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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 12, Pages 2195–2211 (Mi zvmmf74)  

This article is cited in 2 scientific papers (total in 2 papers)

Hertzian contact problem: Numerical reduction and volumetric modification

E. B. Aleksandrova, V. G. Vil'keb, I. I. Kosenkoa

a Russian State University of Tourism and Service, Cherkizovo-1, Moscow oblast, 141221, Russia
b Moscow State University, Moscow, 119992, Russia

Abstract: A technique for the analytical formulation and numerical implementation of an elastic contact model for rigid bodies in the framework of the Hertzian contact problem is described. The normal elastic force and the semiaxes of the contact area are computed so that the problem is sequentially reduced to a scalar transcendental equation depending on complete elliptic integrals of the first and second kinds. Based on the classical solution to the Hertzian contact problem, an invariant volumetric force function is proposed that depends on the geometric characteristics of interpenetration of two undeformed bodies. The normal forces computed using the force function agree with results obtained previously for non-Hertzian contact of elastic bodies. As an example, a ball bearing is used to compare the contact dynamics of elastic bodies simulated in the classical Hertzian model and its volumetric modification.

Key words: Hertzian contact model, existence and uniqueness theorem, volumetric contact model, ball bearing model.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:12, 2226–2240

Bibliographic databases:

UDC: 519.634
Received: 18.01.2008
Revised: 23.04.2008

Citation: E. B. Aleksandrov, V. G. Vil'ke, I. I. Kosenko, “Hertzian contact problem: Numerical reduction and volumetric modification”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2195–2211; Comput. Math. Math. Phys., 48:12 (2008), 2226–2240

Citation in format AMSBIB
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\paper Hertzian contact problem: Numerical reduction and volumetric modification
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 48
\issue 12
\pages 2195--2211
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2530574}
\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 12
\pages 2226--2240
\crossref{https://doi.org/10.1134/S0965542508120129}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kosenko I.I., Aleksandrov E.B., “Implementation of the Contensou-Erismann tangent forces model in the Hertz contact problem”, Multibody Syst. Dyn., 24:3 (2010), 281–301  crossref  mathscinet  zmath  isi  elib  scopus
    2. Zobova A.A., “A review of models of distributed dry friction”, Pmm-J. Appl. Math. Mech., 80:2 (2016), 141–148  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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