Bending and buckling analysis of functionally graded graphene platelets reinforced composite plates supported by local elastic foundations based on simple refined plate theory

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate’s thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin’s method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail.