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Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*

C. Pozzolini, M. Salaun (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam...

Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*

C. Pozzolini, M. Salaun (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam...

Some estimates for the oscillation of the deformation gradient

Vratislava Mošová (2000)

Applications of Mathematics

As a measure of deformation we can take the difference D φ → - R , where D φ → is the deformation gradient of the mapping φ → and R is the deformation gradient of the mapping γ → , which represents some proper rigid motion. In this article, the norm ∥ D φ → - R ∥ L p ( Ω ) is estimated by means of the scalar measure e ( φ → ) of nonlinear strain. First, the estimates are given for a deformation φ → ∈ W 1 , p ( Ω ) satisfying the condition φ → | ∂ Ω = id → . Then we deduce the estimate in the case that φ → ( x ) is a bi-Lipschitzian deformation and φ → | ∂ Ω ≠ id → .

Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics

Frédéric Feyel (2002)

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

A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.

Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics

Frédéric Feyel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.

Some qualitative results for the linear theory of binary mixtures of thermoelastic solids.

F. Martínez, R. Quintanilla (1995)

Collectanea Mathematica

In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.

Some regularity results for minimal crystals

L. Ambrosio, M. Novaga, E. Paolini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( i . e . a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is ℋ 1 -negligible and is empty...

Some regularity results for minimal crystals

L. Ambrosio, M. Novaga, E. Paolini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space (i.e. a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is ℋ 1 -negligible and is...

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