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Displaying 101 – 120 of 141

Residual a posteriori error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.

Résumé d'une Conférence sur la théorie mathématique de l'élasticité, faite aux élèves de l'École Polytechnique (promotion de 1877-1879).

Resal, H. (1879)

Journal de Mathématiques Pures et Appliquées

Shape and topological sensitivity analysis in domains with cracks

Alexander Khludnev, Jan Sokołowski, Katarzyna Szulc (2010)

Applications of Mathematics

The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...

Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin (2009)

Mathematical Modelling of Natural Phenomena

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

Singularity problems in linear elastodynamics

Bruno Carbonaro, Remigio Russo (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Small amplitude homogenization applied to models of non-periodic fibrous materials

David Manceau (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.

Solvability and asymptotics of solutions of crack-type boundary-contact problems of the ocuple-stress elasticity.

Chkadua, O. (2003)

Georgian Mathematical Journal

Some qualitative problems of the linear elasticity theory.

Gachechiladze, Roland, Maisaia, Otar (1998)

Memoirs on Differential Equations and Mathematical Physics

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

Martin Balazovjech, Miloslav Feistauer, Jaromír Horáček, Martin Hadrava, Adam Kosík (2018)

Applications of Mathematics

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic...

Spectral estimates of vibration frequencies of anisotropic beams

Luca Sabatini (2023)

Applications of Mathematics

The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.

Stabilisation exponentielle d’une équation des poutres d’Euler-Bernoulli à coefficients variables

My Driss Aouragh, Naji Yebari (2009)

Annales mathématiques Blaise Pascal

Dans ce travail, nous étudions la propriété de base de Riesz et la stabilisation exponentielle pour une équation des poutres d’Euler-Bernoulli à coefficients variables sous un contrôle frontière linéaire dépendant de la position (resp. l’angle de rotation), de la vitesse et de la vitesse de rotation dans le contrôle force (resp. moment). Nous montrons qu’il existe une suite de fonctions propres généralisées qui forme une base de Riesz de l’espace d’énergie considéré, et qu’il y a stabilité exponentielle...

Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions

Hang Yu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µin three dimensions, $div (μ (\nabla u + \nabla u^{t})) + \nabla (λ div u) + V u = 0$ whereλ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.

Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions*

Hang Yu (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µ in three dimensions, $div (μ (\nabla u + \nabla u^{t})) + \nabla (λ div u) + V u = 0$ where λ and μ are Lipschitz continuous and V∈L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.

Sul problema di contatto tra piastre

Aldo Maceri (1992)

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

Si studia il problema di contatto tra due piastre sottili linearmente elastiche, incastrate al bordo, poste inizialmente a distanza $δ$ e trasversalmente caricate. Si fa l'ipotesi che il contatto tra le due piastre, a deformazione avvenuta, sia privo di attrito. Il problema dell'equilibrio elastico è formulato per via variazionale in termini di lavori virtuali o, equivalentemente, di minimo del funzionale dell'energia. Il quadro analitico di riferimento è quello della teoria delle disequazioni variazionali...