The Influence of Lateral Boundary Conditions on the Asymptotics in Thin Elastic Plates

DOI10.1137/S0036141098333025zbMath0958.74034MaRDI QIDQ4943682

Isabelle Gruais, Monique Dauge, Andreas Rössle

Publication date: 19 March 2000

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

singular perturbationlinear elasticityvariational formulationboundary layersoptimal error estimatesKirchhoff-Love plate theorymembrane equationslateral boundary conditionsvanishing thicknessinfinite asymptotic expansionthree-dimensional plate theory

Mathematics Subject Classification ID

Related Items (24)

Uniform Elliptic Estimate for an Infinite Plate in Linear Elasticity ⋮ Asymptotically correct boundary conditions for the higher-order theory of plate bending ⋮ KOITER ESTIMATE REVISITED ⋮ Full weak uniqueness in anisotropic time-dependent Mindlin theory for plates ⋮ On the generalization of Reissner plate theory to laminated plates. I: Theory ⋮ A posteriori boundary layer detection and resolution in \textit{hpq}-adaptive finite element methods for 3D-based hierarchical plate and shell models ⋮ On singularities of solution of the elasticity system in a bounded domain with angular corner points ⋮ Higher-order responses of three-dimensional elastic plate structures and their numerical illustration byp-FEM ⋮ Approximation of thin three-dimensional plates with smooth lateral surface by polygonal plates ⋮ Finite element approximations of the Lamé system with penalized ideal contact boundary conditions ⋮ 3D-based hierarchical models and \(hpq\)-approximations for adaptive finite element method of Laplace problems as exemplified by linear dielectricity ⋮ Homogenization of Kirchhoff plates with oscillating edges and point supports ⋮ Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. I: Hierarchical modeling and approximations ⋮ Edge layers in thin elastic plates ⋮ The asymptotics of natural oscillations of a long two-dimensional Kirchhoff plate with variable cross-section ⋮ Interior estimates with optimal regularity for a plate model in linear elasticity ⋮ Asymptotic Estimates of Hierarchical Modeling ⋮ Multiscale Expansions for Linear Clamped Elliptic Shells ⋮ Analysis of boundary layer effects due to usual boundary conditions or geometrical defects in elastic plates under bending: an improvement of the Love-Kirchhoff model ⋮ hp-FEM for three-dimensional elastic plates ⋮ HIERARCHICAL MODELING BASED ON MIXED PRINCIPLES: ASYMPTOTIC ERROR ESTIMATES ⋮ AN IMPROVED BIHARMONIC MODEL: INCORPORATING HIGHER-ORDER RESPONSES OF THE PLATE BENDING PHENOMENA ⋮ A criterion for the existence of the essential spectrum for beak-shaped elastic bodies ⋮ On the accuracy of Reissner–Mindlin plate model for stress boundary conditions

This page was built for publication: The Influence of Lateral Boundary Conditions on the Asymptotics in Thin Elastic Plates