A series of elasticity solutions for flexural responses of functionally graded annular sector plates

Abstract

This paper aims at investigating the flexural responses of transversely isotropic functionally graded (FG) annular sector plates subjected to biharmonic loads, where the material parameters are assumed to vary arbitrarily along the thickness direction and the cylindrical boundaries is simply supported at the two radial edges and arbitrary at the two circumferential edges. Based on the extended England-Spencer plate theory, a series of analytical solutions to FG annular sector plates are derived by virtue of the mid-plane displacements of the plate, which can be expressed by four analytic functions of the complex variable, and the corresponding unknown constants can be determined by the boundary conditions at two circumferential edges. In order to validate the proposed analytical solutions, a finite element (FE) model is built to obtain numerical solutions for comparison, which shows that the obtained deflection and stress components are coherent with those from the FE results. Furthermore, two typical biharmonic loads are taken in the numerical examples to discuss the effects of material gradient index, boundary conditions and thickness-to-radius ratio on the flexural responses of the plate in detail. This work gives exact 3D analytical solutions for the FG annular sector plates, which not only provide an in-depth understanding of their mechanical behaviors and a new theoretical route for the analysis of engineering structures, but also serve as benchmark to check analytical solutions based on any simplified plate theories or numerical solutions to the same problem.