摘要
为了精确计算三维静电场中圆柱形和圆台形电极表面的电场强度,基于柱坐标变换提出了柱面曲边四边形边界元法。该方法中积分的区域为柱面,求解函数采用柱面上柱坐标线性插值,单元的外法线方向取严格的柱面法线方向。计算结果表明,与平面直边单元相比,在网格剖分节点相同时,柱面曲边四边形边界元法的计算精度明显提高。在计算精度要求相同时,柱面曲边四边形边界元法节点数较少,具有计算速度快,占用内存少等优点。
In order to calculate the electric field intensities of cylindrical or conical electrodes in 3-D electrostatic fields precisely, the cylindrical and conical surface curve quadrangular BEMs which are based on cylindrical coordinates transformation are put forward. Firstly, owing to the cylindrical coordinates system being orthogonal system, the cylindrical or conical surface in rectangular coordinates system is transformed to rectangular region in （ φ, z） plane which is an abstract plane. And one-to-one mapping is built up from cylindrical or conical surface in rectangular coordinates system to rectangular region in （φ,z） plane. From differential area variable on cylindrical or conical surface to differential area variable on （φ,z） plane, Jacobian is given. Secondly, according to one-to-one mapping relation, if the cylindrical or conical surface is meshed by quadrangular elements corresponding nodes on （φ, z） plane are connected lines which form plane straight side quadrangles. These plane straight side quadrangles correspond to cylindrical or conical surface curve quadrangles. Thus integrals on cylindrical or conical surface curve quadrangles can obtain by calculating integrals on plane straight side quadrangles in （ φ, z） plane. Thirdly, because unknown function is linearly interpolated along cylindrical coordinates on （φ,z） plane, according to one-to-one mapping relation, unknown function is linearly interpolated along cylindrical coordinates on cylindrical or conical surface. Finally, directions of outward normal line to element and cylindrical or conical surface are strictly unanimous, and formulae of the unit normal vector of cylindrical and conical surface are given. The calculating results show that, at the condition of the same meshing, compared with high precise finite element（FE） results, the cylindrical and conical surface curve quadrangular BEM results are consistent with FE, whereas results of the plane straight side quadrangles which are also in rectangular coordinates system have big errors. Hence compared with plane straight side BEM, on the condition of the same nodes the precision of the cylindrical and conical surface curve quadrangular BEMs are higher obviously, and on the condition of the same precision the cylindrical and conical surface curve quadrangular BEMs require less nodes, consequently required memory and calculated time can be decreased greatly.
出处
《高电压技术》
EI
CAS
CSCD
北大核心
2007年第1期132-135,共4页
High Voltage Engineering
关键词
静电场计算
边界元法
圆柱面曲边四边形
圆柱形电极
圆台形电极
electrostatic field calculation
boundary element method
cylinder surface curve quadrangle
cylinder electrode
cone electrode
作者简介
李亚莎 1967-，男，博士生，研究方向为电磁场数值计算。电话：（010）51971619；E-mail：chwld92@yahoo．com.cn.
王泽忠 1960-，男，博士，教授，博导，现从事电磁场分析计算、电力系统电磁兼容和电磁测量等科学研究和教学工作。
