摘要
推导一种精确的Bernoulli-Euler变截面梁单元,解决了传统变截面梁单元在结构稳定性分析中存在的计算精度较低的问题,以常见的外形沿轴向按线性变化的变截面梁为例,给出梁单元的精确刚度阵。放弃传统有限元通过插值理论构建变形场,并通过虚位移原理获取单元刚度阵的方法,直接从计入二阶效应的单元平衡微分方程中得到变截面梁的载荷位移关系,进而得到有限元格式的变截面梁精确刚度阵。借助于变截面梁单元刚度阵,可导致与精确的微分方程解析法同样的计算精度。通过与几个经典算例和ANSYS计算结果比较表明:该精确刚度阵可直接应用于结构稳定性分析,获得变截面梁结构精确的欧拉临界力。
The exact stiffness matrix of the tapered Bernoulli-Euler beam is proposed, whose profile is assumed to be varying linearly, and it can be incorporated into stability analysis with high accuracy. The Bernoulli-Euler theory of bending is used to describe the motion of the beam. Classical finite element method to obtain stiffness matrix is replaced by interpolation method and the principle of virtual work. Solving the governing differential equation of motion with second-order effects, the force- displacement relation is obtained. In the formulation of finite element method, the derived stiffness matrix has the same accuracy with the solution of exact differential equations. The results are compared with some classical ones and ANSYS＇s. It shows that the proposed exact stiffness matrix offers an accurate and effective tool for stability analysis of tapered beam structures, and obtains the exact Euler critical force.
出处
《工程力学》
EI
CSCD
北大核心
2008年第12期60-64,78,共6页
Engineering Mechanics
基金
国家科技支撑计划项目(2006BAJ12B03-2)
