Instability investigation for rotating thin spherical membrane

Abstract

A fluid-filled truncated spherical membrane fixed along its truncated edge to a horizontal, rigid and frictionless plane and spinning around a center axis was investigated. A two-parameter Mooney–Rivlin model was used to describe the material of the membrane. The truncated sphere was modeled in 3D using finite element meshes with different symmetry properties. A quadratic function was used for interpolating hydro-static pressure, giving a symmetric tangent stiffness matrix, thereby reproducing the conservative problem. Various problem settings were considered, related to the spinning, and different instability behaviors were observed. Multi-parametric problems were defined, generalized paths including primary and secondary paths were followed. Stability of the multi-parametric problem was evaluated using generalized eigenvalue analysis based on the total differential matrix for the constrained problem. Numerical results showed that mesh symmetry affected the simulated stability behavior. Fold line evaluations showed the parametric effects on critical solutions.