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Structural Engineering and Mechanics
  Volume 65, Number 1, January10 2018 , pages 121-128

Dynamic analysis of the agglomerated SiO2 nanoparticles-reinforced by concrete blocks with close angled discontinues subjected to blast load
Hassan Bakhshandeh Amnieh and Mohammad Saber Zamzam

    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.
Key Words
    weak instability; numerical instability; overshoot; structure-dependent integration method
Hassan Bakhshandeh Amnieh: School of Mining, College of Engineering, University of Tehran, Iran
Mohammad Saber Zamzam: Department of Mining Engineering, Faculty of Engineering, University of Kashan, Iran

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