Keystone v15: plate & shell bending — the MITC4 Reissner–Mindlin element#676
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Keystone's first out-of-plane analysis. Adds a from-scratch MITC4 plate element (assumed-natural-strain transverse shear, tied at the edge midpoints, so it does not shear-lock in the thin limit), a rectangular plate mesher, a solver (static under uniform/point/hydrostatic load with free/SS/clamped edges and corner supports, smooth recovered Mx/My/Mxy/principal-moment fields, and free-vibration modes by subspace iteration), eight canonical scenarios across five materials, and a new Plate Bending studio with an orbitable flat-shaded 3-D deflected surface, a contour view, animated mode shapes and a live FE-vs-Timoshenko check. Four new closed-form benchmarks (SS & clamped square under UDL, SS square point load, SS fundamental frequency) all pass — badge now 88/88 — each matched to a fraction of a percent against Timoshenko & Woinowsky-Krieger. Verified rendering end-to-end in headless Chromium. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HyixyGQHuUL7EFNkXM94Ud
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Keystone v15 — Plate & Shell Bending (out-of-plane FEM)
Everything in Keystone so far bends in its own plane (trusses, frames, plane-stress membranes). A floor slab, a bridge deck, a pressure-vessel wall, a manhole cover, a silicon die all bend out of plane — a different element family (3 DOF/node: a transverse deflection
wand two rotationsθx, θy) and a whole new chapter. This PR adds it, built from scratch.Why MITC4
A naive 4-node Reissner–Mindlin plate shear-locks: as the plate thins, spurious transverse-shear stiffness makes it come out orders of magnitude too stiff. The MITC4 element (Dvorkin & Bathe, 1984) replaces the directly-differentiated shear with an assumed covariant shear field tied at the four edge midpoints, mapped back through the Jacobian — locking-free in the thin limit, still valid for thick plates. It's the workhorse plate/shell element in real FE codes.
What's here
engine/plate.ts— the MITC4 element: Q4 shape functions & Jacobian, the bending B-matrix, the assumed-natural-strain shear B-matrix (the anti-locking heart), theD_b/D_sconstitutive matrices, 12×12 stiffness + consistent mass (translational + rotary inertia), pressure load, and Gauss-point moment / principal-moment recovery. Pure & deterministic.engine/platemesh.ts— structured rectangular plate mesher (3 DOF/node) + edge-node sets.engine/platesolve.ts— global assembly on the existing sparseAssembler/CSR + PCG; free / simply-supported / clamped edges + corner supports; static solve under uniform / point / hydrostatic load; smooth nodal moment field (Gauss→node extrapolation, matching the app's Q4/Q8 recovery); free-vibration modesK φ = ω² M φby subspace (Bathe) iteration.engine/platepresets.ts— 8 scenarios (SS slab, clamped cover, 2:1 panel, point-loaded SS/clamped squares, corner-supported flat slab, cantilever plate, hydrostatic tank wall) × 5 materials, with the classical Timoshenko coefficients.ui/PlateStudio.tsx— a new Plate Bending tab: an orbitable 3-D deflected surface (flat-shaded on the true deflected normal, painter-sorted, drag to orbit / scroll to zoom) draped with deflection orMx / My / Mxy / M₁, a top-down contour view, animated mode shapes, and a live FE-vs-Timoshenko read-out.Validation (the same "trust the numbers" contract as the rest of Keystone)
Four new closed-form benchmarks wired into the live badge — now 88/88, all green — each matched against Timoshenko & Woinowsky-Krieger:
w_c = 0.004062 q a⁴/Dw_c = 0.00126 q a⁴/Dw_c = 0.01160 P a²/Df₁ = π²(2/a²)√(D/ρt)/2πVerified end-to-end in headless Chromium: the simply-supported slab renders as a clean 3-D sag, the numbers match theory, badge green, zero runtime errors.
Scope
Every changed file is inside
projects/keystone-fea-b3k9/(Golden Rule).node scripts/verify-project.mjs keystone-fea-b3k9passes: scope + conformance + lint + build.🤖 Generated with Claude Code
https://claude.ai/code/session_01HyixyGQHuUL7EFNkXM94Ud
Generated by Claude Code