Tbilisi Mathematical Journal

A quadrature approach to the generalized frictionless shearing contact problem

Elçin Yusufoğlu and İlkem Turhan Çetinkaya

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this study, the generalization of a frictionless contact problem in case of shearing deformation for an elastic inhomogeneous half space is presented. The basic equations of the elasticity theory and Fourier transform technique are applied to the problem to derive the system of singular integral equations. The obtained system of singular integral equations is solved by a quadrature approach. The numerical results are presented for the case of $N=1$, $N=2$, $N=3$, where $N$ denotes the number of the punches whose base are flat.

Article information

Source
Tbilisi Math. J., Volume 13, Issue 1 (2020), 83-96.

Dates
Received: 24 September 2019
Accepted: 24 December 2019
First available in Project Euclid: 24 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1585015222

Digital Object Identifier
doi:10.32513/tbilisi/1585015222

Subjects
Primary: 45E05: Integral equations with kernels of Cauchy type [See also 35J15]
Secondary: 45F15: Systems of singular linear integral equations 74B05: Classical linear elasticity

Keywords
contact problems elasticity theory integral equations

Citation

Yusufoğlu, Elçin; Turhan Çetinkaya, İlkem. A quadrature approach to the generalized frictionless shearing contact problem. Tbilisi Math. J. 13 (2020), no. 1, 83--96. doi:10.32513/tbilisi/1585015222. https://projecteuclid.org/euclid.tbilisi/1585015222


Export citation

References

  • S.M. Aizikovich, V.M. Aleksandrov, A.V. Belokon, L. Ý Krenev and Ý. S. Trubchik, Contact problems of the theory of elasticity for non-homogeneous medium, Fizmatli (2006) (In Russian).
  • A. Vasiliev, S. Volkov, S. Aizikovich and Y.R. Jeng, Axisymmetric contact problems of the theory of elasticity for inhomogeneous layers, Journal of Applied Mathematics and Mechanics, 94 (9) (2014), 705-712.
  • N.V. Generalova and Ye.V. Kovalenko, The effect of a strip-shaped punch on a linearly deformable foundation strengthened by a thin covering, Journal of Applied Mathematics and Mechanics, 59 (5) (1995), 789-795.
  • B.M. Singh, J. Rokne, R.S. Dhaliwal and J. Vrbik, Contact problem for bonded nonhomogeneous materials under shear loading, International Journal of Mathematics and Mathematical Sciences, 29 (2003), 1821-1832.
  • V. Kahya, A. Birinci and R. Erdol, Frictionless Contact Problem Between Two Orthotropic Elastic Layers, World Academy of Science, Engineering and Technology International Journal of Civil, Architectural Science and Engineering Vol:1 No:1, 2007.
  • A. Torun, A contact problem for nonhomogeneous half plane, Dumlupinar University, Science and technology institute (2015), Kutahya.
  • N.I. Muskheleshvili, Singular Integral Equations, Edited by J.R.M. Rodok, (1997) Noordhoff International publishing Leyden.
  • F. Erdogan, G.D. Gupta and TS. Cook, Numerical solution of singular integral equations. In: Sih GC, editor. Method of analysis and solution of crack problems. Leyden: Noordhoff International Publishing, 1973.
  • V.A. Babeshko, E.V. Glushkov and N.V. Glushkova, Methods for constructing the Green function of a stratified elastic half-space, Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 27 (1) (1987), 93-101.
  • V.M. Aleksandrov, B.I. Smetanin and B.V. Sobol, Thin Stress Concentrators in Elastic Solids, Nauka (1993), Moskow.
  • F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quaterly of Applied Mathematics, 30 (1972), 525-534.