THIRD MAIN PROBLEM OF THE THEORY OF ELASTICITY FOR THE LAYER WITH A LONGITUDINAL THICK-WALLED TUBE

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Автор: Miroshnikov V.Yu. PhD, associate professor Kharkiv National University of Construction and Architecture
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Анотация: This paper proposes an approach to solving the substantially spatial problem of the theory of elasticity for the layer with a longitudinal circular cylindrical tube located therein. The layer and tube are rigidly fixed togeth- er. It is necessary to study the stress-strain state of the elastic bodies of both the layer and tube. On the lower boundary of the layer, displacements are given; on the upper boundary of the layer and the in- ner surface of the tube, stresses; on the boundary of the layer and tube, conjugation conditions. The solution to the spatial problem of the theory of elasticity is obtained using the generalized Fourier method in relation to the system of Lamé's equations in the cylindrical coordinates associated with the tube, and the Cartesian coordinates associated with the boundaries of the layer. By satisfying both the boundary and conjugation conditions, we ob- tain infinite systems of linear algebraic equations that are solved by the truncation method. As a result, we obtain displacements and stresses at different points of both the elastic layer and elastic tube. A numerical analysis of the stress-strain state of the elastic body of the layer and tube is carried out. Graphs of the normal stresses on the inner and outer surfaces of the tube are presented. The indicated stress-strain graphs show that the greatest stress in the tube arises on its internal surface. In addition, in comparison with the given function, there is a very slow decrease in the stresses along the z axis. The proposed method can be used to cal- culate tunnels in rocks and other structures and parts whose calculation schemes coincide with the statement of the problem in this paper. The given stress-strain analysis can be used to select geometric design parameters at the initial design stage.
Ключевые слова: Keywords: thick-walled tube in the layer, Lame's equation, generalized Fourier method.  
Данные для цитирования: Miroshnikov V.Yu. PhD, associate professor Kharkiv National University of Construction and Architecture, . THIRD MAIN PROBLEM OF THE THEORY OF ELASTICITY FOR THE LAYER WITH A LONGITUDINAL THICK-WALLED TUBE. Восточно Европейский Научный Журнал. Технические науки. ; ():-.



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