Locking free isogeometric formulations of curved thick beams

We are interested in this work in methods that alleviate shear and membrane locking, typically involved in thick plates and shells. We investigate the use of higher order NURBS to address static straight and curved Timoshenko beam with several approaches usually used in standard locking free finite elements. Among theses methods, two main new strategies have been developed for NURBS: selective reduced integration and B ¯ projection method. Although the simplicity of implementation and the low computational cost suggest that the first method is attractive, this approach is difficult to be generalized to arbitrary polynomial order and continuity. Conversely, the B ¯ one offers a global formalism suitable to tackle every NURBS problem and appears then as the most serious concurrent. The resulting NURBS B ¯ element, which happens to be equivalent to a NURBS mixed element, provides robust and accurate results. The performance of the two methods is assessed on several numerical examples, and comparisons are made with other published techniques to prove their effectiveness.