An adaptive approach with the Element-Free-Galerkin method

The Element-Free-Galerkin-method may be regarded as an alternative to the Finite-Element-method especially for problems with discontinuities, e.g. crack propagation problems. The EFG-method differs from the FEM by using the Moving-Least-Squares-interpolation. The behaviour of this interpolation is strongly influenced by a weighting function, which rules the influence of nodal variables on variables in arbitrary spatial points. With an appropriate selection of the weighting function derivatives of field functions of any desired order are continuous throughout the problem domain within the MLS-interpolation. Hence, gradients of stresses and strains may be calculated throughout the problem domain with a high accuracy. Furthermore, the configuration of nodes is quite flexible, as nodes are not ordered by an element connectivity. Nodes are easily introduced, moved or discarded. The latter characteristics make the EFG-method especially suitable for adaptive schemes. A scheme based on strain gradients is discussed in this paper. It is applied to several linear and physically nonlinear problems with high stress-resp. strain gradients and singularities. Continued mesh refinement in areas of high gradients is derived. The convergence behaviour is investigated for cases, where analytical solutions are available.