MULTISTEP TIME INTEGRATION FOR DISCONTINUOUS STRESS WAVE PROPAGATION IN 3-DIMENSIONAL HETEROGENEOUS SOLIDS

Abstract eng:
We had presented the multistep time integration algorithm for computing the discontinuous stress wave propagation for one and two dimensional heterogeneous solids [1]. It demonstrated several numerical examples to show high performance for the discontinuous stress wave propagation in two dimension as well as one dimension problems. This study extends our proposed algorithm to three 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 heterogeneous solids are always different each other. This multistep time integration are performed separately using their different critical time step sizes for the larger time step domain(L) and the smaller time step domain(S). This study adopts the elementby-element decomposition of the extensional and shear component in order to reduce the dispersion errors [2~3]. The component-wise partitioned equations of motion for the element-by-element decomposition is also simultaneously applied to every heterogeneous domains as shown in following equations. In addition, our algorithm utilized the kinematic and kinetic continuity conditions that the accelerations and the interface loads at the interface nodes should coincide. We will show the good results and the salient features of our proposed algorithm for computing the discontinuous stress wave propagation for three dimensional heterogeneous solids.

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