Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation

Izydorek, Marek and Janczewska, Joanna and Waterstraat, Nils and Zgorzelska, Anita (2018) Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation. Nonlinear Analysis. Real World Applications, 39 . pp. 451-463. ISSN 1468-1218. (doi:https://doi.org/10.1016/j.nonrwa.2017.07.008) (Full text available)

Abstract

We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.

Item Type: Article
Uncontrolled keywords: Bifurcation, Buckling, Winkler foundation
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 05 Feb 2017 14:31 UTC
Last Modified: 18 Aug 2018 23:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60224 (The current URI for this page, for reference purposes)
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