A corotational isogeometric assumed natural strain shell element in updated lagrangian formulation for general geometric nonlinear analysis of thin-walled structures

Abstract

A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems.