Buckling of a thin spherical shell inside a spherical cavity of a contracting massive body

The problem of buckling of a thin elastic spherical shell inside a spherical cavity of uniformly contracting massive body is considered. This problem arises, for example, when designing pressure vessels made of composite materials with a thin metal cap layer. It is assumed that at the beginning of the compression the shell fits tightly against the wall of the cavity (to the rigid frame). An algorithm for searching the equilibrium state of the shell in the supercritical state is described. As a result of solving the problem, among other things, critical values of compressive strain and shell configuration in the supercritical state were obtained.