[1]宋启根.球函数的近似表示式及直线变厚圆板的轴对称弯曲[J].东南大学学报(自然科学版),1981,11(1):1-17.[doi:10.3969/j.issn.1001-0505.1981.01.001]
　Song Qi-gen.Approximate Expressions of Legendre Functions and Axisymmetrical Bendings of Circular Plates with Linearly Varying Thickness[J].Journal of Southeast University (Natural Science Edition),1981,11(1):1-17.[doi:10.3969/j.issn.1001-0505.1981.01.001]
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球函数的近似表示式及直线变厚圆板的轴对称弯曲()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
11
期数:
1981年第1期
页码:
1-17
栏目:
本刊信息
出版日期:
1981-03-20

文章信息/Info

Title:
Approximate Expressions of Legendre Functions and Axisymmetrical Bendings of Circular Plates with Linearly Varying Thickness
作者:
宋启根
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Author(s):
Song Qi-gen
关键词:
厚圆板;  轴对称弯曲;  球函数;  超几何函数;  收敛速度;  计算精度;  计算方法;  表示式;  适用范围;  近似式
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1981.01.001
摘要:
本文第一部分导出了球函数P_p^?（x）及Q_p^?（x）的近似表示式,该式对所有实宗量x都适用。探讨了这些表示式的适用范围、计算精度或收敛速度。当|q|=|m|≤3时这些表示式在大多情况下便于计算并比较准确。这些表示式还可以计算起几何函数F（-p,1+p;1+m;（1-x）/2）的近似值。直线变厚圆板的轴对称弯曲当泊松比 p=0.3或 v=1（?）3时曾被广泛研究过。借助于上述球函数的近似表示式,本文第二部分对这一弯曲问题的计算方法作了改进,并研究了过去很少研讨的有关问题。为了考察 v 对内力的影响,对 v=0及v=0.5的板作了内力分析。计算表明,在变厚圆板中这一影响是显著的。
Abstract:
Approximate expressions of Legeudre functions P~q_p(x)and Q~q_p(x)which may be used for any real argument x are presented in the first part of this paper. The valid rigions,the accuracy of calculation or the speed of convengence of these expressions are studied.In most cases these expressions are convenient for calculation and give good accuracy provided |q|=|m|3.These expressions thenmay be applied to calculate the approximate value of the hypergeometric fuucfion F(-p,1+p; 1+m;(1-x)/2). The axially symmetrical bending of circular plates with linearly varying thickness has been widely studied only for Poisson’s ratio v=0.3 or v=1/3.In the second part of this paper,with the aid of the foregoing approximate expressions of Legendre functions,method of calculation for this bending problem is improved and some problems which have rarely been discussed hitherto are also studied.To examine the effect of v on stress distribution,stress analysis of the plate for v=0 and v=0.5 is investigated.It is shown that the effect of v is considerable in a plate with varying thickness.

相似文献/References:

[1]宋启根.球函数的近似表示式及直线变厚圆板的轴对称弯曲[J].东南大学学报(自然科学版),1980,10(1):1.[doi:10.3969/j.issn.1001-0505.1980.01.001]
　Song Qi-gen.Approximate Expressions of Legendre Functions and Axisymmetrical Bendings of Circular Plates with Linearly Varying Thickness[J].Journal of Southeast University (Natural Science Edition),1980,10(1):1.[doi:10.3969/j.issn.1001-0505.1980.01.001]

更新日期/Last Update: 2013-05-01