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Integral equations of elastic equilibrium for a composite space with given ring gaps along the interface plane. (English. Russian original) Zbl 0876.73009
Phys.-Dokl. 39, No. 12, 839-842 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 339, No. 6, 746-749 (1994).
Following A. Ya. Aleksandrov and Yu. L. Solov’ev [Spatial problems of elasticity theory, Moscow, Nauka (1978)], the authors discuss the following boundary value problem for the generalized analytic functions: find $$\Phi_k$$, $$\Psi_k$$ analytic in the half-plane $$D_k$$ $$(k=1,2)$$, $$\partial D_1=\Gamma=\partial D_2$$, $$D_1\cup\Gamma\cup D_2=$$ complex plane, $$\Gamma$$ is the real axis, with the boundary conditions $$\Phi_k(t)- \overline{\Psi_k(t)}= f_k(t)$$, $$t\in L$$, $$a_1\Phi_1(t)= b_1\overline{\Psi_1(t)}+ c_1\Phi_2(t)$$, $$a_2\Psi_1(t)= b_2 \overline{\Phi_1(t)}+ c_2\Psi_2(t)$$, $$t\in\Gamma\setminus L$$, where $$a_k,b_k,c_k$$ are given constants, and $$f_k(t)$$ is a given function. The problem is reduced to a singular integral equation.
##### MSC:
 74B05 Classical linear elasticity 74S30 Other numerical methods in solid mechanics (MSC2010) 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, $$p$$-analytic, etc.)