The objective of this paper is to identify the optimal load selection at the intermediate time point of the ρ_∞-Bathe time integration method. We study the truncation errors of the scheme in homogeneous and forced responses for various parameters. The optimal load at the sub-step is determined by minimizing the global truncation errors of forced responses. A numerical impulse analysis shows that the optimal load at the sub-step thus established actually corresponds to numerical impulses at the three- and four-point Newton-Cotes formulas for the second- and third-order accuracy cases, respectively. We illustrate the findings of our theoretical study in example solutions of two-dimensional structural dynamics and wave propagation problems. With the optimally selected load at the sub-step, more accurate solutions can be obtained in some analyses.

本文的目的是确定在 ρ _∞的中间时间点的最佳负载选择-沐浴时间积分法。我们研究了该方案在各种参数的均匀和强制响应中的截断误差。通过最小化强制响应的全局截断误差来确定子步骤的最佳负载。数值脉冲分析表明，由此建立的子步骤的最佳载荷实际上分别对应于二阶和三阶精度情况下三点和四点牛顿-科特斯公式的数值冲击。我们在二维结构动力学和波传播问题的示例解决方案中说明了我们的理论研究结果。通过在子步优化选择负载，可以在某些分析中获得更准确的解决方案。