The element-free Galerkin method in large deformations

Abstract

The engineering design process which involves alternate stages of model construction and analysis, can be carried out more efficiently if the analyses are performed on a numerical model, rather than an actual prototype. To this point, the finite element method has been the most widely used numerical technique for the analysis of solids, due primarily to its ability to accurately model complex geometries. However, the finite element mesh loses accuracy rapidly when the elements become distorted, as occurs in problems involving large deformations and fracture propagation. On April 28, 1995 Stephen Beissel from Alliant Techsystems has described a relatively new class of numerical techniques, the element-free Galerkin method, achieved by expansion of the solution in a basis of moving least-squares functions, as opposed to the piecewise polynomial basis of the finite element method. This results in an element-free mesh of nodes with variable connectivities, allowing for greater flexibility in the configuration of nodes. He presented several formulations along with example calculations comparing them with the finite element method.