薄壁杆系结构的梁元分析模型

Beam Element Analytical Model of Thin-walled Beam Structure

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型。在空间梁元分析模型的基础上,采用了一种改进的位移模式,考虑了薄壁杆件可能发生的拉压、剪切、弯曲、扭转和翘曲等各变形形式以及它们的耦合效应,得出了相应的单元形函数;同时从工程应变的定义出发,采用Taylor级数展开的方法,建立了单元的五阶近似正应变表达式;并建立了相应的薄壁单元刚度方程,从而得出了局部坐标系下单元刚度矩阵的显式。根据本文所导出的薄壁梁元分析模型,编制了相应的结构计算程序。通过算例验证了本文所推导的单元刚度矩阵,同时通过与传统空间梁元计算模型计算结果的比较,阐述了截面翘曲对薄壁杆系结构的影响。

In this paper, a kind of thin-walled beam element analytical model that can be used in the elastic analysis of thin-walled beam structure was presented. Based on the space beam element analytical model, an improved displacement model was adopted. It can consider the possible patterns of the deformation of thin-walled beam, such as tension or compression, shear, bending, torsion and warping, and their coupling effect. Thus the element shape function was derived. According to the definition of Green strain, the expression of normal strain of element was constituted using the method of expanding Taylor series. And the corresponding thin-walled element stiffness equation was formulated. The apparent formulation of element stiffness matrix under the local coordination was attained. According to the thin-walled beam element analytical model obtained by this paper, the interrelated structural calculating program was worked out. The numerical example validates the element stiffness matrix. Finally the comparison between the space beam model and the thin-walled beam model indicates the effect of section warping on the thin-walled beam structure.