|Journal||Journal of Mechanical Engineering – Problemy Mashynobuduvannia|
|Publisher||A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||0131-2928 (Print), 2411-0779 (Online)|
|Issue||Vol. 21, no. 3, 2018 (September)|
|Cited by||J. of Mech. Eng., 2018, vol. 21, no. 3, pp. 65-74|
Minavar Mir-Salim-zade, Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences (9, F. Agaev str., Baku, AZ1141, Azerbaijan), e-mail: email@example.com, ORCID: 0000-0003-4237-0352
On the basis of the methods of the theory of elasticity, a mathematical description of the model of partial closure of a system of slits in a perforated isotropic medium with foreign transverse inclusions is given. Such a medium can be considered as a perforated unrestricted plate, reinforced by a system of stringers of a very narrow cross section. It is believed that the medium is weakened by a periodic system of circular holes and rectilinear variable width slits. The variable width of the slits is comparable to elastic deformations. A method of solving the periodic elastic problem and an explicit method of constructing complex potentials corresponding to the unknown normal displacements along rectilinear slits are applied. General representations of solutions are constructed, that describe a class of problems with a periodic distribution of stresses outside circular holes and slits with contact zones. To determine the unknown contact stresses and sizes of contact zones, a singular integral equation is obtained, that reduces to a system of nonlinear algebraic equations. The system of algebraic equations can be solved by the method of successive approximations. As a result, the contact stresses and sizes of contact zones have been found.
Keywords: perforated plate, stringers, rectilinear variable width slits, contact stresses, contact zones
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Received 24 May 2018
Published 30 September 2018