Abstract: Based on the classical shell theory and Sanders nonlinear strain-displacement relationship, the geometric nonlinear ordinary differential governing equations of power-law functionally graded material (P-FGM) shallow spherical shells under thermal mechanical loads are derived. One-dimensional heat conduction temperature field along the thickness and normal uniformly distributed load are considered in the derivation. The two-point boundary value problem composed of the governing equations and clamped boundary condition is solved by the shooting method. Some typical buckling equilibrium paths and bistable configurations of FGM shallow spherical shells are obtained. The influence of parameters on the snap-through buckling behavior of FGM shallow spherical shells under thermal mechanical load is analyzed. The results show that when the temperature rises, the upper critical load of the shells increases significantly and the lower critical load does not change obviously. When gradient index increases, the upper and lower critical loads of the shells decrease significantly. When the constituent material modulus increases, the upper and lower critical loads of the shells increase significantly. When bottom circle radius and thickness are given, the upper and lower critical loads of the shells increase significantly with the decrease of the radius of curvature of the shells middle surface. When middle surface curvature radius and thickness of the shells are given, with the increase of the radius of the bottom circle, the lower critical load of the spherical shell decreases significantly, and the upper critical load is almost unchanged.

Key words: FGM, shallow spherical shell, non-uniform temperature field, normal uniformly distributed load, snap-through buckling, shooting method