A stability result concerning the obstacle problem for a plate

Pozzolini, Cédric; Léger, Alain

doi:10.1016/j.matpur.2008.07.005

Cited by 7 publications

(3 citation statements)

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“…The contact reaction˜ n (u) = D 2ũ f is a positive measure, possibly singular, and its support included in the contact zone, denoted ⌦ C . For more details see [31]. The reaction force between the obstacle and the plate can be approximated bỹ…”

Section: Weak Formulation Under Solid Plate Displacements Assumptionsmentioning

confidence: 99%

Nitsche-based models for the unilateral contact of plates

2021

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This paper aims to present different Nitsche-based models for the unilateral contact of plate structures. Our analysis is based on the consideration of Nitsche’s method on a 3D structure with kinematic assumptions of thin or thick plate theories. This approach is compared to that of Gustafsson, Stenberg and Videman which consists of Nitsche’s method applied directly on a 2D plate model. To simplify the presentation, we focus on the contact of an elastic plate with a rigid obstacle. The different approaches are compared numerically in terms of reliability compared to the 3D elastic model. The aim of this paper is to present different Nitsche based models for the unilateral contact of plate structures. Our analysis is based on the consideration of Nitsche’s method on a 3D structure with kinematic assumptions of thin or thick plate theories. This approach is compared to the one of Gustafsson, Stenberg and Videman which consists of Nitsche's method directly applied on a 2D plate model. To simplify the presentation, we focus on the contact of an elastic plate with a rigid obstacle. The different approaches are numerically compared in terms of reliability compared to the 3D elastic model.

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Section: Weak Formulation Under Solid Plate Displacements Assumptionsmentioning

confidence: 99%

Nitsche-based models for the unilateral contact of plates

2021

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“…In the static case, for example, a stability result concerning the obstacle problem for a plate is considered in [PL08].…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions of o.d.e. systems with a lipchitz non linearity

Rousselet¹

2011

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In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider existence and solution with fixed point methods; this method is constructive and provides a numerical algorithm which is under study. We describe the method for a static case example and we address periodic solutions of differential systems arising in the vibration of structures.

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“…In fact, since the seminal work [5], regularity for the obstacle problem for the biharmonic parabolic equation has received less attention than the same issue for the obstacle problem for second-order parabolic equations. The only regularity result regarding the obstacle problem for the biharmonic parabolic equation we are aware of is [15], whereas [6,8,18,19] are devoted to the elliptic analogue. As in [15], we can prove that −ζ(t) is actually a non-negative bounded Radon measure on D for a.e.…”

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confidence: 99%