On the mathematical foundation of the \((1,1,2)\)-plate model
type: Item
instance of: scholarly article
title: On the mathematical foundation of the \((1,1,2)\)-plate model
zbMATH Open document ID: 0962.74036
DOI: 10.1016/S0020-7683(98)00071-7
published in: International Journal of Solids and Structures
publication date: 2001-05-28T00:00:00Z
review text: This paper considers the plate problem in three-dimensional linear elastostatics in the framework of hierarchical modelling with the help of the energy projection method. In particular, the so-called \((1,1,2)\)-bending model is discussed with emphasis on the applicability of unmodified three-dimensional material laws. It is shown that in some sense the \((1,1,2)\)-bending model is the simplest asymptotically correct model in the hierarchical family. The authors present error estimates for the deviation of the \((1,1,2)\)-solution from the Kirchhoff solution as well as from the three-dimensional solution. The results are illustrated by a numerical example.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74G10
zbMATH DE Number: 1342473
zbMATH Keywords: three-dimensional linear elastostatics
zbMATH Keywords: energy projection method
zbMATH Keywords: polynomial approximation
zbMATH Keywords: \((1,1,2)\)-bending model
zbMATH Keywords: three-dimensional material laws
zbMATH Keywords: asymptotically correct model
zbMATH Keywords: Kirchhoff solution
author: Andreas Rössle
author: M. Bischoff
author: W. L. Wendland
author: E. Ramm
reviewed by: Wilfried Becker
MaRDI profile type: Publication
full work available at URL: s0020-7683(98)00071-7
OpenAlex ID: W1972651902
Wikidata QID: Q127754038
description: scientific article; zbMATH DE number 1342473