Stress state of the box shell under the indentation of two inclusions

Abstract

Thin-walled structures are widely used in various fields in modern technologies of mechanical engineering, construction, aviation industry, shipbuilding, rocket engineering, oil, gas and other industries. Variety of forms of such structures, various loading conditions and pinning, presence of defects and inhomogeneities lead to wide range of different formulations of the problems of research on strength characteristics of such structures and methods used for this purpose. The characteristic feature of this type of problems is the difficulty of their analytical or numerical solving. Assessment of convergence of numerical method solution requires the ability to compare the numerical results with analytical solution results of the corresponding problem.The research is devoted to solving the problem of stress state of box-shell with rectangular profile and infinite length under the indentation of two symmetrically arranged thin rigid inclusions. The problem is reduced to a system of integral equations. The solution is sought in the space of functions that have nonintegrable singularities using the apparatus of the regularization of divergent integrals. Obtained infinite system of linear algebraic equations is solved by the method of reduction. There are obtained the numerical values of the upsettings of inclusions depending on inclusions length and ratios of geometric dimensions of the cross-section of the shell.