摘要
基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。
On the basic assumptions of the Euler-Bemoulli beam, a new method based on the static condensation to obtain the stiffness matrix of tapered beam element is proposed, whose sections are continuously changing along its axial direction, and then, by use of the moving coordinate method, the analysis of large displacement, large rotation but small strain tapered beam structures is proposed. Firstly, according to the interpolation theory and the nonlinear finite element theory, the tangent stiffness matrix of the tapered beam element with 3-node is deduced. Then, the degrees of freedom of the middle node are eliminated by the static condensation method, and a new tapered 2-node beam element is given. Combined with the moving coordinate method, the following coordinate with simple supported is established, and the large displacement total equilibrium equation is obtained. Finally, a numerical example shows that the proposed tapered beam element has high efficiency, and it can be used for nonlinear analysis of structures withtapered beam.
出处
《工程力学》
EI
CSCD
北大核心
2013年第10期257-263,共7页
Engineering Mechanics
基金
国家科技支撑计划项目(2011BAJ02B01-02)
关键词
有限单元法
变截面梁单元
静力凝聚
随动坐标法
几何非线性
finite element method
tapered beam element
the static condensation
moving coordinate method
geometric nonlinerity
