Thin-walled beams: A derivation of Vlassov theory via \(\Gamma\)-convergence

DOI10.1007/s10659-006-9094-9zbMath1107.74029OpenAlexW2027463241MaRDI QIDQ873163

Lorenzo Freddi, Roberto Paroni, Antonino Morassi

Publication date: 28 March 2007

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-006-9094-9

zbMATH Keywords

asymptotic analysislinearly elastic cantilever

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Classical linear elasticity (74B05) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (13)

NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART I ⋮ Thin walled beams with residual stress ⋮ The theory of thin-walled rods of open profile as a result of asymptotic splitting in the problem of deformation of a noncircular cylindrical shell ⋮ Theory of thin thermoelastic rods made of porous materials ⋮ On the theory of porous elastic rods ⋮ Residually stressed beams ⋮ On the Variational Derivation of the Kinematics for Thin-Walled Closed Section Beams ⋮ One-dimensional von Kármán models for elastic ribbons ⋮ On variational dimension reduction in structure mechanics ⋮ NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II ⋮ Asymptotically exact Korn's constant for thin cylindrical domains ⋮ Linear models of a stiffened plate via \(\Gamma \)-convergence ⋮ On Korn’s constant for thin cylindrical domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• On the junction of elastic plates and beams
• On the dependence of the constant in Korn's inequality on parameters characterizing the geometry of the region
• On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity

This page was built for publication: Thin-walled beams: A derivation of Vlassov theory via \(\Gamma\)-convergence