無元素法高斯積分與置點積分耦合之研究

On the Coupling of Gaussian Quadrature and Collocation Integration in the Element Free Glerkin Method

莊清鏘(Ching-Chiang Chuang) ； 黃致榮(Chih-Jung Huang) ； 王仲宇(Chung-Yue Wang)

《中國土木水利工程學刊》 23卷4期 (2011/12) Pp. 385-394

https://doi.org/10.6652/JoCICHE.201112_23(4).0004

摘要

本研究主要探討無元素法弱化方程用背景網格積分的適用性。無元素法模擬問題時不需要事先建立節點關聯的元素，弱化方程常用高斯背景網格積分，積分網格與積分區域不重合時常以積分點位在積分區域的內、外做為積分點參與積分運算的準則，此方式容易因積分點權重影響計算的精確和穩定性。不同於高斯積分，置點積分每個積分點權重相同，只要積分點數足夠就可以得到精確、穩定的結果。本研究將結合高斯積分與置點積分法計算無元素法的弱化方程，並比較傳統高斯積分和置點積分的結果，說明高斯耦合置點積分的優越性。

關鍵字

無元素法 ； 變動式最小平方近似法 ； 高斯積分 ； 置點積分

並列摘要

The suitability of integrating the corresponding weak form with background cells by element free Galerkin method is discussed. In the element free Galerkin method, the connectivity of nodes is not necessary in pre-processing. The weak form is usually integrated with Gaussian-background cell, and the integration cells may not fall into the integration domain completely as the integration cell is independent of the integration domain. Then the location of the integration point is taken as the judging principle for integration. However, the accuracy and stability may be influenced by integration point weighting, and the weighting values of collocation integration are the same, which is different from the Gaussian quadrature. Therefore, acceptable results may be obtained if the number of integration points is large enough. The main purpose of this research is coupling Gaussian quadrature and collocation integration, and the coupled method is compared with traditional Gaussian quadrature method and collocation integration method, which proves the superiority of the coupling method.

並列關鍵字

element free Galerkin method ； moving least squares method ； Gaussian quadrature ； collocation integration