Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials
type: Item
instance of: scholarly article
title: Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials
zbMATH Open document ID: 0618.73012
DOI: 10.1007/BF00251231
author: Douglas N. Arnold
author: Richard S. Falk
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: (From the authors' abstract.) The authors consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained (compliance tensor is semi- definite), and formulate a simple necessary and sufficient condition for the fundamental boundary value problem to be well-posed. For materials fulfilling the condition, they establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application the authors determine the orthotropic materials for which the fundamental problems are well-posed in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, they derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unkown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 4003597
zbMATH Keywords: equations of linear homogeneous anisotropic elasticity
zbMATH Keywords: internally constrained
zbMATH Keywords: necessary and sufficient condition
zbMATH Keywords: continuous dependence
zbMATH Keywords: displacement
zbMATH Keywords: stress
zbMATH Keywords: elastic moduli
zbMATH Keywords: ellipticity
zbMATH Keywords: orthotropic materials
zbMATH Keywords: well-posed
zbMATH Keywords: Young's moduli
zbMATH Keywords: shear moduli
zbMATH Keywords: Poisson ratios
zbMATH Keywords: unconstrained
zbMATH Keywords: two-dimensional constrained material
zbMATH Keywords: reduction to a single scalar equation
reviewed by: G. Jaiani
MaRDI profile type: Publication
Wikidata QID: Q59039297
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full work available at URL: https://doi.org/10.1007/bf00251231
OpenAlex ID: W2109359973
description: scientific article; zbMATH DE number 4003597