Nonlinear axisymmetric buckling analysis of the FGM sandwich shallow spherical shells under thermomechanical loads

Abstract

Functionally graded material (FGM) sandwich shallow spherical shells are promising composite sandwich structures for modern engineering applications. In this paper, the axisymmetric snap-through buckling of spherical shells under uniform external pressure and non-uniform temperature rise along the shell thickness was studied. Based on the classical shell theory and the Sanders nonlinear kinematics equations, we established a two-point boundary value problem (BVP) posed by the displacement-type nonlinear ordinary differential equations governing the axisymmetric buckling of the FGM sandwich shallow spherical shells and the clamped boundary conditions. Then, the solutions of the above BVP were obtained using the numerical shooting method. The influence of initial term numbers of the infinite series defining the non-uniform temperature field on the accuracy of the solution was examined. Numerical calculations showed that a considerable initial term number of the series were needed to obtain the applicable solutions for engineering. Some valuable conclusions were drawn through detailed parameter studies. As the radius of the bottom circle increases, the lower critical load of shells decreases, the jump amplitude of buckling increases, and the upper critical load remains almost unchanged. The upper and lower critical loads and the jump amplitude increase as the circle radius of the middle surface of shells decreases. When the thickness of shells increases, their upper and lower critical loads increase, whereas the jump amplitude of buckling reduces. The gradient index has a significant effect on the steady-state response of pre-buckling spherical shells but little effect on that of post-buckling spherical shells. When the temperature rises, the upper critical load and the buckling jump amplitude of shells increase, but the lower critical load decreases. When the gradient index is greater (less) than about 0.35, the upper critical load decreases significantly (increases slightly) with the increase in the relative thickness of the FGM core. The present numerical results are well consistent with the finite element results and those in the available literature.