Step 2: formulation

Read First

/AGENTS.md
/docs/ABAQUS_SUBROUTINE_AGENT_DESIGN.md
/docs/ARCHITECTURE.md
/docs/ADR.md
/.codex/skills/abaqus-subroutine-formulation/SKILL.md
/docs/requirements/uel-3d-euler-beam.md
/docs/research/uel-3d-euler-beam-research.md
/docs/formulations/README.md

Task

Create /docs/formulations/uel-3d-euler-beam.md.

Define the implementable finite element formulation for the first 3D Euler-Bernoulli beam UEL scope. Include:

Element topology, node ordering, local axes, and DOF ordering.
Required material and section parameters.
Local 12x12 stiffness matrix terms for axial, torsion, bending about local 2, and bending about local 3.
Transformation matrix from local to global coordinates and orientation-vector validation.
Internal force/residual relation for static small-displacement analysis.
AMATRX and RHS contribution rules by LFLAGS for the supported procedure subset.
Numerical tolerances for zero length, near-parallel orientation vector, non-positive section/material properties, and matrix symmetry.
State variable policy. If no persistent state is needed, state that SVARS is not used except optional diagnostics approved by requirements.
Output recovery quantities that external CSV validation should compare.

Do not define the full Abaqus ABI signature here unless needed to express formulation responsibilities; the interface step owns the ABI contract.

Do not create or modify Fortran source, tests, reference artifacts, or implementation plans in this step.

Tests To Write First

None. This is a formulation artifact step.

Acceptance Criteria

python -m unittest discover -s scripts -p "test_*.py"
python scripts/validate_reference_artifacts.py
python scripts/validate_workspace.py

The step is complete only when /docs/formulations/uel-3d-euler-beam.md has enough matrix, residual, and transformation detail for a later implementation step to code without inventing physics.

Validation Notes

Keep solver-result validation as externally generated ODB-extracted CSV evidence.
Update /phases/uel-3d-euler-beam/index.json step 2 with completed, error, or blocked and a concrete summary or reason.

Forbidden

Do not add JavaScript/TypeScript/npm fallback.
Do not run Abaqus analyses from this project.
Do not generate reference CSVs.
Do not create Fortran production source.
Do not break existing tests.

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