屈曲杆大挠度弹性曲线的摄动解及其不完全分岔问题的奇异摄动解法
The Perturbation Solution of the Large Elastic Curve of Buckled Bars and the Singular Perturbation Method for Its Imperfect Bifurcation Problem
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摘要: 本文用摄动法求解了屈曲杆大挠度情况下的弹性曲线,并考虑支座处的缺陷对分岔(失稳)问题的影响,用奇异摄动的不完全分岔理论进行了计算,给出了分岔图解,并对其物理意义进行了讨论.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.
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[1] 铁木辛柯,《弹性稳定理论》,第二版,科学出版社(1965). [2] Matkowsky,B.J.and E.L.Reiss,Singular perturbations of bifurcations,SIAM T,Appl,Math.,33,2(1977). [3] Iooss,Grard and D,D,Joseph,Elementary Stability and Bifurcation Theory,Springer-Verlag(1980). -
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