Postbuckling of free edge Reissner–Mindlin plates elastically supported on a two-parameter foundation and subjected to biaxial compression and transverse loads

A postbuckling analysis is presented for a rectangular Reissner–Mindlin plate with all four free edges subjected to biaxial compression combined with a transverse central patch load and resting on a two-parameter (Pasternak-type) elastic foundation. The lateral pressure is first converted into an initial deflection and the initial geometric imperfection of the plate is also taken into account. The formulations are based on Reissner–Mindlin plate theory considering the first order shear deformation effect, including plate-foundation interaction. The analysis uses a mixed Galerkin-perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates with all four free edges under combined loading conditions and 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, transverse shear deformation, plate aspect ratio, loaded area parameter and initial lateral pressure are studied. Typical results are presented in dimensionless graphical form.