An isogeometric method for linear nearly-incompressible elasticity with local stress projection

Abstract

In this paper, we propose an isogeometric method for solving the linear nearly-incompressible elasticity problem. The method is similar to the B̄ formulation where the volumetric strain is projected on a lower degree spline space in order to prevent volumetric locking. In our method, we adopt a local projection on a coarser mesh, chosen in order to guarantee optimal convergence. Moreover the locality of the projector allows to maintain the sparsity of the stiffness matrix, that is, the efficiency of the method. The analysis of the method is based on the inf–sup stability of the associated mixed formulation via a macro-element technique for spline functions. The numerical tests confirm the theory of the method.