修正多重尺度法在求解圆簿板具有很大挠度问题时的应用<sup>*</sup>

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

修正多重尺度法在求解圆簿板具有很大挠度问题时的应用^*

基金项目: * 国家自然科学基金资助的课题

Shanghai Institute of Applied Mathematics and Mechanics; Shanghai University of Technology, Shanghai

摘要: 本文利用修正的多重尺度法^[1～2]重新研究固支圆薄板在均匀压力作用下,挠度很大时解的渐近性态.结果表明与钱伟长教授用首创的合成展开法求解该问题^[3]的结果相一致,但较后者更简捷.本文结果还表明文[4]中所指出文[1～2]方法的局限性是非本质的,并改正文[3]中一些计算错误.
- 圆板 /
- 大挠度 /
- 修正多重尺度法 /
- 复合展开法 /
- 渐近解
Abstract: In this paper, asymptotic behaviour of the solution to the problem of a thin damped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in [1-2]. The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in [3]. However, by contrast, the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in [3]. It is also shown that the restriction of the method of paper [1-2] pointed out in paper [4] is not essential, and several computation errors in [3] are corrected as well.
- circular plate /
- large deflection /
- the modified method of multiple scales /
- the method of composite expansions /
- asymptotic solution

[1]	江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲问题(Ⅰ),应用数学和力学,3(5)(1982),629-640.
[2]	江福汝,环形和圆形薄板在各种支承条件下的非对称弯曲问题(Ⅱ),应用数学和力学,5(2)(1984), 191-204.
[3]	Chien Wei-zang, Asymptotic behavior of a thin clamped circular plate under uniform norm al pressure at very large deflection,The Science Reports of Nationdl Tsing Huo Univ.,5(1)(1948), 71-94.
[4]	周焕文,奇异摄动法在薄板和薄壳的弯曲问题中的若干应用,应用数学和力学,5(4) (1984).481-488.