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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 2, Pages 306–327 (Mi vsgtu1471)

Mechanics of Solids

A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

Yu. M. Streliaiev

Zaporizhzhya National University, Zaporizhzhya, 69600, Ukraine

Abstract: Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

Keywords: elastic body, contact problem, Coulomb friction, quasistatic problem, integral equation, uniqueness of solution, regularizing equation, iterative process

DOI: https://doi.org/10.14498/vsgtu1471

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Bibliographic databases:

UDC: 539.3
MSC: 74M15, 74M10
Original article submitted 24/I/2016
revision submitted – 27/IV/2016

Citation: Yu. M. Streliaiev, “A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:2 (2016), 306–327

Citation in format AMSBIB
\Bibitem{Str16} \by Yu.~M.~Streliaiev \paper A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2016 \vol 20 \issue 2 \pages 306--327 \mathnet{http://mi.mathnet.ru/vsgtu1471} \crossref{https://doi.org/10.14498/vsgtu1471} \zmath{https://zbmath.org/?q=an:06964489} \elib{http://elibrary.ru/item.asp?id=27126244}