zbMATH — the first resource for mathematics

Symmetric weak-form integral equation method for three-dimensional fracture analysis. (English) Zbl 0906.73074
A symmetric Galerkin boundary element method is developed for the analysis of linearly elastic isotropic three-dimensional solids containing fractures. The formulation is based upon a weak-form displacement integral equation and a weak-form traction integral equation. These integral equations are only weakly singular, and their validity requires only that the boundary displacement data are continuous, hence, allowing standard \(C^0\) elements to be employed. As part of the numerical implementation, a special crack-tip element is developed which has a feature in that there exist degrees of freedom associated with the nodes at the crack front.

74S15 Boundary element methods applied to problems in solid mechanics
74R99 Fracture and damage
Full Text: DOI
[1] Kanninen, M.F.; Popelar, C.H., Advanced fracture mechanics, (1980), Oxford University Press · Zbl 0463.73110
[2] Brebbia, C.A.; Dominguez, J., Boundary elements, an introductory course, (1992), Computational Mechanics Publications · Zbl 0780.73002
[3] Cruse, T.A., Boundary element analysis in computational fracture mechanics, (1988), Kluwer Academic Publishers · Zbl 0648.73039
[4] Martin, P.A.; Rizzo, F.J., Hypersingular integrals: how smooth must the density be?, Int. J. numer. methods engrg., 39, 687-704, (1996) · Zbl 0846.65070
[5] Bonnet, M.; Bui, H.D., Regularization of the displacement and traction BIE for 3D elastodynamics using indirect methods, ()
[6] Mi, Y.; Aliabadi, M.H., Dual boundary element method for three-dimensional fracture mechanics analysis, Engrg. anal. bound. elem., 10, 161-171, (1992)
[7] Young, A., A single-domain boundary element method for 3-D elastostatic crack analysis using continuous elements, Int. J. numer. methods engrg., 39, 1265-1293, (1996) · Zbl 0894.73207
[8] Forth, S.C.; Keat, W.D., Three-dimensional nonplanar fracture model using the surface integral method, Int. J. frac., 77, 243-262, (1996)
[9] Gray, L.J.; Martha, L.F.; Ingraffea, A.R., Hypersingular integrals in boundary element analysis, Int. J. numer. methods engrg., 39, 387-404, (1990) · Zbl 0717.73081
[10] Guiggiani, M.; Krishnasamy, G.; Rizzo, F.J.; Rudolphi, T.J., Hypersingular boundary integral equations. A new approach to their numerical treatment, (), 211-220 · Zbl 0765.73072
[11] Bui, H.D., An integral equation method for solving the problem of a plane crack of arbitrary shape, J. mech. phys. solids, 25, 29-39, (1977) · Zbl 0355.73074
[12] Weaver, J., Three-dimensional crack analysis, Int. J. solids struct., 13, 321-330, (1977) · Zbl 0373.73093
[13] Sládek, V.; Sládek, J., Three-dimensional crack analysis for an anisotropic body, Appl. math. modeling, 6, 374-380, (1982) · Zbl 0492.73102
[14] S. Li and M.E. Mear, Singularity-reduced integral equations for discontinuities in elastic media, in preparation.
[15] Liu, Y.; Rudophi, T.J., Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations, Engrg. anal. bound. elem., 8, 301-311, (1991)
[16] Sládek, V.; Tanaka, M., Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity, Int. J. numer. methods engrg., 36, 1609-1628, (1993) · Zbl 0772.73091
[17] Cruse, T.A.; Richardson, J.D., Non-singular somigliana stress identities in elasticity, Int. J. numer. methods engrg., 39, 3273-3304, (1996) · Zbl 0886.73005
[18] Huang, Q.; Cruse, T.A., On the non-singular traction-BIE in elasticity, Int. J. numer. methods engrg., 37, 2041-2072, (1994) · Zbl 0832.73076
[19] Gu, H.D.; Yew, C.H., Finite element solution of a boundary equation for mode-I embedded three-dimensional fracture, Int. J. numer. methods engrg., 26, 1525-1540, (1988) · Zbl 0636.73087
[20] Bonnet, M., Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity, Engrg. anal. bound. elem., 15, 93-102, (1995)
[21] Nedelec, J.C., Integral equations with non integrable kernels, Integral equations and operator theory, 5, 563-572, (1982) · Zbl 0479.65060
[22] Ghosh, N.; Mukherjee, S., A new boundary element method formulation for three-dimensional problems in linear elasticity, Acta mech., 67, 107-119, (1987) · Zbl 0612.73085
[23] Demkowicz, L.; Karafiat, A.; Oden, J.T., Variational (weak) form of the hypersingular formulation for the Helmholtz exterior boundary-value problems, ()
[24] Chang, C.C.; Mear, M.E., A boundary element method for two-dimensional linear elastic fracture analysis, Int. J. frac., 74, 219-251, (1995)
[25] Li, H.B.; Han, G.M., A new method for evaluating singular integral in stress analysis of solids by the direct boundary element method, Int. J. numer. methods engrg., 21, 2071-2098, (1985) · Zbl 0576.65129
[26] L. Xiao and M.E. Mear, A technique for the efficient evaluation of nearly singular integrals, in preparation.
[27] Williams, M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. appl. mech., 19, (1952)
[28] Barsoum, R., On the use of isoparametric finite elements in linear fracture mechanics, Int. J. numer. methods engrg., 10, 25-37, (1976) · Zbl 0321.73067
[29] Stern, M., Families of consistent conforming elements with singular derivative fields, Int. J. numer. methods engrg., 14, 409-421, (1979) · Zbl 0408.73071
[30] Benthem, J.P., The quarter-infinite crack in a half space; alternative and additional solutions, Int. J. solids struct., 16, 119-130, (1980) · Zbl 0463.73125
[31] Nakamura, T.; Parks, D.M., Three-dimensional stress field near the crack front of a thin elastic plate, J. appl. mech., 55, 805-813, (1988)
[32] Murakami, Y., ()
[33] Sládek, V.; Sládek, J., Three-dimensional curved crack in an elastic body, Int. J. solids struct., 5, 425-436, (1983) · Zbl 0512.73086
[34] Xu, G.; Ortiz, M., A variational boundary integral method for the analysis for 3-D cracks of arbitrary geometry modeled as continuous distributions of dislocation loops, Int. J. numer. methods engrg., 36, 3675-3701, (1993) · Zbl 0796.73067
[35] Raju, I.S.; Newman, J.C., Three-dimensional finite-element analysis of finite-thickness fracture specimens, Nasa tn d-8414, (1977)
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.