Dynamic Integrity of Hyperelastic Spherical Membranes

Thin-walled elastomeric membranes are found in many engineering fields, being usually subjected to large deformation. Both geometrical and material nonlinearities play an important role in their static and dynamic behavior. Spherical membrane under internal pressure is a rather common problem and may present various coexisting stable solutions due to their high nonlinearity. Their response depends on the adopted constitutive law and the related material parameters. The aim of this work is to study the static and dynamic nonlinear behavior of a spherical membrane under internal pressure and investigate how the competing stable solutions may influence their dynamic integrity. Here, the Ogden model is adopted given its generality, and the nonlinear equation of motion of a preloaded membrane is obtained and solved by numerical integration and continuation techniques. To study the dynamic integrity of competing solutions, the global (GIM) and local (LIM) integrity measures and the integrity factor (IF) are adopted. For this, a numerical strategy based on the Monte Carlo method is proposed. The numerical results demonstrate the influence of competing solutions on the global dynamic behavior and safety of the structure. Furthermore, they validate the Monte Carlo technique as an efficient numerical tool for integrity quantification.