|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. 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: firstname.lastname@example.org, 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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- Finkel, V. M. (1977). Fizicheskiye osnovy tormozheniya razrusheniya [Physical principles of inhibition of fracture]. Moscow: Metallurgiya, 360 p. (in Russian).
- Parton, V. Z., & Morozov, Ye. M. (1985). Mekhanika uprugo-plasticheskogo razrusheniya [Mechanics of elastic-plastic fracture]. Moscow: Nauka, 504 p. (in Russian).
- Mirsalimov, V. M. (1986). Some problems of structural arrest of cracks. Soviet materials science, vol. 22, iss. 1, pp. 81–85. https://doi.org/10.1007/BF00720871
- Tolkachev, V. M. (1964). Peredacha nagruzki ot stringera konechnoy dliny k beskonechnoy i polubeskonechnoy plastine [Transfer of a load from a stringer of finite length to an infinite and semi-infinite plate]. Dokl. AN SSSR, vol. 154, no. 4, pp. 86–88 (in Russian).
- Dolgikh, V. N. & Filshtinskiy, L. A. (1976). Ob odnoy modeli regulyarnoy kusochno-odnorodnoy sredy [On a model of a regular piecewise homogeneous medium]. Izv. AN SSSR. Mekhanika Tverdogo Tela, no. 2, pp. 158–164 (in Russian).
- Vanin, G. A. (1985). Mikromekhanika kompozitsionnykh materialov [Micromechanics of Composite Materials]. Kyiv: Nauk. dumka, 302 p. (in Russian).
- Broyek, D. (1980). Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow: Vyssha shkola, 368 pp. (in Russian).
- Cherepanov, G. P. (1983). Mekhanika razrusheniya kompozitsionnykh materialov [Mechanics of destruction of composite materials]. Moscow: Nauka, 296 p. (in Russian).
- Maksimenko, V. N. (1988). Influence of riveted stiffeners on crack development around a hole. Journal of Applied Mechanics and Technical Physics, vol. 29, iss. 2, pp. 287–293. https://doi.org/10.1007/BF00908597
- Savruk, M. P. & Kravets, V. S. (1994). Reinforcement of a thin cracked plate by a system of parallel stringers. Materials Science, vol. 30, iss. 1, pp. 95–104. https://doi.org/10.1007/BF00559023
- Savruk, M. P. & Kravets, V. S. (1995). Two-dimensional problems of the theory of elasticity for reinforced cracked plates. Materials Science, vol. 31, iss. 3, pp. 350–362. https://doi.org/10.1007/BF00558558
- Savruk, M. P & Kravets, V. S. (1999). Effect of breaks in riveted stringers on the elastic and limiting equilibrium of a cracked plate. Materials Science, vol. 35, iss. 3, pp. 339–348. https://doi.org/10.1007/BF02355477
- Mir-Salim-zade, M. V. (2005). A crack with interfacial bonds in an isotropic medium strengthened with a regular system of stringers. Mechanics of Composite Materials, vol. 41, iss. 6, pp. 519–526. https://doi.org/10.1007/s11029-006-0005-8
- Mir-Salim-zade, M. V. (2007). Fracture of an isotropic medium strengthened with a regular system of stringers. Mechanics of Composite Materials, vol. 43, iss. 1, pp. 41–50. https://doi.org/10.1007/s11029-007-0004-4
- Mirsalimov, V. M. & Mustafayev, A. B. (2014). Tochnoye resheniye kontaktnoy zadachi o chastichnom vzaimodeystvii beregov shcheli peremennoy shiriny pri deystvii temperaturnogo polya [Exact solution of the contact problem on the partial interaction of variable width slit faces under the action of a temperature field]. Problemy Mashinostroyeniya −Journal of Mechanical Engineering, vol. 17, no. 3, pp. 33–37 (in Russian).
- Mustafayev, A. B. (2014). Vzaimodeystviye beregov shcheli peremennoy shiriny pri izgibe polosy (balki) pod vozdeystviyem temperaturnogo polya [Interaction of variable width slit faces with the bending of a strip (beam) under the influence of a temperature field]. Mekhanika Mashin, Mekhanizmov i Materialov − Mechanics of Machines, mechanisms and Materials, no. 3, pp. 30–36 (in Russian).
