摘要
工程实际中任意非规则边界问题的数学模型建立困难,导致参数不易求解和优化。应用近代复变共形映射理论,利用三角插值和法线迭代收敛方法,将任意复杂边界域转化为单位圆域,系统地建立了二者间的共形映射函数。针对挤压（拔制）异型材模具精密快速加工设计问题,求解了模具相似成形塑性流动的数学模型,建立了圆角方型材精密挤压（拔制）模具模腔数学模型及优化函数方程,使模腔快速CAD/CAM一体化成为可能。
It is especially difficult to model the irregular geometry boundary region in engineering problems, which makes analytical solution and optimization of parameters very hard. Conformal mapping method is adopted to transform the complicated region to unit circle disk. To solve the conformal mapping function, complex triangle interpolation theory with iterative method and normal convergence is presented. And FFT algorithm is used to solve the coefficients. For symmetrical region, fast algorithm is realized by simplification. This method is realized by computer program and is validated to solves mathematics model of similar forming plastic stream in exact extruding/drawing. At last, die mathematical model and optimized function equation of arc square product are built.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2002年第9期83-86,共4页
Journal of Mechanical Engineering
基金
国家自然科学基金资助项目(50075076)
关键词
优化设计
共形映射
三角插值
模具
Optimal design Conformal mapping Triangle interpolation Die
