Thermal Buckling of Imperfect Deep Functionally Graded Spherical Shell

Abstract

Thermal buckling analysis of deep imperfect functionally graded (FGM) spherical shell is considered in this paper. A mixture of ceramic and metal is considered for the FGM shell and the material properties, such as the modulus of elasticity and coefficient of thermal expansion, vary by a power law function through the thickness. Employing the Sanders non-linear kinematic relations, total potential energy function is derived and the equilibrium and stability equations are obtained for the imperfect shell. Approximate solutions satisfying the simply supported boundary condition are assumed and using the Galerkin method the error due to the approximation is minimized. The geometrically imperfect shell is considered and three types of thermal loadings, such as the uniform temperature rise (UTR), linear temperature rise through the thickness (LTR), and non-linear temperature rise through the thickness (NLTR) are considered and their associated buckling temperatures are obtained. The effects of different temperature functions and the magnitude of initial geometric imperfection are examined on the thermal buckling loads of the shell.