Calculates deflection and bending stresses for flat plates under pressure, per Roark's Formulas for Stress and Strain: rectangular plates with all edges simply supported (exact Navier series, uniform or hydrostatic load) or all edges clamped (verified tabulated coefficients), and circular plates with simply supported or clamped edges (exact closed forms). Colour-coded heatmaps for deflection, σx, σy and von Mises stress, a centreline profile, yield utilisation at your design factor, and the required thickness for the entered load.
Inputs: material preset (S275, S355, 304 and 316 stainless, 6082 and 5083 aluminium, or custom E/ν/Sy), plate dimensions (long side a, short side b, thickness t), and pressure in any of Pa, kPa, MPa, bar, mm H₂O, m H₂O or psi.
Outputs: maximum deflection, governing bending stresses with their locations (plate centre or clamped edge), von Mises stress, yield utilisation, flexural rigidity D, plus colour-coded plan heatmaps and a centreline profile chart for deflection, σx, σy and von Mises stress. The tool warns when deflection exceeds t/2, where linear thin-plate theory is no longer reliable.
Method: Navier double-sine series, exact solution for the biharmonic plate equation with simply-supported boundary conditions on all four edges (Roark's Formulas for Stress and Strain, Table 11.4, Case 1a). 225 odd-numbered series terms (m,n = 1 to 29) are summed, giving convergence to better than 0.01% on deflection at the plate centre.
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Free, runs in the browser, nothing uploaded. Every result should be verified against the applicable code or standard before use in design.