【摘要】 多时间步长方法常用于求解有限元动力学空间多尺度问题,可分为单元重叠与非重叠两种形式。单元非重叠形式的多时间步长方法涉及边界数据的插值过程,造成计算不稳定、精度不高。为了提高多时间步长方法计算稳定性与求解精度,基于节点分割与重叠边界单元,提出一种改进的多时间步长计算方法。结合显式积分格式数据传递规律与重叠单元,分区边界数据由动力学方程显式求出,算法实施过程简单。采用能量方法分析了算法的稳定性能,给出了算法一般性稳定条件。稳定性分析结果表明改进方法的稳定性只由分区内部单元特性决定,重叠单元不影响算法的稳定性能,这扩展了改进方法的适用范围。数值算例结果表明该算法具有较高的计算精度,能量校验进一步证实了算法的稳定性能。更多还原

【Abstract】 The multi-time step method,which can be divided into overlapping and non-overlapping,is a classical method to deal with the spatial multiscale problem of finite element dynamics analysis.The interpolation process of the boundary node is involved in the non-overlapping multi-time step method which makes the calculation process unstable and inaccurate.Combined the finite element model node segmentation with overlapping boundary element,an improved multi-time step computing method is proposed to improve computational stability and accuracy.The data transfer laws and overlapping element are combined with the explicit integral scheme.The subdomain boundary node can be calculated explicitly by the dynamic equation and the implementation process is simple.The stability of the algorithm is analyzed by the energy method.The analysis results show that the stability of the improved method is determined only by the characteristics of the internal cells in the partition area.The overlap elements do not affect the stability of the algorithm,which extends the application scope of the proposed method.The numerical example shows that the algorithm has high calculation accuracy,and the stability of the algorithm is further confirmed by the energy check.更多还原