Benchmark solution of the dynamic response of a spherical shell at finite strain

This paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. The equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge-Kutta schemes. Accuracy and convergence of the proposed method are evaluated by means of numerical examples with finite deformations and material non-linearities and inelasticity.