An augmented Lagrangian approach to essential boundary conditions in meshless methods

The problem of boundary conditions enforcement in meshless methods has been solved in the literature by several approaches. In the present paper, the moving least-squares (MLS) approximation is introduced in the total potential energy functional for the elastic solid problem and an augmented Lagrangian term is added to satisfy essential boundary conditions. The method can be easily extended to any kind of constraint for the approximation variables. The solution is found by iterating alternatively on approximation variables and on Lagrange multipliers. The advantages of the proposed formulation are: (a) theability to deal with thesameapproach with any constraint type; (b) thenumbe r of thevariable s is not increased by theLagrangemultiplie rs; (c) theHe ssian of thefunctional w.r.t. theapproximation variables is banded, well conditioned and strictly positive de