Enrichment of the boundary element method through the partition of unity method for mode I and II fracture analysis

Simpson, Robert Napier and Trevelyan, J. 2009. Enrichment of the boundary element method through the partition of unity method for mode I and II fracture analysis. Presented at: 10th International Conference on Boundary Element Techniques (BETEQ), Athens, Greece, 22-24 July 2009. Published in: Sapountzakis, E. J. and Aliabadi, M. H. eds. Advances in Boundary Element Techniques X. Southampton: EC Ltd, pp. 55-61.

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Abstract

The present method offers an approach to 2D fracture problems where certain basis functions that are known to capture the required crack tip displacement field are incorporated in a boundary element formulation through the Partition of Unity Method. The same basis functions that were used by Mo¨es et al. in the implementation of the Extended Finite Element Method (XFEM) [1] for fracture analysis are used. It is found, in the simple case of a straight crack, that these reduce to rather simple expressions for the boundary element implementation.With the introduction of these basis functions, additional unknown coefficients are produced which are accommodated by providing additional collocation points. To allow the evaluation of asymmetric crack problems, enrichment was applied to the Dual Boundary Element Method (DBEM) [2] with certain modifications made to the Displacement and Traction Boundary Integral Equations. With the inclusion of enrichment functions, analytical expressions can no longer be used for the evaluation of the strongly singular and hypersingular terms and instead a specially adapted numerical quadrature routine is used. The method was tested on both Mode I and Mode II problems where substantial increases in accuracy were gained for a small increase in degrees of freedom (DOF).

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TJ Mechanical engineering and machinery
Publisher:	EC Ltd
ISBN:	9780954778361
Last Modified:	19 Mar 2016 23:05
URI:	https://orca.cardiff.ac.uk/id/eprint/38330

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