Avoiding shear locking for the Timoshenko beam problem via isogeometric collocation methods

In this work we study isogeometric collocation methods for the Timoshenko beam problem, considering both mixed and displacement-based formulations. In particular, we show that locking-free solutions are obtained for mixed methods independently on the approximation degrees selected for the unknown fields. Moreover, several numerical tests are provided in order to support our theoretical results and to show the good behavior and the flexibility of isogeometric collocation methods in this context.

► We study isogeometric collocation methods for the Timoshenko beam problem.
► We show that locking-free solutions are obtained independently of the approximation degrees selected for the unknown fields.
► We develop a rigorous error analysis.
► We present several numerical tests supporting the theoretical results.