Note sur les conditions de résistance d'un tube elliptique, dont l'épaisseur est faible, soumis à l'action d'une pression uniforme intérieure.
Note sur les équations générales de la théorie mathématique de l'élasticité en coordonnées curvilignes
Notes on some recent methods in bifurcation theory
Notes on stresses for manifolds.
Nouvelles propriétés des courbes et relation de dispersion en élasticité linéaire
In the case of an elastic strip we exhibit two properties of dispersion curves λn,n ≥ 1, that were not pointed out previously. We show cases where λ'n(0) = λ''n(0) = λ'''n(0) = 0 and we point out that these curves are not automatically monotoneous on . The non monotonicity was an open question (see [2], for example) and, for the first time, we give a rigourous answer. Recall the characteristic property of the dispersion curves: {λn(p);n ≥ 1} is the set of eigenvalues of Ap, counted with their...
Nouvelles propriétés des courbes et relations de dispersion en élasticité linéaire
Novel procedure to compute a contact zone magnitude of vibrations of two-layered uncoupled plates.
Null controllability of a thermoelastic plate.
Numerical algorithm for the computation of the slip-line field
Numerical analysis and simulations of quasistatic frictionless contact problems
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.
Numerical analysis of a frictionless viscoelastic piezoelectric contact problem
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 scheme...
Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
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 for efficient discretization....
Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids
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 for efficient...
Numerical analysis of a Stokes interface problem based on formulation using the characteristic function
Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates...
Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM
This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc:= . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD)...
Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM*
This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping...
Numerical Analysis of Evolution Problems in Nonlinear Small Strains Elastoviscoplasticity.
Numerical analysis of history-dependent quasivariational inequalities with applications in contact mechanics
A new class of history-dependent quasivariational inequalities was recently studied in [M. Sofonea and A. Matei, History-dependent quasivariational inequalities arising in contact mechanics. Eur. J. Appl. Math. 22 (2011) 471–491]. Existence, uniqueness and regularity results were proved and used in the study of several mathematical models which describe the contact between a deformable body and an obstacle. The aim of this paper is to provide numerical analysis of the quasivariational inequalities...
Numerical analysis of parallel replica dynamics
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by...
Numerical Analysis of the Equations of Small Strains Quasistatic Elastoviscoplasticity.