Investigation of geometric nonlinear stability of sandwich functionally graded (SFGM) spherical shells under uniform external pressure using an analytical approach

Abstract

The geometric nonlinear response of spherical shells made of sandwich functionally graded material (SFGM) under uniform external pressure incorporating the effects of transverse shear deformations is considered. The equilibrium and compatibility nonlinear differential equations can be solved by using the modified interaction method. All of the equations are developed based on the first-order shear deformation theory (FSDT). In the present study, the geometric nonlinear problem has been solved for special boundary conditions including movable and fixed clamped supports in the meridional direction. A closed-form nonlinear load-deflection relationship is developed for SFGM shell which expresses the equilibrium path of the shell.

Keywords:

• Geometric nonlinear stability
• spherical shells
• sandwich functionally graded materials
• power-law functions
• closed-form formula