Thermal and mechanical instability of an imperfect shallow spherical cap

In this article, the thermal and mechanical buckling loads of a cap of a shallow spherical shell of isotropic material and geometrically imperfect shell are considered. The equilibrium and stability equations are based on Donnell - Mushtari - Velasov (DMV) theory and are derived using the variational method. The Sander's nonlinear strain-displacement relations are used. The shell is under external pressure for mechanical loading and uniform temperature rise and radial temperature difference for thermal loadings. A simply supported boundary condition is assumed. The solutions for thermal and mechanical buckling loads are obtained using the stability equations and the Galerkin method. One-term approximation for the middle-plane shell displacement is considered. The expressions for the thermal and mechanical buckling loads are obtained analytically and are given by closed-form solutions.