材料非線形性を有する一次元棒における応力波伝播解析へのセルオートマトンの応用

概要

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We have investigated the properties of the numerical methods for analyzing the stress wave propagation which is caused by a longitudinal impact of a cylindrical bar by a one-dimensional model. It is shown that the one-dimensional model possesses some physical properties for the numerical calculation by applying an exponential function as the constitutive equation. We have treated the numerical method which keeps the physical properties intrinsically possessed by the system. Namely, we have focused on Cellular Automaton (CA) scheme which is derived from the integrable difference scheme by means of the ultra discrete limit. We have compared the CA scheme with the integrable difference scheme and the general-purpose methods such as Euler method and Leapfrog method on the efficiency of the calculation. The properties of the CA scheme for the present analysis are revealed. Especially, it is shown that the CA scheme can maintain a certain accuracy for the long time behavior of the stress wave propagation and the interaction between the waves.
2010-06-25