因果性に基づく減衰モデルの動的陽解法への適用性検討

<p>　In recent years, time history response analysis has been carried out using a more elaborate three-dimensional model. The dynamic explicit method does not require solving simultaneous equations and is suitable for parallel computing. However, if the damping model is Stiffness-proportional damping and Rayleigh damping, the stability conditions become stricter than the mass-proportional damping, and it is necessary to make the analysis time step finer.</p><p>　There are many unclear points about the damping, but a model in which the attenuation ratio is almost constant is desired in terms of engineering.</p><p>　Co-authored Nakamura proposed two causal damping models called Causal Hysteretic damping and Extended Rayleigh damping. Compared with the conventional Rayleigh damping, two causal damping models can be analyzed with a damping ratio that is constant over a wide range. However, the formulation and verification of these damping models was based on the dynamic implicit method.</p><p> </p><p>　Therefore, the purpose of this report is to examine the applicability of two causal damping models to the dynamic explicit method. We also confirm that using two causal damping models may improve computational efficiency compared to using a conventional damping model. First, the outline of two causal damping models and the outline of the dynamic explicit method that approximates the velocity term by backward difference are shown. Furthermore, numerical analysis was performed using a simple multi-degree-of-freedom model and a model of shell elements with about 3000 nodes, and the applicability was examined. Since this is the initial stage of research, we examined its applicability in elastic linear problems.</p><p> </p><p>　As a result, followings were obtained.</p><p>1) Using two causal damping models, it was confirmed that the dynamic explicit method exhibits the same performance as the dynamic implicit method by a simple multi-degree-of-freedom model.</p><p>2) Two causal damping models could be applied to the dynamic explicit method, which approximates the velocity term by backward difference, by the model of shell elements with about 3000 nodes. In addition, it was confirmed by comparing the two causal damping models and the mode damping that the damping ratio can be evaluated constant and accurately over a wide frequency range.</p><p>3) Two causal damping models and conventional Rayleigh damping require the velocity term to be solved by dynamic explicit method that approximates the backward difference. It was revealed that two causal damping models may have a larger analysis time step than the conventional Rayleigh damping model.</p>