Buckling modes in pantographic lattices

Ivan Giorgio; Alessandro Della Corte; Francesco dell'Isola; David J. Steigmann

doi:10.1016/j.crme.2016.02.009

Buckling modes in pantographic lattices

Ivan Giorgio ^1,² ; Alessandro Della Corte ^3,²; Francesco dell'Isola ^1,²; David J. Steigmann ^4,²

¹ Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, 00184 Roma, Italy
² International Research Center for the Mathematics and Mechanics of Complex Systems, Università dell'Aquila, Italy
³ Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, 00184 Roma, Italy
⁴ Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA

Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 487-501.

Abstract
Résumé

We study buckling patterns in pantographic sheets, regarded as two-dimensional continua consisting of lattices of continuously distributed fibers. The fibers are modeled as beams endowed with elastic resistance to stretching, shearing, bending and twist. Included in the theory is a non-standard elasticity due to geodesic bending of the fibers relative to the lattice surface.

Nous étudions le flambage de milieux continus bidimensionnels. Ces milieux, que nous appelons « feuilles pantographiques », sont constitués par un réseau formé de deux familles orthogonales de fibres parallèles. Ces fibres sont considérées comme des poutres élastiques reliées entre elles à chaque intersection par une liaison pivot. Le modèle bidimensionnel continu utilisé généralise celui des plaques, puisqu'il prend en compte l'énergie élastique liée à la courbure des fibres dans le plan de la structure.

Received: 2015-10-22
Accepted: 2016-02-06
Published online: 2016-04-04

DOI: 10.1016/j.crme.2016.02.009

Keywords: Pantographic structures, Buckling, Second gradient models, Geodesic bending, Non-linear elasticity
Mots-clés : Structures pantographiques, Flambage, Milieux continus du second gradient, Flexion géodésique, Élasticité non linéaire

Author's affiliations:

Ivan Giorgio ^{1, 2}; Alessandro Della Corte ^{3, 2}; Francesco dell'Isola ^{1, 2}; David J. Steigmann ^{4, 2}

¹ Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, 00184 Roma, Italy
² International Research Center for the Mathematics and Mechanics of Complex Systems, Università dell'Aquila, Italy
³ Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, 00184 Roma, Italy
⁴ Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA

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     author = {Ivan Giorgio and Alessandro Della Corte and Francesco dell'Isola and David J. Steigmann},
     title = {Buckling modes in pantographic lattices},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {487--501},
     publisher = {Elsevier},
     volume = {344},
     number = {7},
     year = {2016},
     doi = {10.1016/j.crme.2016.02.009},
     language = {en},
}

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Ivan Giorgio; Alessandro Della Corte; Francesco dell'Isola; David J. Steigmann. Buckling modes in pantographic lattices. Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 487-501. doi : 10.1016/j.crme.2016.02.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.009/

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