Isogeometric collocation for the Reissner–Mindlin shell problem

Abstract

We present an isogeometric collocation formulation for the Reissner-Mindlin shell problem. After recalling the necessary basics on differential geometry and the shell governing equations, we show that the standard approach of expressing the equilibrium equations in terms of the primal variables is not a suitable way for shells due to the complexity of the underlying equations. We then propose an alternative approach, based on a stepwise formulation, and show its numerical implementation within an isogeometric collocation framework. The formulation is tested successfully on a set of benchmark examples, which comprise important aspects like locking and boundary layers. These test show that locking effects can be conveniently avoided by using high polynomial degrees. An accompanying study on the computational time also confirms that high polynomial degrees are preferable in terms of computational efficiency.