浅析质量矩阵对动力计算精度的影响  

ANALYSIS OF THE INFLUENCE OF MASS MATRIX ON THE PRECISION OF DYNAMIC CALCULATION

作　　者：张尧 董军 李国华 王秀芳 ZHANG Yao;DONG Jun;LI Guo-hua;WANG Xiu-fang(Beijing Higher Institution Engineering Research Center of Structural Engineering and New Materials,Beijing University of Civil Engineering and Architecture,Beijing 100044,China)

机构地区：[1]北京建筑大学土木与交通工程学院工程结构与新材料北京市高等学校工程研究中心,北京100044

出　　处：《工程力学》2023年第S01期11-18,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51808025);北京市自然科学基金项目(8202012);长江学者和创新团队发展计划项目(IRT_17R06);北京建筑大学北京未来城市设计高精尖创新中心项目(UDC2019021424);北京建筑大学金字塔人才培养工程项目(JDYC20200329)。

摘　　要：通过一致质量矩阵和集中质量矩阵的显式表达,对比分析了质量矩阵对Euler-Bernoulli梁理论和两结点双线性插值梁理论动力计算精度的影响。并通过Python有限元程序的数值模拟,揭示了两结点双线性插值梁的优越性。理论推导和数值分析结果表明:梁单元动力计算前必须进行网格剖分;网格密度的增大并不能提高Euler-Bernoulli梁集中质量矩阵的动力精度,而一致质量矩阵的收敛性显著高于集中质量矩阵。The influence of mass matrix on dynamic calculation accuracy of Euler-Bernoulli beam theory and two-node bilinear interpolation beam theory is compared and analyzed by displaying uniform mass matrix and concentrated mass matrix.The superiority of two-node bilinear interpolation beam is revealed by numerical simulation using the finite element program Python.The results of theoretical derivation and numerical analysis show that the grid must be divided before the dynamic calculation of beam element.The increase of mesh density does not improve the dynamic accuracy of Euler-Bernoulli beam using concentrated mass matrix,while the convergence of uniform mass matrix is significantly higher than that of concentrated mass matrix.

关 键 词：有限元 质量矩阵 两结点双线性插值梁 Euler-Bernoulli 转动质量 

分 类 号：TU311.3[建筑科学—结构工程]