MULTISTEP TIME INTEGRATION FOR STRESS WAVE PROPAGATION IN HETEROGENEOUS SOLIDS: ONE DIMENSIONAL PROBLEM

Abstract eng:
This study presents the multistep time integration algorithm for computing the stress wave propagation for 1-dimensional heterogeneous solids. Since the critical time step size is determined according to the characteristic length of the element and the speed of the stress wave, the respective critical time step sizes of two heterogeneous materials are different each other. The present algorithm deals with two different domain separately: the larger time step domain (L) and the smaller time step domain (S). The equation of motions in two domain can be written as shown in Eq. (1). The subscripts L and S designate the larger time step domain and the smaller time step domain respectively, and two Lagrange multipliers, ?L and ?S , are the interface loads at the interface nodes between two solids. The accelerations and the interface loads and at the interface nodes should be continuous kinematically and kinetically as described in Eq. (1). Where the localized Lagrange multiplier, Uf, means the displacement at the reference node of the interfaces[1]. Numerical integrations are performed separately with two different time step size for the larger time step domain and the smaller time step domain. We adopted the pushforward-pullback time integration to obtain high accuracy and reduce the dispersion errors[2]. This study demonstrates several numerical problems of stress wave propagation in one dimensional heterogeneous solids to show salient features and performance. The work has been partially supported by the BK21 plus program (21A20131712520) through the National Research Foundation funded by the Ministry of Education of Korea as a visiting professor in the Department of Mechanical Engineering, Korea University, and the National Research Foundation of Korea (MSIP, 2012M2A8A4026290).

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