An analytical solution for nonlinear cylindrical bending of functionally graded plates

In this paper, the nonlinear cylindrical bending of a functionally graded plate is studied. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the material properties follows a simple power-law distribution in terms of the volume fractions of constituents. The von Karman strains are used to construct the nonlinear equilibrium equations of the plates subjected to in-plane and transverse loadings. The governing equations are reduced to linear differential equation with nonlinear boundary conditions yielding a simple solution procedure. The results show that the functionally graded plates exhibit different behavior from plates made of pure materials in cylindrical bending. Also, it is shown that the linear plate theory is inadequate for analysis of functionally graded plate even in the small deflection range.