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FESADev/.codex/skills/fem-formulation-spec/references/analysis-families.md
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2026-09-05 15:14:21 +09:00

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Structural Analysis Family Guidance

Read only the family selected by the approved requirements. Coupled features apply each relevant section and define the coupling terms explicitly.

Common

Check DOF ordering, boundary conditions, units, coordinate transforms, rigid-body modes, element orientation, residual convention, output location, and conservation or equilibrium identities.

Linear static

Define linearization assumptions, stiffness symmetry expectations, load assembly, constraint treatment, reactions, patch tests, rigid-body/null-space checks, and mesh-convergence quantities.

Nonlinear static

Define configuration and strain/stress measures, state update, residual and consistent tangent, load/time parameter, convergence norms, increment/cutback behavior, path dependence, and energy or work checks.

Modal, eigenvalue, and buckling

Define matrix problem, boundary conditions, mass or geometric stiffness, eigensolver target, normalization, repeated-mode handling, sign/phase invariance, residual norms, and mode correlation. Distinguish linearized buckling from nonlinear collapse.

Dynamics

Define mass and damping, initial conditions, time integration, stability and algorithmic dissipation, load history, time-step convergence, energy balance, frequency/phase measures, and modal truncation where applicable.

Contact and constraints

Define gap and normal orientation, active-set/search semantics, normal and tangential laws, enforcement method, consistent contributions, state transitions, penetration/slip measures, and action-reaction checks.

Material nonlinearity

Define admissible state, yield/failure surface, flow/evolution laws, integration algorithm, consistent material tangent, history initialization, loading/unloading cases, and single-point constitutive tests.

Do not apply an irrelevant checklist merely for completeness. If the family is ambiguous and the choice changes physical meaning or acceptance, return needs-user-decision.