开孔薄板屈曲状态的存在性

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基金项目: 国家教委博士点基金资助项目

The Existence of Buckled States on a Perforated Thin Plate

摘要: 基于[1,2]中对于开孔薄板建立的广义von Kármán理论,本文系统地研究了沿开孔薄板的每一条边界受自身平衡的面内外力作用时开孔薄板屈曲状态的存在性,这一工作全面地推广了[3,4]中的结果.
- 开孔薄板 /
- 多连通城域 /
- 修正von Kármán理论 /
- 屈曲状态 /
- 分支理论
Abstract: On the basis of the generalized von Kármán theory for perforated thin plates established in [1,2], the existence of buckled states for perforated plates subjected to self-equilibrating inplane forces along each edge systematically is investigated. This work completely generalizes the results in [3, 4].
- perforated plate /
- multi-connected region /
- modified von Kármán theory /
- buckled state /
- bifurcation theorem

[1]	朱正佑、程昌钧,关于开孔薄板大挠度问题的一般数学理论,力学学报,18(2) (1986),123-135.
[2]	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
[3]	Berger, M., On yon Kármán equation and the buckling of a thin elastic plate Ⅰ: The clamped plate, Comm. Pure Appl. Math., 20, 4 (1967), 687-719.
[4]	Berger, M. and P. File, On von kármán equation and the buckling of a thin elastic plate Ⅱ, Comm. Pure Appl. Math., 21, 3 (1968), 227-241.
[5]	Adams, R. A., Sobolev Spaces, Academic Press, New York (1975).
[6]	Rektorys, Karel, Variational Methods in Mathematics, Science and Engineering, D. Reidel Publishing Company(1975).
[7]	钱伟长,《广义变分原理》,科学出版社(1985),
[8]	Berger, M., An eigenvalue problem for non-linear elliptic partial differential equation, Trans. A. M. S., 120(1965), 154-184.
[9]	Agnon, S., The L_p approach to the Dirichiet problem, Ann. Scuola di Pisa, 13(1959), 504-448.
[10]	Dunford, Nelson and Jacob T., Schwartz, Linear Operators, Part Ⅰ: Generai Theory, INC., New York (1958).
[11]	朱正佑、程昌钧,《分支问题的数值计算方法》,兰州大学出版社(1989).
[12]	Chow, Shui-nee and Jack K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York, Berlin, Heidelberg (1982).