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A meshless method with enriched weight functions for three‐dimensional crack propagation
Author(s) -
Duflot Marc
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1530
Subject(s) - regularized meshless method , singularity , meshfree methods , planar , singular boundary method , simple (philosophy) , domain (mathematical analysis) , set (abstract data type) , extension (predicate logic) , fracture mechanics , mathematics , computer science , mathematical analysis , structural engineering , finite element method , engineering , philosophy , computer graphics (images) , epistemology , boundary element method , programming language
The propagation of cracks in three dimensions is analysed by a meshless method. The cracks are modelled by a set of triangles that are added when the propagation occurs. Since the method is meshless, no remeshing of the domain is necessary during the propagation. To avoid using a large number of degrees of freedom, the stress singularity along the front of the cracks is taken into account by an enrichment of the shape functions of the meshless method by means of appropriate weight functions. This enrichment technique is an extension of the technique that proved to be successful in two dimensions in a previous paper. Several algorithms for efficiently implementing the meshless method in three dimensions are detailed. The accuracy of the enrichment is first assessed on simple examples and some results of non‐planar propagation of multiple cracks are then presented. Copyright © 2005 John Wiley & Sons, Ltd.