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ENRICHED ELEMENT‐FREE GALERKIN METHODS FOR CRACK TIP FIELDS
Author(s) -
FLEMING M.,
CHU Y. A.,
MORAN B.,
BELYTSCHKO T.
Publication year - 1997
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/(sici)1097-0207(19970430)40:8<1483::aid-nme123>3.0.co;2-6
Subject(s) - galerkin method , stress intensity factor , finite element method , degrees of freedom (physics and chemistry) , mathematics , set (abstract data type) , function (biology) , partial differential equation , fracture (geology) , mathematical analysis , stress (linguistics) , stress field , structural engineering , computer science , physics , materials science , engineering , linguistics , philosophy , quantum mechanics , evolutionary biology , composite material , biology , programming language
The Element‐Free Galerkin (EFG) method is a meshless method for solving partial differential equations which uses only a set of nodal points and a CAD‐like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom. © 1997 by John Wiley & Sons, Ltd.