用局部Petrov-Galerkin方法分析弹性杆振动问题  

Analysis for Vibration Problems of Elastic Bars by the Meshless Local Petrov-Galerkin Method

作　　者：熊渊博[1] 曾纪杰[2] 

机构地区：[1]湖南大学工程力学系,湖南长沙410082 [2]湖南理工学院机电系,湖南岳阳414000

出　　处：《岳阳师范学院学报（自然科学版）》2004年第1期61-64,共4页Journal of Yueyang Normal University

基　　金：湖南省自然科学基金 ( 0 2JJY40 71)资助项目

摘　　要：提出一维弹性动力问题的局部Petrov -Galerkin方法 ,这是一种真正的无网格方法。这种方法采用移动最小二乘函数来近似解变量 ,并且采用移动最小二乘近似函数的权函数作为加权残值法的权函数。文中对形成的离散动力学方程用Newmark方法求解 ,计算实例表明 :局部Petrov -Galerkin方法是一种很有效的求解弹性动力学问题的方法。The Meshless Local Petrov-Galerkin (MLPG) method is utilized to analyze the vibration problem of a bars in the paper. It was a truly meshless method. It used the moving least square approximation as a trial function, and used the weighted function of the moving least square approximation as a test function of the weighted residual method. The local weak formulation is derived from the dynamic partial differential equation. The Newmark methods is used for the time integration scheme. Numerical examples,free and forced vibration analyses for bar, show that the local Petrov-Galerkin method was applicable and effective for solving the vibration problem of elastic body.

关 键 词：无网格局部Petrov—Galerkin方法 移动最小二乘法 弹性体振动 Newmark方法 

分 类 号：O326[理学—一般力学与力学基础]