Static response and free vibration of two-dimensional functionally graded metal/ceramic open cylindrical shells under various boundary conditions

The free vibration and static response of a two-dimensional functionally graded (2-D FGM) metal/ceramic open cylindrical shell are analyzed using 2-D generalized differential quadrature method. The open cylindrical shell is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. This paper presents a novel 2-D power-law distribution for ceramic volume fraction of 2-D FGM that gives designers a powerful tool for flexible designing of structures under multifunctional requirements. Various material profiles in two radial and axial directions are illustrated using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated, and to validate the results, comparisons are made with the available solutions for FGM cylindrical shells. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the mechanical stresses and natural frequency than conventional 1-D FGM. The achieved results confirm that natural frequency and mechanical stress distribution can be modified to a required manner by selecting an appropriate volume fraction profile in two directions.