Displaying similar documents to “Numerical analysis of the quasistatic thermoviscoelastic thermistor problem”

Frictional contact of an anisotropic piezoelectric plate

Isabel N. Figueiredo, Georg Stadler (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Young-measure approximations for elastodynamics with non-monotone stress-strain relations

Carsten Carstensen, Marc Oliver Rieger (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density φ . Their time-evolution leads to a nonlinear wave equation u t t = div S ( D u ) with the non-monotone stress-strain relation S = D φ plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding...

Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices

Iñigo Arregui, José Jesús Cendán, Carlos Parés, Carlos Vázquez (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method...

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

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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.

Stabilization methods in relaxed micromagnetism

Stefan A. Funken, Andreas Prohl (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential u and magnetization 𝐦 . In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming P 1 - ( P 0 ) d -element in d = 2 , 3 spatial dimensions...

Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete...

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids

Carsten Carstensen, Petr Plecháč (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm...

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...