Non-Linear Analysis of Functionally Graded Sector Plates with Simply Supported Radial Edges Under Transverse Loading

In this study, nonlinear bending of functionally graded (FG) circular sector plates with simply supported radial edges subjected to transverse mechanical loading has been investigated. Based on the first-order shear deformation plate theory with von Karman strain-displacement relations, the nonlinear equilibrium equations of sector plates are obtained. Introducing a stress function and a potential function, the governing equations which are five non-linear coupled equations with total order of ten are reformulated into three uncoupled ones including one linear edge-zone equation and two nonlinear interior equations with total order of ten. The uncoupling makes it possible to present analytical solution for nonlinear behavior of FG sector plates with simply-supported radial edges via perturbation technique and Fourier series method. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified by comparison with the existing ones in the literature. The effects of non-linearity, material constant and boundary conditions on bending of an FG sector plate are studied. It is shown that in bending analysis of functionally graded sector plates, linear theory is solely applicable for w/h  and is inadequate for analysis of fully simply supported FG sector plates even in the small deflection range.