Isogeometric analysis of shells

This work is concerned with the isogeometric analysis of shells. A new hierarchic family of NURBS-based shell finite elements is developed. Besides a shear-rigid 3-parameter shell element formulation with Kirchhoff-Love kinematics, both a shear flexible 5-parameter Reissner-Mindlin-type and a 7-parameter 3D shell element which accounts for thickness change are derived. Compared to existing isogeometric shell elements the hierarchy showing up in the shell mechanics is transferred to the parameterization of the kinematic shell equations by gradually enhancing the minimalistic 3-parameter shell model with additional degrees of freedom in order to systematically increase the approximation quality of the shell formulation. This represents the key innovation of this thesis with significant benefits both with regard to finite element technology and model adaptivity. The continuity requirements on the displacement functions for the proposed hierarchic shell models are C1, which can be naturally satisfied with the applied higher-continuity NURBS discretizations. All shell models of the hierarchy utilize a pure displacement ansatz. Due to the concept of a hierarchic parameterization both transverse shear locking and curvature thickness locking are avoided by default for the Reissner-Mindlin-type and the 3D shell formulations. In order to remove membrane locking two new strategies for higher-order and higher-continuity discretizations – a NURBS-based Discrete Strain Gap method and a mixed displacement-stress formulation – are developed and applied to the in-plane part of the isogeometric shell finite elements, which ultimately lead to isogeometric shell element formulations that are completely free from geometric locking.