正交各向异性椭圆板的弹性失稳

基金项目: 国家教委博士点基金

Elastic Instability of an Orthotropic Elliptic Plate

摘要: 本文以von Kármán型方程为基础并利用一般分支理论讨论了正交各向异性椭圆板在面内边缘均布压力作用下的弹性失稳.利用Liapunov-Schmidt过程证明了单特征值处分支解的存在性并利用小摄动展开得到了分支解的渐近表达式.最后利用有限单元法计算了正交各向异性椭圆板的临界载荷并进行了板的过屈曲分析,还考察了材料和几何参数对稳定性的影响.
- 正交各向异性 /
- 椭圆板 /
- 弹性稳定性 /
- 临界载荷 /
- 摄动解 /
- 过屈曲性态
Abstract: On the basis of von Karman equations and using the general bifurcation theory,the elastic instability of an orthotropic elliptic plate whose edge is subjected to a uniform plane compression is discussed.Following the well-known Liapunov-Schmidt process the existance of bifurcation solution at a simple eigenvalue is shown and the asymptotic expression is obtained by means of the perturbation expansion with a small parameter.Finally,by using the finite element method,the critical loads of the plate are computed and the post-buckling behavior is analysed.And also the effect of material and geome trie parameters on the stability is studied.
- orthotropic /
- elliptic plate /
- elastic instability /
- critical load /
- bifurcation solution /
- post-buckling behavior

[1]	Voinovsky-Krieger,S.,The stability of a clamped elliptic plate under uniform compression,J.Appl.Mech.,4(1937),177.
[2]	Shibaoka,Yoshiv,On the buckling of an elliptic plate with clamped edge I,Journal of the Physical Society of Japan,11,10(1956),1088.
[3]	Shibaoka,Yoshiv,On the buckling of an elliptic plate with clamped edge II,Journal of the Physical Society of Japan,12,5(1957),529.
[4]	Berger,M.,On von Kármán equation and the buckling of a thin elastic plate I,The clamped plate.Comm.Pure Appl.Math.,20(1967),687.
[5]	Berger,M.and P.Fife,On von Kármán equation and the buckling of a thin elastic plate II,Comm.Pure Appl.Math.,21(1968),227.
[6]	程昌钧,《杆与板的分叉与屈曲》.兰州大学力学系讲义(1986).
[7]	Adams,R,A.,《索伯列夫空间》,叶其孝等译,人民教育出版社(1983).
[8]	Rektorys,Karel,Variational Methods in Mathematics,Science and Engineering,D.Reidl Publishing Company(1975).
[9]	Zienkiewicz,O.C.and Y.K.Cheung,The Finite Element Method in Structural and Continuum Mechanics,McGraw-Hill(1967).