Duality Method for Solving 3D Contact Problems with Friction

R. V. Namm; Намм Р. В.; G. I. Tsoy; Цой Г. И.

doi:10.31857/S0044466923070104

Duality Method for Solving 3D Contact Problems with Friction

Authors: Namm R.V.¹, Tsoy G.I.¹
Affiliations:
1. Computing Center, Far Eastern Branch, Russian Academy of Sciences
Issue: Vol 63, No 7 (2023)
Pages: 1225-1237
Section: МАТЕМАТИЧЕСКАЯ ФИЗИКА
URL: https://journals.rcsi.science/0044-4669/article/view/136208
DOI: https://doi.org/10.31857/S0044466923070104
EDN: https://elibrary.ru/ZXTRJO
ID: 136208

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Abstract
About the authors
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Abstract

The article studies a 3D contact problem with Coulomb friction for an elastic body resting on a rigid support. The solution of the quasi-variational formulation of the problem is defined as a fixed point of some mapping that associates the given force of the normal reaction of the support with the value of the normal stress in the contact zone. The fixed point is sought by the method of successive approximations, the convergence of which is proved using modified Lagrange functionals. The results of the numerical solution using finite element modeling and the proximal gradient method are presented.

Keywords

elastic body, friction force, nonlinear boundary conditions, modified Lagrange functional, fixed point

About the authors

R. V. Namm

Computing Center, Far Eastern Branch, Russian Academy of Sciences

Email: rnamm@yandex.ru
680000, Khabarovsk, Russia

G. I. Tsoy

Computing Center, Far Eastern Branch, Russian Academy of Sciences

Author for correspondence.
Email: tsoy.dv@mail.ru
680000, Khabarovsk, Russia

References

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