梁杆结构二阶效应分析的一种新型梁单元

推导了一种计及梁杆二阶效应的新型两结点梁单元。首先依据插值理论构造了三结点Euler-Bernoulli梁单元的位移场:使用五次Hermite插值函数建立梁单元的侧向位移场,二次Lagrange插值函数建立梁单元的轴向位移场,进而由非线性有限元理论推导了单元的线性刚度矩阵和几何刚度矩阵,然后使用静力凝聚方法消除三结点梁单元中间结点的自由度,从而得到一种考虑轴力效应的新型两结点梁单元。实例分析表明,此新型梁单元具有很高的计算精度,使用此单元进行梁杆结构分析可获得相当准确的二阶位移和内力。

A NEW BEAM ELEMENT FOR SECOND-ORDER EFFECT ANALYSIS OF BEAM STRUCTURES

A new two-node beam element considering the second-order effect of beams is developed. Based on the interpolation theory, the displacement fields of the three-node Euler-Bernoulli beam element are constructed at first: the quintic Hermite interpolation polynomial is used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then the linear and geometric stiffness matrices of the three-node beam element are derived according to the nonlinear finite element theory. Finally the degrees of freedom of the middle node of the element are eliminated using the static condensation method, and a new two-node beam element including axial-force effect is obtained. The results of several examples show that the second-order displacements and internal forces with high precision can be obtained with this new beam element.