應用無網格Galerkin法於一維梁之靜力與動力分析

Abstract

無網格法為近十幾年來逐漸日趨成熟的演算法，相較於傳統的有限元素法，其具有不需使用網格建立形狀函數之特點，讓無網格法擺脫有限元素法在處理某些問題遭遇到的限制。但由於無網格法發展並未如有限元素法的歷史悠久並且成熟，在許多研究方面仍待拓展。一維梁是簡單的問題且有解析解，本研究利用無網格法分析一維問題，重點在於探討無網格法之參數對於分析誤差的影響，以便有利於日後將無網格法應用到更複雜之問題。

The meshfree method has attracted lots of attentions from the researchers in the field of numerical analysis in the recent two decades. The meshfree method has the advantage over the finite element method on constructing shape function without predefining meshes. The development of the meshfree method is still far away from maturity. Accordingly, the main purpose of the work is to study comprehensively the convergence behaviors of the solutions obtained from the element free Galerkin method. The element free Galerkin method is applied to analyze a beam under static loading and to determine the natural frequencies of a beam. The used shape functions are constructed by the moving least squares method or radial basis function approach. The accuracy of the solutions influenced by the parameters such as the type of weighting function and basis function, the number of nodes is extensively investigated.