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Keywords = unilateral quasistatic contact problem

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10 pages, 297 KiB  
Article
An Approximation of Solutions for the Problem with Quasistatic Contact in the Case of Dry Friction
by Nicolae Pop, Miorita Ungureanu and Adrian I. Pop
Mathematics 2021, 9(8), 904; https://doi.org/10.3390/math9080904 - 19 Apr 2021
Cited by 5 | Viewed by 2956
Abstract
In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get [...] Read more.
In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get the necessary optimality conditions, we use some regularization techniques, and this leads us to a problem of control for an inequality of the variational type. The optimal control problem consists, in our case, of minimizing a sequence of optimal control problems, where the control variable is given by a Neumann-type boundary condition. The state system is represented by a limit of a sequence, whose terms are obtained from the discretization, in time with finite difference and space with the finite element method of a regularized quasistatic contact problem with Coulomb friction. The purpose of this optimal control problem is that the traction force (the control variable) acting on one side of the boundary (the Neumann boundary condition) of the elastic body produces a displacement field (the state system solution) close enough to the imposed displacement field, and the traction force from the boundary remains small enough. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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