An Explicit Time Integration Method Based on the Verlet Scheme with Improved Characteristics in Numerical Dispersion

Abstract

This article is about a modification of Verlet’s time integration method. First, a one-step version of the basic scheme is described. Subsequently, a diagonal matrix is introduced in the scheme to improve the behavior of Verlet’s method with respect to period elongation. The generic coefficient of this diagonal matrix is defined by referring to the frequency which locally dominates the structural dynamics of the correlated unknown. Since the computation of these coefficients is algorithmic, the method presented does not involve the adjustment of any parameter. Furthermore, the presented modification does not alter the excellent amplitude decay and stability characteristics of the original method. As a result, a second order one-step explicit time integration scheme with desirable accuracy and stability properties is obtained. Several numerical examples for nonlinear problems are conducted to show the ability of the presented method to reduce unwanted period distortion. Computational algorithms can automate repetitive design tasks, saving designers time and effort. In this sense, these computational tools provide designers with detailed data insights that can guide decision-making processes. Once implemented, algorithms become effective and useful tools for increasing productivity and creating more robust designs. However, the reliability of the results is a prerequisite for the success of these approaches. In the context of the dynamic behavior of structures, the present work improves a preexisting computational tool to reproduce the motion of the system under study. Practical engineering applications for linear and nonlinear dynamic analysis can then be addressed by introducing data rigor into the design. Starting from appropriate mathematical models for the analyzed structures, the presented algorithm provides an accurate description of the resulting displacements and stresses. All this through a calculation effort comparable to that of the previous method. As demonstrated by the tests carried out, the simulation for the control of suspension systems as well as the seismic response to earthquake excitation on buildings can represent applicative implications in the engineering field.