• Title, Summary, Keyword: unconditional stability

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Numerical dissipation for explicit, unconditionally stable time integration methods

  • Chang, Shuenn-Yih
    • Earthquakes and Structures
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    • v.7 no.2
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    • pp.159-178
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    • 2014
  • Although the family methods with unconditional stability and numerical dissipation have been developed for structural dynamics they all are implicit methods and thus an iterative procedure is generally involved for each time step. In this work, a new family method is proposed. It involves no nonlinear iterations in addition to unconditional stability and favorable numerical dissipation, which can be continuously controlled. In particular, it can have a zero damping ratio. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it can save many computationally efforts when compared to the currently available dissipative implicit integration methods.

Performances of non-dissipative structure-dependent integration methods

  • Chang, Shuenn-Yih
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.91-98
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    • 2018
  • Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

A virtual parameter to improve stability properties for an integration method

  • Chang, Shuenn-Yih
    • Earthquakes and Structures
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    • v.11 no.2
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    • pp.297-313
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    • 2016
  • A virtual parameter is introduced into the formulation of the previously published integration method to improve its stability properties. It seems that the numerical properties of this integration method are almost unaffected by this parameter except for the stability property. As a result, it can have second order accuracy, explicit formulation and controllable numerical dissipation in addition to the enhanced stability property. In fact, it can have unconditional stability for the system with the instantaneous degree of nonlinearity less than or equal to the specified value of the virtual parameter for the modes of interest for each time step.

Dynamic analysis of the agglomerated SiO2 nanoparticles-reinforced by concrete blocks with close angled discontinues subjected to blast load

  • Amnieh, Hassan Bakhshandeh;Zamzam, Mohammad Saber
    • Structural Engineering and Mechanics
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    • v.65 no.1
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    • pp.121-128
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    • 2018
  • Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

Feasible Scaled Region of Teleoperation Based on the Unconditional Stability

  • Hwang, Dal-Yeon;Blake Hannaford;Park, Hyoukryeol
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.1
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    • pp.32-37
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    • 2002
  • Applications of scaled telemanipulation into micro or nano world that shows many different features from directly human interfaced tools have been increased continuously. Here, we have to consider many aspects of scaling such as force, position, and impedance. For instance, what will be the possible range of force and position scaling with a specific level of performance and stability\ulcorner This knowledge of feasible staling region can be critical to human operator safety. In this paper, we show the upper bound of the product of force and position scaling and simulation results of 1DOF scaled system by using the Llewellyn's unconditional stability in continuous and discrete domain showing the effect of sampling rate.

AN EFFICIENT SECOND-ORDER NON-ITERATIVE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC TELEGRAPH EQUATIONS

  • Jun, Young-Bae;Hwang, Hong-Taek
    • The Pure and Applied Mathematics
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    • v.17 no.4
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    • pp.289-298
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    • 2010
  • In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.

Unconditional stability for explicit pseudodynamic testing

  • Chang, Shuenn-Yih
    • Structural Engineering and Mechanics
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    • v.18 no.4
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    • pp.411-428
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    • 2004
  • In this study, a newly developed unconditionally stable explicit method is employed to solve momentum equations of motion in performing pseudodynamic tests. Due to the explicitness of each time step this pseudodynamic algorithm can be explicitly implemented, and thus its implementation is simple when compared to an implicit pseudodynamic algorithm. In addition, the unconditional stability might be the most promising property of this algorithm in performing pseudodynamic tests. Furthermore, it can have the improved properties if using momentum equations of motion instead of force equations of motion for the step-by-step integration. These characteristics are thoroughly verified analytically and/or numerically. In addition, actual pseudodynamic tests are performed to confirm the superiority of this pseudodynamic algorithm.

Identification of Feasible Scaled Teleoperation Region Based on Scaling Factors and Sampling Rates

  • Hwang, Dal-Yeon;Blake Hannaford;Park, Hyoukryeol
    • Journal of Mechanical Science and Technology
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    • v.15 no.1
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    • pp.1-9
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    • 2001
  • The recent spread of scaled telemanipulation into microsurgery and the nano-world increasingly requires the identification of the possible operation region as a main system specification. A teleoperation system is a complex cascaded system since the human operator, master, slave, and communication are involved bilaterally. Hence, a small time delay inside a master and slave system can be critical to the overall system stability even without communication time delay. In this paper we derive an upper bound of the scaling product of position and force by using Llewellyns unconditional stability. This bound can be used for checking the validity of the designed bilateral controller. Time delay from the sample and hold of computer control and its effects on stability of scaled teleoperation are modeled and simulated based on the transfer function of the teleoperation system. The feasible operation region in terms of position and force scaling decreases sharply as the sampling rate decreases and time delays inside the master and slave increase.

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A family of dissipative structure-dependent integration methods

  • Chang, Shuenn-Yih;Wu, Tsui-Huang;Tran, Ngoc-Cuong
    • Structural Engineering and Mechanics
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    • v.55 no.4
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    • pp.815-837
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    • 2015
  • A new family of structure-dependent integration methods is developed to enhance with desired numerical damping. This family method preserves the most important advantage of the structure-dependent integration method, which can integrate unconditional stability and explicit formulation together, and thus it is very computationally efficient. In addition, its numerical damping can be continuously controlled with a parameter. Consequently, it is best suited to solving an inertia-type problem, where the unimportant high frequency responses can be suppressed or even eliminated by the favorable numerical damping while the low frequency modes can be very accurately integrated.

A novel two sub-stepping implicit time integration algorithm for structural dynamics

  • Yasamani, K.;Mohammadzadeh, S.
    • Earthquakes and Structures
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    • v.13 no.3
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    • pp.279-288
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    • 2017
  • Having the ability to keep on yielding stable solutions in problems involving high potential of instability, composite time integration methods have become very popular among scientists. These methods try to split a time step into multiple sub-steps so that each sub-step can be solved using different time integration methods with different behaviors. This paper proposes a new composite time integration in which a time step is divided into two sub-steps; the first sub-step is solved using the well-known Newmark method and the second sub-step is solved using Simpson's Rule of integration. An unconditional stability region is determined for the constant parameters to be chosen from. Also accuracy analysis is perform on the proposed method and proved that minor period elongation as well as a reasonable amount of numerical dissipation is produced in the responses obtained by the proposed method. Finally, in order to provide a practical assessment of the method, several benchmark problems are solved using the proposed method.