Asymptotic study of a frictionless contact problem between two elastic bodies

Letoufa, Yassine; Benseridi, Hamid; Dilmi, Mourad

doi:10.22436/jmcs.016.03.04

Cited by 3 publications

(6 citation statements)

References 10 publications

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“…To prove (59), we use those similar steps as in [2,5,[9][10][11], by integrating (46) from 0 to z, and taking into account A i3j3 depending only on x, we obtain…”

Section: Limit Problem and Main Resultsmentioning

confidence: 99%

“…where λ ε , μ ε > 0 are the Lamé coefficients (see [13] pp. 102-103) corresponds to the homogeneous and isotropic case of elastic materials, and has been studied in [2,3,5]. Thus also, the Stokes flow in [11] can be recovered when λ ε tends to 0.…”

Section: Journal Of Function Spacesmentioning

confidence: 99%

“…One of the objectives of this study is to obtain twodimensional equation that allows a reasonable description of the phenomenon occurring in the three-dimensional domain by passing the limit to 0 on the small thickness of the domain (3D). Let us mention for example [1][2][3][4][5][6][7][8] in which the authors worked on the asymptotic behavior for the linearized elasticity system with different boundary conditions. Some problems of Newtonian or non-Newtonian fluids are considered in [9][10][11] where the authors proved a limit problem that gives a distribution of velocity and pressure through the weak form of the Reynolds equation.…”

Section: Introductionmentioning

confidence: 99%

“…See another situation in [4] where the paper concerns asymptotic derivation of frictionless contact models for elastic rods on a foundation with normal compliance. Recently, the authors in [5,12] have proved the asymptotic behavior of a frictionless contact problem between two elastic bodies, when the vertical dimension of the two domain reaches zero. However, all these papers have been only restricted in a homogeneous and isotropic case of elastic materials.…”

Section: Introductionmentioning

confidence: 99%

“…The present work is a follow-up of [2,3,5] to study the heterogeneous and anisotropic situation with Tresca's friction.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Study of the Anisotropic Static Elasticity System in Thin Domain

Letoufa

Boulaaras

Benseridi

et al. 2021

Journal of Function Spaces

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We study the asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin domain of ℝ 3 which has a fixed cross-section in the ℝ 2 plane with Tresca friction condition. The novelty here is that stress tensor has given by the most general form of Hooke’s law for anisotropic materials. We prove the convergence theorems for the transition 3D-2D when one dimension of the domain tends to zero. The necessary mathematical framework and (2D) equation model with a specific weak form of the Reynolds equation are determined. Finally, the properties of solution of the limit problem are given, in which it is confirmed that the limit problem is well defined.

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“…To prove (59), we use those similar steps as in [2,5,[9][10][11], by integrating (46) from 0 to z, and taking into account A i3j3 depending only on x, we obtain…”

Section: Limit Problem and Main Resultsmentioning

confidence: 99%

Section: Journal Of Function Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The present work is a follow-up of [2,3,5] to study the heterogeneous and anisotropic situation with Tresca's friction.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Study of the Anisotropic Static Elasticity System in Thin Domain

Letoufa

Boulaaras

Benseridi

et al. 2021

Journal of Function Spaces

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On the asymptotic study of transmission problem in a thin domain

Benseghir

Benseridi

Dilmi

2018

Journal of Inverse and Ill-Posed Problems

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In this paper, we study the theoretical analysis of a frictionless contact between two general elastic bodies in a stationary regime in a three-dimensional thin domain {\Omega^{\varepsilon}} with Tresca friction law. Firstly, the problem statement and variational formulation are presented. We then obtain the estimates on displacement independently of the parameter ε. Finally, we obtain the main results concerning the limit of a weak problem and its uniqueness.

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Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions

Boudersa¹,

Benseridi²

2022

J. Math. Computer Sci.

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In this paper, we consider the stationary problem in three dimensional thin domain Ω ε with maximal monotone graph and Tresca conditions. In the first step, we present the problem statement and give the variational formulation. We then study the asymptotic behavior when one dimension of the domain tends to zero. In the latter case a specific Reynolds limit equation is obtained and the uniqueness of the displacement of the limit problem are proved.

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Asymptotic study of a frictionless contact problem between two elastic bodies

Cited by 3 publications

References 10 publications

A Study of the Anisotropic Static Elasticity System in Thin Domain

A Study of the Anisotropic Static Elasticity System in Thin Domain

On the asymptotic study of transmission problem in a thin domain

Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions

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