空间钢框架几何非线性分析的新梁-柱单元

A new beam-column element for nonlinear analysis of space steel frames

基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部六个应力分量,考虑了结构变形过程中由于力矩空间转动引起的连带弯矩影响及弓形效应,采用可计入单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及力矩转动属性的空间钢框架梁-柱单元几何非线性切线刚度矩阵.利用框架节点的平衡条件对单元刚度矩阵进行简化,得到了结构整体的几何刚度矩阵.并通过算例证明了本方法的精确度和有效性.

According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components has been taken into account to consider the induced moments generated by rotation of the initial moment about the other axes in the deformation of the structure from the C1 to the C2 configuration and the bowing effect has also been considered. The cubic polynomial interpolation function which can be used to consider the element shearing deformation has been applied to derive the geometrical nonlinear stiffness matrix of the space steel frame beam-column element considering shear effects and the rotational characteristic feature of moments in detail, and the incremental stiffness equations for the structure are yielded based on the conditions of compatibility at nodal points of space frames. The accuracy and efficiency Of the proposed analytical method are verified by numerical examples.