含有任意多个椭圆孔弹性板的应力场计算

本文应用弹性力学的复变函数理论,用多保角变换的方法,导出了含有任意多个椭圆孔的无限大弹性板多复变量应力函数的表达式。每个孔的大小、位置和孔边作用的载荷均为任意指定。板的无限远处作用有和坐标轴方向一致的均匀拉压载荷P_x,P_y和均匀剪切载荷P_(xy)。并在孔边进行复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。编制了相应的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。

Stress Calculation in an Elastic Plate Containing Multiple Elliptical Holes

On the basis of mathematical elastic theory, multiple-complex-variable stress functions are used to calculate the stress field in an infinite elastic plate with multiple elliptical holes of which sizes and locations are arbitrary. The plate is subjected to uniform loads . Px, Py , and Pxy at infinity, and arbitrary loads on the hole boundary. The stress functions are expanded into complex Fourier series on the hole boundary. The undetermined coefficients of the stress functions are then determined by the comparing coefficients method. A FORTRAN77 program is realized. Known solutions in the literature are used to verify the method, which shows that the method is yery effective.