Abstract: The difference between the theory heat input and the heat input calculated by Gauss numerical integral method, which was input by Gauss heat source was discussed, when the different integral zone and mesh element size were taken into account. The numerical result is close to theory value when length side of integral zone is equal to 3 times the effective radius of heat source. The lager zone couldn't improve numerical integral precision. The numerical integral result is lower than theory value when the value of Gauss Point is gained by shape function but higher when it was gained by Gauss distribution function. The numerical precision is very high when the mesh element size is 1/6 times the size of integral zone or 1/2 times the effective radius of heat source. The smaller element size couldn't improve numerical precision.

Key words: Gauss heat source model , Gauss integration , Welding temperature field

摘要： 讨论了当焊接热源为高斯热源时,采用不同大小的积分区域和网格单元尺寸,由高斯数值积分得到
的热输入与理论热输入之间的差异。认为当积分矩形区域的边长为3R(R 为热源有效半径)时,数值积分得到的热
输入量就非常接近理论热数量,增大积分区域尺寸对结果精度的影响有限。高斯点函数值采用形函数给出时,积分
结果偏小,而直接用已知函数给出时,积分结果偏大。等分数为3,即网格单元尺寸为积分区域尺寸的1/6或有效热
源半径的1/2时,数值积分的精度已非常高,网格单元尺寸更进一步减小时对精度提高的作用有限。

关键词: 高斯热源模型 , 高斯积分 , 焊接温度场