Improved State-Space Approach Based on Lumped Mass Matrix for Transient Analysis of Large-Scale Locally Nonlinear Structures

被引:0
|
作者
Sun, Baoyin [1 ,2 ,3 ]
Xuan, Jiaheng [3 ]
Gao, Long [3 ]
Wang, Kai [3 ]
Ou, Jinping [4 ]
机构
[1] State Key Lab Bldg Safety & Built Environm, Beijing 100029, Peoples R China
[2] Natl Engn Res Ctr Bldg Technol, Beijing 100029, Peoples R China
[3] Hohai Univ, Coll Civil & Transportat Engn, Nanjing 210024, Peoples R China
[4] Harbin Inst Technol, Sch Civil & Environm Engn, Shenzhen 518055, Peoples R China
基金
中国国家自然科学基金; 中国博士后科学基金;
关键词
transient analysis; state-space approach; lumped mass; local nonlinear; nonlinear force corrector; DYNAMIC-ANALYSIS; ACCURACY;
D O I
10.3390/buildings14092735
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
Due to the assumption of acceleration variation in traditional step-by-step integration methods such as Newmark, sufficiently small time steps are required to ensure numerical stability and accuracy in dynamic systems. In contrast, the state-space approach, based on piecewise interpolation of discrete load functions, does not rely on predetermined acceleration assumptions and has demonstrated high efficiency in terms of stability and accuracy. The original state-space method requires the calculation of the inverse of the structural mass in the transition matrix. However, when a lumped mass matrix is used, this computation renders the entire mass matrix singular, resulting in an invalid solution expression. To address this issue, this study proposes an improved state-space approach for the transient analysis of large-scale structural systems with local nonlinearities. In this approach, a nonlinear force corrector is introduced as an external force term applied to the linear elastic system to account for the nonlinear behavior of locally yielding components. Consequently, the original nonlinear dynamic system can be transformed into an equivalent linear elastic transient system. Furthermore, based on the lumped mass matrix, a first-order ordinary differential state-space equation for such an equivalent linear elastic transient system is derived. Simulation results from three transient system examples show that the state-space approach outperforms the Newmark method in terms of accuracy and stability for dynamic systems characterized by high frequency and low damping. The prediction results show that the state-space approach appears to be insignificantly affected by the choice of the consistent or lumped mass matrix. The numerical results show that the root-mean-square errors between the consistent and lumped matrices in the top displacement time histories of a 15-storey plane frame under various seismic intensities are all less than 1%, and in the base reaction time histories responses the discrepancies are only about 0.5%, indicating that the use of lumped mass matrices is quite reliable. When many nodes or degrees of freedom have no assigned mass, the dimensionality of the state-space equation can be significantly reduced using the lumped mass approach. Therefore, the simulation of large-scale systems can be simplified by employing the improved state-space approach with lumped mass matrices, yielding results nearly identical to those obtained using traditional methods. In conclusion, the improved state-space approach has great potential for the simulation of transient behavior in large-scale systems with local nonlinearities.
引用
收藏
页数:25
相关论文
共 12 条
  • [1] Improved Formulation in Mixed-Based State-Space Approach for Large Displacement Inelastic Analysis of Frames
    Jafari, V.
    Rahimian, M.
    Vahdani, S. H.
    JOURNAL OF ENGINEERING MECHANICS, 2011, 137 (03) : 196 - 204
  • [2] A state-space approach for dynamic analysis of sliding structures
    Wang, YP
    Liao, WH
    Lee, CL
    ENGINEERING STRUCTURES, 2001, 23 (07) : 790 - 801
  • [3] Improved Craig-Bampton method for transient analysis of structures with large-scale plastic deformation
    Qian, Peng-bo
    Qian, Lin-fang
    Yin, Xiao-chun
    JOURNAL OF VIBROENGINEERING, 2017, 19 (02) : 812 - 830
  • [4] An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model
    Sheng Xiang
    Bin Cheng
    Feng-yu Zhang
    Miao Tang
    China Ocean Engineering, 2022, 36 : 682 - 696
  • [5] An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model
    Xiang Sheng
    Cheng Bin
    Zhang Feng-yu
    Tang Miao
    CHINA OCEAN ENGINEERING, 2022, 36 (05) : 682 - 696
  • [6] An improved model order reduction method for dynamic analysis of large-scale structures with local nonlinearities
    Li, Wenxiong
    Chen, Suiyin
    APPLIED MATHEMATICAL MODELLING, 2023, 120 : 786 - 811
  • [7] An improved time-domain response estimation method for floating structures based on rapid solution of a state-space model
    Lu, Hongchao
    Tian, Zhe
    Zhou, Lin
    Liu, Fushun
    OCEAN ENGINEERING, 2019, 173 : 628 - 642
  • [8] Equivalent continuum modeling method for transient response analysis of large space truss structures with nonlinear elastic joints
    Liu, Fushou
    Jin, Dongping
    Li, Xinyuan
    Wei, Guo
    ACTA MECHANICA, 2023, 234 (08) : 3499 - 3517
  • [9] Imperfect and multilayered magneto-electro-elastic nanoplates bending response analysis based on the nonlocal state-space approach
    Ngak, F. P. Ewolo
    Ntamack, G. E.
    Azrar, L.
    Alnefaie, K.
    COMPOSITE STRUCTURES, 2023, 324
  • [10] An analysis of the accuracy and formation of criterion for comparing two versions of the trilateration approach to the acoustic flaw detection of large-scale industrial structures
    A. Sh. Mekhtiev
    N. A. Abdullaev
    Kh. G. Asadov
    Russian Journal of Nondestructive Testing, 2014, 50 : 713 - 718