用多复变量应力函数计算任意多连通弹性平面问题
The Calculation of the MultipIy-Connected Elastic Plane Problems by Means of Stress Functions of Multiple Complex Variables
-
摘要: 本文应用弹性力学的复变函数理论,用多保角变换的方法,导出了任意多连通无限大弹性板的多复变量应力函数表达式。在边界上进行复Fourier级数展开,用待定系数法确定应力函数的未知系数,从而计算弹性板的应力场,以含有任意多个任意位置椭圆孔的无限板为例,编制了相应的多工况运行的FORTRAN77标准化程序,进行了考题和算例分析,给出了级数的收敛状况和孔边周向应力的分布图,结果表明本方法对处理多连通无限大弹性平面问题行之有效。Abstract: On the basis of mathematical elastic theory, the stress functions of multiple complex variables are derived in an infinite multiply-connecied plate by using,nultiple conformal represeniations. The funciions are developed in Fou ries series on unit circles,the unknown coefficients of the functions are deiermined by cornparing coefficient method, then the stresses in the plaie can be calculaied. A plate conlaining multiple elliptical hofes is discussed, the corresponding FORTRAN77 program is finished. Two examples are given, they show that this method is very effective and convenient.
-
Key words:
- holes /
- plate /
- stress calculation
-
[1] 西田正孝.《应力集中》(李安定等译),机械工业出版社.北京(1986). [2] Г.Н.萨文、В.И.杜尔契,《应力集中手册》(张正国译),黑龙江科学技术出版(1983). [3] 黄炎.《局部应力及其应用》,机械工业出版社,北京(1990). [4] 航空工业部科学技术委员会,《应力集中系数手册》,高等教育出版社,北京(1990). [5] Lin Chih-bing, On the stresses in a plate containing two circular holes, J. of Applied Physics, 19, 1(1948), 77-81. [6] Ukadgaonker. V, G., Stress analysis of a plate containing two circular holes having tangential stresses, AIAA Journal, 18, 1(1980), 125-128. [7] 穆斯海里什维里,《数学弹性力学的几个基本木问题》(赵惠元译,王柔怀校),科学出版社.北京(1958). [8] 徐芝纶.《弹性力学》(第二版),人民教育出版社,北京(l1978). [9] 杜庆华、余寿文、姚振汉,《弹性理论》,科学出版社,北京(1986). [10] 樊大均.《数学弹性力学》.新时代出版社(1983). -
点击查看大图
计量
- 文章访问数: 2015
- HTML全文浏览量: 58
- PDF下载量: 713
- 被引次数: 0
下载:
