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本文根据薄壁杆件的约束扭转理论,对薄壁杆系结构有限元分析中的几个基本问题进行了探讨。明确指出一般的薄壁杆件的单元刚度矩阵是建立在两种坐标系下的混合单元刚度矩阵;提出用坐标变换的方法可以把混合单元刚度矩阵变换到统一的形心主惯性坐标系中,从而解决了由于截面的形心与扭转中心不在同一点而给建立结构有限元方程带来的困难;同时提出了三种典型的结点模型,以及各自在有限元分析中的处理方法,使得反映截面翘曲的广义结点位移фx在结点的连续性的概念较为明确。
Based on the theory of constrained torsion of thin-walled rods, this paper discusses several basic problems in the finite element analysis of thin-walled rods. It is pointed out that the unit stiffness matrix of general thin-walled members is the stiffness matrix of mixed units established in the two coordinate systems. It is proposed that the method of coordinate transformation can transform the stiffness matrix of the mixed elements into a unified centroid-based principal inertial coordinate system. It solves the difficulty of establishing the structural finite element equation due to the fact that the centroid of the section is not in the same position as the torsion center. At the same time, three typical model nodes are proposed, and their respective processing methods in the finite element analysis are analyzed. The concept of the continuity of the generalized node displacement фx in section warp is more clear.