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 s...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 1998-08, Vol.162 (1), p.203-222
Main Authors: Häussler-Combe, U., Korn, C.
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Fracture mechanics (crack, fatigue, damage...)
Fracture mechanics, fatigue and cracks
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Solid mechanics
Structural and continuum mechanics
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(97)00344-7