基于流动坐标系的3维空间动力非线性有限元方法  

A nonlinear dynamic finite element method in 3D space based on the Co-rotational formulation

作　　者：王涛[1] 刘德贵[1] 胡安杰[1] WANG Tao;LIU Degui;HU Anjie(School of Civil Engineering and Architecture,Southwest University of Science and Technology,Mianyang,621000,China)

机构地区：[1]西南科技大学土木工程与建筑学院,四川绵阳621000

出　　处：《振动与冲击》2018年第16期14-23,37,共11页Journal of Vibration and Shock

基　　金：国家自然科学基金(51708468);四川省教育厅项目(15ZB0122);西南科技大学博士基金(16ZX7117)

摘　　要：为了考虑3维空间中柔性结构大幅振动的几何非线性振动效应,建立了基于流动坐标系(CR列式)的Newmark-β非线性有限元动力时程计算方法。在动力时程计算的每一个时间步中,考虑结构的几何非线性,考虑初始应力和重力的时变效应,通过平衡迭代计算,得到有限元模型各个节点的位移、速度、加速度。开发了使用杆、梁单元的有限元计算程序,并提供了详细的计算方法与计算流程。设计了多个算例,计算得到了柔性结构在3维空间的非线性振动现象,依据非线性振动理论解释了现象的原理。通过算例与ANSYS的进行了对比,结果表明:算法与程序编制正确可靠,计算效率高,适用于柔性结构在3维空间中大幅度非线性振动的计算与研究。Considering the geometric nonlinear effect of large amplitude vibration of flexible structures in 3 Dimension(3D)space,a nonlinear dynamic FEM time-history Newmark-βmethod was built based on the Co-rotational formulation theory.In each step of time-history calculation,geometric nonlinearity,time variant effect of stress and gravity in the structure were considered.The equilibrium iteration calculation was used to get the displacement,velocity,acceleration of the nodes in the FE model.An FEM program which used link and beam elements was developed.The methods and calculation flow were discussed.Three numerical examples were designed.The calculation results reflect the nonlinear vibration of the flexible structures in 3D space.And these phenomena were explained by the nonlinear vibration theory.The computational results of the samples were compared with ANSYS.The results indicate that the algorithm and program are reliable and efficient,which can be applied for large amplitude vibration calculation and investigation on flexible construction in 3D space.

关 键 词：有限元方法 3维空间 流动坐标系 几何非线性 动力时程 

分 类 号：TB115[理学—数学]