Robust and Efficient Large Deformation Analysis of Kirchhoff–love Shells: Locking, Patch Coupling and Iterative Solution

Abstract

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of thin walled structures. They make it possible to meet the C 1 requirement in the interior of surface patches, to avoid the use of finite rotations and to reduce the number of unknowns compared to shear flexible models. Locking elimination, patch coupling and iterative solution are crucial points for a robust and efficient nonlinear analysis and represent the main focus of this work. Patch-wise reduced integrations are investigated to deal with locking in large deformation problems discretized via a standard displacement-based formulation. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified, allowing to avoid locking without resorting to a mixed formulation. The Newton method with mixed integration points (MIP) is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden and a superior robustness with respect to the standard Newton scheme. A simple penalty approach for coupling adjacent patches, applicable to either smooth or non-smooth interfaces, is proposed. An accurate coupling, also for a nonmatching discretization, is obtained using an interface-wise reduced integration while the MIP iterative scheme allows for a robust and efficient solution also with very high values of the penalty parameter.