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Displaying 81 –
100 of
221
We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems...
In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformable
obstacle. The beam is assumed to be situated horizontally and to move, in both horizontal and
tangential directions, by the effect of applied forces. The left end of the beam is clamped
and the right one is free. Its horizontal displacement is constrained because of the presence
of a deformable obstacle, the so-called foundation, which is modelled by a normal compliance contact condition.
The effect...
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl. 2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class . However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational Mech....
A simple dynamical problem involving unilateral contact and dry friction of Coulomb
type is considered as an archetype. We are concerned with the existence and uniqueness of
solutions of the system with Cauchy data. In the frictionless case, it is known
[Schatzman, Nonlinear Anal. Theory, Methods Appl.2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class
C∞. However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational...
We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction
and adhesion on a part of his boundary. After discretizing the variational formulation with respect
to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting
technique enables us to obtain the existence of incremental solutions with bounds independent of the
regularization parameter. We finally obtain the existence of a quasistatic solution...
A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.
The plane Signorini problem is considered in the cases, when there exist non-trivial rigid admissible displacements. The existence and uniqueness of the solution and the convergence of piecewise linear finite element approximations is discussed.
The purpose of this paper is to derive and study a new asymptotic
model for the equilibrium state of a thin anisotropic
piezoelectric plate in frictional contact with a rigid obstacle.
In the asymptotic process, the thickness of the piezoelectric
plate is driven to zero and the convergence of the unknowns is
studied. This leads to two-dimensional Kirchhoff-Love plate
equations, in which mechanical displacement and electric potential
are partly decoupled. Based on this model numerical examples are
presented...
The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion which...
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. We deduce that...
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...
The 2D-Signorini contact problem with Tresca and Coulomb friction
is discussed in infinite-dimensional Hilbert spaces. First, the
problem with given friction (Tresca friction) is considered. It
leads to a constraint non-differentiable minimization problem. By
means of the Fenchel duality theorem this problem can be transformed
into a constrained minimization involving a smooth functional. A
regularization technique for the dual problem motivated by augmented
Lagrangians allows to apply an...
Currently displaying 81 –
100 of
221