Non-linear analysis of functionally graded plates in cylindrical bending based on a new refined shear deformation theory

A new refined shear deformation theory for the nonlinear cylindrical bending behavior of functionally graded (FG) plates is developed in this paper. This new theory is based on the assumption that the transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The plates are subjected to pressure loading, and their geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of plate are assumed to vary according to the power law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy and the results are compared to the classical, the first-order and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the nonlinear cylindrical bending behavior of functionally graded plates.