On the distribution of stresses in circular infinite cylinder with cylindrical cavities
Abstract
Nonaxisymmetric boundary value problem of elasticity theory for multiconnected body with cylindrical boundaries is investigated. The solution is constructed as a superposition of basic solutions of the Lame equation in coordinate systems related to the centers of body boundary surfaces. Boundary conditions are satisfied exactly by the generalized Fourier method. The numerical analysis of stresses in the areas of their greatest concentration is carried out.
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References
Abramian, B. L. On the problem of axisymmetric deformation of a circular cylinder / B. L. Abramian // Dokl. AS Arm. SSR. - 1954. - V. 19, No 1. - P. 3-12 (in Russian).
Valov, G. M. About axially symmetric deformation solid circular cylinder of finite length / G. M. Valov // Prikl. Math. Mech. - 1962. - V. 26, Issue 4. - P. 650-667 (in Russian).
Prokopov, V. K. Axisymmetric problem of elasticity theory for isotropic cylinder / V. K. Prokop ov // Tr. Leningr. polytech. Ins. - 1950. - No 2. - P. 286-304 (in Russian).
Lur'e, A. I. Three-dimensional problems of the theory of elasticity / A. I. Lur'e - M.: Gostechizdat, 1955. - 492 p. (in Russian).
Gomilko, A. M. Homogeneous solutions in the problem of equilibrium of an elastic cylinder of finite length / A. M. Gomilko, V. T. Grinchenko, V. V. Meleshko // Teor. prikl. mech. - 1989. - No 20. - P. 3-9 (in Russian)
Grinchenko, V. T. Axisymmetric problem of elasticity theory for a semiinfinite circular cylinder / V. T. Grinchenko // Prikl. mech. - 1965. - V. 1, No 1. - P. 109-119 (in Russian).
Grinchenko, V. T. Axisymmetric problem of elasticity theory for thick-walled cylinder of finite length / V. T. Grinchenko // Prikl. mech. - 1967. - V. 3, No 8. - P. 93-103 (in Russian).
Grinchenko, V. T. Equilibrium and steady-state oscillations of elastic b o dies of finite dimensions / V. T. Grinchenko. - Kiev: Nauk. dumka, 1978. - 264 p. (in Russian).
Meleshko, V. V. Equilibrium of an elastic finite cylinder under axisymmetric discontinuous normal loadings [Text] / V. V. Meleshko, Yu. V. Tokovyy // J. Eng. Math. - 2013. - V. 78. - P. 143-166.
Tokovyy, Yu. V. Axisymmetric stresses in finite elastic cylinder under normal pressure, evenly distributed over the surface of the side / Yu. V. Tokovyy // Prikl. problemi mech. math. - 2010. - Issue 8. - P. 144-151 (in Ukrainian).
Arutynian, N. Kh. Behavior of solutions of problems of elasticity theory in unb ounded domains with parab oloidal and cylindrical inclusions or cavities / N. Kh. Arutynian, A. B. Movchan, S. A. Nazarov // Usp. mech. 1987. - V. 10, No 4. - P. 3-91 (in Russian).
Chirstensen, R. Intro duction to mechanics of comp osites / R. Christensen. - M.: Mir, 1982. - 334 p. (in Russian).
Vanin, G. A. Micromechanics of comp osite materials / G. A. Vanin. - K.: Nauk. Dumka. - 1985. - 304 p. (in Russian).
Vihak, V. M. Exact solution of the axisymmetric thermo elasticity problem for a long cylinder sub jected to varying with-resp ect-to-length loads [Text] / V. M. Vihak, A. V. Yasinskyy, Yu. V. Tokovyy, A. V. Rychahivskyy // J Mech Behav Mater. - 2007. - No 18. - P. 141-148.
Williams, D. K. Pip e-anchor discontinuity analysis utilizing p ower series solutions, Bessel functions, and Fourier series [Text] / D. K. Williams, W. F. Ranson // Nucl Eng Des. - 2003. - No 220. - P. 1-10.
Zhong, Z. Analysis of a transversely isotropic ro d containing a single cylindrical inclusion with axisymmetric eigenstrains [Text] / Z. Zhong, Q. P. Sun // Int. Journal of Solids and Structures. - 2002. - V. 39, Issue 23. - P. 5753-5765.
Nikolaev, A. G. Stress distribution in the cylindrical sample of material with two parallel cylindrical cavities / A. G. Nikolaev, E. A. Tanchik // Vopr. pro ekt. proizv. constr. LA. - Issue 4(76). - Kh., 2013. - P. 26-35 (in Russian).
Nikolaev, A. G. Stress state in the cylindrical sample with two parallel cylindrical fibers / A. G. Nikolaev, E. A. Tanchik // Av.-cosm. tech. technol. - 2013. - No 6(103). - P. 32-38 (in Russian).
Nikolaev, A. G. Addition theorems of solutions of Lame equation / A. G. Nikolaev. - Kh.: KhAI, 1993. - 109 p. - Dep. in GSTB of Ukraine 21.06.93, No 1178 - Uk 93 (in Russian).
Nikolaev, A. G. Generalized Fourier metho d in three-dimensional problems of elasticity / A. G. Nikolaev, V. S. Protsenko. - Kh.: KhAI, 2011. - 344 p. (in Russian).
Nikolaev, A. G. Justification of Fourier method in the basic boundary value problems in the theory of elasticity for some three-dimensional canonical domains / A. G. Nikolaev // Dokl. NAN Ukr. - 1998. - No 2. - P. 78-83 (in Russian).
Leb edev, N. N. Sp ecial functions and its applications / N. N. Leb edev // M.: Phis.-math. lit. - 1963. - 358 p. (in Russian).
Kantorovich, L. V. Functional Analysis / L. V. Kantorovich, G. P. Akilov. - M.: Nauka, 1977. - 742 p. (in Russian).
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