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柔性物体的碰撞动力学是工程实际中的一个重要问题。获得问题的动力响应是一个有挑战性的任务,通常通过数值计算来完成。首次采用离散奇异卷积法分析碰撞动力学问题,并通过钢球碰撞柔性杆的算例来研究几种数值方法的有效性。数值方法包括常规的有限元法、离散奇异卷积法、谱有限元法和提出的改进谱有限元法,将各种方法获得的算例的数值结果与理论解比较来研究方法的有效性。研究结果表明,采用恰当的常规有限元长度后,提出的改进谱有限元法给出的接触应力的结果最精确。另外还发现,离散奇异卷积法可以用于求解碰撞问题。
The collision dynamics of flexible objects is an important issue in engineering practice. Get the problem of dynamic response is a challenging task, usually by numerical calculation to complete. For the first time, a discrete singular convolution method is used to analyze the dynamics of collisions. The validity of several numerical methods is studied by the example of a collision of a steel ball with a flexible rod. The numerical methods include the conventional finite element method, the discrete singular convolution method, the spectral finite element method and the improved spectral finite element method. The numerical results obtained by the various methods are compared with the theoretical solutions to study the validity of the method. The results show that the proposed method of improved spectral finite element method gives the most accurate contact stress with the proper length of conventional finite element. In addition, we find that the discrete singular convolution method can be used to solve the collision problem.