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An explicit time integration algorithm for linear and non-linear finite element analyses of dynamic and wave problems

机译：一种用于动态和波动问题的线性和非线性有限元分析的显式时间积分算法

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摘要

Purpose The purpose of this paper is to propose a new explicit time integration algorithm for solution to the linear and non-linear finite element equations of structural dynamic and wave propagation problems.Design/methodology/approach The algorithm is completely explicit so that no linear equation system requires solving, if the mass matrix of the finite element equation is diagonal and whether the damping matrix does or not. The algorithm is a single-step method that has the simple starting and is applicable to the analysis with the variable time step size. The algorithm is second-order accurate and conditionally stable. Its numerical stability, dissipation and dispersion are analyzed for the dynamic single-degree-of-freedom equation. The stability of the multi-degrees-of-freedom non-proportional damping system can be evaluated directly by the stability theory on ordinary differential equation.Findings The performance of the proposed algorithm is demonstrated by several numerical examples including the linear single-degree-of-freedom problem, non-linear two-degree-of-freedom problem, wave propagation problem in two-dimensional layer and seismic elastoplastic analysis of high-rise structure.Originality/value A new single-step second-order accurate explicit time integration algorithm is proposed to solve the linear and non-linear dynamic finite element equations. The algorithm has advantages on the numerical stability and accuracy over the existing modified central difference method and Chung-Lee method though the theory and numerical analyses.
机译：目的本文的目的是提出一种新的显式时间积分算法，以解决结构动力和波传播问题的线性和非线性有限元方程。设计/方法/方法该算法是完全显式的，因此没有线性方程有限元方程的质量矩阵是否为对角线，以及阻尼矩阵是否为对角线，则需要求解。该算法是一种单步方法，具有简单的启动方法，适用于时间步长可变的分析。该算法是二阶准确且条件稳定的。针对动态单自由度方程分析了其数值稳定性，耗散和色散。可以通过常微分方程的稳定性理论直接评估多自由度非比例阻尼系统的稳定性。发现该算法的性能通过包括线性单度阻尼在内的多个数值示例进行了证明。自由问题，非线性两自由度问题，二维层中的波传播问题以及高层结构的地震弹塑性分析。原始物/值一种新的单步二阶精确显式时间积分算法提出求解线性和非线性动力有限元方程的方法。通过理论和数值分析，与现有的改进的中心差分法和Chung-Lee法相比，该算法在数值稳定性和精度上具有优势。

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  • 来源
    《Engineering Computations》 |2019年第1期|161-177|共17页
  • 作者

    Zhao Mi; Li Huifang; Cao Shengtao; Du Xiuli;

  • 作者单位

    Beijing Univ Technol, Minist Educ, Key Lab Urban Secur & Disaster Engn, Beijing, Peoples R China|Beijing Univ Technol, Beijing Collaborat Innovat Ctr Metropolitan Trans, Beijing, Peoples R China;

    Beijing Univ Technol, Minist Educ, Key Lab Urban Secur & Disaster Engn, Beijing, Peoples R China|Beijing Univ Technol, Beijing Collaborat Innovat Ctr Metropolitan Trans, Beijing, Peoples R China;

    China Acad Bldg Res, Beijing, Peoples R China;

    Beijing Univ Technol, Minist Educ, Key Lab Urban Secur & Disaster Engn, Beijing, Peoples R China|Beijing Univ Technol, Beijing Collaborat Innovat Ctr Metropolitan Trans, Beijing, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Structural dynamics; Finite element analysis; Explicit time integration; Single-step algorithm; Stability and accuracy; Wave propagation;

    机译：结构动力学;有限元分析;显式时间积分;单步算法;稳定性和准确性;波传播;

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