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

作者: Namm R.V.¹, Tsoy G.I.¹
隶属关系:
1. Computing Center, Far Eastern Branch, Russian Academy of Sciences
期: 卷 63, 编号 7 (2023)
页面: 1225-1237
栏目: Mathematical physics
URL: https://rjonco.com/0044-4669/article/view/665021
DOI: https://doi.org/10.31857/S0044466923070104
EDN: https://elibrary.ru/ZXTRJO
ID: 665021

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详细

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.

关键词

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

作者简介

R. Namm

Computing Center, Far Eastern Branch, Russian Academy of Sciences

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

G. Tsoy

Computing Center, Far Eastern Branch, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: tsoy.dv@mail.ru
680000, Khabarovsk, Russia

参考

Hlavaček I., Haslinger Ya., Nečas I., Lovišhek Ya. Numerical solution of variational inequalities. New York: Springer-Verlag, 1988.
Kikuchi N., Oden J.T. Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia: SIAM, 1988.
Namm R., Tsoy G. A modified duality scheme for solving a 3D elastic problem with a crack // Commun. Comput. Inf. Sci. 2019. V. 1090. P. 536–547.
Намм Р.В., Цой Г.И. Модифицированная схема двойственности для решения упругой задачи с трещиной // Сиб. журн. вычисл. матем. 2017. Т. 20. № 1. С. 47–58.
Namm R., Tsoy G. Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces // Open Comput. Sci. 2020. V. 10. № 1. P. 276–282.
Вихтенко Э.М., Намм Р.В. Схема двойственности для решения полукоэрцитивной задачи Синьорини с трением // Ж. вычисл. матем. и матем. физ. 2007. Т. 47. № 12. С. 2023–2036.
Namm R., Tsoy G., Vikhtenko E., Woo G. Variational method for solving contact problem of elasticity // CEUR Workshop Proc. 2021. V. 2930. P. 98–105.
Вихтенко Э.М., Максимова Н.Н., Намм Р.В. Функционалы чувствительности в вариационных неравенствах механики и их приложение к схемам двойственности // Сиб. журн. вычисл. матем. 2014. Т. 17. № 1. С. 43–52.
Haslinger J., Kučera R., Dostal Z. An algorithm for the numerical realization of 3D contact problems with Coulomb friction // J. Comput. Appl. Math. 2004. V. 164–165. P. 387–408.
Kravchuk A.S., Neittaanmäki P.J. Variational and quasi-variational inequalities in mechanics. Dordrecht: Springer, 2007.
Haslinger J., Kučera R., Vlach O., Baniotopoulos C.C. Approximation and numerical realization of 3D quasistatic contact problems with Coulomb friction // Math. Comput. Simul. 2012. V. 82. P. 1936–1951.
Glowinski R. Numerical methods for nonlinear variational problems. New York: Springer, 1984.
Trémolières R., Lions J.-L., Glowinski R. Numerical analysis of variational inequalities. Amsterdam: North-Holland, 1981.
Namm R.V., Tsoy G.I. Solution of the static contact problem with Coulomb friction between an elastic body and a rigid foundation // J. Comput. Appl. Math. 2023. V. 419. P. 114725.
Beck A., Teboulle M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems // SIAM J. Imaging Sciences. 2009. V. 2. P. 183–202.
Gustafsson T., McBain G.D. scikit-fem: A Python package for finite element assembly // J. Open Source Softw. 2020. V. 5. № 5. P. 2369.
Сорокин А.А., Макогонов С.В., Королев С.П. Информационная инфраструктура для коллективной работы ученых Дальнего Востока России // Научно-техническая информация. Серия 1: Организация и методика информационной работы. 2017. № 12. С. 14–16.