A fully "locking-free" isogeometric approach for plane linear elasticity problems: a stream function formulation

In this paper, we study plane incompressible elastic problems by means of a ''stream-function'' formulation such that a divergence-free displacement field can be computed from a scalar potential. The numerical scheme is constructed within the framework of NURBS-based isogeometric analysis and we take advantage of the high continuity guaranteed by NURBS basis functions in order to obtain the displacement field from the potential differentiation. As a consequence, the obtained numerical scheme is automatically locking-free in the presence of the incompressibility constraint. A Discontinuous Galerkin approach is proposed to deal with multiple mapped, possibly multiply connected, domains. Extensive numerical results are provided to show the method capabilities.