3.5 Plate Bending (plates)
Purpose: Thin rectangular plate under uniform lateral pressure — deflection and bending moments.
Method: FEM — Mindlin/Reissner-style plate discretization (3 DOF/node: $w, \theta_x, \theta_y$); Gauss integration.
Key behavior: Biharmonic plate equation in weak form; moments from curvature:
M_x = -D(\partial^2 w/\partial x^2 + \nu\,\partial^2 w/\partial y^2), \quad D = \frac{E t^3}{12(1-\nu^2)} $$[^indicative-bending-stress-and-deflection-checks] **Inputs:** $L$, $W$, thickness $t$, $E$, $\nu$, pressure $q$, mesh density, boundary type. **Outputs:** deflection grid, $M_x, M_y, M_{xy}$, peaks, contour-style plots. **Design codes:** Indicative bending stress and deflection checks. **UI:** Modern `inputs`/`results`. **Gaps:** Single rectangular plate; limited boundary catalog; validation quality low in maturity matrix. --- [^indicative-bending-stress-and-deflection-checks]: Indicative bending stress and deflection checks.