Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Bifurcations in the regularized Ericksen bar model

Grinfeld, M. and Lord, G.J. (2008) Bifurcations in the regularized Ericksen bar model. Journal of Elasticity, 90 (2). pp. 161-173. ISSN 0374-3535

[img]
Preview
PDF (strathprints013398.pdf)
Download (328Kb) | Preview

    Abstract

    We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Muller's conjecture [18] concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of Muller's conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a "loop" structure that characterizes (k, 3k) bifurcations.

    Item type: Article
    ID code: 13398
    Keywords: microstructure, lyapunov–schmidt analysis, ericksen bar model, numerical statistics, elasticity, Probabilities. Mathematical statistics, Mathematics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Mrs Carolynne Westwood
    Date Deposited: 12 Nov 2009 14:58
    Last modified: 16 Mar 2012 19:11
    URI: http://strathprints.strath.ac.uk/id/eprint/13398

    Actions (login required)

    View Item

    Fulltext Downloads: