Abstract
Contact problems for elastic hollow cylinders made of an inhomogeneous material are considered. The cylinders are subjected to uniformly distributed internal or external pressure and interact with a stiff shroud or finite-length insert. Poisson’s ratio (Young’s modulus) of the elastic material varies along the radial coordinate. The problem equations are reduced to integral equations with respect to contact pressures. A singular asymptotic method, which is fairly effective for contact regions of sufficiently large length, is applied to solve the problem.
Similar content being viewed by others
References
V. A. Lomakin, Theory of Elasticity of Inhomogeneous Bodies (Lenand, Moscow, 2014) [in Russian].
V. V. Kalinchuk and T. I. Belyankova, Dynamics of the Surfaces of Inhomogeneous Media (Fizmatlit, Moscow, 2009) [in Russian].
V. V. Kalinchuk and T. I. Belyankova, “Dynamic Contact Problem for a Pre-Stressed Cylindrical Tube Filled with a Fluid,” Prikl. Mat. Mekh. 73 (2), 289–302 (2009).
M. V. Abramovich, E. M. Kolosova, and M. I. Chebakov, “Contact Problem in the Presence of Friction Forces in the Contact Region for a Three-Component Cylindrical Base,” Prikl. Mat. Mekh. 78 (1), 262–269 (2014).
M. I. Chebakov and E. M. Kolosova, “Contact Interaction of a Shroud and a Hollow Cylinder Containing a Defect with a Variable Internal Pressure,” Ekol. Vest. Nauch. Ts. Chernomor. Ekon. Sotrud., No. 3, 75–83 (2014).
T. I. Belyankova, V. V. Kalinchuk, and V. A. Lyzhov, “Specific Features of the Dynamics of a Three-Layer Hollow Cylinder,” Ekol. Vest. Nauch. Ts. Chernomor. Ekon. Sotr., No. 4, 19–32 (2015).
A. I. Lur’ye, Three-Dimensional Problems of the Elasticity Theory (Gostekhteoretizdat, Moscow, 1955) [in Russian].
V. M. Alexandrov and B. L. Romalis, Contact Problems in Machine Engineering (Mashinostroenie, Moscow, 1986) [in Russian].
V. M. Alexandrov and D. A. Pozharskii, Three-Dimensional Contact Problems (Kluwer, Dordrecht, 2001).
D. A. Pozharskii, “Contact Problem for a Hollow Cylinder,” Prikl. Mat. Mekh. 81 (6), 727–733 (2017).
E. A. Kuznetsov, “Pressure of a Circular Cylinder on a Half-Space with a Variable Poisson’s Ratio over the Depth,” Izv. Akad. Nauk SSSR, Mekh. Tv. Tela, No. 1, 73–86 (1985).
A. N. Borodachev, “Elastic Equilibrium of an Inhomogeneous Layer over its Thickness,” Prikl. Mekh. 24 (8), 30–35 (1988).
D. A. Pozharskii, “Elastic Equilibrium of an Inhomogeneous Wedge with a Variable Poisson’s Ratio,” Prikl. Mat. Mekh. 80 (5), 614–621 (2016).
M. E. Gurtin, “The Linear Theory of Elasticity,” in Handbuch der Physik, Vol. VIa/2 (Springer-Verlag, Berlin, 1972), pp. 1–296.
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983) [in Russian].
Reference Book on Special Functions, Eds. by M. Abramovits and I. Stigan (Nauka, Moscow, 1979) [in Russian].
B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, New York-London, 1958).
E. I. Grigolyuk and V. M. Tolkachev, Contact Problem of the Theory of Plates and Shells (Mashinostroenie, Moscow, 1980) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.A. Pozharskii, N.B. Zolotov.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 6, pp. 130–138, November-December, 2019.
Rights and permissions
About this article
Cite this article
Pozharskii, D.A., Zolotov, N.B. Contact Problems for Hollow Cylinders Made of an Inhomogeneous Material. J Appl Mech Tech Phy 60, 1088–1095 (2019). https://doi.org/10.1134/S0021894419060142
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894419060142