Nonlinear bending of simply supported rectangular Reissner–Mindlin plates under transverse and in-plane loads and resting on elastic foundations

A nonlinear analysis is presented for a simply supported, rectangular moderately thick plate subjected to transverse central patch load and in-plane compressive loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner–Mindlin plate theory considering the first order shear deformation effect, and including the plate–foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the load–deflection curves and load–bending moment curves. Numerical examples are presented that relate to the performances of moderately thick plates subjected to combined loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences played by a number of effects, among them foundation stiffness, loaded area, the plate aspect ratio, transverse shear deformation and initial compressive load are studied. Typical results are presented in dimensionless graphical form.