Asymptotic Analysis of Linearly Elastic Flexural Shells Subjected to an Obstacle in Absence of Friction

Piersanti, Paolo

doi:10.1007/s00332-023-09916-y

Cited by 3 publications

(3 citation statements)

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“…It can be shown, in the same fashion as [8,21], that the operator β is monotone, bounded and non-expansive. Lemma 2.1.…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 88%

“…The notation for differential geometry and functional analysis used in this article is drawn from the monographs [1] or [2]. For related references on the topic, we also refer to [3][4][5][6][7][8][9][10][11].…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 99%

“…For the second batch of the numerical experiments, we consider once again the mesh size 0 < ℎ << 1, we couple κ with ε in the same fashion as [8] and we let ε 0. The numerical results…”

Section: (A) Example 1: Cylindrical Shellsmentioning

confidence: 99%

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On the numerical corroboration of an obstacle problem for linearly elastic flexural shells

Peng,

Piersanti,

Shen

2024

Phil. Trans. R. Soc. A.

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In this article, we study the numerical corroboration of a variational model governed by a fourth-order elliptic operator that describes the deformation of a linearly elastic flexural shell subjected not to cross a prescribed flat obstacle. The problem under consideration is modelled by means of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Sobolev space and is known to admit a unique solution. Qualitative and quantitative numerical experiments corroborating the validity of the model and its asymptotic similarity with Koiter’s model are also presented. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.

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“…It can be shown, in the same fashion as [8,21], that the operator β is monotone, bounded and non-expansive. Lemma 2.1.…”

Section: Penalty Methods For Flexural Shell Modelmentioning

confidence: 88%