The Existence of Buckled States on a Perforated Thin Plate

Cheng Chang-jun; Yang Xiao

Volume 13 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(8): 699-709

Cheng Chang-jun, Yang Xiao. The Existence of Buckled States on a Perforated Thin Plate[J]. Applied Mathematics and Mechanics, 1992, 13(8): 699-709.

Citation:

Cheng Chang-jun, Yang Xiao. The Existence of Buckled States on a Perforated Thin Plate[J]. Applied Mathematics and Mechanics, 1992, 13(8): 699-709.

Citation:

Cheng Chang-jun, Yang Xiao. The Existence of Buckled States on a Perforated Thin Plate[J]. Applied Mathematics and Mechanics, 1992, 13(8): 699-709.

PDF( 674 KB)

The Existence of Buckled States on a Perforated Thin Plate

Department of Mechanics, Lanzhou University, Lanzhou

Received Date: 1991-04-22
Publish Date: 1992-08-15

Abstract

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

FullText(HTML)

References(12)

References

[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).

Relative Articles

[1]	WANG Pingyuan, LI Cheng, YAO Linquan. Bending and Buckling of Functionally Graded Nanoplates Based on the Nonlocal Strain Gradient Theory[J]. Applied Mathematics and Mechanics, 2021, 42(1): 15-26. doi: 10.21656/1000-0887.410188
[2]	LI Ruoyu, WANG Tianhong. Thermo-Mechanical Buckling Analysis of Thin Plates[J]. Applied Mathematics and Mechanics, 2020, 41(8): 877-886. doi: 10.21656/1000-0887.400308
[3]	SHI Feng, MA Hongying, SUN Yizhen, XIANG Song, WANG Yanbing, LUAN Tingting. Buckling Analysis of Composite Laminate Plates Based on the n-order Shear Deformation Theory[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1346-1357. doi: 10.21656/1000-0887.410061
[4]	ZOU Sen, LIU Yong, WANG Qi. Numerical Study on Passive Control of Airfoil-Vortex Interaction Based on Slotted Leading Edges[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1159-1168. doi: 10.21656/1000-0887.400028
[5]	LIU Wu-fa, GONG Zhen-bang, WANG Qin-que. Investigation on Kane Dynamic Equations Based on Screw Theory for Open-Chain Manipulators[J]. Applied Mathematics and Mechanics, 2005, 26(5): 577-584.
[6]	Yang Wenxiong. Mathematical Theory of k Multiplier[J]. Applied Mathematics and Mechanics, 2000, 21(3): 307-314.
[7]	SONG Tian-shu, LIU Dian-kui. An Application of Theoretical Solutions About Cylindrical Shells With Small Openings[J]. Applied Mathematics and Mechanics, 2000, 21(9): 961-965.
[8]	Zhang Jianwu, Li Qi, Shu Yongping. On the Refined First-Order Shear Deformation Plate Theory of Kûrmûn Type[J]. Applied Mathematics and Mechanics, 2000, 21(5): 477-482.
[9]	E Guokang. Modification in the Theory on Flexural-Torsional Buckling of Structures[J]. Applied Mathematics and Mechanics, 1997, 18(10): 911-920.
[10]	Shen Huishen. Kármán-Type Equations for a Higher-order Shear Deformation Plate Theory and Its Use in the Thermal Postbuckling Analysis[J]. Applied Mathematics and Mechanics, 1997, 18(12): 1059-1073.
[11]	Cheng Changiun, Yang Xiao. The Mathematical Models and Generalized Variational Principles of Nonlinear Analysis for Perforated Thin Plates[J]. Applied Mathematics and Mechanics, 1996, 17(2): 105-114.
[12]	He Lu-wu, Cheng Chang-jun. A Method of Determining Buckled States of Thin Plates at a Double Eigenvalue[J]. Applied Mathematics and Mechanics, 1992, 13(4): 307-311.
[13]	He Lu-wu, Cheng Chang-jun. The Buckled States of Rectangular Plates[J]. Applied Mathematics and Mechanics, 1992, 13(5): 401-406.
[14]	He Lu-wu, Cheng Chang-jun. The Buckled States of Annular Sandwich Plates[J]. Applied Mathematics and Mechanics, 1992, 13(7): 599-604.
[15]	Shang Xin-chun. Tensile Instability of Nonlinear Spherical Membrane with Large Deformation[J]. Applied Mathematics and Mechanics, 1991, 12(10): 927-933.
[16]	Shen Hui-shen, Chen Tie-yun. A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(6): 515-528.
[17]	Shen Hui-chuan. Further Study of the Relation of von Karman Equation for Elastic Large Deflection Problem and Schrodinger Equation for Quantum Eigenvalues Problem[J]. Applied Mathematics and Mechanics, 1987, 8(6): 539-546.
[18]	Qin Sheng-li, Zhang Ai-shu. On the Problems of Buckling of an Annular Thin Plate[J]. Applied Mathematics and Mechanics, 1985, 6(2): 175-190.
[19]	Shen Hui-chuan. The Relation of von Karman Equation for Elastic Large Deflection Problem and Schrodinger Equation for Quantum Eigenvalues Problem[J]. Applied Mathematics and Mechanics, 1985, 6(8): 711-723.
[20]	Liu Cheng-qun. Note on the Critical Variational State in Elasticity Theory[J]. Applied Mathematics and Mechanics, 1984, 5(6): 895-901.