On the local enforcement of Dirichlet boundary conditions in meshless methods

The solution of elliptic systems of partial differential equations requires the imposition of appropriate boundary conditions (BC’s). There are basically two types of BC’s1: the essential (Dirichlet) and the natural (Neumann). In the present work we discuss the enforcement of the former type within the framework of weak form based methods. Especially interesting are the ways to accomplish this task when the domain approximation functions do not possess inter-polatory character. A general method is proposed to locally enforce these conditions based on a hybrid-displacement model arising from a non-conventional finite element formulation. The conditions that must be fulfilled by both the approximations of the displacements in the domain and the tractions on the essential boundary are identified