On the Stability of Hyperelastic Spherical and Cylindrical Shells Subjected to External Pressure Using a Numerical Approach

Abstract

In this paper, the incremental equilibrium equations and corresponding boundary conditions for the isotropic, hyperelastic and incompressible shells are derived and then employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature (GDQ) method is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. The results are in full agreement with the previously obtained results and the effects of thickness and mode number are studied on the shell’s stability. For the spherical and cylindrical shells of arbitrary thickness which are subjected to external hydrostatic pressure, the symmetrical buckling takes place at a value of [Formula: see text] which depends on the geometric parameter [Formula: see text] and the mode number [Formula: see text], where [Formula: see text] and [Formula: see text] are the undeformed inner and outer radii, respectively, and [Formula: see text] is the ratio of the deformed inner radius to the undeformed inner radius.