电邮这篇文章 Solution to contact problem between an elastic body and a rigid base covered with a layer of deformable material
- 作者: Namm R.V1, Tsoy G.I1
-
隶属关系:
- Computing Center of the Far Eastern Branch of the Russian Academy of Sciences
- 期: 卷 65, 编号 8 (2025)
- 页面: 1408–1422
- 栏目: Mathematical physics
- URL: https://bakhtiniada.ru/0044-4669/article/view/308334
- DOI: https://doi.org/10.31857/S0044466925080081
- EDN: https://elibrary.ru/VIZATE
- ID: 308334
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
A contact problem for an elastic body with a base covered with a deformable layer is studied. The layer is rigid-elastic, i.e., it begins to deform when the yield strength is reached and exerts the normal pressure on the body, which depends on the penetration of the body into the layer. For the rigid base, the Signorini condition is used. The existence of a solution to the problem is proved using weak Schauder’s fixed-point theorem. The results of numerical simulation using the finite element method are presented.
作者简介
R. Namm
Computing Center of the Far Eastern Branch of the Russian Academy of Sciences
Email: rnamm@yandex.ru
Khabarovsk, Russia
G. Tsoy
Computing Center of the Far Eastern Branch of the Russian Academy of Sciences
Email: tsoy.dv@mail.ru
Khabarovsk, Russia
参考
- Hlavacek I., Haslinger J., Necas I., Lovishek J. Solution of variational inequalities in mechanics. 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.
- Kravchuk A.S., Neittaanmaki P.J. Variational and quasi-variational inequalities in mechanics. Dordrecht: Springer, 2007.
- Dostal Z., Kozubek T., Sadowska M., Vondrak V. Scalable algorithms for contact problems. Cham: Springer, 2023.
- Glowinski R. Numerical methods for nonlinear variational problems. New York: Springer, 1984.
- Tremolieres R., Lions J.-L., Glowinski R. Numerical analysis of variational inequalities. Amsterdam: North-Holland, 1981.
- Haslinger J., Kucera 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.
- Haslinger J., Kucera 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.
- Namm R.V., Tsoy G.I. Duality analysis of the frictionless contact problem between linear elastic body and rigid-plastic foundation // Siberian Electronic Math. Rep. 2025. V. 22. №1. P. 274–293.
- Sofonea M., Migorski S. Variational-Hemivariational inequalities with applications. New York: Chapman & Hall, 2017.
- Sofonea M., Shillor M. Tykhonov well-posedness and convergence results for contact problems with unilateral constraints // Technologies. 2021. V. 9. №1. P. 1–25.
- 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. A modified duality scheme for solving a 3D elastic problem with a crack // Commun. Comput. Inf. Sci. 2019. V. 1090. P. 536–547.
- 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.
- 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.
- 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.
- Намм Р.В., Цой Г.И. Метод двойственности для решения 3D контактной задачи с трением // Ж. вычисл. матем. и матем. физ. 2023. Т. 63. №7. С. 1225–1237.
- Golikov A.I., Evtushenko Yu.G. Generalized Newton's method for linear optimization problems with inequality constraints // Proc. Steklov Inst. Math. 2014. V. 284. P. 96–107.
- Mangasarian O.L. A generalized Newton method for absolute value equations // Optim. Lett. 2009. V. 3. P. 101–108.
- Bertsekas D.P. Constrained optimization and Lagrange multiplier methods. Nashua: Athena Scientific, 1996.
- Namm R.V., Woo G.-S., Xie S.-S., Yi S.-C. Solution of semicoercive Signorini problem based on a duality scheme with modified Lagrangian functional // J. Korean Math. Soc. 2012. V. 49. №4. P. 843–854.
- 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. Сер. 1: Организация и методика информационной работы. 2017. №12. C. 14–16.
补充文件
