On the effects of nodal distributions for imposition of essential boundary conditions in the MLPG meshfree method.

Abstract

Imposition of essential boundary conditions in meshfree methods is made difficult because the shape functions used do not possess the delta property. Various procedures have been proposed including penalty, Lagrange multipliers and collocation. It is shown in this paper that the success of a procedure depends on the arrangement of the nodal points. Certain methods of imposing boundary conditions are shown not to work for unstructured nodal arrangements. Much previous work has been demonstrated using structured grids thus hiding these drawbacks.