Singularity theory, rod theory, and symmetry-breaking loads
type: Item
instance of: scholarly article
title: Singularity theory, rod theory, and symmetry-breaking loads
zbMATH Open document ID: 0678.58007
author: John F. Pierce
published in: Lecture Notes in Mathematics
publication date: 1992-09-17T00:00:00Z
review text: The author studies from a mathematically advanced point of view three- dimensional buckling of rods where both the rod geometry and the loading are rotationally symmetric. It is well-known that for such problems after loss of stability not only one equilibrium but a whole orbit of equilibria will be obtained. The main question the author asks is: How is the orbit changed under a perturbation of the loading? For this purpose a nice presentation of the Kirchhoff and Cosserat rod theories in modern mathematical notation is given. The analysis is performed first by reducing the infinite-dimensional problem defined on a function space by means of the Lyapunov-Schmidt-method to one which is defined on a finite-dimensional space and second by application of the concepts of singularity theory. The main result is a classification theorem for certain classes of perturbation of loads for the orbit breaking problem. Finally some comments are made concerning the general imperfection sensitivity problem making use of the concept of unfoldings. The presentation is clear and good to understand. The book should certainly find an interested readership both in the applied mathematics and in the theoretical mechanics community.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 58-02
Mathematics Subject Classification ID: 58D05
zbMATH DE Number: 43043
zbMATH Keywords: bifurcation
zbMATH Keywords: orbit breaking
zbMATH Keywords: Lyapunov-Schmidt
zbMATH Keywords: perturbation
zbMATH Keywords: Kirchhoff
zbMATH Keywords: Cosserat
zbMATH Keywords: unfoldings
reviewed by: Hans Troger
MaRDI profile type: Publication
DOI: 10.1007/BFB0093780
description: scientific article; zbMATH DE number 43043