Developments of the mixed grid isogeometric Reissner–Mindlin shell: Serendipity basis and modified reduced quadrature

Abstract

In this paper, we use the Serendipity basis in the isogeometric Reissner–Mindlin shell formulation to facilitate the fiber vector definition. The Serendipity basis and the NURBS basis are used here to express the shell fiber rotations and the mid-surface translations respectively. Results show that they perform nearly the same with the Lagrange/NURBS formulation, but with savings in the number of rotational degrees of freedom. We also study the transverse shear locking phenomenon and give a modified reduced quadrature scheme. It can improve the efficiency and to some extent relieve the locking without introducing hourglass modes. The linear decreasing, from outer elements to inner elements, quadrature point distribution also prevents the oscillation of the solutions in the coarse meshes.