김경종
64 lines
2.2 KiB
Markdown
64 lines
2.2 KiB
Markdown
# Step 2: formulation-spec
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## Read These Files First
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Read the following files before editing:
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- `/AGENTS.md`
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- `/docs/PRD.md`
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- `/docs/ARCHITECTURE.md`
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- `/docs/ADR.md`
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- `/docs/requirements/euler-beam-3d.md`
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- `/docs/research/euler-beam-3d-research.md`
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- `/docs/formulations/README.md`
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## Task
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Create `/docs/formulations/euler-beam-3d-formulation.md`.
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The formulation must define the implementation contract for the C++ kernel. Include:
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- local coordinate system: local `x` from node 1 to node 2; local `y` from the user orientation vector projected normal to local `x`; local `z = x cross y`
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- local DOF order: `[u1, v1, w1, rx1, ry1, rz1, u2, v2, w2, rx2, ry2, rz2]`
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- section constants: `E`, `G`, `A`, `J`, `Iy`, `Iz`
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- local 12x12 stiffness matrix terms for:
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- axial: `EA/L`
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- torsion: `GJ/L`
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- bending in local `x-y` using `EIz`
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- bending in local `x-z` using `EIy`
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- transformation matrix convention and global stiffness equation `K_global = T^T K_local T`
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- end-force recovery equation `f_local = K_local u_local`
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- validation tolerances for unit tests, using deterministic double comparisons
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- singular and invalid input handling:
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- zero or near-zero length throws `std::invalid_argument`
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- nonpositive `E`, `G`, `A`, `J`, `Iy`, or `Iz` throws `std::invalid_argument`
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- orientation vector parallel to beam axis throws `std::invalid_argument`
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Use compact matrices and named scalar coefficients so the implementation step can transcribe directly.
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Do not create C++ files in this step.
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## Tests To Write First
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- No C++ test is required in this documentation-only step.
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## Acceptance Criteria
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```powershell
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python -m unittest discover -s scripts -p "test_*.py"
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python scripts/validate_workspace.py
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```
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## Verification Notes
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1. Confirm the matrix is symmetric by construction.
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2. Confirm local/global transformation convention is unambiguous.
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3. Update `phases/euler-beam-3d/index.json` step 2:
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- success: `"status": "completed"`, `"summary": "3D Euler beam formulation contract added"`
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- failure after retries: `"status": "error"`, `"error_message": "<specific error>"`
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- blocked: `"status": "blocked"`, `"blocked_reason": "<specific reason>"`
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## Forbidden
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- Do not modify requirements, source, tests, or reference artifacts.
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