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Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Karl Kunisch, Georg Stadler (2005)

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

The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Karl Kunisch, Georg Stadler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an...

Global asymptotic stabilisation of an active mass damper for a flexible beam

Laura Menini, Antonio Tornambè, Luca Zaccarian (1999)

Kybernetika

In this paper, a finite dimensional approximated model of a mechanical system constituted by a vertical heavy flexible beam with lumped masses placed along the beam and a mobile mass located at the tip, is proposed; such a model is parametric in the approximation order, so that a prescribed accuracy in the representation of the actual system can be easily obtained with the proposed model. The system itself can be understood as a simple representation of a building subject to transverse vibrations,...

Homogenization of many-body structures subject to large deformations

Philipp Emanuel Stelzig (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an initial brittle bond with their neighbors. Noninterpenetration...

Homogenization of many-body structures subject to large deformations

Philipp Emanuel Stelzig (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an...

Il problema monolaterale di contatto dinamico con attrito di una trave su una fondazione alla Hetényi: un approccio agli elementi finiti

Luigi Ascione, Giancarlo Bilotti (1988)

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

L'ipotesi di contatto monolaterale tra strutture di fondazione e terreno assume un significato importante in tutti quei problemi tecnici, nei quali l'area di contatto tra struttura e fondazione diviene percentualmente piccola, sia per la rigidezza relativa dei corpi a contatto, sia per la condizione di carico, soprattutto in presenza di carichi ribaltanti come possono adesempio essere le forze sismiche. In questo contesto sono stati sviluppati negli ultimi anni diversi studi, che riguadano però...

Ingham type theorems and applications to control theory

Claudio Baiocchi, Vilmos Komornik, Paola Loreti (1999)

Bollettino dell'Unione Matematica Italiana

Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.

Iteratively solving a kind of Signorini transmission problem in a unbounded domain

Qiya Hu, Dehao Yu (2005)

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

In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...

Iteratively solving a kind of signorini transmission problem in a unbounded domain

Qiya Hu, Dehao Yu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...

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