Bezier曲面三角形边界元法及其在特高压绝缘子串电场计算中的应用

Research and application of Bezier curved surface trilateral BEM for calculating UHV insulators electric fields

为了在用边界元法计算三维静电场电位和电场分布时能够得到较精确结果，提出了Bezier曲面三角形边界元方法．该方法用ANSYS建模和二阶剖分，利用剖分得至U的节点坐标信息和面积坐标系下对应的Bernstein基函数构造双2次Bezier曲面参数方程，再利用面积比值法构造对应于Bezier曲面顶点节点的形状函数，由Bezier曲面参数方程和形状函数可得到Bezier曲面边界元方程．以计算导体球的电场和电位分布为例进行验算，由计算结果可知：在计算相同剖分节点的情况下，Bezier曲面三角形边界元法比一阶平面三角形边界元法具有更高的计算精度．最后，将Bezier曲面三角形边界元法应用于特高压绝缘子串的电场计算．

In order to determine the electric field and the potential distribution of 3D electrostatic field accurately by using the boundary element method （BEM）,this paper proposes Bezier curved surface trilateral BEM. This method uses ANSYS to build the model and second-order element to mesh the boundary sur face. Making use of the second-order element node information and corresponding Bernstein basis functions which are in the area coordinates construct the corresponding Bezier curve parameter equation. Using area ratio method constructs shape function which is correspond to the surface trilateral element. Last the Bezier curved surface boundary element equation can be obtained by Bezier curve parameter equation and the surface element shape function. In this paper, the electric field and potential distribution calculation of spherical electrode is given. The calculating results show that when the grid nodes is equal, calculation precision of Bezier curved surface trilateral BEM is obviously improved in compared with the first-order plane trilateral BEM. Finally, the Bezier curved surface trilateral BEM is applied to UHV insulator string electric field calculation.