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Shape optimization for dynamic contact problems

Andrzej Myśliński (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.

Shape optimization in contact problems

Haslinger, Jaroslav (1986)

Equadiff 6

Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization

Jaroslav Haslinger, Oldřich Vlach (2005)

Applications of Mathematics

Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.

Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI

Alexandros Markopoulos, Petr Beremlijski, Oldřich Vlach, Marie Sadowská (2023)

Applications of Mathematics

The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the Coulomb friction problem leads to an implicit variational inequality which can be written as a fixed point problem. Furthermore, it is known that the discretized problem is uniquely solvable for small coefficients of friction. Since the considered problem is nonsmooth, we exploit the generalized Mordukhovich’s differential calculus to compute the needed...

Study of a contact problem with normal compliance and nonlocal friction

Arezki Touzaline (2012)

Applicationes Mathematicae

We consider a static frictional contact between a nonlinear elastic body and a foundation. The contact is modelled by a normal compliance condition such that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element...

Study of a viscoelastic frictional contact problem with adhesion

Arezki Touzaline (2011)

Commentationes Mathematicae Universitatis Carolinae

We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...