Analysis of functionally graded plates resting on elastic foundation and subjected to non-linear hygro-thermo-mechanical loading

In the present study, a new fifth-order shear and normal deformation theory is developed and applied for the bending analysis of functionally graded (FG) plates resting on two-parameter Winkler–Pasternak elastic foundation subjected to non-linear hygro-thermo-mechanical loading. The theory involves the effects of transverse shear and normal deformations, i.e. thickness stretching. Navier’s solution technique is used to obtain analytical solutions for simply supported FG plates. The results are presented in non-dimensional form and are compared with previously published results in the literature. The present study has the following novelties. The present polynomial-type theory is computationally simpler than non-polynomial-type plate theories which are mathematically complicated, tedious and more cumbersome. For the accurate structural analysis of composite plates under hygro-thermal loading, consideration of thickness coordinate up to third-order polynomial is not sufficient. Therefore, in the present theory, thickness coordinate is expanded up to fifth-order polynomial to get the accurate displacements and stresses. Transverse normal stress/strain plays an important role in the modeling of thick plates which is neglected by many theories available in the literature.