Recursive Derivation of One-Dimensional Models from Three-Dimensional Nonlinear Elasticity

DOI10.1177/1081286506075357zbMath1175.74046OpenAlexW2112952034MaRDI QIDQ3629994

Nicolas Meunier

Publication date: 2 June 2009

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286506075357

zbMATH Keywords

elasticityvariational methodsasymptotic expansionsrodsstrings

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Strings (74K05)

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Cites Work

• Unnamed Item
• Asymptotic behaviour of thin interphases within the large deformation case
• A variational definition of the strain energy for an elastic string
• A justification of a nonlinear model in plate theory
• A justification of nonlinear properly invariant plate theories
• Statics of curved rods on account of torsion and flexion
• Existence of minimizers for non-quasiconvex integrals
• Dérivation des modèles de plaques membranaires non linéaires à partir de l'élasticité tri-dimensionnelle
• The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function
• Nonlinear problems of elasticity