Advanced Studies in Pure Mathematics

Analysis of an evolutionary variational inequality arising in elasticity quasi-static contact problems

Nicolae Pop

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Abstract

In this paper, we present the strong and the variational form of a dynamic contact problem with friction. We derive the result and obtain an incremental formulation by space discretization with finite element method and by time discretization with finite difference method of the dynamic contact problem. As well we describe the solution strategies for spatially discrete system and the condition for stability of the solution. Difficulties caused by the discontinuity of the Coulomb's friction law (passage from sliding to adhesion), are tried to be passed over using the Newton-Raphson iterative techniques, and their success depends also on the small value of the parameter, from the regularized friction law.

Article information

Source
Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 225-235

Dates
Received: 26 December 2006
Revised: 12 October 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447657

Digital Object Identifier
doi:10.2969/aspm/05310225

Mathematical Reviews number (MathSciNet)
MR2582421

Zentralblatt MATH identifier
05608565

Subjects
Primary: 74S05: Finite element methods 74M10: Friction 74M15: Contact 74H15: Numerical approximation of solutions 74H30: Regularity of solutions 39A11

Keywords
Unilateral contact problem dry friction laws finite element method finite difference method Newmark algorithm Newton-Raphson method

Citation

Pop, Nicolae. Analysis of an evolutionary variational inequality arising in elasticity quasi-static contact problems. Advances in Discrete Dynamical Systems, 225--235, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05310225. https://projecteuclid.org/euclid.aspm/1543447657


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