Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅰ)

Bissanga Gabriel; Jiang Furu

Volume 19 Issue 10

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(10): 865-877

Bissanga Gabriel, Jiang Furu. Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅰ)[J]. Applied Mathematics and Mechanics, 1998, 19(10): 865-877.

Citation:

PDF( 527 KB)

Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅰ)

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

Received Date: 1997-04-25
Rev Recd Date: 1998-05-30
Publish Date: 1998-10-15

Abstract

Abstract

In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions. Theseries solutions are constructed, the boundary layer effects are analysed and their asymptotics are proved.
- circular plate,
- large deflection,
- boundary layer effect,
- asymptotics,
- modified method of multiple scales

FullText(HTML)

References(6)

References

[1]	Chien Weizang,Large deflection of a circular clamped plate under uniform pressure,J.Phy.,7(1947),102-113.
[2]	Chien Weizang,Asymptotic behaviour of a thin clamped circular plate under uniform normal pressure at very large deflecion,The Science Report of National Tsing Hua University,5(1)(1948),71-94.
[3]	钱伟长、叶开沅,圆薄板大挠度问题,中国物理学报,10(3)(1954),209-238.
[4]	Chuen Yuan Chia,Non-Linear Analysis of Plates,McGraw-Hill,International Book Compary,New-York(1980).
[5]	A.C.沃耳密尔著,《柔韧板与柔韧壳》,卢文达、黄择言、卢鼎霍译,科学出版社(1963).
[6]	乔宗椿,修正多重尺度法在求解圆薄板具有很大挠度问题时的应用,应用数学和力学,14(10)(1993),903-912.

Relative Articles

[1]	XU Weizheng, HUANG Yu, LI Tong, LI Yexun, FU Hua, WANG Yanping, ZHENG Xianxu. Study on the Influence of Deformation Mode Assumption on Plastic Deformation of Circular Plates Under Impact Loading[J]. Applied Mathematics and Mechanics, 2025, 46(5): 591-599. doi: 10.21656/1000-0887.450285
[2]	LONG Lian-chun, ZHANG Chao-ya. Response Analysis of Thin Circular Plates in the Local Gaussian Temperature Field[J]. Applied Mathematics and Mechanics, 2016, 37(4): 391-403. doi: 10.3879/j.issn.1000-0887.2016.04.007
[3]	WANG Yun, XU Rong-qiao, DING Hao-jiang. Free Axisymmetric Vibration of FGM Circular Plates[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1009-1014. doi: 10.3879/j.issn.1000-0887.2009.09.001
[4]	LAI Shao-yong, FU Qing-long. The Asymptotic Theory of Initial Value Problems for Semilinear Perturbed Wave Equations in Two Space Dimensions[J]. Applied Mathematics and Mechanics, 2003, 24(1): 74-82.
[5]	Shu Xuefeng, Zhang Xiaoqing, Zhang Jinxiang. Thermoelastic Free Vibration of Clamped Circular Plate[J]. Applied Mathematics and Mechanics, 2000, 21(6): 647-654.
[6]	Wang Peiguang. Asymptotic and Oscillation for a Class of First Order Neutral Differential Equation[J]. Applied Mathematics and Mechanics, 1999, 20(6): 654-660.
[7]	Bissanga Cabriel, Jiang Furu. Application of the Modified Method of Multiple Scales to the Bending Problems for Circular Thin Plate at Very Large Deflection and the Asymptotics of Solutions(Ⅱ)[J]. Applied Mathematics and Mechanics, 1999, 20(4): 358-362.
[8]	Qian Weizhang. The First-Order Approximation of Non-Kirchhoff-Love Theory for Elastic Circular Plate with Fixed Boundary under Uniform Surface Loading(Ⅱ)[J]. Applied Mathematics and Mechanics, 1997, 18(2): 95-103.
[9]	Jie Min. On the Liapunov’s Stability of a Clamped Orthotropic Round Plate under Radial Axisymmetrical Impact Load[J]. Applied Mathematics and Mechanics, 1996, 17(2): 145-149.
[10]	Chien Wei-zang, Ru Xue-ping. A Further Study of the Theory of Elastic Circular Plates with Non-Kirchhoff-Love Assumptions[J]. Applied Mathematics and Mechanics, 1995, 16(2): 95-106.
[11]	Qiao Zong-chun. Application of the Modified Method of Multiple Scales to Solving the Problem of a Thin Clamped Circular Plate a Very Large Deflection[J]. Applied Mathematics and Mechanics, 1993, 14(10): 903-912.
[12]	Zhao Ya-pu, Hsueh Dah-wei. The Dynamic Plastic Behavior of a Simply Supported Circular Plate in a Damping Medium with Finite-Deflections[J]. Applied Mathematics and Mechanics, 1991, 12(10): 871-878.
[13]	Zheng Xiao-ping Ye Tian-qi Chen Bai-ping, . An Analytical Method for a Mixed Boundary Value Problem of Circular Plates under Arbitrary Lateral Loads[J]. Applied Mathematics and Mechanics, 1991, 12(9): 787-793.
[14]	Liu Rea-huai, Zhu Gao-qiu. Further Study on Large Deflection of Circular Sandwich Plates[J]. Applied Mathematics and Mechanics, 1989, 10(12): 1041-1047.
[15]	Chou Huan-wen, Yin Chuan-yan. The Perturbation-Iterative Method Applied to the Problems of the Large Deflection of the Elastic Circular Thin Plates[J]. Applied Mathematics and Mechanics, 1988, 9(4): 297-304.
[16]	Chen Shan-lin, Zhang Li-ying. The Large Deflection on Problem of Circular Plate on Elastic Foundation and in Conjunction with Linear Elastic Structure[J]. Applied Mathematics and Mechanics, 1986, 7(4): 325-333.
[17]	Yang Chia-shih, Xie Zhi-cheng. Perturbation Method in the Problem of Large Deflections of Circular Plates with Nonuniform Thickness[J]. Applied Mathematics and Mechanics, 1984, 5(2): 255-261.
[18]	Liu Ren-huai, Shi Yun-fang. Exact Solution for Circular Sandwich Plate with Large Deflection[J]. Applied Mathematics and Mechanics, 1982, 3(1): 11-23.
[19]	Chen Shan-Tin. Chien’s Solution and Its Asymptotic Behavior in Large Deflection of Circular Plates[J]. Applied Mathematics and Mechanics, 1982, 3(4): 513-518.
[20]	Chen Shan-lin. Elastic Behavior of Uniformly Loaded Circular Corrugated Plate with Sine-shaped Shallow Waves in Large Deflection[J]. Applied Mathematics and Mechanics, 1980, 1(2): 261-272.