×

zbMATH — the first resource for mathematics

Regularization in 3D for anisotropic elastodynamic crack and obstacle problems. (English) Zbl 0773.73029
Summary: We propose a unified method of generating a regularized integral equation in the double layer potential approach for 3D anisotropic elastodynamics. Our regularization preserves the causality in the time-domain. The method is based on a special decomposition of the hypersingular kernel which appears in the integral representation of the stress tensor.

MSC:
74J20 Wave scattering in solid mechanics
74R99 Fracture and damage
74E10 Anisotropy in solid mechanics
45F15 Systems of singular linear integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] V. Sladek and J. Sladek, Transient elastodynamic three-dimensional problems in cracked bodies. Appl. Math. Model. 8 (1984) 2-10. · Zbl 0525.73110 · doi:10.1016/0307-904X(84)90169-0
[2] H.D. Bui, An integral equations method for solving the problems of a plane crack of arbitrary shape. J. Mech. Phys. Solids 25 (1977) 29-39. · Zbl 0355.73074 · doi:10.1016/0022-5096(77)90018-7
[3] M. Bonnet, Méthode des équations intégrales régularisées en élastodynamique. Bulletin de la direction des études et recherches, EDF, France (1987).
[4] E. Z. Polch, T.A. Cruse and C.-J. Huang, Traction BIE solutions for flat cracks. Comp. Mech. 2 (1987) 253-267. · Zbl 0616.73093 · doi:10.1007/BF00296420
[5] N. Nishimura and S. Kobayashi, A regularized boundary integral equation method for elastodynamic crack problems. Comp. Mech. 4 (1989) 319-328. · Zbl 0675.73065 · doi:10.1007/BF00301390
[6] J.-C. Nedelec, Le potentiel de double couche pour les ondes élastiques. Internal report no99 of Centre de Mathématiques appliquées, Ecole Polytechnique, France (1983).
[7] A. Bamberger, Approximation de la diffraction d’ondes élastiques: une nouvelle approche (I), (II), (III). Internal report no91, 96, 98 of Centre de Mathématiques appliquées, Ecole Polytechnique, France (1983). · Zbl 0571.73020
[8] P.A. Martin and F.J. Rizzo, On boundary integral equations for crack problems. Proc. Roy. Soc. London (A) 421 (1989) 341-355. · Zbl 0674.73071 · doi:10.1098/rspa.1989.0014
[9] E. Bécache, Résolution par une méthode d’équations intégrales d’un problème de diffraction d’ondes élastiques transitoires par une fissure. Ph.D. of the University PARIS 6 (1991).
[10] E. Bécache, A variational boundary integral equation method for an elastodynamic antiplane crack. Int. J. for Numerical Meth. in Eng. 36 (1993). · Zbl 0772.73088
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.