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将Newmark-β法中常平均加速度法的基本假定与精细积分法耦合,对积分项的计算引入指数矩阵的Taylor级数展开式,提出了动力方程的显式耦合级数解,设计了相应的时程积分算法,并应用在结构的地震反应分析中。分析表明,由于该方法是显式的,在质量矩阵为对角矩阵时,不需要计算耦联的方程组,因此可以有效地减少内存占用和机时耗费。该方法的稳定性条件显然满足,其精度可根据Taylor级数展开式的截断阶数进行灵活控制。算例表明该方法对地震作用的有效性和适应性。
The basic assumption of the normal average acceleration method in the Newmark-β method is coupled with the fine integral method. The integral term is introduced into the Taylor series expansion of the exponential matrix, and the explicit coupled series solution of the dynamic equation is proposed. Cheng integral algorithm, and applied in the structural seismic response analysis. The analysis shows that, since the method is explicit, it is not necessary to calculate the coupled equations when the mass matrix is a diagonal matrix, thus effectively reducing memory consumption and time cost. The stability conditions of the method are obviously satisfied, and its accuracy can be flexibly controlled according to the truncation order of Taylor Series expansion. The example shows the validity and adaptability of the method to the earthquake.