Y. PROTSEROV, N. VAYSFELD . Torsion problem for elastic multilayered finite cylinder with circular crack[J]. Applied Mathematics and Mechanics, 2017 , 38(3) : 423 -438 . DOI: 10.1007/s10483-017-2173-7

[1] Mykhas'kiv, V., Stankevych, V., Zhbadynskyi, I., and Zhang, C. 3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half-spaces. International Journal of Fracture, 159(2), 137-149(2009)
[2] Chang, D. and Kotousov, A. A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness. Fatigue and Fracture of Engineering Materials & Structures, 37(11), 1254-1267(2014)
[3] Lee, D. S. The problem of internal cracks in an infinite strip having a circular hole. Acta Mechanica, 169, 101-110(2004)
[4] Savruk, M. P., Osiv, P. N., and Prokopchuk, I. V. Numerical Analysis in Plane Problems of the Crack's Theory (in Russian), Naukova Dumka, Kyiv (1989)
[5] Morozov, N. F. Mathematical Questions of the Crack's Theory (in Russian), Nauka, Moskow (1984)
[6] Vorovich, I. I. and Babeshko, V. A. Dynamical Mixed Problems of the Elasticity Theory for the No Classical Areas (in Russian), Nauka, Moskow (1979)
[7] Hakobyan V. Mixed Boundary Value Problems On Interaction of Continuum Deformable Bodies with the Different Types Stress Concentrators (in Russian), Gitutyan, Yerevan (2014)
[8] Babeshko, V. A., Ratner, S. V., and Syromyatnikov, P. V. Anisotropic bodies with inhomogeneities:the case of a set of cracks. Mechanics of Solids, 42(5), 700-709(2007)
[9] Uflyand, Y. S. Integral Transformations in the Problems of the Elasticity Theory (in Russian), Nauka, Moskow (1967)
[10] Guz, A. N. and Dyshel, M. S. Fracture and buckling of thin panels with edge crack in tension. Theoretical and Applied Fracture Mechanics, 36(1), 57-60(2001)
[11] Akiyawa, T., Hara, T., and Shibua, T. Torsion of an infinite cylinder with multiple parallel circular. Theoretical & Applied Mechanics Japan, 50, 143-173(2001)
[12] Huang, G. Y., Wang, Y. S., and Yu, S. W. Stress concentration at a penny-shaped crack in a nonhomogeneous medium under torsion. Acta Mechanica, 180(1-4), 107-115(2005)
[13] Kaman, M. O. and Mehmet, R. G. Cracked semi-infinite cylinder and finite cylinder problems. International Journal of Engineering Science, 44(20), 1534-1555(2006)
[14] Malits, P. Torsion of a cylinder with a shallow external crack. International Journal of Solids and Structures, 46, 3061-3067(2009)
[15] Suzuki, K., Shibuya, T., and Koizumi, T. The torsion of hollow cylinder with two or infinite parallel external circular cracks. Bulletin of JSME, 23(179), 637-643(1980)
[16] Yantian, L. and Hong, Y. Torsion of a finite length laminar composite circular cylinder debonded over a penny shaped area. Engineering Fracture Mechanics, 31(1), 1-8(1988)
[17] Li, Y. D., Zha, H., and Xiong, T. The cylindrical interface crack in a layered tubular composite of finite thickness under torsion. European Journal of Mechanics-A/Solids, 39, 113-119(2013)
[18] Kushnir, R. M., Protsyuk, B. V., and Synyuta, V. M. Quasistatic temperature stresses in a multiplayer thermally sensitive cylinder. Materials Science, 40(4), 433-445(2004)
[19] Ayzikovich, S., Alexandrov, V., Vasil'ev, A., Krenev, L., and Trubchik, I. The Analytical Solutions of the Mixed Axysimmetrical Problems for the Functional-Gradient Materials (in Russian), Fizmatlit, Moscow (2011)
[20] Gasparyan, A. and Mkchitaryan, S. M. On the stress state of the composite in the form of the packet from the arbitrary finite quantity of the elastic layers during the antiplane deformation. Izv. Nats. Akad. Nauk Armen. Mekh., 63(2), 10-20(2010)
[21] Popov, G. Y. and Gribnyak, S. T. Solving problems in mechanics for layered media. International Applied Mechanics, 16(10), 68-74(1980)
[22] Vaysfeld, N. Nonstationary problem of stress concentration near a spherical crack, situated inside a truncated cone. Mathematical Methods and Physico-Mechanical Fields, 47(3), 134-143(2004)
[23] Vaysfeld, N. and Popov, G. The torsion of the conical layered elastic cone. Acta Mechanica, 225(1), 67-76(2014)
[24] Protserov, Y. S. The axisymmetric torsion problem for the multilayered cylinder of finite length (in Russian). Odessa National University Proceedings Mathematics and Mechanics, 3(23), 76-83(2014)
[25] Nowacki, W. A dynamical problem of thermoelasticity. Archiwum Mechaniki Stosowanej, 9(3), 325-334(1957)
[26] Popov, G. Y. The Elastic Stress' Concentration Around Dies, Cuts, Thin Inclusions and Reinforcements (in Russian), Nauka, Moskow (1982)
[27] Kamke, E. Differentialgleichungen:Losungsmethoden und Losungen, I, Gewohnliche Differentialgleichungen, Teubner, Leipzig (1977)
[28] Popov, G. Y., Abdimanov, S. A., and Ephimov, V. V. Green's Functions and Matrixes of the One-Dimensional Boundary Problems (in Russian), Raczah, Almati (1999)
[29] Bateman, H. and Erdelyi, A. Higher Transcendental Functions, McGraw-Hill, New York (1953)
[30] Gradshtein, L. and Rygik, L. The Tables of Integrals, Series and Products (in Russian), Nauka, Moscow (1963)
[31] Marichev, O. The Method of Special Function Integrals' Calculation (in Russian), Nauka, Minsk (1978)