一种新型高效的几何非线性梁-柱单元  

A New Efficient Geometric Nonlinear Beam-Column Element

作　　者：王震[1,2,3] 李国强 WANG Zhen;LI Guoqiang(College of Civil Engineering, Tongji University, Shanghai 200092, China;State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;Shanghai Ershiye Construction Co. I.td Shanghai 201999, China;China MCC20 Group Corp. Ltd. , Shanghai 201999, China)

机构地区：[1]同济大学土木工程学院,上海200092 [2]上海二十冶建设有限公司,上海201999 [3]中国二十冶集团有限公司,上海201999 [4]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《建筑钢结构进展》2018年第3期26-32,共7页Progress in Steel Building Structures

基　　金：国家自然科学基金(51120185001)

摘　　要：进行杆系结构有限元分析时,为得到足够精确的数值解往往需要将构件划分为大量的单元。单元数量的增加不仅会极大的增加计算代价,还易产生数值计算不收敛的问题。在梁-柱单元位移函数中引入了轴力的影响,将传统三次位移函数改进为四次位移函数,并推导得到了新型几何非线性梁-柱单元。新单元几何非线性刚度矩阵中考虑了单元位形变化对平衡方程的影响及单元位形变化对几何方程的影响,进而可以考虑二阶效应、弓形效应。采用新单元编制了有限元程序,算例分析表明:该新梁-柱单元精度得到了显著改善,可以极大减少非线性有限元模型的单元数量,在分析柱的稳定、梁悬链线效应等极限问题时具有显著优势。To get an accurate simulation result, more elements are needed in numerical simulations. This will not only increase the computational cost significantly,but also reach the computational divergence more easily. Instead of using traditional Hermitian cubic interpolation function,the axial force is considered in element deformation in this paper, and a fourth order interpolation function is derived to form a new beam-column element. The influence of element deformation on the equilibrium equation and geometric equation is considered in the new element,known as the second-order effect and bowing effect. A finite element program is written to verify the efficiency and accuracy of the new element comparing to B23 element in ABAQUS software. It can be concluded that the element number can be greatly reduced under the same accuracy, and more superior in dealing with limit analysis, such as the stability of columns and catenary effect of beams.

关 键 词：梁-柱单元 几何非线性 单元刚度矩阵 二阶效应 弓形效应 

分 类 号：TU311[建筑科学—结构工程]