BUCKLING AND SURFACE WRINKLING OF AN ELASTIC GRADED CYLINDER WITH ELASTIC MODULUS ARBITRARILY VARYING ALONG RADIAL DIRECTION

Abstract

This paper investigates the buckling and surface wrinkling phenomena of an elastic graded cylinder under axial compression. We develop a semi-analytical finite element model based on elastic stability theory and the work of Lee et al. [Journal of Mechanics and Physics of Solids56 (2008) 858–868], which enables us to determine the critical compressive strain and corresponding wrinkling wavelength of a soft cylindrical structure with the shear modulus arbitrarily varying along the radial direction. A number of examples of practical interest have been explored to validate the proposed method, including: (i) surface wrinkling a soft cylinder with a hard outer surface, (ii) surface wrinkling of a soft cylindrical tube with a hard inner surface layer, (iii) buckling of a soft cylinder with an embedded hard layer, (iv) surface wrinkling of a soft cylinder covered by a bilayer, and (v) surface wrinkling of an elastic graded soft cylinder covered by a hard layer. The results demonstrate that the proposed method is valid for all these situations. In comparison to conventional finite element method, the discretization and meshing in the present method are much easier and the degrees of freedom involved are much smaller.