김경종
77 lines
4.2 KiB
Markdown
77 lines
4.2 KiB
Markdown
# 3D Euler-Bernoulli Beam Kernel Numerical Review
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## Metadata
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- feature_id: euler-beam-3d
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- source_formulation: docs/formulations/euler-beam-3d-formulation.md
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- status: pass-for-implementation-planning
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- owner_agent: numerical-review-agent
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- date: 2026-06-12
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## Review Verdict
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- verdict: pass-for-implementation-planning
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- reason: the formulation has a bounded kernel scope, explicit DOF order, closed-form local stiffness, unambiguous transform convention, and concrete invalid-input behavior.
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## Critical Findings
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- No blocking numerical defects were found for kernel implementation planning.
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- The formulation is not a full solver release contract. Parser, assembly, HDF5 output, reference comparison, and physics sanity remain downstream gates.
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## Numerical Risk Assessment
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- rigid_body_modes: expected six zero-energy modes for the unconstrained element. Implementation tests must include at least rigid global translation and local/global force consistency.
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- patch_test: solver-level patch testing is blocked until assembly and parser integration exist.
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- symmetry: local stiffness is symmetric by construction; global stiffness remains symmetric if `K_global = T^T K_local T` is used consistently.
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- positive_definiteness: isolated element stiffness is positive semidefinite, not positive definite. Positive definiteness requires enough constraints in a solver model.
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- hourglass: not applicable to closed-form Euler-Bernoulli beam stiffness.
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- shear_locking: Timoshenko shear terms are excluded, so shear locking is not introduced by this kernel increment.
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- volumetric_locking: not applicable.
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- distortion: curved geometry and offsets are out of scope; zero or near-zero length must be rejected.
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- singular_jacobian: zero length is the relevant singular mapping case.
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- conditioning: very slender elements or large stiffness ratios can be ill-conditioned; tests should use moderate deterministic values.
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- convergence: not applicable to this linear element kernel.
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## Consistency Checks
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- units: pass. `EA/L`, `GJ/L`, `EI/L^3`, `EI/L^2`, and `EI/L` have the expected force/displacement or moment/rotation dimensions for the matching DOF pairs.
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- dimensions: pass. The element vector is 12x1 and stiffness is 12x12.
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- signs: pass for the documented DOF order; local `v-rz` and `w-ry` coupling signs are explicitly stated.
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- dof_ordering: pass. The formulation keeps node 1 DOFs followed by node 2 DOFs.
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- coordinate_transforms: pass. `u_local = T*u_global`, `K_global = T^T*K_local*T`, and `f_global = T^T*f_local` are mutually consistent.
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- matrix_vector_dimensions: pass.
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- integration_weights: not applicable because the kernel uses closed-form stiffness.
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- output_locations: pass for element end forces only; stress/strain recovery is explicitly out of scope.
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## Verification Readiness
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- unit_tests:
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- model topology accepts `ElementTopology::beam2`.
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- local stiffness representative entries match named coefficients.
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- local stiffness is symmetric within `1.0e-10`.
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- local force recovery equals `K*u`.
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- invalid length and nonpositive section constants throw `std::invalid_argument`.
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- axis-aligned transform produces global stiffness equal to local stiffness.
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- rotated global stiffness remains symmetric.
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- rigid global translation produces near-zero global end forces.
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- simple axial extension produces equal and opposite axial end forces.
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- parallel orientation vector throws `std::invalid_argument`.
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- patch_tests: future solver integration gate.
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- mms_or_mes: not required for this closed-form kernel increment.
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- benchmark_reference_comparison: future gate after reference artifacts exist.
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- missing_evidence: no missing evidence blocks kernel implementation.
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## Required Revisions
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### Formulation Agent
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- None before implementation planning.
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### Research Agent
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- None before implementation planning.
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### Reference Model Agent
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- Future reference model artifacts remain required before release readiness, but they are not required for this kernel implementation.
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## Downstream Handoff
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### Implementation Planning Agent
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- Use the verification readiness list as the minimum C++ TDD checklist.
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- Keep tests deterministic and avoid ill-conditioned constants.
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### Reference Model Agent
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- Define future solution-verification models separately from these kernel-only unit tests.
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