On variational dimension reduction in structure mechanics

DOI10.1007/s10659-014-9473-6zbMath1305.74016arXiv1305.3170OpenAlexW2053260384MaRDI QIDQ2255565

Roberto Paroni, Paolo Podio-Guidugli

Publication date: 17 February 2015

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

Full work available at URL: https://arxiv.org/abs/1305.3170

zbMATH Keywords

linear elasticitybeam theory\(\Gamma\)-convergenceplate theory

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Classical linear elasticity (74B05) Plates (74K20) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (6)

Quasistatic delamination of sandwich-like Kirchhoff-Love plates ⋮ Pointwise error estimate for a consistent beam theory ⋮ A justification of the Timoshenko beam model through Γ-convergence ⋮ Linear models for thin plates of polymer gels ⋮ On the Kirchhoff-Love hypothesis (Revised and Vindicated) ⋮ On the validation of theories of thin elastic structures

Cites Work

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• An exact derivation of the thin plate equation
• A variational definition of the strain energy for an elastic string
• The Reissner-Mindlin plate theory via \(\Gamma\)-convergence
• Thin-walled beams: A derivation of Vlassov theory via \(\Gamma\)-convergence
• Asymptotic expansions by \(\Gamma \)-convergence
• The general theory of homogenization. A personalized introduction
• Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
• Thin-walled beams: the case of the rectangular cross-section
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• The equations of motion of a plate with residual stress
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• The Passage from Discrete to Continuous Variational Problems: a Nonlinear Homogenization Process
• A JUSTIFICATION OF THE REISSNER–MINDLIN PLATE THEORY THROUGH VARIATIONAL CONVERGENCE
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Validation of Classical Beam and Plate Models by Variational Convergence

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