无单元法应用于欧拉梁的动力特性分析
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摘要
基于广义移动最小二乘法建立了同时考虑挠度和转角双变量的无单元法用于欧拉梁的动力计算.与传统有限元法相比,该方法只需输入节点信息无需定义单元,具有前处理简单的优势;与只考虑挠度的单变量无单元法相比,该方法具有更高的插值精度.运用双变量无单元法计算了4种不同边界条件欧拉梁的自振圆频率和振型,通过与理论解、有限元解、单变量无单元解的比较,表明无单元法在动力分析中的应用是可行的,欧拉梁的计算同时考虑挠度和转角双变量是必要的,该法在高阶振型计算中具有精度优势.
Based on the generalized moving least square method,a new element-free Galerkin(EFG) double-variable approximation is proposed for dynamic analysis of Euler beam.Compared with finite element method(FEM),only individual nodal data is required in the current method so that its preprocessor is fairly easy.In contrast to the single-variable approximation which is constructed only using the nodal coefficients of deflection,the present approximation has smaller interpolation error.Natural frequencies and natural modes of four Euler beams with different boundary conditions are calculated by the current method.By comparing with theoretical solution,FEM and single-variable EFG,it is conclude that double-variable EFG is feasible on dynamic analysis and it is necessary to consider both the deflection and rotation nodal variable.This method is more accurate than FEM in higher-order modes calculation of Euler beam.
Based on the generalized moving least square method,a new element-free Galerkin(EFG) double-variable approximation is proposed for dynamic analysis of Euler beam.Compared with finite element method(FEM),only individual nodal data is required in the current method so that its preprocessor is fairly easy.In contrast to the single-variable approximation which is constructed only using the nodal coefficients of deflection,the present approximation has smaller interpolation error.Natural frequencies and natural modes of four Euler beams with different boundary conditions are calculated by the current method.By comparing with theoretical solution,FEM and single-variable EFG,it is conclude that double-variable EFG is feasible on dynamic analysis and it is necessary to consider both the deflection and rotation nodal variable.This method is more accurate than FEM in higher-order modes calculation of Euler beam.
引文
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[2]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,1998.
[3]Belytschko T,Lu Y Y,Gu L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineer-ing,1994,37:229-256.
[4]Lu Y Y,Belytschko T,Gu L.A new implementation of the element free Galerkin method[J].Computer Methods in AppliedMechanics and Engineering,1994,113:397-414.
[5]Atluri S N,Cho J Y,Kim HG.Analysis of thin beams,using the meshless local Petrov-Galerkin method,with generalizedmoving least squares interpolations[J].Comput Mech,1999,24:324-334.
[6]杨玉英,李晶.无网格Galerkin方法中权函数的研究[J].塑性工程学报,2005,12(4):5-9.
[7]吴琛.基于小波变换及无单元法的结构动力仿真分析[D].福州:福州大学,2007.
[8]张雄,刘岩.无网格法[M].北京:清华大学出版社,2004.
[9]帕兹M.结构动力学———理论与计算[M].李裕澈,刘勇生译.北京:地震出版社,1993.
[10]袁驷,叶康生,Williams F W,等.杆系结构自由振动精确求解的理论和算法[C]//崔京浩.第十四届全国结构工程学术会议论文集.北京:工程力学杂志社,2005:159-165.
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