关于伽辽金法的一点注记  

A NOTE ON GALERKIN METHOD

作　　者：陈波[1] 李映辉[1] 李翔宇 CHEN Bo;LI Yinghui;LI Xingyu(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu,610031,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都610031

出　　处：《力学与实践》2022年第2期393-396,共4页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11872319)。

摘　　要：伽辽金法作为一种数值方法,广泛用于各种数学物理工程问题。教科书和一些文献关于伽辽金法试函数的选取存在一些争议,本文通过应用该法求解轴向力作用下悬臂梁的静动力学问题为例,证实仅选取满足位移而不满足力边界条件的试函数时,即使增加试函数的个数,可能也无法获得正确的计算结果。Galerkin method is a numerical method widely used in mathematics, physics, and engineering problems. There are some controversies among textbooks and some literature about the selection of trial functions. To make an example, this paper uses Galerkin method to solve the static and dynamic problems of a cantilever beam under the axial load. It is proved that correct results cannot be obtained when choosing trial functions that satisfy only displacement but not force boundary conditions, even if increasing the number of trial functions.

关 键 词：伽辽金法 试函数 轴向力 悬臂梁 

分 类 号：O302[理学—力学]