复变函数法解析在轴对称变形问题中的应用

对于轴对称变形问题,如果能取合适的坐标系就可变换成用复变函数法能够解析的平面流动问题,即将平面流动问题广义地理解为只与两个坐标有关的流动问题。基于这种处理方法,本文对圆柱体的镦粗和圆棒、线材的挤压、拉拔进行了解析。结果证明,在实践上与采用同样变形区形状的其它上界法解析的结果完全一致,在理论上证明了只要坐标选取适当、复变函数选取合适,就可利用复变函数法进行塑性加工问题的解析。

Application of Complex Function Analysis to Asymmetrically Deformation Problem

The asymmetric deformation problem can be transformed into aplane flow one to which the complex function analysis will be available if acoordinate system is taken up properly,i.e. a plane flow problem is considered,in a generalized manner,as only related to two coordinate axes. Basd on such atreatment, an analysis is made for cylinder's upsetting, extrusion of round barsand wire drawing. The practical results show entirely in conformity withthose by different upper bond methods, providing that the shape of deforma-tion zone taken on is the same. It is also proved theoretically that the complexfunction method is applicable to the analysis of other plastic forming problemsonly if a coordinate system is taken properly with the complex function select-ed appropriately.