Антиплоская деформация равномерно кусочно-однородного пространства с периодической системой полубесконечных внутренних трещин

Abstract

In this paper, we have constructed a solution for the problem of antiplane deformation of a uniformly piecewise homogeneous space of two alternately repeating heterogeneous layers of equal thickness from different materials, which are relaxed on their median planes by two semi-infinite, periodic parallel tunneling cracks. A system of defining equations of the problem is derived in the form of a system of two singular equations of the first kind, with respect to contact stresses acting in the contact zones on the median planes of heterogeneous layers, the solution of which, in the general case, is constructed by the method of mechanical quadrature. In the particular case when the cracks in the heterogeneous layers are the same, the solution of the problem is reduced to the solution of two independent equations and their closed solutions are constructed. The defining singular integral equation of the problem is also obtained in the case when there are no cracks in one of the heterogeneous layers. In the general case, a numerical calculation was carried out and patterns of changes in contact stresses and intensity factors of destructive stresses at the end points of cracks were determined depending on the physical and mechanical and geometric parameters of the problem, which are the ratios of the shear moduli of the layers and the ratio of the layer thickness and crack lengths.