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

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。

On the basis of the mathematical elastic theory,the stress functions of multiple complex variables are derived in an infinite multiply-connected plate by using multiple conformal representations The functions are developed in Fourier Series on unit circles.the unknown coefficients of the functions are determined by comparing coefficient method,then the stresses in the plate can be calculated.A plate containing multiple elliptical holes is discussed, the corresponding FORTR- AN 77 program is finished.Two examples are given,they show that this method is Yery effective and convenient.