Nonlinear analysis of simply supported Reissner–Mindlin plates subjected to lateral pressure and thermal loading and resting on two-parameter elastic foundations

A nonlinear analysis is presented for a simply supported, Reissner–Mindlin plate subjected to a transverse central patch load and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The two cases of thermal postbuckling of initially pressurized plates and of nonlinear bending of initially heated plates are considered. The temperature fields considered are associated with a non-uniform parabolic distribution over the plate surface and a linear through-the-thickness temperature gradient, respectively. The material properties are assumed to be independent of temperature. The formulations are based on the Reissner–Mindlin plate theory, considering the first order shear deformation effect and including the plate-foundation interaction and thermal effects. The analysis uses a perturbation technique to determine the thermal postbuckling and nonlinear bending response of the plate. The numerical illustrations concern the thermal postbuckling and nonlinear bending behavior of moderately thick plates resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, plate aspect ratio, transverse shear deformation, thermal load ratio, loaded area and the amount of initial lateral pressure as well as initial thermal bending stress are studied.