- Mirsalimov, V. M. & Mustafayev, A. B. (2015). Solution of the problem of partial contact between the faces of a slot of variable width under the action of temperature fields. Materials Science, vol. 51, iss.1, pp. 96–103. https://doi.org/10.1007/s11003-015-9814-z
- Mirsalimov, V. M. & Mustafayev, A. B. (2015). A contact problem on partial interaction of faces of a variable thickness slot under the influence of temperature field. Mechanika, vol. 21, iss. 1, pp. 19–22. https://doi.org/10.5755/j01.mech.21.1.10132
- Mirsalimov, V. M. (2016). Simulation of partial closure of a variable width slot with interfacial bonds in end zones in an isotropic medium. International. Journal of Damage Mechanics, vol. 25, iss. 2, pp. 266–279. https://doi.org/10.1177/1056789515585178
- Mir-Salim-zade, M. V. (2016). Zakrytiye shcheli, iskhodyashchey iz kontura krugovogo otverstiya v stringernoy plastine [Closure of a slit originating from the contour of a circular hole in a stringer plate]. Vestn. Chuvash. ped. un-ta im. I. Ya. Yakovleva. Ser. Mekhanika predelnogo sostoyaniya − I. Yakovlev Chuvash State Pedugogical University Bulletin. Series: Mechanics of a Limit State, no. 1(27). , pp. 78–89 (in Russian).
- Mir-Salim-zade, M. V. (2016). Partial Contact of the Faces of a Slot of Variable Width in a Plate Reinforced by Stringers. Materials Science, vol. 52, iss. 3, pp. 323–329. https://doi.org/10.1007/s11003-016-9960-y
- Gasanov, Sh. G. (2017). Resheniye kontaktnoy zadachi dlya ploskosti, oslablennoy shchelyu peremennoy shiriny, v neodnorodnom napryazhennom pole [Solution to the contact problem for the plane weakened by a variable width gap in a non-uniform stressed field]. Problemy Mashinostroyeniya − Journal of Mechanical Engineering, vol. 20, no. 2, pp. 29–36 (in Russian). https://doi.org/10.15407/pmach2017.02.029
- Mir-Salim-zada, Minavar V. (2017). Contact problem for a stringer plate weakened by a periodic system of variable width slots. Structural Engineering and Mechanics, vol. 62, iss. 6. pp. 719–724. https://doi.org/10.12989/sem.2017.62.6.719
- Mustafayev, A. B. (2017). Slowing down of the growth of a crack of variable width under the influence of a temperature field. Journal of Applied Mechanics and Technical Physics, vol. 58, iss. 1, pp. 148–154. https://doi.org/10.1134/S0021894417010163
- Muskhelishvili, N. I. (1966). Nekotoryye osnovnyye zadachi matematicheskoy teorii uprugosti [Some basic problems of the mathematical theory of elasticity]. Moscow: Nauka, 707 p. (in Russian).
- Panasyuk, V. V., Savruk, M. P., & Datsyshin, A. P. (1976). Raspredeleniye napryazheniy okolo treshchin v plastinakh i obolochkakh [Distribution of stresses near cracks in plates and shells]. Kyiv: Nauk. dumka, 444 p. (in Russian).
- Ladopoulos, E. G. (2000). Singular integral equations, linear and non-linear theory and its applications in science and engineering. Berlin: Springer Verlag, 552 p. https://doi.org/10.1007/978-3-662-04291-5_10
- Muskhelishvili, N. I. (1968). Singulyarnyye integralnyye uravneniya [Singular integral equations]. Moscow: Nauka, 512 p. (in Russian).
- Mirsalimov, V. M. (1987). Neodnomernyye uprugoplasticheskiye zadachi [Non-dimensional elastic-plastic problems]. Moscow: Nauka, 256 p. (in Russian).
- Savruk, M. P. & Kazberuk, A. (2017). Stress concentration at notches. Springer International Publishing, 498 p. https://doi.org/10.1007/978-3-319-44555-7
Received: 24 May 2018