改进共旋坐标法的Timoshenko梁单元非线性分析

为提高空间Timoshenko梁单元非线性问题的计算精度，在共旋坐标法的基础上，提出了一种改进的Timoshenko梁单元几何非线性分析方法。利用虚功原理得到改进空间梁单元的刚度矩阵；使用有限质点法中的逆向运动思路计算单元局部坐标系下的刚体旋转矩阵；根据整体坐标系与局部坐标系之间旋转角度的转化以及微分关系，求得空间梁单元的切线刚度矩阵；编制了相应的有限元程序，对多个经典的大变形结构进行几何非线性分析。计算结果印证了该文所提出改进方法的正确性，同时与传统共旋坐标法相比，具有更高的精度。

NONLINEAR ANALYSIS OF TIMOSHENKO BEAM ELEMENT BASED ON IMPROVED COROTATIONAL FORMULATION

An improved geometrically nonlinear analysis method based on corotational formulation is proposed to improve the computation accuracy of nonlinear problems of spatial Timoshenko beam element. The stiffness matrix of the improved spatial beam element is obtained by using the principle of virtual work; The rigid-body rotation matrix of the element in local coordinate system is calculated by using the reverse motion approach in finite particle method; The tangent stiffness matrix of the spatial beam element is obtained according to the transformation and differential relationship of the rotation angle between the global coordinate system and the local coordinate system; A finite element program is made to analyze the geometric nonlinearity of several typical large deformation structures. The results show that the improved method proposed in this paper is correct and has higher accuracy than the traditional corotational formulation.