摘要
推导了一种新型的空间两结点非线性Euler-Bernoulli梁单元。使用传统有限元方法的插值理论构造了空间三结点Euler-Bernoulli梁单元的位移场:二次Lagrange插值函数建立单元的扭转和轴向位移场;五次Hermite插值函数建立单元的横向位移场,然后推导了此空间三结点梁单元的切线刚度矩阵,随后使用静力凝聚方法消除三结点梁单元内部结点的自由度,从而得到一种新型的空间两结点Euler-Bernoulli梁单元。通过结构稳定算例证明:一个新型梁单元的计算精度相当于3个―4个传统非线性两结点梁单元,每根杆件使用一个单元离散就可得到非常准确的临界载荷。
A spatial two-node nonlinear Euler-Bernoulli beam element is derived. The displacement fields of the spatial three-node beam element are constructed using the interpolation theory of the conventional finite element method. The quadratic Lagrange interpolation polynomial is used for the torsional and axial displacement fields and the quintic Hermite interpolation polynomial for the transverse displacement fields. Then the linear and geometric stiffness matrices of the three-node beam element are derived from the displacement fields. A three-dimensional two-node beam element is developed by eliminating the degrees of freedom of the interior node of the three-node element using the static condensation method. The results of several structural buckling examples show that only one of the new beam element has the same accuracy with that of 3-4 conventional two-node beam elements and the critical force with high accuracy can be obtained even each beam is discretized into one element.
出处
《工程力学》
EI
CSCD
北大核心
2009年第4期86-91,共6页
Engineering Mechanics
关键词
梁杆结构
结构稳定
有限单元法
空间三结点梁单元
静力凝聚
framed structures
structural buckling
the finite element method
spatial three-node beam element
static condensation
