Static analysis of variable thickness two-directional functionally graded annular sector plates fully or partially resting on elastic foundations by the GDQ method

In this paper, bending analysis of two-directional functionally graded circular/annular sector plates with variable thickness fully and partially resting on elastic foundations is investigated, for the first time. The material properties vary simultaneously in transverse and radial directions according to a power-law distribution of the volume fraction of the constituents. Based on the first-order shear deformation theory and using the concept of physical neutral surface, the governing equations are derived. A polynomial-based generalized differential quadrature method is then employed to solve the set of governing partial differential equations for various combinations of boundary conditions. The validity and accuracy of the results are demonstrated by comparison with existing results in the literature. Effects of boundary conditions, power-law indices, thickness variation, two-parameter elastic foundations, and geometrical parameters on static responses of circular/annular sector plates subjected to uniform and non-uniform loading are studied in detail. It is found that the physical neutral surface varies in radial direction owing to variations of Young's modulus and thickness in radial direction.