开孔簿板非线性分析的数学模型和广义变分原理<sup>*</sup>

程昌钧; 杨骁

开孔簿板非线性分析的数学模型和广义变分原理^*

程昌钧,
杨骁

兰州大学力学系兰州 730000

基金项目: * 国家教委博士点基金

计量
- 文章访问数: 2197
- HTML全文浏览量: 126
- PDF下载量: 572
- 被引次数: 0
出版历程
- 收稿日期: 1995-02-22
- 刊出日期: 1996-02-15

The Mathematical Models and Generalized Variational Principles of Nonlinear Analysis for Perforated Thin Plates

Department of Mechanics, Lanzbou University, Lanzbou, Gansu 730000, P. R. China

摘要

摘要: 基于薄板非线性弯曲的Kirchhoff-Kármán假设.本文提出了在任意中面边界条件下任意开孔薄板非线性分析的三类边值问题并建立了相应的广义变分原理.能够看到在本文中提出的数学模型完全是一种新的不同于Karman理论的模型.这些数学模型能够应用于任意中面边界条件下开孔薄板的非线性分析和稳定性分析.
- 开孔薄板 /
- 非线性分析 /
- 数学模型 /
- 广义变分原理
Abstract: On foe basis of the Kirchoff-Kármán hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.
- perforated thin plate /
- non-linear analysis /
- mathematical model /
- generalized variational principle

HTML全文

参考文献(13)

[1]	P,M,Naghdi,The theory of plates zad shells,Handbuck der Physik,Vla/2,ed.C,Truesdell,Springer-Verlag,Berlin,Heidelberg,New York(1972).
[2]	Zhu Zhengyou and Cheng Changjun,General mathematical theory of large deflections of thin plates with some holes,Acta Mechanics Sinica,2(3)(1986),278-288.
[3]	程昌钧、吕小安,关于开孔薄板大挠度问题的一般数学理论(续),力学学报,21(2)(1989),193-203.
[4]	程昌钧、朱正佑,《结构的屈曲和分叉》,兰州大学出版社(1991).
[5]	Cheag Changjun and Zhu Zhengyou,The buckled states of annular plates,Scientia Sinica,Series A,19(9)(1986),956-965.
[6]	Cheng Changjun,Duan Wei and D,F,Parker,Elastic instability of polar orthotropic annular plates,Int,J.Engag.Sci.,27(2)(1989),109-121.
[7]	Cheng Chan,gjun and A,J.M.Spencer,Nor-axisymmetric instability of polar orthotropic annular plates,J.Engag.Math.,23(1989),29-51.
[8]	Cheng Changjun and Lid Xiaoan,Buckling and post-buckling of znnular plats in shearing(Ⅰ):Buckling and(Ⅱ):Post-buckling,Com.Methods Appl.Mech.Engng.,92(2)(1991),157-172,173-191.
[9]	吕小安,开孔圆柱壳的非线性理论与稳定性间题,兰州大学博士学位论文(1990).
[10]	何录武,夹层板的屈曲和分支,兰州大学博士学位论文(1990).
[11]	程昌钧、杨晓,开孔薄板屈曲状态的存在性,应用数学和力学,13(8)(1992),699-709.
[12]	Yang Xiao and Cheng Changjun,Variationzl principles on perforated thin plates and finite element method of buckling and post-buckling analysis,Acts Mechanics Sinica,7(2)(1991),1-10.
[13]	钱伟长,《变分法及有限元》,科学出版社(1980).