Effects of shear deformation on Mechanical and thermo-mechanical nonlinear stability of FGM shallow spherical shells subjected to uniform external pressure

Abstract

In the present paper, the asymmetrical nonlinear response of a clamped functionally graded shallow spherical shell is subjected to uniform external pressure. It considers the effects of thermal stresses by both of the theories, Classical Laminate Theory, CLT and First-Order Shear Deformation Theory FSDT. Material properties are graded in the thickness direction according to the power-law distribution in terms of the volume fraction of the constituents. Mechanical and thermo-mechanical properties are assumed to be temperature-independent and linear elastic. All of the governing equations are derived by aid of first-order transverse shear deformation theory considering geometrical nonlinearity. The nonlinear differential equation system is solved employing Galerkin method. Buckling and post-buckling analysis have been done according to one-term deformation mode by the closed form relation of load-deflection that shows the equilibrium path. Parametric studies are conducted to bring out the effects of shear deformation on the equilibrium path in different geometries and boundary conditions. Numerical results are presented in graphical arrangement, showing that the geometrical nonlinear equilibrium paths. The effects of shear deformation on the equilibrium path are considered by comparing the results from FSDT and CLT and was verified by nonlinear finite-element method.