Symmetry and bifurcation in three-dimensional elasticity. II
type: Item
instance of: scholarly article
title: Symmetry and bifurcation in three-dimensional elasticity. II
zbMATH Open document ID: 0536.73010
DOI: 10.1007/BF00963840
author: D. R. J. Chillingworth
author: J. E. Marsden
author: Yieh-Hei Wan
published in: Archive for Rational Mechanics and Analysis
publication date: 1983-01-01T00:00:00Z
review text: [For part I see ibid. 80, 295-331 (1982; Zbl 0509.73018).] Under the physical assumptions that the undeformed state of a body is stress free (i.e., the manifold has an embedding in \({\mathbb{R}}^ 3\) on which the stress function is zero), and that a certain condition is imposed on the energy (the system is strongly elliptic and its linearized theory satisfies the stability condition), the authors continue their investigation on the number of solutions to the partial differential equations of elastostatics and the stability of such solutions, along with their bifurcation diagrams. The treatment is heavily mathematical, but a few examples are given; it is a pity that so few attempts have been made to state or, more dangerously, to paraphrase the mathematical results in the language of engineering. Once again the authors have given a tour de force in their application of mathematics to continuum mechanics.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 74G99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 3852509
zbMATH Keywords: symmetry
zbMATH Keywords: three-dimensional elasticity
zbMATH Keywords: undeformed state
zbMATH Keywords: stress free
zbMATH Keywords: certain condition is imposed on the energy
zbMATH Keywords: number of solutions
zbMATH Keywords: elastostatics
zbMATH Keywords: bifurcation diagrams
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3852509