Abstract
The paper deals with the numerical solution techniques for the traction boundary integral equation (BIE), which describes the opening (and sliding) displacements of the surface of the traction loaded crack or arbitrary planform embedded in an elastic infinite body (buried crack problem). The traction BIE is a singular integral equation of the first kind for the displacement gradients. Its solution poses a number of numerical problems, such as the presence of derivatives of the unknown function in the integral equation, the modeling of the crack front displacement gradient singularity, and the regularization of the equation's singular kernels. All of the above problems have been addressed and solved. Details of the algorithm are provided. Numerical results of a number of crack configurations are presented, demonstrating high accuracy of the method.
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Blandford, G.E.; Ingraffea, A.R.; Liggett, J.A. (1981): Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Numer. Meth. Eng. 17, 387–404
Bui, H. D. (1977): An integral equation method for solving the problem of plane crack of arbitrary shape: J. Mech. Physics and Solids 25, 23–39
Cruse, T.A. (1969): Numerical solutions in three-dimensional clastostatics. Int. J. of Solids and Struct. 5, 1259–1274
Cruse, T.A.; Van Buren, W. (1971): Three-dimensional elastic stress analysis of a fracture specimen with an edge crack: Int. J. Fract. Mech., 7, 1–15
Cruse, T.A. (1975): Boundary-integral equation method for three-dimensional elastic fracture mechanics analysis. AFOSRTR-75-0813, Accession No. ADA-11060, 13–20
Cruse, T.A. (1978): Two-dimensional BIE fracture mechanics analysis. Appl: Math: Model. 2, 287–293
Guidera, J.T.; Lardner, R.W. (1975): Penny shaped cracks. J. Elast. 5, 59–73
Henshell, R.D.; Shaw, K.G. (1975): Crack tip elements are unnecessary. Int. J. Numer. Meth: Eng. 9, 495–509
Hinton, E.; Campbell, J.S. (1974): Local and global smoothing of discontinuous finite element functions using a least squares method. Int. J. Numer. Meth. Eng. 8, 461–480
Labeyrie, J.; Chauchot, P. (1984): On the crack tip singularities in 3-D BEM, Boundary Elements VI. Proc. 6th Int. Conf. on Board the Liner the Queen Elizabeth 2, Southampton to New York. Berlin, Heidelberg, New York: Springer
Polch, E.Z. ; Cruse, T.A. ; Huang, C.-J.: Buried crack analysis with an advanced traction BIE algorithm. In: Advanced Topics in Boundary Element Analysis. T.A. Cruse, A.B. Pifko, and H. Armen, (eds) Presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, Miami Beach, Florida, Nov. 17–22, 1985
Putot, C.J. (1980): Une nouvelle methode de fissures planes. Thèse, Université Paris VI
Rizzo, F.J.; Shippy, D.J. (1977): An advanced boundary integral equation method for three-dimensional thermoelasticity. Int. J. Numer. Meth. Eng. 11, 1753–1768
Tada, H.; Paris, P.; Irwin, G. (1973): The stress analysis of cracks handbook. Del Research Corporation
Weaver, J. (1977): Three-dimensional crack analysis. Int. J. Solids Struct. 13, 321–330
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Communicated by S.N. Atluri, October 12, 1986
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Polch, E.Z., Cruse, T.A. & Huang, C.J. Traction BIE solutions for flat cracks. Computational Mechanics 2, 253–267 (1987). https://doi.org/10.1007/BF00296420
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DOI: https://doi.org/10.1007/BF00296420