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A quadrature approach to the generalized frictionless shearing contact problem. (English) Zbl 1448.74081
Summary: 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.
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74B05 Classical linear elasticity
74S99 Numerical and other methods in solid mechanics
Full Text: DOI Euclid
[1] 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).
[2] 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. · Zbl 1298.74184
[3] 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. · Zbl 0918.73092
[4] 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. · Zbl 1130.74447
[5] 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. · Zbl 1180.74044
[6] A. Torun, A contact problem for nonhomogeneous half plane, Dumlupinar University, Science and technology institute (2015), Kutahya.
[7] N.I. Muskheleshvili, Singular Integral Equations, Edited by J.R.M. Rodok, (1997) Noordhoff International publishing Leyden.
[8] 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. · Zbl 0265.73083
[9] 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. · Zbl 0617.73064
[10] V.M. Aleksandrov, B.I. Smetanin and B.V. Sobol, Thin Stress Concentrators in Elastic Solids, Nauka (1993), Moskow. · Zbl 0805.73013
[11] F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quaterly of Applied Mathematics, 30 (1972), 525-534. · Zbl 0236.65083
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