带刚臂空间梁元的几何非线性有限元分析

A GEOMETRICAL NONLINEAR FINITE ELEMENT ANALYSIS OF 3-D BEAM ELEMENT WITH RIGID ARMS

为解决应用空间梁元进行结构的几何非线性分析时所存在的相交处刚性连接问题,根据刚臂在受力后只有刚体运动而本身不变形的特点,将刚臂视为空间矢量,利用空间矢量有限转动公式及微分方法,导出了结构坐标系下刚臂两端的位移和杆端力的总量及增量关系。结合常规空间梁元非线性切线刚度矩阵,得到了两端带任意刚臂的空间梁元切线刚度矩阵显式表达式。依据此算法编制了相应的非线性有限元计算程序,对弯梁、框架等结构进行了空间几何非线性分析。计算结果表明:应用两端带任意刚臂的空间梁元可以很好地解决前面提到的问题,且其有限元分析格式与不带刚臂的空间梁元完全一致,具有很好的实用性。

In order to solve the problem of a rigid link when a 3-D beam element is applied to structural geometrical nonlinear analysis, the relationships of total amount and incremental for the displacement and the end force of ends of rigid arms in a global coordinate system are presented via a treating rigid arm as a spatial vector and then employing its finite rotation formula and differential method, based on the characteristics of the forced rigid ann having no deformation but rigid motion. The explicit expressions of the nonlinear tangent stiffness matrix of a 3-D beam element with rigid arms in both ends are obtained by Combining the traditional nonlinear tangent stiffness matrix of a 3-D beam element. A finite element program based on the algorithm is developed to analyze the geometric nonlinear behaviors of the curved beam and frame structures. Numerical results demonstrate that the proposed 3-D beam element can solve the structural analysis of a 3-D beam with rigid links. Moreover, this beam element is valid and practicable due to its consistent format with the general beam element without rigid arms.