reconstruct the full displacement after substitution, and recover constrained reaction from K*d-F, equivalently Rc=Kcf*df+Kcc*dc-Fc, rather than a separate end-force sum.	execution	Correctly handle nonzero constraints and equilibrium.	Approved design §7; formulation §§15, 16.5	must	Constraint/load integration and residual tests	RHS, full displacement, and constrained reactions match the approved partition equations.	Residual normalized 1e-10	formulation-agent; numerical-review-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-028	The sole authoritative solver output shall be HDF5 results.h5; the writer shall complete a temporary file before replacing the final path and shall leave no incomplete final file after a writer failure.	output	Prevent ambiguous or partial results.	Approved design §9; ADR-005	must	HDF5 integration/atomicity tests	Success produces the final file and injected failure leaves no incomplete final results.h5.	N/A	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-029	HDF5 schema v0 shall contain /metadata, /model/nodes, /model/elements, /steps/<step-name>/frames/0/nodal/displacement, /steps/<step-name>/frames/0/nodal/reaction, /steps/<step-name>/frames/0/element/end_force_local, /steps/<step-name>/frames/0/element/section_resultant, /steps/<step-name>/frames/0/element/generalized_strain, /steps/<step-name>/frames/0/element/stress_s11, and /diagnostics.	output	Give downstream comparison a stable schema root.	Approved design §9	must	HDF5 schema test	Every named path exists at frame 0 with documented identity and rank/component contracts.	Exact paths	io-definition-agent; reference-verification-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-030	HDF5 metadata/model identity shall record schema version, solver version, source input identity, unit-system label, coordinate convention, element formulation, stable internal IDs, and instance/source-label mappings; ordinary input shall use user-consistent-unspecified, while the approved cantilever comparison shall apply its external SI contract without inferring SI from .inp alone.	output	Make results auditable without guessing units or identity.	Approved design §9; ADR-005	must	Metadata/schema test; reference contract review	Every field is present, ordinary runs use the exact label, and legacy comparison records external SI provenance.	Exact labels and identity	io-definition-agent; reference-model-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-031	Output shall include every node's global displacement/reaction in [UX, UY, UZ, URX, URY, URZ], local endpoint equilibrium end actions in [FX,FY,FZ,MX,MY,MZ], endpoint section resultants in [N,T,My,Mz], and generalized strain/resultant values at the two Gauss points, independent of Abaqus output requests.	output	Separate equilibrium, section, and generalized results.	Approved design §§8, 9	must	Recovery unit tests; HDF5 schema test	Every component order and endpoint/Gauss location matches the contract in runs with and without output requests.	Analytical 1e-9; reference policy where applicable	formulation-agent; io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-032	The solver shall output axial S11 at both Gauss points and each input section point, or at centroid (0,0) with source=fesa-default when section points are absent; transverse/torsional shear stress shall not be recovered, and Abaqus beam-stress reference comparison shall remain explicit N/A while analytical/unit and HDF5 schema tests remain mandatory.	output	Retain useful stress recovery without inventing a reference baseline.	Approved design §§2.2, 8.3, 12	must	Stress unit/analytical test; HDF5 schema test; report review	Correct stress rows and fallback label exist, no shear stress is emitted, and reference report marks stress N/A.	Analytical relative 1e-9; Abaqus reference N/A	formulation-agent; io-definition-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-033	The CLI shall support fesa.exe <model.inp> --output <results.h5>, default output to the current directory's results.h5, use exit codes 0=success, 2=usage, 3=input, 4=model, 5=solver, 6=HDF5, and emit severity, code, file, line, keyword, entity_identity, and message diagnostics to stderr in deterministic order.	output	Stabilize automation and failure classification.	Approved design §10	must	CLI integration and diagnostic ordering tests	Default/explicit output works and every failure class returns its exact code and complete ordered fields.	Exact codes, fields, and order	io-definition-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-034	Every production C++ behavior shall be developed in one step as GoogleTest RED -> GREEN -> VERIFY, with a related C++ test file, focused CTest evidence, full MSVC x64 Debug build/CTest evidence, at least one discovered test, and no new warning under the FESA target's /W4 /WX policy.	verification	Enforce project TDD and warning policy.	Approved design §§11.1, 11.4; ADR-012	must	Implementation report; build/CTest logs	The related test fails first, then focused/full tests pass, discovery finds tests, and FESA emits no warning.	Zero test failures and new warnings	implementation-planning-agent; implementation-agent; build-test-executor-agent	approved
FESA-REQ-LS3DEB-035	Numerical tests shall satisfy normalized 1e-12 for stiffness symmetry and two-point-Gauss/closed-form agreement, normalized 1e-10 for rigid-mode and linear-system residual, and relative 1e-9 for analytical solutions, while checking six rigid modes, rank 6, positive deformation energy, transformation orthogonality/energy invariance, prescribed-displacement recovery, and axial/torsion/two-plane bending benchmarks.	verification	Detect sign, integration, rank, and transform defects.	Approved design §§11.2, 11.3; formulation §18	must	Unit, analytical, and orchestration tests	Every listed invariant and analytical case passes at its stated threshold.	1e-12 matrix; 1e-10 residual; 1e-9 analytical	formulation-agent; numerical-review-agent; implementation-planning-agent	approved
