A regularized boundary integral equation method for elastodynamic crack problems. (English) Zbl 0675.73065

Summary: This paper presents a double layer potential approach of elastodynamic BIE crack analysis. Our method regularizes the conventional strongly singular expressions for the traction of double layer potential into forms including integrable kernels and 0th, 1st and 2nd order derivatives of the double layer density. The manipulation is systematized by the use of the stress function representation of the differentiated double layer kernel functions. This regularization, together with the use of B-spline functions, is shown to provide accurate numerical methods of crack analysis in 3D time harmonic elastodynamics.


74R05 Brittle damage
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI


[1] Budreck, D. E.; Achenbach, J. D. (1988): Scattering from three-dimensional planar cracks by the boundary integral equation method. J. Appl. Mech. 55, 405-412 · Zbl 0663.73073 · doi:10.1115/1.3173690
[2] Bui, H. D. (1977): An integral equations method for solving the problem of a plane crack of arbitrary shape. J. Mech. Phys. Solids 25, 29-39 · Zbl 0355.73074 · doi:10.1016/0022-5096(77)90018-7
[3] Green, A. E.; Zerna, W. (1954): Theoretical elasticity. London: Oxford University Press · Zbl 0056.18205
[4] Guo, Q. C.; Nishimura, N.; Kobayashi, S. (1987): Elastodynamic analysis of a crack by BIEM. Proc. 4th Jn. Nat. Symp. BEM, pp. 197-202 (in Japanese) · Zbl 0825.73539
[5] Irwin, G. P. (1962): Crack-extension force for a part-through crack in a plate. J. Appl. Mech. 29, 651-654
[6] Itou, S. (1980): Dynamic stress concentration around a rectangular crack in an infinite elastic medium. Z. Angew. Math. Mech. 60, 381-388 · Zbl 0454.73081 · doi:10.1002/zamm.19800600806
[7] Kobayashi, S.; Nishimura, N. (1982): Transient stress analysis of tunnels and cavities of arbitrary shape due to travelling waves. In: Banerjee, P. K.; Shaw, R. P. (eds.): Developments in boundary element methods II, pp. 177-210. London: Applied Science Publishers
[8] Kupradze, V. D.; Gegelia, T. G.; Basheleishvili, M. O.; Burchuladze, T. V. (1979): Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Amsterdam: North-Holland
[9] Lachat, J. C.; Watson, J. O. (1976): Effective numerical treatment of boundary integral equations. Int. J. Numer. Methods Eng. 10, 991-1005 · Zbl 0332.73022 · doi:10.1002/nme.1620100503
[10] Martin, P. A.; Wickham, G. R. (1983): Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results. Proc. R. Sec. London Ser. A 390, 91-129 · Zbl 0537.73017 · doi:10.1098/rspa.1983.0124
[11] Nedelec, J. C. (1986): The double layer potential for periodic elastic waves in R 3. In: Du, Q. (ed.): Boundary elements, pp. 439-448. Oxford: Pergamon Press · Zbl 0622.73026
[12] Nishimura, N.; Kobayashi, S. (1987): On the regularisation of the differentiated double layer potentials in elasticity. Proc. 4th Jn. Nat. Symp. BEM, pp. 49-54 (in Japanese)
[13] Nishimura, N.; Kobayashi, S. (1988): An improved boundary integral equation method for crack problems. In: Cruse, T. A. (ed.): Advanced boundary element method pp. 279-286. Proc. IUTAM symp. 1987, San Antonio/TX. Berlin, Heidelberg, New York: Springer
[14] Polch, E. Z.; Cruse, T. A.; Huang, C.-J. (1987): Traction BIE solutions for flat cracks. Comput. Mech. 2, 253-267 · Zbl 0616.73093 · doi:10.1007/BF00296420
[15] Sládek, V.; Sládek, J. (1984): Transient elastodynamic three-dimensional problems in cracked bodies. Appl. Math. Modelling 8, 2-10 · Zbl 0525.73110 · doi:10.1016/0307-904X(84)90169-0
[16] Takakuda, K. (1985): Stress singularities near crack front edges. Bull. JSME 28, 225-231
[17] Takakuda, K.; Koizumi, T.; Shibuya, T. (1985): On integral equation methods for crack problems. Bull. JSME 28, 217-224
[18] Watson, J. O. (1982): Hermitian boundary elements for plane problems of fracture mechanics. Res. Mech. 4, 23-42
[19] Weaver, J. (1977): Three-dimensional crack analysis. Int. J. Solids Struct. 13, 321-330 · Zbl 0373.73093 · doi:10.1016/0020-7683(77)90016-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.