求解刚-柔组合结构的隐式-显式混合法

摘要

A new kind of hybrid algorithm of explicit and implicit method was presented in this paper, in which explicit method was used in calculating flexible substructure which has major degrees-of-freedom and then implicit method was used in calculating rigid substructure which has minor degrees-of-freedom. This method takes advantage of unconditional stability of explicit method and high calculation efficiency of implicit method. The stability requirement of the hybrid algorithm is described by the highest natural frequency of flexible substructure other than the highest natural frequency of the entire structure, which avoids too strict requirement in choice of time step size resulted from local high rigidity. This method can achieve high efficiency when being used in such conditions as calculation of soli-structure interaction and liquid-structure interaction. Numerical examples proved the correctness of the hybrid algorithm.%针对整体柔性、局部刚性的组合结构系统的动力反应分析,推出了一种隐式-显式混合算法的逐步积分方法.这种混合求解方法,在一个算法步中,对柔性部分采用显式方法求解,对刚性部分则采用隐式方法求解,充分利用了隐式算法无条件稳定的优点和显式算法计算高效的优点.混合法稳定域大小表达式中的频率为柔性部分的最高频率,而不是整体结构的最高频率,这就避开了局部刚性导致显式算法时间步长需要过于细化的缺点.这种方法可以作为一种高效的逐步积分方法,用来求解土-结构相互作用、液固耦合系统等的动力反应.算例表明了方法的正确性.