An elementary exclusion principle for Michell trusses

Ross Granowski

doi:10.1016/j.crma.2012.10.030

Calculus of Variations

An elementary exclusion principle for Michell trusses
[Un principle elémentaire dʼexclusion pour les treillis de Michell]

Présenté par : Étienne Ghys

Ross Granowski ¹

¹ School of Mathematics, Georgia Institute of Technology, 686, Cherry Street, Atlanta, GA 30332-0160, USA

Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 991-995.

Résumé
Abstract

Nous étendons le principe dʼexclusion des treillis de Michell énoncé dans Figueraoa et al. (2012) [2], à des structures obtenues par supperposition dʼun nombre dénombrable de barres. De plus, notre principle dʼexclusion sʼapplique en tout point de la structure à analyser.

The exclusion optimality principle for Michell trusses established in Figueraoa et al. (2012) [2] is extended to frames which consist of countably many bars or rods. Furthermore, our extended exclusion principle can be applied to any point of the support of the frame under analysis.

Reçu le : 2012-08-30
Accepté le : 2012-10-29
Publié le : 2012-11-01

DOI : 10.1016/j.crma.2012.10.030

Affiliations des auteurs :

Ross Granowski ¹

¹ School of Mathematics, Georgia Institute of Technology, 686, Cherry Street, Atlanta, GA 30332-0160, USA

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Ross Granowski. An elementary exclusion principle for Michell trusses. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 991-995. doi : 10.1016/j.crma.2012.10.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.030/

Bibliographie
Cité par

[1] G. Bouchitté; W. Gangbo; P. Seppecher Michell trusses and lines of principal action, Mathematical Models and Methods in Applied Sciences, Volume 18 (2008) no. 9, pp. 1571-1603

[2] E. Figueraoa; A. Hill; D. Lusco; R. Ryham Cutting corners in Michell trusses, Portugalie Mathematica, Volume 69 (2012) no. 2, pp. 95-112

[3] W. Gangbo Discrete decomposition of discrete forces, 2011 www.math.gatech.edu/~gangbo/ (unpublished lecture notes, cf.)

[4] A.G. Michell The limits of economy of material in framed-structures, Philosophical Magazine Ser. 6, Volume 8 (1904), pp. 589-597

[5] R. Skelton; M. de Oliveira Optimal tensegrity structures in bending: The discrete Michell truss, Journal of Franklin Institute, Volume 347 (2010), pp. 257-283

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