The integral equation method in the theory of the layers with set of cavities and galleries

Abstract

A method of solution of boundary problem is developed for the integral equations’ systems arising in the difficulty of structural behavior evaluation of block structures which represent underground constructions containing multiple shaft tunnels. The same problem appears in the study of multilayer materials behavior. These materials have connections with parallel different-sized cavities of a large extent. The method is based on reduction of boundary problems to the integral equations’ systems with a kernel representing matrix-function of high order. The latter circumstance complicates the study and the solution of the initial boundary problem by methods of reducing it to the Fredholm’s combined equations of the second kind. A factorization method, which allows study the behavior of the solution characteristics more optimally, will be developed in order to investigate the combined equations. This can be achieved by designing of factorization approach to the analysis of higher-order matrix-functions. The approach makes it possible to construct the conditions of boundary problem’s solutions by using some kind of algorithm of successive approximations. The conditions describe both the behavior of contact voltages in the zones of jointing of partitions with multipart layers and the behavior of motions in the inter-partitions zones.