Non-linear analysis of functionally graded circular plates under asymmetric transverse loading

Based on the first-order shear deformation plate theory with von Karman non-linearity, the non-linear axisymmetric and asymmetric behavior of functionally graded circular plates under transverse mechanical loading are investigated. Introducing a stress function and a potential function, the governing equations are uncoupled to form equations describing the interior and edge-zone problems of FG plates. This uncoupling is then used to conveniently present an analytical solution for the non-linear asymmetric deformation of an FG circular plate. A perturbation technique, in conjunction with Fourier series method to model the problem asymmetries, is used to obtain the solution for various clamped and simply supported boundary conditions. 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 results in the literature. The effects of non-linearity, material properties, boundary conditions, and boundary-layer phenomena on various response quantities in a solid circular plate are studied and discussed. It is found that linear analysis is inadequate for analysis of simply supported FG plates which are immovable in radial direction even in the small deflection range. Furthermore, the responses of FG materials under a positive load and a negative load of identical magnitude are not the same. It is observed that the boundary-layer width is approximately equal to the plate thickness with the boundary-layer effect in clamped FG plates being stronger than that in simply supported plates.