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The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.

The role of deviatone and volumetrie non-associativities on strain localization

Ahmed Benallal, Claudia Comi (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A homogeneous solid subject to quasi-static loading in the small strain range is considered. The material model assumed is rate-independent, non-associative and incrementally bilinear. The strain localization conditions are analytically solved using a geometric method. The expressions of the critical hardening moduli, their domains of validity and the form of the strain rate discontinuity are obtained. Finally these results, and in particular the role of hydrostatic and deviatoric non-normality,...

The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...

The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...

The Singularity Expansion Method applied to the transient motions of a floating elastic plate

Christophe Hazard, François Loret (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...

The stability study of a plane engine

Rafał Kołodziej, Tomasz Nowicki (2000)

Applicationes Mathematicae

We study the dynamical properties of a plane engine vibrations modelled by a system of ODE.

The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions

Ivana Pultarová (2005)

Applications of Mathematics

We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...

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