矩形管中对空间立体角积分的计算方法

The computational method of integration for solid angle on lateral surface of the rectangular pipe

根据任意闭合曲面对曲面外任一点所张立体角等于零这一特点,我们提出了积分面转换的计算方法,即把对矩形管侧面的积分转变为对矩形管横截面的积分,同时,在轴向采用线性插值函数的条件下,将矩形管横截面的积分表示成解析形式,从而实现了矩形管侧面对空间任一点所张立体角积分的完全解析表示。

Based on the solid angle that a closed surface opens to an outer point of that is zero, we give a computational method of change of integrating surface, i.e., the integration for lateral surface of rectangular pipe has been changed into the integration for the cross section of the rectangular pipe. Therefore, under the assumption that the interpolation functions between nodal points are linear in direction of axis, the integration for the cross section of the rectangular pipe has been turned into analytic solution, thereby on the lateral surface of rectangular pipe, the integration for solid angle to any point has been completely expressed in analytic solution.