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Numerical resolution of the boundary integral equations for elastic scattering by a plane crack. (English) Zbl 0835.73066
Summary: The problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. We use a variational method, first writing the problem in Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method on the surface of the crack. Numerical tests were made with circular and elliptical cracks. Extensive results are given concerning the crack opening displacement, the scattering cross-section, the back-scattered amplitude and far-field patterns.

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74J20 Wave scattering in solid mechanics
74R99 Fracture and damage
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[1] Bouwkamp, Reports Progress Phys. 17 pp 35– (1954)
[2] Jones, C.P.A.M. 9 pp 713– (1956)
[3] Mal, Int. J. Eng. Sci. 8 pp 381– (1970)
[4] Martin, Proc. R. Soc. Lond. A 390 pp 91– (1983)
[5] and , ’Scattering of elastic waves by a three-dimensional crack’, Boundary Elements VIII Conf., Springer, Berlin 1986, pp. 169-178.
[6] Nishimura, Comput. Mech. 4 pp 319– (1989)
[7] Nédélec, Comput. Methods Appl. Mech. Eng. 8 pp 61– (1976)
[8] ’Approximation de la diffraction d’ondes elastiques (I)’, in Nonlinear Partial Differential Equations and their Applications, Pitman, London, 1984, pp. 48-95.
[9] Hamdi, CRAS sér, II 292 pp 17– (1981)
[10] Ha Duong, Integr. Eq. Oper. Theory 15 pp 426– (1992)
[11] Budreck, J. Appl. Mech. 55 pp 405– (1988)
[12] Lin, J. Acoust. Soc. Am. 82 pp 1442– (1987)
[13] ’Estudo Matemàtico e Numérico da Difracção de Ondas Elàsticas em Fissuras Planas por um Método de Equações Integrais’, Master Thesis, Universidade de Lisboa, Lisbon, 1992.
[14] and , Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin, 1972.
[15] Thèse de Docteur ès Sciences, Université Paris VI, 1987.
[16] Krenk, Phil. Trans. R. Soc. A 308 pp 167– (1982)
[17] , and , Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North Holland, Amsterdam, 1979.
[18] and , ’Ray methods for waves in elastic solids’, Monog. and Studies in Mathematics, Vol. 14, Pitman, London, 1982.
[19] Barratt, Proc. Camb. Phil. Soc. 61 pp 969– (1965)
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