含有整体刚体位移杆件系统的几何非线性分析

GEOMETRIC NONLINEAR ANALYSIS OF TRUSS SYSTEMS WITH RIGID BODY MOTIONS

许多杆件系统中,结构和机构共同存在。应用现有有限元理论很难分析这些杆件系统的几何非线性效应。该文引入多组坐标:总体坐标系、物体坐标系、单元坐标系、节点坐标系和截面坐标系,介绍了一种含刚体位移杆件系统几何非线性效应的共转坐标方法。该文假设梁单元交叉节点为刚性连接,即:节点坐标系和截面坐标系之间的坐标转换矩阵始终不变,明确了杆件结构中节点转动的概念。并且依据有限转动理论,推导出物体在单元坐标系和总体坐标系下的变形转换关系,有效的分解了物体的大转动、大变形效应。进而列出了大变形分析的非线性残量方程。另外,该文用多体系统动力学处理约束的方法,建立了具有复杂边界条件结构的增广约束方程。最后,给出4个算例,验证了所述方法的可行和正确性以及约束增广法处理约束的有效性。

Many truss systems are both structures and mechanisms.So it is hard to solve these problems using the classical FEM theory.Aiming at dealing with the geometric nonlinear effect of these systems,this paper presents a co-rotational method using a series of coordinate systems which include global coordinate,body-fixed coordinate,element coordinate,node coordinate and section coordinate.It is supposed that the cross-section nodes are rigidly connected,namely the transformation matrix between the node coordinate and the section coordinate is invariable,thus the rotational concept is clearer.Subsequently,the deformational conversion relationship between element coordinate and global coordinate is attained based on the finite rotation theory,and it is shown that the large rotation and deformation are appropriately converted into small strain effect.Then,the nonlinear formulation of the residual forces is obtained.In addition,this paper gives a new augmented constraint method which is widely used in multi-body dynamics to deal with complicated displacement boundary conditions.Finally,four numerical examples are given to verify the method of this paper.