Nonlinear Analysis of Structures with Negative Stiffness Based on Force Analogy Method

李钢; 李凯; 余丁浩; 杨树标

doi:10.13409/j.cnki.jdpme.2018.02.003

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Nonlinear Analysis of Structures with Negative Stiffness Based on Force Analogy Method

更新时间：2025-12-11

- Nonlinear Analysis of Structures with Negative Stiffness Based on Force Analogy Method
- Vol. 38, Issue 2, Pages: 216-223(2018)
- 作者机构：
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- DOI：10.13409/j.cnki.jdpme.2018.02.003
  CLC： U311.3
- Published：2018
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[1]李钢,李凯,余丁浩,杨树标.基于拟力法的负刚度非线性分析[J].防灾减灾工程学报,2018,38(02):216-223.

李钢, 李凯, 余丁浩, et al. Nonlinear Analysis of Structures with Negative Stiffness Based on Force Analogy Method[J]. 2018, 38(2): 216-223.
[1]李钢,李凯,余丁浩,杨树标.基于拟力法的负刚度非线性分析[J].防灾减灾工程学报,2018,38(02):216-223. DOI： 10.13409/j.cnki.jdpme.2018.02.003.

李钢, 李凯, 余丁浩, et al. Nonlinear Analysis of Structures with Negative Stiffness Based on Force Analogy Method[J]. 2018, 38(2): 216-223. DOI： 10.13409/j.cnki.jdpme.2018.02.003.

摘要

拟力法是一种高效的结构非线性分析方法

当结构进入非线性状态时

拟力法仅需对一个代表局部塑性且规模较小的矩阵进行迭代运算

从而避免了传统方法对规模较大的整体刚度矩阵的分解运算。拟力法在处理负刚度问题时

结构的非线性特征由局部塑性矩阵集中体现。研究了负刚度条件下拟力法中局部塑性矩阵的正负定特性及条件数与最小特征值等数值特征

得到了第二刚度系数对矩阵数值特征的影响规律

并与传统方法中整体刚度矩阵的相应特征进行了对比分析。结果表明

结构进入负刚度状态时

拟力法中局部塑性矩阵将表现为非正定性

且相比于整体刚度矩阵

数值模拟表明其具有条件数少、数值精度高的特征。最后通过数值算例验证了拟力法在计算负刚度问题的优势与计算能力。

Abstract

The force analogy method（FAM）is an effective numerical method for structural nonlinear analysis.When nonlinearity occurs at some small regions of structure

FAM only need to factorize a relative small local plastic matrix rather than the large global stiffness matrix in the traditional method.For the negative stiffness problem in FAM

structural nonlinear characteristics are mainly reflected by the local plastic matrix.In this paper

the numerical features of the local plastic matrix in the case of negative stiffness

such as the positive definite or negative definite

the condition number and the minimum eigenvalue

are studied.The influence of the second stiffness coefficient of material constitutive on numerical features is obtained

and the comparisons with the traditional method are done.Results show that when the structure is in the negative stiffness state

the local plastic matrix in FAM is non-positive definite.Numerical simulation indicates that the presented approach has a smaller condition number and higher numerical accuracy than the global stiffness matrix.Finally

the advantages and computing capability of the FAM for the negative stiffness problem was verified by numerical examples.

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references

基于拟力法的纤维梁有限元非线性分析方法 [J]. 李钢,余丁浩,李宏男. 建筑结构学报 . 2016(09)

单自由度结构体系抗地震倒塌能力研究 [J]. 施炜,叶列平,陆新征. 建筑结构学报 . 2014(09)

力-变位关系全过程模拟的有限元位移控制新方法 [J]. 杜修力,曹惠,金浏. 工程力学 . 2012(01)

Newmark积分方法在负刚度时的数值稳定性分析 [J]. 李爽,翟长海,刘洪波,谢礼立. 哈尔滨工业大学学报 . 2011(08)

基于拟力法的MBC非线性控制 [J]. 李钢,刘啟凤,李宏男. 振动工程学报 . 2010(03)

基于拟力法的消能减震结构地震反应分析 [J]. 李钢,李宏男,李瀛. 土木工程学报 . 2009(04)

往复荷载下钢筋混凝土柱受力性能的数值模拟 [J]. 汪训流,陆新征,叶列平. 工程力学 . 2007(12)

病态方程的复合结构解法 [J]. 邹积麟,钱稼茹. 清华大学学报(自然科学版) . 2001(Z1)

Newmark法在负刚度条件下的收敛性和稳定性 [J]. 吴云芳. 重庆建筑大学学报 . 2001(01)

动力方程的一种直接积分方法在负刚度条件下的收敛性和稳定性 [J]. 吴云芳. 世界地震工程 . 2000(02)

非线性结构动力方程求解的显式差分格式的特性分析 [J]. 李小军,廖振鹏. 工程力学 . 1993(03)

极限后负刚度模型对RC框架结构地震倒塌反应的影响 [J]. 杜修力,李小军,尹之潜. 计算结构力学及其应用 . 1993(02)

负屈服刚度条件下数值积分的收敛性和稳定性 [J]. 程民宪. 力学学报 . 1988(01)

钢筋混凝土结构考虑负刚度的随机层恢复力模型的研究 [D]. 李剑群. 四川大学 2004

负刚度条件下结构动力分析的数值稳定性及一种计算方法 [A]. 苗启松,袁驷,陈肇元.岩土力学数值方法的工程应用——第二届全国岩石力学数值计算与模型实验学术研讨会论文集[C]. 1990

建筑抗震弹塑性分析[M]. 中国建筑工业出版社 , 陆新征, 2009

Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness [J] . Hong-Nan Li,Chunxu Qu,Linsheng Huo,Satish Nagarajaiah. Journal of Sound and Vibration . 2015

Nonlinear hysteretic behavior simulation of reinforced concrete shear walls using the force analogy method [J] . Gang Li,Feng Zhang,Yu Zhang,Hong‐Nan Li. Struct. Design Tall Spec. Build. . 2015 (7)

Nonlinear seismic analysis of reinforced concrete frames using the force analogy method [J] . Gang Li,Yu Zhang,Hong‐Nan Li. Earthquake Engng Struct. Dyn. . 2014 (14)

Inelastic Dynamic Response of Structures Using Force Analogy Method [J] . Kevin K. F. Wong,Rong Yang. Journal of Engineering Mechanics . 1999 (10)

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