Nonlinear thermomechanical stability of shear deformable FGM shallow spherical shells resting on elastic foundations with temperature dependent properties

This paper presents an analytical approach to investigate the nonlinear stability of clamped functionally graded material (FGM) shallow spherical (SS) shells and circular plates resting on elastic foundations, subjected to uniform external pressure and exposed to thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Formulations for axisymmetrically deformed SS shells are based on the first order shear deformation theory taking geometrical nonlinearity, initial geometrical imperfection and interaction of Pasternak type elastic foundations into consideration. Approximate solutions are assumed to satisfy clamped immovable boundary conditions and Galerkin method is applied to derive expressions of buckling loads and load–deflection curves for FGM SS shells. Specialization of these expressions gives corresponding relations of FGM circular plates, and an iterative algorithm is adopted to obtain buckling temperatures and postbuckling temperature–deflection curves for thermally loaded FGM circular plates. The effects of material, geometry and foundation parameters, imperfection and temperature dependence of material properties on the nonlinear response of FGM SS shells and circular plates are analyzed and discussed in detail.