On the Variational Derivation of the Kinematics for Thin-Walled Closed Section Beams

DOI10.1007/978-1-4020-8774-5_9zbMath1208.74069OpenAlexW2163503153MaRDI QIDQ5390440

Roberto Paroni, Antonino Morassi, Lorenzo Freddi

Publication date: 1 April 2011

Published in: IUTAM Symposium on Relations of Shell Plate Beam and 3D Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4020-8774-5_9

zbMATH Keywords

Young measuresdimension reductionnonlinear elasticityGamma-convergence

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10)

Cites Work

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• A variational definition of the strain energy for an elastic string
• Thin-walled beams: A derivation of Vlassov theory via \(\Gamma\)-convergence
• An introduction to \(\Gamma\)-convergence
• Asymptotic derivation of a general linear model for thin-walled elastic rods
• Thin-walled beams: the case of the rectangular cross-section
• A nonlinear model for inextensible rods as a low energy \(\varGamma\)-limit of three-dimensional nonlinear elasticity
• Torsion of thin tubes: A justification of some classical results
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• Torsion of thin tubes with multicell cross-section
• Asymptotic analysis of Poisson's equation in a thin domain and its application to thin-walled elastic beams and tubes
• An Asymptotic Analysis of the Flexure Problem for Thin Tubes

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