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Bifurcation and stability of a three‐hinged rod under a conservative load
Author(s) -
Rajendran S.,
Leung A. Y. T.,
Starr A. G.,
Chan J. K. W.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990220)44:5<657::aid-nme522>3.0.co;2-0
Subject(s) - bifurcation , parameter space , gravitational singularity , codimension , mathematics , bifurcation diagram , singularity theory , singularity , pitchfork bifurcation , structural stability , saddle node bifurcation , mathematical analysis , symmetry (geometry) , bifurcation theory , geometry , physics , nonlinear system , structural engineering , engineering , quantum mechanics
The bifurcation solutions and their stability of a three‐hinged rod under conservative compressive force are investigated. The equations for the system are non‐linear, and possess some symmetry properties. The symmerty group concepts are employed to exploit these symmetry properties. The symbolic computer software, Mathematica , is used for the analytical and numerical solutions. The loci of codimension‐one singularity are plotted on a two‐dimensional control parameter space. These curves partition the parameter space into regions of qualitatively similar bifurcation diagrams. The bifurcation solutions and their stability at typical points in the parameter diagram, and the perturbation of codimension‐one singularities are discussed. Copyright © 1999 John Wiley & Sons, Ltd.