Global interpolating MLS shape functions for structural problems with discrete nodal essential boundary conditions

Abstract

The moving least squares (MLS)-based element-free Galerkin method (EFGM) has been widely studied, yielding valuable results and becoming a robust mesh-free technique for structural analysis. Due to the non-interpolating nature of MLS shape functions, the EFGM procedure leads to stiffness and mass matrices based on nodal parameters instead of true nodal displacements. The interpolating moving least squares (IMLS) methods with singular weight functions or the weighted nodal least squares (WNLS) methods were proposed in order to arrange the formulation in terms of actual displacements at the nodes. In this work, a later transformation matrix to retrieve the classic stiffness and mass matrices is discussed and numerically tested in problems with discrete prescribed displacements at boundaries, for which a straightforward finite element method (FEM)-type imposition of boundary conditions is possible.