Analytically Modeling of Complicated Boundary Simply-connected Region Conformal Mapping
XU Chen-xiao,ZHU Heng-jun,QI Hong-yuan(1-College of Mechanical, Electronic & Control Engineering, Northern Jiaotong University, Beijing 100044)
It is difficult to model the irregular geometry simply-connected region in engineering problems, which makes analytical solution and optimization of parameters very hard. Conformal mapping method is adopted to transform the complicated contact region to unit circle disk. To solve the conformal mapping function, complex triangular interpolation with iterative and normal convergence is presented. And FFT algorithm is used to solve the coefficients. For symmetrical region, a fast algorithm is realized by simplification. Using this method, it is possible to obtain analytical solution and optimized parameters. The method is realized by a computer program and its effect is presented with an example.