共旋梁单元几何非线性分析的子结构方法

Substructure method for geometric nonlinear analysis of corotational beam elements

采用有限元方法分析结构的非线性行为必须进行多次迭代求解,因此在保证非线性计算精度的同时提高其计算效率是关键。该文以内含2个平面梁单元的子结构为例,建立一种平面梁结构基于共旋法与子结构的几何非线性分析方法。共旋法具有将刚体位移从结构的大位移中扣除而得到准确的小变形的特点,子结构法则能将内部节点的自由度凝聚到边界节点从而大大减少结构非线性平衡方程组的阶数,该文将两者结合并利用有较好的通过荷载和位移极限点功能的修正弧长法编制了计算程序,对荷载-位移曲线具有“位移跳跃”或“荷载跌落”显著特征的数个算例进行分析,与已有文献的结果对比验证了方法及程序的正确性。

The nonlinear behavior of structures analyzed shall be solved through multiple iterations when the finite element method is applied,and it is essential to enhance computational efficiency while ensuring computational accuracy.In this study,with a substructure comprising two plane beam elements taken as an example,a geometric nonlinear analysis method is established for plane beam structures utilizing the corotational method and substructure.The corotational method can precisely calculate small deformations by subtracting rigid body displacements from substantial structural displacements,while the substructure method may condense the degrees of freedom of inner nodes to boundary nodes,significantly reducing the order of nonlinear equilibrium equations.By combining the two methods,a calculation program is developed based on the modified arc-length method with excellent loading and displacement limit point capabilities.With the calculation program,several examples featuring loading-displacement curves with"displacement jumps"or"load drops"in existing literature were analyzed and compared,and the accuracy of the proposed method and the developed program was validated.