Rectangular thin plates in bending: notes
This form uses a polynomial expansion for w as indicated in form's formulae (hit the 'Formulas' button, equations enforcing boundary conditions not shown).
The coefficients of the expansion are calculated by means of strain energy minimization. The expression used for strain energy is shown in the 'Formulas' as .
This expression includes the terms due to shear strain, according to the model exposed in Art.39 of Timoshenko's Theory of Plates and Shells 2nd ed. The correction with respect to the usual simple bending theory is of limited significance except for relatively very thick plates.
For concentrated loads or loads distributed over a small area this method does not provide the local peak stresses that may be obtained by other means: care should be exercised, based onto supplemental analyses, when assessing plate strength in such cases.