An effective boundary element method for analysis of crack problems in a plane elastic plate
 Yan Xiangqiao
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A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the cracktip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right cracktip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e., a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
 Cruse, T A Numerical evaluation of elastic stress intensity factors by boundary integral equation method[A]. In: Swedlow, J L eds. (1972) Surface Cracks Physics Problems and Computational Solutions[C]. ASME, New York, pp. 153170
 Cruse, T A (1978) Two dimensional BIE fracture mechanics analysis[J]. Appl Math Modeling 2: pp. 287293 CrossRef
 Blandford, G E, Ingraffea, A R, Liggett, J A (1981) Twodimensional stress intensity factor computations using the boundary element method[J]. Internat J Numer Methods Engrg 17: pp. 387404 CrossRef
 Crouch, S L, Starfield, A M (1983) Boundary Element Method in Solid Mechanics[M]. Geore Allon & Unwin, London
 Pan, E (1997) A general boundary element analysis of 2D linear elastic fracture mechanics[J]. Internat J Fracture 28: pp. 4159 CrossRef
 Portela, A, Aliabadi, M H, Rook, D P (1992) The dual boundary element method: effective implementation for crack problems[J]. Internat J Numer Methods Engrg 33: pp. 12691287 CrossRef
 Mi, Y, Aliabadi, M H (1992) Dualboundary element method for three dimensional fracture mechanics analysis[J]. Engineering Analysis with Boundary Elements 10: pp. 161171 CrossRef
 Tanaka, M, Itoh, H (1987) New crack elements for boundary element analysis of elastostatics considering arbitrary stress singularities[J]. Appl Math Modelling 11: pp. 357363 CrossRef
 Cruse, T A (1989) Boundary Element Analysis in Computational Fracture Mechanics[M]. Kluwer, Dordrecht
 Aliabadi, M H, Rooke, D P (1991) Numerical Fracture Mechanics[M]. Computational Mechanics Publications, Kluwer, Dordrecht, Southampton
 Aliabadi, M H (1997) Boundary element formulation in fracture mechanics[J]. Applied Mechanics Review 50: pp. 8396 CrossRef
 Xiangqiao, Yan (2004) A special cracktip displacement discontinuity element[J]. Mechanics Research Communications 31: pp. 651659 CrossRef
 Kitagawa, H, Yuuki, R (1977) Analysis of the nonlinear shaped cracks in a finite plate by the conformal mapping method[J]. Trans Japan Soc Mech Engrs 43: pp. 43544362
 Murakami, Y (1978) A method of stress intensity factor calculation for the crack emanating from an arbitrarily shaped hole or the crack in the vicinity of an arbitrarily shaped hole[J]. Trans Japan Soc Mech Engrs 44: pp. 423432
 Murakami, Y (1987) Stress Intensity Factors Handbook[M]. Pergamon Press, New York
 Erdogan, F, Gupta, G D, Ratwani, M (1974) Interaction between a circular inclusion and an arbitrarily oriented crack[J]. ASME J Appl Mech 41: pp. 10071013
 Title
 An effective boundary element method for analysis of crack problems in a plane elastic plate
 Journal

Applied Mathematics and Mechanics
Volume 26, Issue 6 , pp 814822
 Cover Date
 20050601
 DOI
 10.1007/BF02465433
 Print ISSN
 02534827
 Online ISSN
 15732754
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 stress intensity factor
 boundary element method
 displacement discontinuity
 cracktip element
 TB33
 74R10
 74S15
 Industry Sectors
 Authors

 Yan Xiangqiao ^{(1)}
 Author Affiliations

 1. Research Laboratory on Composite Materials, Harbin Institute of Technology, 150001, Harbin, P. R. China