Elastodynamic crack problems in an anisotropic medium through a complex variable approach

Piva, A.

doi:10.1090/qam/860897

Author: A. Piva
Journal: Quart. Appl. Math. 44 (1986), 441-445
MSC: Primary 73M05; Secondary 73C03
DOI: https://doi.org/10.1090/qam/860897
MathSciNet review: 860897
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The complex variable approach is used to obtain closed-form solutions to elastodynamic crack problems in a strip of anisotropic elastic medium, with one plane of symmetry, under antiplane shear stress. The two problems examined involve a finite-length crack propagating in an infinitely long strip of finite width when the edges are subjected either to constant displacements or shearing stresses. The special cases corresponding to either an orthotropic medium or an isotropic medium are recovered.

R. J. Tait and T. Bryant Moodie, Complex variable methods and closed form solutions to dynamic crack and punch problems in the classical theory of elasticity, Internat. J. Engrg. Sci. 19 (1981), no. 2, 221–229. MR 660549, DOI https://doi.org/10.1016/0020-7225%2881%2990022-7
R. J. Tait and T. Bryant Moodie, On a problem in the dynamic theory of cracks, Quart. Appl. Math. 39 (1981/82), no. 3, 419–423. MR 636245, DOI https://doi.org/10.1090/S0033-569X-1981-0636245-4
F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. Translation edited by I. N. Sneddon. MR 0198152
B. M. Singh, T. Bryant Moodie, and J. B. Haddow, Closed-form solutions for finite-length crack moving in a strip under antiplane shear stress, Acta Mech. 38 (1981), no. 1-2, 99–109. MR 602014, DOI https://doi.org/10.1007/BF01351465

H. T. Danyluk and B. M. Singh, Closed form solutions for a finite length crack moving in an orthotropic layer of finite thickness, Lett. Appl. Eng. Sci. 22, 637–644 (1984)

S. G. Lekhnitskii, Anisotropic plates, Gordon & Breach, Philadelphia, 1968