Optimal control of friction coefficient in Signorini contact problems

2021 ◽  
Author(s):  
El‐Hassan Essoufi ◽  
Abderrahim Zafrar
Keyword(s):  
Optimal Control ◽  
Friction Coefficient ◽  
Contact Problems ◽  
Signorini Contact

SET-VALUED PSEUDOMONOTONE MAPS AND DEGENERATE EVOLUTION INCLUSIONS

1999 ◽  
Vol 01 (01) ◽  
pp. 87-123 ◽  
Author(s):  
KENNETH L. KUTTLER ◽  
MEIR SHILLOR
Keyword(s):  
Weak Solution ◽  
Friction Coefficient ◽  
Frictional Contact ◽  
Contact Problems ◽  
Pseudomonotone Operator ◽  
Unique Weak Solution ◽  
Dynamical Models ◽  
Evolution Inclusions ◽  
Theory Of Evolution ◽  
Pseudomonotone Maps

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are [Formula: see text] where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems.We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution.This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.

Analysis of beam contact problems via optimal control theory

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Dewey H. Hodges ◽  
Robert R. Bless
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Contact Problems

Optimal control for antiplane frictional contact problems involving nonlinearly elastic materials of Hencky type

2017 ◽  
Vol 23 (3) ◽  
pp. 308-328 ◽  
Author(s):  
Andaluzia Matei ◽  
Sorin Micu ◽  
Constantin Niţǎ
Keyword(s):  
Optimal Control ◽  
Frictional Contact ◽  
Variational Equation ◽  
Optimal Solution ◽  
Contact Problems ◽  
Point Of View ◽  
Friction Laws ◽  
Convergence Results ◽  
Positive Exponent ◽  
Nonlinearly Elastic

We consider an antiplane contact problem modeling the friction between a nonlinearly elastic body of Hencky type and a rigid foundation. We discuss the well-posedness of the model by considering two friction laws. Firstly, Tresca’s law is used to describe the friction force and leads to a variational inequality. Alternatively, a regularizing power law with a positive exponent r is considered and gives, from the mathematical point of view, a variational equation. In both contexts, we address a boundary optimal control problem by minimizing, on a nonconvex set, a cost functional with two arguments. We show the existence of at least one optimal pair for each problem. Finally, we deliver some convergence results proving that the optimal solution of the regular problem tends, when r goes to zero, to an optimal solution of the first one.

Optimal control of static contact in finite strain elasticity

2020 ◽  
Vol 26 ◽  
pp. 95
Author(s):  
Anton Schiela ◽  
Matthias Stoecklein
Keyword(s):  
Optimal Control ◽  
Finite Strain ◽  
Path Following ◽  
Contact Problems ◽  
Finite Deformations ◽  
Elastic Contact ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Static Contact ◽  
Convergence Of Sequences

We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

Analytical Models for the Deformation and Adhesion Components of Rubber Friction

1978 ◽  
Vol 6 (1) ◽  
pp. 3-47 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Friction Coefficient ◽  
Solution Method ◽  
Complex Modulus ◽  
Contact Problems ◽  
Analytical Models ◽  
Exact Results ◽  
Fourier Methods ◽  
Rubber Friction ◽  
Linear Viscoelastic ◽  
Deformation Component

Abstract Fourier methods of analysis are employed to develop linear viscoelastic stress and displacement solutions for use in contact problems, and then some exact results for contact area and the deformation component of the friction coefficient are derived for materials whose complex modulus obeys a power law in frequency. A model for predicting waves of detachment resulting from adhesion is proposed, and it is shown that an analogy exists whereby the solution method for sliding without adhesion can be used to predict these waves and the resulting frictional force.

Sign in / Sign up

Export Citation Format

Share Document