Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Abstract

Thin structures like shells are highly susceptible to mechanical instabilities. They can undergo large nonlinear elastic deformations while exhibiting combined bending and stretching modes of deformation. Here, we propose a new displacement-based finite element (FE) formulation based on the isogeometric discretization of Koiter’s nonlinear shell theory and use of the method of dynamic relaxation (DR) to solve equilibrium configurations of problems involving fine-scale and hierarchical wrinkling and buckling. No imperfection seeding is required to trigger instabilities. The use of the NURBS basis provides a rotation-free, conforming, higher-order spatial continuity such that curvatures and membrane strains can be computed directly from interpolating the position vectors of the control points using spatial finite differences. The pseudo-dissipative FE dynamical system is updated through explicit time integration and made scalable for parallel computing using a message passing interface (MPI). The proposed FE method is successfully benchmarked against several numerical and experimental results.