A simple and efficient hybrid discretization approach to alleviate membrane locking in isogeometric thin shells

Abstract

This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based surface discretizations, and can thus be run with existing isogeometric finite element codes. Also, the stresses can be recovered straightforwardly. The effectiveness of the proposed approach in alleviating, if not eliminating, membrane locking is demonstrated through the rigorous study of the convergence behavior of several classical benchmark problems. Accuracy gains are particularly large in the membrane stresses. The approach is formulated here for quadratic NURBS, but an extension to other discretization types can be anticipated. The same applies to other constraints and associated locking phenomena.