An efficient and robust rotational formulation for isogeometric Reissner-Mindlin shell elements

This work is concerned with the development of an efficient and robust isogeometric Reissner-Mindlin shell formulation for the mechanical simulation of thin-walled structures. Such structures are usually defined by non-uniform rational B-splines (NURBS) surfaces in industrial design software. The usage of isogeometric shell elements can avoid costly conversions from NURBS surfaces to other surface or volume geometry descriptions. The shell formulation presented in this contribution uses a continuous orthogonal rotation described by Rodrigues' tensor in every integration point to compute the current director vector. The rotational state is updated in a multiplicative manner. Large deformations and finite rotations can be described accurately. The proposed formulation is robust in terms of stable convergence behavior in the nonlinear equilibrium iteration for large load steps and geometries with large and arbitrary curvature, and in terms of insensitivity to shell intersections with kinks under small angles. Three different integration schemes and their influence on accuracy and computational costs are assessed. The efficiency and robustness of the proposed isogeometric shell formulation is shown with the help of several examples. Accuracy and efficiency is compared to an isogeometric shell formulation with the more common discrete rotational concept and to Lagrange-based finite element shell formulations. The competitiveness of the proposed isogeometric shell formulation in terms of computational costs to attain a pre-defined error level is shown.