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Development of efficient methods of determination of an intense-strained state of thin-walled constructional designs with inclusions, reinforcements and other stress raisers is an important problem both with theoretical, and from the practical point of view, considering their wide practical application. Aim: The aim of this research is to develop the analytical mathematical method of studying of an intense-strained state of infinite plate with cross-shaped embedment at a bend. Materials and Methods: The method of boundary elements is an efficient way of the boundary value problems solution for systems of differential equations. The methods based on boundary integral equations get wide application in many branches of science and technique, calculation of plates and shells. One of methods of solution of a numerous class of the integral equations and systems arising on the basis of a method of boundary integral equations is the analytical method of construction of these equations and systems to Riemann problems with their forthcoming decision. Results: The integral equation for the analysis of deflections and the analysis of an intense-strained state of a thin rigid plate with rigid cross-shaped embedment is received. The precise solution of this boundary value problem is received by reduction to a Riemann problem and its forthcoming solution. An asymptotical behavior of contact efforts at the ends of embedment is investigated.

Development of effective methods of determining the stress-strain state thin-walled structures with inclusions, reinforcements and other stress concentrators is an important task, both from a theoretical and practical point of view, by reason of their great practical application. Aim: The aim of the research is to analyze the elastic-deformed state of a spherical shallow shell. Materials and Methods: In this work, based on the generalized scheme of integral transformations, a constructive method of direct numerical-analytical solutions of boundary value problem of calculating the stress-strain state of a spherical shallow shell with the inclusion in bending is proposed. Results: The results of numerical calculations are presented. Calculations allow predicting the value of deformation of the cylindrical shells structure with reinforcements and determining the optimum parameters for the design or manufacture. The obtained results can be used in determining the strength characteristics of structural elements that consist of composite materials. The article contains comparative analysis of the results and demonstrates the effectiveness of the method for solving this class of problems.