用保角映射法求解多层套扁挤压筒内的应力  

STRESS CALCULATION OF FLAT CONTAINER BY CONFORMAL MAPPING METHOD

作　　者：王匀[1] 刘全坤[1] 

机构地区：[1]合肥工业大学材料科学与工程学院,合肥230009

出　　处：《机械工程学报》2005年第10期80-83,共4页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(50075022)。

摘　　要：生产大型铝型材用扁挤压筒内孔近似椭圆,属多连通域,难以采用常规的单连体平面问题的复变函数保角映射法,应力求解困难。结合单连体复变函数法和留数定理给出了受内压扁挤压筒的应力求解公式和例子,并与有限元模拟结果进行了比较分析。结果表明理论解和数值解在全域范围内基本一致,从而解决了保角映射法应用于扁挤压筒实际工程应力计算的主要障碍,为模具强度设计提供了依据。Flat container is used to extrude large aluminum profiles. Because of the inner-hole geometry of fiat container is approximate to ellipse, it is difficult to apply conventional conformal mapping method of single-connect region to stress calculation. The stress calculation formula and example of pressed fiat container are given through complex function of single-connect region and residue theory. By the comparison with simulated result obtained by analysis, it shows that the theoretic solution is in good accord with numerical solution and conformal mapping method can be applied to practical stress calculation of flat container. Furthermore, the method gives support to the design of fiat container.

关 键 词：保角映射 扁挤压筒 应力 解析解 数值解 保角映射法 应力计算 求解公式 复变函数法 多层 

分 类 号：O175.1[理学—数学] TK83[理学—基础数学]