FESA-REQ-LS3DEB-036	The approved B33 reference comparison shall group rows by the same model, step/frame, quantity, and component, compute reference_scale only from read-only Abaqus values, and apply absolute_floor + 1e-6 * reference_scale to every matched row.	tolerance	Give zero and nonzero rows one deterministic rule.	Approved design §11.3; ADR-014	must	Comparison unit/integration test; report review	Every group uses the Abaqus-only maximum absolute scale and every matched row uses the exact formula.	Relative coefficient 1e-6	reference-model-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-037	For the approved SI bundle, displacement and rotation shall use absolute_floor=1e-9, force and moment shall use absolute_floor=1e-3, and a zero component scale shall use the applicable absolute floor alone.	tolerance	Preserve dimensional meaning near zero.	Approved design §11.3; ADR-014	must	Comparison tests with zero/near-zero rows	Each quantity uses its exact SI floor and zero-scale groups use no relative contribution.	SI 1e-9 displacement/rotation; 1e-3 force/moment	reference-model-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-038	Reference values shall not be zero-clamped and rows shall not be dropped; missing, extra, duplicate, nonfinite, schema-mismatched, or identity-mismatched rows shall fail before tolerance evaluation.	tolerance	Prevent false passes through omission or clamping.	Approved design §§11.3, 12; ADR-014	must	Negative comparison tests	Every listed invalid case fails before numeric comparison and zero values remain unchanged.	No ignored invalid rows	reference-verification-agent	approved
FESA-REQ-LS3DEB-039	The verification report shall record every row decision and maximum absolute error, component-scale normalized error, RMS error, norm error, and worst row/component for each compared quantity.	tolerance	Make the pass/fail decision auditable.	Approved design §11.3; ADR-014	must	Verification report schema/review	Per-row decisions and all required aggregate/worst metrics are present for every quantity.	Report completeness	reference-verification-agent; release-agent	approved
FESA-REQ-LS3DEB-040	The V0 reference baseline shall use the exact read-only files reference/cantilever beam/cantilever beam.inp, reference/cantilever beam/cantilever beam displacements.csv, reference/cantilever beam/cantilever beam reactions.csv, and reference/cantilever beam/cantilever beam elemental forces.csv without rename, rewrite, correction, or restoration; absent metadata.json is allowed by project-wide policy and README.md is N/A for this approved legacy bundle.	reference	Protect the approved correctness baseline.	Approved design §12; ADR-010, ADR-014	must	Artifact inventory; Git diff review	Exact filenames exist and no reference file is added, removed, renamed, or content-modified.	Exact path/content identity	reference-model-agent; reference-verification-agent; release-agent	approved
FESA-REQ-LS3DEB-041	Before comparison, artifact validation shall confirm all four files, TYPE=B33, expected CAE report headers, unique row keys, and finite values; failure shall be classified as needs-reference-artifacts or schema-mismatch and comparison shall not start.	reference	Detect stale B31 or malformed evidence.	Approved design §§6.3, 12	must	Artifact-check integration test	All checks pass before comparison and every failure uses an approved classification.	Exact inventory and schema	reference-model-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-042	Reference verification shall compare displacement by source-node identity (U1/U2/U3/UR1/UR2/UR3), reaction by source-node identity (RF1/RF2/RF3/RM1/RM2/RM3), and node-station-normalized section resultant by SF1->N, SM1->My, SM2->Mz, SM3->T; adjacent interior endpoints shall first agree within approved tolerance and shall not be averaged to hide a mismatch.	reference	Compare equivalent quantities despite legacy station rows.	Approved design §§8.2, 12	must	Reference comparison test/report	All components match by source identity and interior endpoints pass before deterministic representative selection.	Requirements 036 and 037 policy	io-definition-agent; reference-model-agent; reference-verification-agent	approved
FESA-REQ-LS3DEB-043	Reference comparison shall run only after build/test passes; physics sanity shall run only after reference comparison passes and shall check global force/moment equilibrium, reaction sign, displacement direction, symmetry, element section-force consistency, and normalized residual; release readiness shall require all prior gate evidence and known limitations.	governance	Keep numerical similarity distinct from physical/release approval.	Approved design §§11, 12, 13	must	Gate evidence audit	Each downstream report cites the preceding pass and physics evidence covers all six checks before release review.	Relevant upstream tolerances	coordinator-agent; physics-evaluation-agent; release-agent	approved
FESA-REQ-LS3DEB-044	FESA agents and Harness shall not execute Abaqus, Nastran, or another reference solver and shall not create, modify, rename, or restore reference artifacts; release documentation shall not claim support for any Out Of Scope behavior.	governance	Prevent baseline contamination and scope inflation.	Approved design §§2.2, 12; ADR-010	must	Process audit; Git diff; release documentation review	No reference execution or artifact mutation occurs and every exclusion is recorded without a support claim.	N/A	coordinator-agent; reference-model-agent; release-agent	approved

