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

  • Yasamani, K. (Malek-ashtar University of Technology) ;
  • Mohammadzadeh, S. (College of Engineering, School of Civil Engineering, University of Tehran)
  • Received : 2017.08.05
  • Accepted : 2017.10.12
  • Published : 2017.09.25

Abstract

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.

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