Selecting the load at the intermediate time point of the ρ∞-Bathe time integration scheme

Abstract

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.