Showing papers on "Meshfree methods published in 1997"
TL;DR: In this paper, an enriched EFG formulation for fracture problems is proposed and two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the Asymptotics Fields.
Abstract: SUMMARY The Element-Free Galerkin (EFG) method is a meshless method for solving partial di⁄erential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom. ( 1997 by John Wiley & Sons, Ltd.
622 citations
TL;DR: In this paper, a meshless Petrov-Galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of Shepard functions, and conditions on test functions and trial functions for nonintegrable pseudo-derivatives for Petrov Galerkin method which pass the patch test.
139 citations
TL;DR: In this article, a three-dimensional meshless method, the element-free Galerkin (EFG) method, is described, which is intended for dynamic problems with geometric and material nonlinearities solved with explicit time integration.
Abstract: The formulation and implementation of a three-dimensional meshless method, the element-free Galerkin (EFG) method, are described. The formulation is intended for dynamic problems with geometric and material nonlinearities solved with explicit time integration, but some of the developments are applicable to other solution methods. The mechanical formulation is posed in the reference configuration so that the shape functions and their derivatives need to be computed only once. A method for speeding up the calculation of shape functions and their derivatives is presented. Results are presented for sloshing problems and Taylor bar impact problems, including an impact problem in which the bar impacts with an angle of obliquity.
70 citations