具有初始缺陷弹性板的稳定性分析

Analysis of Stability on Elastic Plates with lnitial lmperfections

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

摘要: 本文以Marguerre方程为基础,用奇异性理论研究了初始挠度缺陷以及横向载荷对弹性板屈曲后分叉解的影响。借助于普适开折的原理,在单特征值局部邻域内将该问题的失稳分析转化为三次代数方程的讨论,从而确定出分叉解的性态。同时绘出了在不同参数下的分叉解文,讨论了几何缺陷和横向载荷对特征值的影响。
- 缺陷普适开折 /
- 特征值 /
- 分叉
Abstract: On the basis of Marguerre equations,the influence on a bifurcation diagram of am elatic plate affected by initial deflection imperfection and transverse loading is studied with the help of the singularity theory.Thes paper applies universal unfoldingprinciples,it is put forward that the unstable analysis of thes problem can transform into the study of a triple algebraic equation in the neighborhood of a simple eigenvalue.Thus the bifurcated states are decided,and the bifurcation diagrams are drawn up following distinct paramentrs. Then the quantitative series of interfering with eigenvalues are discussed.
- imperfection /
- universal unfolding /
- eigenvalue

[1]	J.M.T.Thompson and G.W.Hunt,Dangers of structural optimization,Engineering Optimization,1(1974),99-110.
[2]	S.Timoshenko and S.Woinowsky-Krieger,Theory of Plates and Shells,McGraw-Hill,New York(1959).
[3]	J.M.Coan.The influence of curvature on the buckling of structures.J.Appl.Mech.,18(1951),143.
[4]	K.Marguerre,Zur thcurie gckrummten plane grosser formanderung,Proc.5th Intl.Cong.Appl.,Mech.,John Wiley & Sons Inc.,New York(1938).93-101.
[5]	Chin Chuenyuan,Nonlinear Analysis of Plates,McGraw-Hill.New York(1980),93-107.
[6]	Xu Kaiyu,Buckling of a rectangular plate with small initial deflection,ICNM-Ⅱ Proc.ed.by Chien Weizang.Peking University Press,Beijing(1992)630-632.
[7]	T.Poston and 1.Stewart.Catastrophe Theory and Its Applications,Pitman,London(1978).
[8]	Z.Gaspar,Critical imperfection theroy.J.Strut.,Mech.,11(1983).297-325.
[9]	M.Golubitsky and D.Schaeffer,A theroy for imperfect bifurcation via singularity theory,Conun.Pure Appl.,Math.,32(1979),21-98.
[10]	M.Berger,On von Karman equations and the buckling of a thin elastic plate L,The clamped plate,Comm.Pure Appl.Mech.20(1967),687-719.
[11]	程昌钧、朱正佑.《结构的屈曲与分叉》,兰州大学出版社(1991).
[12]	张恭庆、林源渠.《泛函分析讲义》.北京大学出版社(1987).
[13]	陈予恕、唐云等.《非线性动力学中的现代分析方法》,科学出版社(1992),88-116.