Nonlinear bending behavior of Reissner–Mindlin plates with free edges resting on tensionless elastic foundations

Abstract

A nonlinear bending analysis is presented for a Reissner–Mindlin plate with four free edges subjected to thermomechanical loads and resting on a tensionless elastic foundation of the Pasternak-type. The mechanical loads consist of transverse partially distributed loads and in-plane edge loads while the temperature field is assumed to exhibit a linear variation through the thickness of the plate. The material properties are assumed to be independent of temperature. The two cases of initially compressed plates and of initially heated plates are considered. The formulations are based on Reissner–Mindlin first order shear deformation plate theory and include the plate-foundation interaction and thermal effects. A set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the nonlinear bending analysis of moderately thick plates with four free edges. A two step perturbation technique is employed in conjunction with this set of admissible functions to determine the load-deflection and load-bending moment curves. An iterative scheme is developed to obtain numerical results without using any prior assumption for the shape of the contact region. The numerical illustrations concern moderately thick plates with four free edges resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results show that the nonlinear bending responses for the conventional and tensionless elastic foundation are quite different.