Giuseppe Creazza, Arturo Natali (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Nei continui bidimensionali isotropi in fase fessurata si dimostra, nella sola ipotesi che le linee di rottura rappresentino univocamente il meccanismo di collasso, la impossibilità di ottenere un moltiplicatore ottimale del carico. La configurazione reale può essere definita considerando anche la capacità deformativa del continuo in esame.
Gérard A. Maugin, Carmine Trimarco (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.
Resal, H. (1879)
Journal de Mathématiques Pures et Appliquées
Maurice Levy (1874)
Bulletin des Sciences Mathématiques et Astronomiques
D. R. J. Chillingworth (1985)
Banach Center Publications
Segev, R. (2000)
Rendiconti del Seminario Matematico
Tark Bouhennache, Yves Dermenjian (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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...
Tark Bouhennache, Yves Dermenjian (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Awrejcewicz, J., Krysko, V.A., Ovsiannikova, O. (2005)
Mathematical Problems in Engineering
Benabdallah, Assia, Naso, Maria Grazia (2002)
Abstract and Applied Analysis
Věra Radochová (1973)
Aplikace matematiky
José Fernández García, Weimin Han, Meir Shillor, Mircea Sofonea (2001)
International Journal of Applied Mathematics and Computer Science
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.
Mikael Barboteu, Jose Ramon Fernández, Youssef Ouafik (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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...
Carsten Carstensen, Petr Plecháč (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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....
Carsten Carstensen, Petr Plecháč (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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...
Yoshiki Sugitani (2017)
Applications of Mathematics
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...
Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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)...
Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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...
D. Blanchard, P. Le Tallec (1987)
Numerische Mathematik
Kamran Kazmi, Mikael Barboteu, Weimin Han, Mircea Sofonea (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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...