Duality Method for Solving 3D Contact Problems with Friction

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 v...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2023-07, Vol.63 (7), p.1350-1361
Main Authors: Namm, R. V., Tsoy, G. I.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Contact stresses
Coulomb friction
Elastic bodies
Finite element method
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Normal stress
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523070096