Nonlinear axisymmetric response of FGM shallow spherical shells with tangential edge constraints and resting on elastic foundations

Abstract

This paper presents an analytical approach to investigate the nonlinear axisymmetric response of functionally graded (FG) shallow spherical shells (SSSs) resting on elastic foundations, exposed to thermal environment and subjected to uniform external pressure. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Formulations are based on the first order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and tangential edge restraints into consideration. Approximate solutions are assumed to satisfy clamped boundary conditions and Galerkin method is applied to derive explicit expressions of buckling loads and load–deflection relations. The effects of material and geometrical properties, foundation stiffness parameters, degree of tangential restraint, temperature field and imperfection on the buckling behavior and load carrying capacity of FG SSSs are analyzed and discussed.