基于近似Woodbury法的杆系结构静力稳定性分析  

Static Stability Analysis for Skeletal Structures Based on Woodbury Approximation Method

作　　者：靳永强 张涛[1] 莫振林 袁永强 李彦滨 周雄雄 JIN Yongqiang;ZHANG Tao;MO Zhenlin;YUAN Yongqiang;LI Yanbin;ZHOU Xiongxiong(China Construction Second Engineering Bureau Ltd.,Beijing 100160,China;China Southuest Geotechnical Inuestigation&Design Institute Co.,Ltd.,Chengdu,Sichuan 610052,China;College of Water Resources and Architectural Engineering,Northuest A&F University,Yangling,Shaanxi 712100,China)

机构地区：[1]中国建筑第二工程局有限公司,北京100160 [2]中国建筑西南勘察设计研究院有限公司,四川成都610052 [3]西北农林科技大学水利与建筑工程学院,陕西杨凌712100

出　　处：《水利与建筑工程学报》2022年第1期148-154,共7页Journal of Water Resources and Architectural Engineering

基　　金：中央高校基本科研业务费专项资金资助(2452020207)。

摘　　要：为了高效求解杆系结构的静力稳定性问题,本文基于多点位移控制算法和近似Woodbury法,提出了一种静力推覆分析方法。该方法以Woodbury公式为理论基础,对多点位移控制的平衡方程进行展开,并结合隔离非线性理论形成了具有刚度矩阵弹塑性分离形式的控制方程,采用近似Woodbury法对控制方程进行高效求解,避免在稳定性分析中整体刚度矩阵的实时求逆运算。通过数值模拟验证了本文方法的有效性和精确性,结果表明:该方法能够较好地追踪失稳后的非线性平衡路径,获得下降段曲线,处理负刚度问题。最后,将本文方法应用于某框架结构的静力稳定性分析中,论证了该方法能高效地获得荷载-位移全过程曲线,完整反映结构的承载力、稳定性及刚度的整个变化历程。An efficient stability analysis method for skeletal structures is proposed by combining the displacement control algorithm with multiple point constraints and the Woodbury approximation method. The inelasticity-separated governing equation including the multiple point displacement constraints is derived based on the Woodbury formula. It is solved by the Woodbury approximation method in the proposed scheme,resulting in an obvious advantage in efficiency for analyzing the stability of skeletal structures. During the analysis,the update and factorization of the global stiffness matrix can be avoided. The feasibility and validity of the proposed method is verified by numerical simulation example.It is indicated that the proposed method can capture the nonlinear equilibrium path and deal with the negative stiffness problem. Finally,the proposed scheme is applied to solve the nonlinear stability problem of a steel frame. Numerical results show that the proposed method can accurately acquire the critical load value in this case where the nonlinear equilibrium path has snap-through buckling situations. Thus,the proposed method has greater potential for obtaining the complete load-displacement curves and solving the negative stiffness problems of skeletal structures.

关 键 词：杆系结构 静力稳定性 近似Woodbury法 隔离非线性理论 

分 类 号：TU375.1[建筑科学—结构工程]