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Computation of multiple bifurcation point

Computation of multiple bifurcation point Purpose – The aim of this paper is to develop a new method for finding multiple bifurcation points in structures. Design/methodology/approach – A brief review of nonlinear analysis is presented. A powerful method (called arc‐length) for tracing nonlinear equilibrium path is described. Techniques for monitoring critical points are discussed to find the rank deficiency of the stiffness matrix. Finally, by using eigenvalue perturbation of tangent stiffness matrix, load parameter associated with multiple bifurcation points is obtained. Findings – Since other methods of finding simple bifurcation points diverge in the neighborhood of critical points, this paper introduces a new method to find multiple bifurcation points. It should be remembered that a simple bifurcation point is a multiple bifurcation point with rank deficiency equal to one. Therefore, the method is applicable to simple critical points as well. Practical implications – Global buckling of the structures should be considered in design. Many structures (specially symmetric space structures) have multiple bifurcation points, therefore, analyst and designer should be aware of these points and should control them (for example, by changing the geometry or other related factors) for obtaining a safe and optimum design. Originality/value – In this paper a robust method to find multiple bifurcation points is introduced. By using this method, engineers can be aware of critical load of multiple bifurcation points to control global buckling of related structures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

Computation of multiple bifurcation point

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References (20)

Publisher
Emerald Publishing
Copyright
Copyright © 2006 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400610671135
Publisher site
See Article on Publisher Site

Abstract

Purpose – The aim of this paper is to develop a new method for finding multiple bifurcation points in structures. Design/methodology/approach – A brief review of nonlinear analysis is presented. A powerful method (called arc‐length) for tracing nonlinear equilibrium path is described. Techniques for monitoring critical points are discussed to find the rank deficiency of the stiffness matrix. Finally, by using eigenvalue perturbation of tangent stiffness matrix, load parameter associated with multiple bifurcation points is obtained. Findings – Since other methods of finding simple bifurcation points diverge in the neighborhood of critical points, this paper introduces a new method to find multiple bifurcation points. It should be remembered that a simple bifurcation point is a multiple bifurcation point with rank deficiency equal to one. Therefore, the method is applicable to simple critical points as well. Practical implications – Global buckling of the structures should be considered in design. Many structures (specially symmetric space structures) have multiple bifurcation points, therefore, analyst and designer should be aware of these points and should control them (for example, by changing the geometry or other related factors) for obtaining a safe and optimum design. Originality/value – In this paper a robust method to find multiple bifurcation points is introduced. By using this method, engineers can be aware of critical load of multiple bifurcation points to control global buckling of related structures.

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and Software – Emerald Publishing

Published: Jul 1, 2006

Keywords: Stability (control theory); Optimization techniques; Structures; Stiffness matrices

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