基于MATLAB/PDEtool的轴对称场分析

MATLAB/PDEtool是非常优秀的二维偏微分有限元求解软件,具有像静电场、静磁场和工频交流电磁场等专业模式,但这些专业模式不能直接用于柱坐标系表示的轴对称场的求解分析。文章推导出了正交坐标系中的泊松方程,并通过柱坐标系中轴对称场的方程形式和直角坐标系中标准二维椭圆型偏微分方程形式的比较,得到了他们坐标之间、系数之间的对应关系,据此用MATLAB/PDEtool对轴对称场进行了求解分析,结果说明本文的方法是有效的。

Analysis of Axisymmetric Filed by MATLAB/PDEtool

MATLAB/PDEtool is excellent software for analyzing a PDE (Partial Differential Equation) problem by 2-D (Two Space Dimensions) FEM (Finite Element Method). MATLAB/PDEtool has some important and common application modes such as Eletrostatics, Magnetostatics, AC Power Electromagnetics, etc.. However, These modes can not be used to analyze a PDE problem in the cylindrical coordinate system directly. The Poisson equation in the orthogonal curvilinear coordinate system is derived in the paper. Comparing the equation form of the axisymmetric magnetostaic filed in the cylindrical coordinate system with that of the standard elliptic equation in the rectangular coordinate system, the corresponding relations between their coordinates and between their coefficients are gained. And then the analysis of an axisymmetric magnetostaic filed problem is demonstrated by MATLAB/PDEtool. The results confirm the methods.