Open Questions

• 이 approved requirements baseline 안에는 사용자 결정을 기다리는 항목이 없다.
• source formulation의 needs-research 상태와 그 문서에 남은 evidence/open-issue 항목은 후속 Research, Formulation Alignment, Numerical Review gate에서 이 승인 baseline에 맞춰 해결해야 하며, 이 Step에서 새 정책으로 해소하지 않는다.
• 이 baseline의 수치, 단위, schema, keyword, reference 경로를 바꾸려면 요구조건 변경 승인과 downstream traceability 갱신이 필요하다.

Downstream Handoff

Research Agent

• B33/Euler–Bernoulli 의미, slender-beam 적용 한계, 두 방향 굽힘·비틀림 benchmark와 source reliability를 조사하되 승인 범위나 tolerance를 바꾸지 않는다.
• 확인된 사실과 추론을 분리하고 unresolved evidence gap을 명시한다.

Formulation Agent

• source formulation의 feature/status를 이 baseline과 정렬하고 DOF 순서, local-axis, theta_y=-dw/dx, 2점 Gauss, stiffness/recovery 부호를 추적한다.
• 요구조건을 충족하는 수학 계약만 정리하고 C++ API나 input/output schema를 설계하지 않는다.

I/O Definition Agent

• 요구조건 009020과 028033을 exact parser/model/HDF5 row schema와 diagnostic 계약으로 구체화한다.
• 최소 HDF5 path, stable source identity, ordinary-run unit label, legacy SI comparison provenance를 보존한다.

Reference Model Agent

• 요구조건 036~044에 따라 read-only legacy inventory, provenance, row keys, component mapping, artifact precheck, tolerance coverage를 계약화한다.
• reference/cantilever beam/의 네 파일은 어떤 방식으로도 변경하지 않는다.

Implementation Planning Agent

• 모든 must row를 테스트에 추적하고 C++ production 작업마다 같은 Step 안에서 RED/GREEN/VERIFY를 증명하는 계획을 작성한다.
• factorization-before-load orchestration, nonzero prescribed displacement, deterministic assembly, atomic HDF5, CLI diagnostics, reference precheck를 독립적으로 검증 가능하게 분해한다.