Refined theory for non-linear buckling of heated composite shallow spherical shells

Abstract The present study deals with static buckling and postbuckling behavior of clamped shallow laminated spherical shell with polar-orthotropic layers subjected to a conservative uniform external pressure and temperature load. The physical properties of the material are assumed to be temperature independent. The variational principle of minimum potential energy of the system is used to obtain the static governing equations in terms of displacements. Five Mindlin-type displacement variables are utilized to take into account a thickness shear. A tenth order system of non-linear differential equations is obtained and its numerical solution is shown for the case of axisymmetric deformation and constant temperature field. A method of solution, including finite difference discretization and modified relaxation procedure, is proposed. Some specific effects inherent to composite shells are found and discussed.