Wrinkling of Elastic Cylinders With Material Properties Varying in Radial Direction

Abstract

Although the instability of graded elastic cylinders has been analyzed by many researchers, most of them focused on the core-shell cylinders and film-substrate structures with inhomogeneous Young’s modulus. For a radially graded elastic cylinder subjected to the axial compression, the variation of Poisson’s ratio may result in the radial and circumferential stresses and thereby affects the critical condition of instability. By assuming linear elasticity with nonlinear kinematics, the governing equation for the incremental stress field is developed for instability analysis of the cylinder with radially graded material properties (Young’s modulus and Poisson’s ratio). Considering the arbitrariness of material properties, the state space technique is implemented and a semi-analytical solution is acquired. The obtained solution is validated by the finite element results. Numerical examples show that the critical condition of instability for graded elastic cylinders is related to whether Poisson’s ratio is assumed to be constant.