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Smoothing Analysis for the Singularity of Patch Functions in Weak-Form Equations

 

Tian Zhongxu   Liu Zhengxing

Department of engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030

Abstract: In weak form equations, singularity problems will be faced when derivatives of patch functions are concerned. This paper concentrates on the disposal of the singularities of the sample and test functions in week forms, So that .to provide some rules for the disposal of the singularity. Through the analysis, the patch functions were smoothing without any change of their property of fitting and integrate property are analyzed. Some computational rules are given to ensure the singularities be disposed of properly while obtaining the discrete forms. These computational are frank and easy to be used. The computational rules can also be some basis of the analysis for the singularity. Two typical elastic problems, Beam bending and thin plate bending problems are disposed of and analyzed. The examples have shown that these rules are useful and reasonable.

 

Key Words: smoothing, weak-form, computational rules, finite element method, discrete operator difference, reproduction

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