变厚度圆板大挠度理论的摄动法
Perturbation Method in the Problem of Large Deflections of Circular Plates with Nonuniform Thickness
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摘要: 本文用对两个小参数的摄动法,对于轴对称圆薄板大挠度问题,在板厚按指数规律变化、载荷为均布的情况下,求出了三级摄动解。所得摄动解在特殊情况下与精确解的比较表明结果是较为理想的。Abstract: In this paper the perturbation method about two parameters is applied to the problem of large deflections of a circular plate with exponentially varying thicknesses under uniform pressure, An asymtotic solution up to the third-order is derived. In comparison with the exact solutions in special cases,the asymtotic solution shows a precise accuracy.
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[1] 钱伟长,轴对称圆薄板在大挠度情形下的一般理论,钱伟长等编著《弹性圆薄板大挠度问题》,中国科学院(1954). [2] 钱伟长,圆板大挠度理论的摄动法,钱伟长等编著《弹性圆薄板大挠度问题》,中国科学院(1954). [3] Chien Wei-zang, Large deflection of a circular plate under uniform pressure, ChineseJournal of Physics,7,2(1947). [4] 铁摩辛柯,S,《板壳理论》,科学出版社(1977). [5] 钱伟长,《奇异摄动理论及其在力学中的应用》,科学出版社(1981). -
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