Reducing the boundary value problems of elasticity theory for cracked bodies to boundary integral equations

A general method has been proposed for constructing integral representations of general solutions and boundary integral equations of multidimensional boundary value problems of mathematical physics for regions with cuts. It involves the use of the theory of generalized functions, and in particular of the surface delta function. At first, the boundary value problems of Dirichlet and Neumann were studied for n-dimensional Poisson and Helmholtz equations in a space with cuts along piecewise-smooth surfaces. After that the method is extended to the case of a system of differential equations. In this way the basic spatial and plane problems of elasticity theory were considered for an anisotropic infinite body with cracks under static and dynamic loading. The corresponding axisymmetric problems were also studied.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 6, pp. 61–71, November–December, 1990.