A state space solution for onset of surface instability of elastic cylinders with radially graded Young's modulus

Abstract

A state space solution is developed to analyze surface instability of cylindrical structures with Young's modulus varying arbitrarily in the radial direction. By using the incremental theory for surface instability of elastic materials, the equilibrium equations for the incremental stress field from a fundamental state are derived for radially graded elastic cylinders subjected to an axial compression, which together with the boundary conditions constitute an eigenvalue problem. In the present work, a state space method is established to solve the eigenvalue problem and predict the critical condition for onset of surface instability. The state space solutions for three typical examples are presented and shown to be in good agreement with the numerical results by the finite element method, including the analytical solution for a thin cylindrical shell. In particular, a transition of the critical buckling mode for a soft cylinder covered by a bilayer is illustrated clearly by the present method. In contrast to the finite element method, the state space method is a semi-analytical approach with higher computational efficiency for arbitrarily graded elastic cylinders, including layered structures.