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*
Application of the Modified Method of Multiple Scales to Solving the Problem of a Thin Clamped Circular Plate a Very Large Deflection
-
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.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.
-
[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. -
点击查看大图
计量
- 文章访问数: 1770
- HTML全文浏览量: 84
- PDF下载量: 532
- 被引次数: 0
下载:
