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Solution of a problem of a boundary crack, outgoing orthogonally from the separation line of two semiplanes with different elastic constants. (English. Russian original) Zbl 0693.73067

Sov. Appl. Mech. 24, No. 1, 84-89 (1988); translation from Prikl. Mekh., Kiev 24, No. 1, 96-101 (1988).
In this paper we obtain the exact solution of the problem of a crack, outgoing orthogonally from the separation boundary of two semiplanes with different elastic constants. Similar problems have been considered earlier; however, in one case the solution of the singular integral equation, to which the problem reduces, has been given numerically, while in another case the results, obtained for the orthotropic case, are not suited for isotropic semiplanes. In another case only the method of reduction of the integral equation to the Riemann boundary value problem has been considered.
The approach used by the authors allows one to isolate the singularities of the solution of the singular integral equation at the outgoing point of the crack to the separation line between the components of the body and to obtain an effective solution of the formulated problem either exactly (as in the case of a semiplane or a piecewise homogeneous plane), or approximately (semiplane, supported band) with the aid of orthogonal polynomials.

MSC:

74R05 Brittle damage
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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