Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity

Abstract

In continuation of a membrane locking-free isogeometric thin-shell formulation for linear and nonlinear analyses, this contribution introduces an extension to trimmed patches in combination with a continuity preserving coupling scheme for multi-patch NURBS models. The latter bears some immanent challenges of CAD-derived designs including arbitrary trimmed geometries, non-conforming patch discretizations and overlapping domains. We address all of them herein and follow a modified Hellinger–Reissner mixed formulation to regain full control over membrane locking effects. We extend the variational formulation consistently following the fundamental aspects of a weighted residual approach to enforce weakly the interface conditions among coupled patches and utilize the finite cell method to handle properly the issue of trimming. We critically assess the performance of the proposed method studying several numerical examples of linear and non-linear elasticity. We compare our method with established developments in this field and demonstrate superior achievements with regard to solution quality, robustness and computational complexity.