Curved p-version C¹ finite elements for the finite deformation analysis of isotropic and composite laminated thin shells in irregular shape

In this work, we generalize our recently developed p-version curved C¹ plate elements to the finite deformation analysis of general isotropic and laminated thin shells with arbitrary curvature and shape. The kinematic formulations are based on the geometrically-exact nonlinear thin shell model where the Kirchhoff-Love hypothesis is strictly implemented during the deformation. Since high accurate curved coarse meshes are required in the implementation of p-version finite element method, the quasi regional mapping technique is employed and modified to obtain the high-order meshes with fitted boundaries. Through this method, shells with irregular shapes can be easily modeled. To avoid dealing the difficult problem of constructing fully C¹ conforming displacement fields on shell surface, the C¹ conformity of present elements is implemented on the selected Gauss-Lobatto nodes, which had been found to be able to produce very fast convergence. Nodal variables including second-order directional derivatives on surfaces are derived and used for element assembly. In this manner, direct construction of displacement fields on shell mid-surface defined by the quasi regional mapping is allowed. Several benchmark problems of large deformation analysis of isotropic and laminated thin shells are presented to illustrate the accuracy as well as robustness of the present method.