横截面呈周期性变化边界的轴类零件受扭应力场的解析研究  

The Research on the Stress Field Analysis Solutions under Torque Loadings of the Shafts with the Periodic Boundary of Cross Section

作　　者：虞世鸣[1] 刘慰俭[1] 

机构地区：[1]上海大学机械电子工程学院

出　　处：《上海大学学报（自然科学版）》1997年第S1期153-157,共5页Journal of Shanghai University:Natural Science Edition

摘　　要：弹性理论处理横截面呈周期性变化边界的轴类零件时，往往受这类零件边界条件的限制，而影响其工程实践的推广应用．本文提出一种方法，其实质是：采用富里埃级数来逼近横截面呈周期性变化边界的轴类零件的边界形状；并应用复变函数论中保角映射原理，将零件复杂的边界形状映像成单位圆，从而使弹性理论可以分析和计算复杂边界轴类零件的应力场；再通过留数的求解实现保角映射的反变换．Elastic theory is restricted practically by the boundary condition in analysis solutions about the shafts with the periodic boundary of cross section.In order to develop this local property,this paper presents a method,which uses Fourier Series to approximate the boundary shapes of the shafts with periodic boundary of cross section,and uses the conformal mapping in Theory of Function of a Complex Variable to make the complicated boundary shapes of the shafts map a unit circle.Thus elastic theory can analyze the stress field solutions of these shafts,and its residue solution solves the inverse transformation of the conformal mapping.

关 键 词：轴类零件 横截面 解析 保角映射 留数 

分 类 号：O345[理学—固体力学]