Discrete equivalent time integration methods for transient analysis

An, Ata Mu

doi:10.1002/nme.755

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…Figures 4 and 5 depict the algorithmic damping ratio and relative period error for several different time integration algorithms (Hulbert, 1992a). An interesting controls perspective on numerical dispersion and dissipation can be found in Muǧan and Hulbert (2001a,b) and Muǧan (2003). In a similar vein, Pegon (2001) characterizes algorithm performance in terms of forced vibration response.…”

Section: Dispersion and Dissipationmentioning

confidence: 98%

Computational Structural Dynamics

Hulbert

2004

Encyclopedia of Computational Mechanics

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This chapter presents an overview and a state‐of‐the art compilation of time integration methods for solving problems of dynamics, with a particular focus on developments that have occurred during the past 25 years. Various classifications of time integration algorithms are provided that assist the reader in understanding the many different types of numerical methods available for solving time‐dependent problems. Time integration algorithms for linear structural dynamics are reviewed thoroughly, from classical Newmark‐type schemes, to recent developments in time finite element‐based approaches. The distinction between linear and nonlinear dynamics is articulated and numerical methods developed for direct application towards solving nonlinear dynamics probems are presented. The chapter concludes with guidelines towards selecting an appropriate time integration method, along with guidelines towards choosing appropriate time step sizes.

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Section: Dispersion and Dissipationmentioning

confidence: 98%

Computational Structural Dynamics

Hulbert

2004

Encyclopedia of Computational Mechanics

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“…Many approaches have been established to solve different dynamic problems, such as structure, fluid flowing, and multi-rigid-body systems [3][4][5][6][7][8][9][10][11][12]. They are mainly classified into two categories: explicit and implicit algorithms.…”

Section: Introductionmentioning

confidence: 99%

A new simple method of implicit time integration for dynamic problems of engineering structures

Zhou

2007

Acta Mech Sin

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This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai's approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.

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“…List of some of the available criteria for investigating the performance of integration algorithms are listed in [3]. One of the studies on the performance evaluation of integration algorithms was carried out by Mugan in which he found that frequency domain analysis can describe all of the time domain properties of an integration algorithm [4]. A frequency domain analysis will also be used in this paper to evaluate different integration algorithms.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Integration Algorithms for Real-Time Hybrid Simulation Using Frequency Domain-Based Error Indicators

Hessabi¹,

Ashasi-Sorkhabi²,

Liu³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Real-time hybrid simulation (RTHS) is a testing method that combines computer simulation (i.e., analytical substructure) with physical testing (i.e., experimental substructure). This enables investigation of dynamic characteristics of load-rate dependent complex structures. To ensure reliable experimental results, even in the presence of sophisticated controllers and compensation methods, it is necessary to evaluate the accuracy of the success of the hydraulic actuators in imposing the command displacements. With recent developments in tracking error monitoring, new indicators have been proposed that are based on frequency domain analysis and can successfully uncouple phase (lag and lead) and amplitude (overshoot and undershoot) errors and quantify them. These new frequency-based error indicators are not structure-specific and can be reliably used to examine the effectiveness of each component of RTHS inner (i.e., servo-control) and outer (i.e., integration algorithm) loops. In this paper, frequency domain-based (FDB) error indicators are employed to evaluate the effectiveness of five commonly-used integration algorithms (i.e. central difference method, explicit Newmark method, discrete state space formulation with a zero-order hold and first-order hold, the state-space formulation by Zhang et al., and the alpha method) in different test scenarios. The applicability of the FDB error indicators to nonlinear systems is first verified through numerical simulations performed on a nonlinear system with predefined parameters. Then these indicators are used to post-process the experimental results obtained from RTHS's with various integration algorithms. The experiments are carried out on a system with a nonlinear analytical substructure and a linear experimental substructure at the University of Toronto. Findings from numerical simulation and experimental results demonstrate that the FDB method is an efficient approach to compare performances of different integration algorithms.

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Discrete equivalent time integration methods for transient analysis

Cited by 6 publications

References 23 publications

Computational Structural Dynamics

Computational Structural Dynamics

A new simple method of implicit time integration for dynamic problems of engineering structures

Comparison of Integration Algorithms for Real-Time Hybrid Simulation Using Frequency Domain-Based Error Indicators

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