Displaying similar documents to “Numerical analysis of a frictionless viscoelastic piezoelectric contact problem”

Dynamic frictional contact of a viscoelastic beam

Marco Campo, José R. Fernández, Georgios E. Stavroulakis, Juan M. Viaño (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Mikaël Barboteu, Krzysztof Bartosz, Piotr Kalita (2013)

International Journal of Applied Mathematics and Computer Science

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We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The...

Numerical analysis and simulations of quasistatic frictionless contact problems

José Fernández García, Weimin Han, Meir Shillor, Mircea Sofonea (2001)

International Journal of Applied Mathematics and Computer Science

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A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.

Dynamic contact problems with velocity conditions

Oanh Chau, Viorica Motreanu (2002)

International Journal of Applied Mathematics and Computer Science

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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...

Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

Weimin Han, Mircea Sofonea (1999)

Applicationes Mathematicae

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We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show...

Thick obstacle problems with dynamic adhesive contact

Jeongho Ahn (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...