Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (4): 345-354.
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Zhou Zhe-wei
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Abstract: This paper presents the large deflection elastic curve of buckled bars through perturbation method, and the bifurcation diagrams including the influence of the imperfection at the base by using singular perturbation method of imperfect bifurcation theory. The physical meaning of the bifurcation diagrams is discussed.
Key words: non-holonomic system, Lindelf’s equation, Chaplygin’s equation, the Vakonomic model, Chetaev’s model
Zhou Zhe-wei. THE PERTURBATION SOLUTION OF THE LARGE ELASTIC CURVE OF BUCKLED BARS AND THE SINGULAR PERTURBATION METHOD FOR ITS IMPERFECT BIFURCATION PROBLEM. Applied Mathematics and Mechanics (English Edition), 1987, 8(4): 345-354.
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[1] Timoshenko,S.P.and J.M.Gere,Theory of Elastic Stability,Second edition,McGraw-Hill(1961). [2] Matkowsky,B.J.and E.L.Reiss,Singular perturations of bifurcations,SIAM.Appl Math.,33,2,Sep.(1977). [3] Iooss,Gérard and D.D.Joseph,Elementary Stability and Bifurcation Theory.Springer-Verlag(1980).
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