A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function

In this work we propose a method which combines the element‐free Galerkin (EFG) with an extended partition of unity finite element method (PUFEM), that is able to enforce, in some limiting sense, the essential boundary conditions as done in the finite element method (FEM). The proposed extended PUFEM is based on the moving least square approximation (MLSA) and is capable of overcoming singularity problems, in the global shape functions, resulting from the consideration of linear and higher order base functions. With the objective of avoiding the presence of singular points, the extended PUFEM considers an extension of the support of the classical PUFE weight function. Since the extended PUFEM is closely related to the EFG method there is no need for special approximation functions with complex implementation procedures, and no use of the penalty and/or multiplier method is required in order to approximately impose the essential boundary condition. Thus, a relatively simple procedure is needed to combine both methods. In order to attest the performance of the method we consider the solution of an analytical elastic problem and also some coupled elastoplastic‐damage problems. Copyright © 2003 John Wiley & Sons, Ltd.