Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory

In the present study, a simple four-unknown exponential shear deformation theory is developed for the bending of functionally graded material (FGM) rectangular plates resting on two-parameter elastic foundation and subjected to nonlinear hygrothermomechanical loading. The elastic properties, coefficient of thermal expansion, and coefficient of moisture expansion of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. Unlike first-order and other higher-order plate theories, the present theory has four independent unknowns. The in-plane displacement field of the present theory uses exponential functions in terms of thickness co-ordinate for calculating out-of-plane shearing strains. The transverse displacement includes bending and shear components. The principle of virtual displacement is employed to derive the governing equations and associated boundary conditions. A Navier solution technique is employed to obtained an analytical solutions. The elastic foundation is modelled as two-parameter Winkler–Pasternak foundation. The numerical results obtained are compared with previously published results wherever possible to prove the efficacy and accuracy of the present theory. The effects of stiffness and gradient index of the foundation on the hygrothermomechanical responses of the plates are discussed.