Comparing hinged and supported rectangular plates

Athanasios Stylianou; Guido Sweers

doi:10.1016/j.crme.2010.08.002

Comparing hinged and supported rectangular plates
[Comparaison d'une plaque rectangulaire simplement appuyée et d'une plaque charnière]

Athanasios Stylianou ¹ ; Guido Sweers ¹

¹ Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Cologne, Germany

Comptes Rendus. Mécanique, Volume 338 (2010) no. 9, pp. 489-492.

Résumé
Abstract

On considère le modèle de Kirchhoff–Love pour des plaques minces simplement appuyées, c'est à dire l'équation aux dérivées partielles du quatrième ordre $Δ^{2} u = f ⩽ 0$ sur une domaine borné Ω de dimension deux avec la condition $u_{| \partial Ω} ⩾ 0$ et supplementée avec les conditions naturelles. Nous démontrons que la solution de ce problème n'est pas identique à la solution d'une plaque charnière dans le cas où cette plaque est rectangulaire. Dans cet dernier cas, les conditions de bord sont $u = Δ u = 0$ .

We consider the Kirchhoff–Love model for the supported plate, that is, the fourth order differential equation $Δ^{2} u = f ⩽ 0$ in a two-dimensional bounded domain Ω with the condition $u_{| \partial Ω} ⩾ 0$ and supplemented with natural boundary conditions. We show that the solution differs from the solution of the hinged plate problem, that is, the bi-Laplace equation with $u = Δ u = 0$ on the boundary, in the case of a rectangular domain.

Reçu le : 2010-05-16
Accepté le : 2010-08-16
Publié le : 2010-09-01

DOI : 10.1016/j.crme.2010.08.002

Keywords: Analytical mechanics, Plates, Supported plate, Hinged plate, Unilateral boundary conditions, Variational inequality, Boundary obstacle
Mots-clés : Mécanique analytique, Plaques, Plaque simplement appuyé, Plaque charnière, Inégalité variationelle, Condition au bord unilatérale

Affiliations des auteurs :

Athanasios Stylianou ¹ ; Guido Sweers ¹

¹ Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Cologne, Germany

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Athanasios Stylianou; Guido Sweers. Comparing hinged and supported rectangular plates. Comptes Rendus. Mécanique, Volume 338 (2010) no. 9, pp. 489-492. doi : 10.1016/j.crme.2010.08.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.08.002/

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Guido Sweers On Sign Preservation for Clotheslines, Curtain Rods, Elastic Membranes and Thin Plates, Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 118 (2016) no. 4, p. 275 | DOI:10.1365/s13291-016-0147-0
Sergey A. Nazarov; Athanasios Stylianou; Guido Sweers Hinged and supported plates with corners, Zeitschrift für angewandte Mathematik und Physik, Volume 63 (2012) no. 5, p. 929 | DOI:10.1007/s00033-012-0195-y
S. A. Nazarov; G. Sweers; A. Stylianou Paradoxes in problems on bending of polygonal plates with a hinged/supported edge, Doklady Physics, Volume 56 (2011) no. 8, p. 439 | DOI:10.1134/s1028335811080027

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