An isogeometric Reissner–Mindlin shell element based on mixed grid

We propose in this article a new isogeometric Reissner–Mindlin degenerated shell element for linear analysis. It is based on the mixed use of non-uniform rational basis spline and Lagrange basis functions in the same domain. The mid-surface of the shell is represented and discretized using non-uniform rational basis spline and the directors of the shell are discretized using Lagrange polynomials. The interpolatory property of Lagrange polynomials gives a natural choice of fiber vectors, thus removing the difficulties in the definition of directors that is seen in most isogeometric Reissner–Mindlin shell elements. The non-uniform rational basis spline representation of the mid-surface allows us to maintain the exact geometry representation characteristic of the isogeometric approach. The independent expressions of displacements and rotations also give users the possibility to use different numbers of degrees of freedom in an element for both kinematic variables. Several numerical examples show that our method is simple, robust, and efficient