|Journal||Journal of Mechanical Engineering|
|Publisher||A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||0131-2928 (Print), 2411-0779 (Online)|
|Issue||Vol. 20, no. 4, 2017 (December)|
|Cited by||J. of Mech. Eng., 2017, vol. 20, no. 4, pp. 45-52|
A solution to the three-dimensional problem of the theory of elasticity is given for the case when stresses are set at the boundaries of parallel cylindrical cavities in an elastic space. A solution to the Lame system of equations is obtained by the generalized Fourier method in the cylindrical coordinates associated with cylinders. Infinite systems of linear algebraic equations, to which the problem is reduced, are solved by the truncation method. As a result, displacements and stresses are found in an elastic body. Numerical results are given for the case of two cylinders.
Keywords: cylindrical cavities in a space, Lamé equations, generalized Fourier method
- Lure, A. I. (1955). Spatial problems in the theory of elasticity. Moscow: Gostehizdat, 492 p.
- Podilchuk, Yu. N. (1979). Three-dimensional problems in the theory of elasticity. Kiyev: Naukova dumka, 240 p.
- Solyanik-Krasa, K. V. (1987). Axisymmetric problem of the theory of elasticity. Moscow: Stroyizdat, 336 p.
- Vasilev, V. Z. (1968). Axisymmetric deformation of an elastic isotropic space with an infinite cylindrical recess. Solid mechanics, vol. 5, pp. 124–129.
- Nikolaev, A. G. & Tanchik, E. A. (2013). Stress distribution in a cylindrical sample of a material with two parallel cylindrical cavities. Questions of design and production of aircraft structures, iss. 4, pp. 40–49.
- Perepelica, V. G., Shmatovskiy, L. D., & Kolomiec, A. N. (2008). The technique of analytical studies of the distribution of stresses in the faces of various forms during mining workings. Geotechnical mechanics, no. 78, pp. 1–33.
- Nikolaev, A. G. & Procenko, V. S. (2011). Generalized Fourier method in the spatial problems of the theory of elasticity. Kharkov: National Aerospace University «KhAI», 344 p.
- Savin, G. N. (1968). Stress distribution near openings. Kiyev: Naukova dumka, 891 p.
Received 31 August 2017
Published 30 December 2017