弱形式方程中分片函数奇异性的光滑化分析

研究弱形式方程中的分片光滑函数因求导数出现的奇异性问题，意在为得到离散格式时正确处理这一问题提供依据。在不改变拟合性质的情况下，将分片函数光滑化，则分步积分公式仍然有效。通过光滑后的函数讨论其积分的性质，总结出了几条计算规则。文中的典型例子说明这些计算规则是合理而有效的。

SMOOTHING ANALYSIS FOR THE SINGULARITY OF PATCH FUNCTIONS IN WEAK-FORM EQUATIONS

In weak form equations, singularity problems will always be faced as far as derivativesof patch functions are concerned. This paper concentrates on the disposal of the singularitiesof sample and test functions in week forms so as to provide some rules for singularity disposal.Through the analysis, the patch functions were smoothed without any change of their fittingproperty and then their integrate property are analyzed. Some computational rules are given toensure the singularities be disposed of properly in discrete form derivation. These computationalrules are proved easy to use. The computational rules can also be regarded as some basis forsingularity analysis. Two typical elastic problems: beam bending and thin plate bending problemsare disposed of and analyzed, showning that these rules are useful and reasonable.