Estimation of the state of constructions and underground structures with a number of the parallel connections

Abstract

Methods for assessing the strength properties of objects such as underground structures, in particular mines, containing parallel tunnels, are being developed, the partitions between which are formed by the material of the seams. Such block constructions made from the metal contained cavities, which are lightening the weight of the object, are used in the branches of machinery, also in aircraft industry for airfoil of power generator. Traditionally the researchers are held for the one fix and then the collected characteristics are accepting for the other objects. At the same time, multiplicity of such objects can lead to the appearance one more fact of offence of resistance connected with the possibility of localization of the stress-strain state in one of the zones of the structure, which leads to exceeding the planned strength parameters. In this study the calculating theory mechanical strength characteristics of such objects is built on the examples of underground constructions. The foundation of the study is the theory of block-level element, basing on factorizing approaches. The problem leads to the research of the system of integral equations of first kind with difference kernel, which is listed to the system of Fredholm integral equations of second kind. With the way of integral evaluation, describing kernels of these equations according to the theory residues, integral equations are managed to be listed to algebraic equations, available for analytical analysis, allowing finding out location of strain and displacement.