@article{M2AN_1994__28_2_141_0, author = {B\'ecache, E. and Ha Duong, T.}, title = {A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {28}, year = {1994}, pages = {141-176}, mrnumber = {1267196}, zbl = {0817.73067}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1994__28_2_141_0} }
Bécache, E.; Ha Duong, T. A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 141-176. http://gdmltest.u-ga.fr/item/M2AN_1994__28_2_141_0/
[1] Formulation variationnelle espace-temps pour le calcul par potentiel retardé d'une onde acoustique, Math. Methods Appl. Sci., 8, 405-435. | MR 859833 | Zbl 0618.35069
and , 1986,[2] Formulation variationnelle espace-temps pour le calcul par potentiel retardé d'une onde acoustique; Problème de Neumann, Math. Methods Appl. Sci., 8, 598-608. | MR 870995 | Zbl 0636.65119
and , 1986,[3] Approximation de la diffraction d'ondes élastiques, une nouvelle approche (I), (II), (III), Technical report, École Polytechnique, CMAP, Rapports Internes n° 91, 96, 98. | Zbl 0571.73020
, 1983,[4] Résolution par une méthode d'équations intégrales d'un problème de diffraction d'ondes élastiques transitoires par une fissure. PhD thesis, Université de Paris 6. Thèse.
, 1991,[5] A Variational Boundary Integral Equation Method for an Elastodynamic Antiplane Crack, Int. J. for Numerical Meth. in Eng., 36, 969-984 | MR 1208455 | Zbl 0772.73088
, 1993,[6] Regularization in 3D for Anisotropic Elastodynamic Crack and Obstacle Problems, J. of Elasticity, 31, 25-46. | MR 1221204 | Zbl 0773.73029
, , , 1993,[7] Boundary elements methods in dynamic analysis, Appl. Mech. Rev., 40, 1-23.
, 1987,[8] Méthode des équations intégrales régularisées en élastodynamyque, PhD thesis, ENPC, Thèse. | MR 884382 | Zbl 0612.73083
, 1986,[9] An intgral equations method for sol ving the problems of a plane crack of arbitrary shape, J. Mech. Phys. Solids, 25, 29-39. | MR 443528 | Zbl 0355.73074
, 1977,[10] Simulation Numérique de Problèmes de Diffraction d'Ondes par une Fisure, PhD thesis, Université Paris VI, Thèse d'État.
, 1984,[11] Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 2. Masson. | Zbl 0642.35001
and , 1985,[12] On the transient acoustic scattering by a flat object, Japan J. Appl. Math., 7, 489-513. | MR 1076300 | Zbl 0719.35063
, 1990,[13] On the boundary integral equations for the crack opening displacement of flat cracks, Integr. Equat. Oper. Th., 15, 427-453. | MR 1155713 | Zbl 0753.45005
, 1992,[14] Boundary-value problems for the System of elasticity theory in unbounded domains. Korn's inequalities, Russian Math. Surveys, 43, 65-119. | MR 971465 | Zbl 0669.73005
and , 1988,[15] Hypersingular boundary integral equations : Their occurrence interpretation, regularization and computation. In P. K. Banerjee and S. Kobayashi, editors, Developments in Boundary Element Methods, vol. 7 ; Advanced Dynamic Analysis, Elsevier Applied Science Publishers.
, and , 1991,[16] Problèmes aux limites non homogènes et Applicaitons, vol. l, Dunod. | Zbl 0165.10801
and , 1968,[17] On multistep time discretization of linear initial-boundary value problems and their boundary integral equations, submitted to Numerische Mathematik. | Zbl 0795.65063
,[18] On boundary integral equations for crack problems, Proc. Roy. Soc. London A, 421, 341-355. | MR 985268 | Zbl 0674.73071
and , 1989,[19] Intégral Equations with non Integrable Kernels, Intégral Equations and Operator Theory, 5, 562-572. | MR 665149 | Zbl 0479.65060
, 1982,[20] Le Potentiel de Double Couche pour les Ondes Élastique, Internal report n° 99, C.M.A.P., École Polytechnique.
, 1983,[21] Boundary Integral Equation Methods in Elastodynamic Crack Problems, In Brebbia, Wendland, and Kuhn, editors, Proc. 9th Int. Conf. BEM, vol. 2 : Stress Analysis Applications, pp. 279-291. Springer-Verlag.
, , , 1987,[22] A regularized boundary integral equation method for elastodynamic crack problems, Computat. Mech., 4, 319-328. | Zbl 0675.73065
and , 1989,[23] On Korn's second inequality, RAIRO, Analyse numérique, 15, 237-248. | Numdam | MR 631678 | Zbl 0467.35019
, 1981,[24] Transient elastodynamic three-dimensional problems in cracked bodies, Appl. Math. Model, 8, 2-10. | MR 734034 | Zbl 0525.73110
and , 1984,[25] Crack Problems in the Classical Theory of Elasticity, John Wiley and Sons. | MR 258339 | Zbl 0201.26702
and ,[26] A Boundary Integral Equation Method for Three-Dimensional Crack Problem in Elasticity, Math. Meth. in the Appl. Sci., 8, 609-623. | MR 870996 | Zbl 0608.73097
, 1986,[27] Boundary Integral Equation for screen problem in R3 Integral Eq. and Oper. Theory, 10, 263. | Zbl 0653.35016
, 1987,[28] Basic Linear Partial Differential Equations, Academic Press. | Zbl 0305.35001
, 1975,