Non-iterative explicit integration algorithms based on acceleration time history for nonlinear dynamic systems

A two-step explicit acceleration integration method (EAIM2) and a three-step explicit acceleration integration method (EAIM3), which are entirely explicit time integration algorithms, are proposed based on acceleration time history. The computation efforts and costs can be observably reduced on account of avoiding matrix inversion and iteration processes in nonlinear systems. Four nonlinear systems are employed to analyze the EAIM2, the EAIM3, the HHT-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha $$\end{document} method, the Newmark explicit method and the generally used Newmark method for comparison purposes. The results show that the highest orders of accuracy of the EAIM2 and the EAIM3 are all of second order. The stability of the proposed methods can remain in a critical state in undamped systems. The puny energy ratio and the periodic energy growth and decay manifest that the proposed methods are endowed with favorable nonlinear stability. The amplitude attenuation of the proposed methods is zero. The proposed methods and the CDM possess the same period elongation. The period error of the proposed methods is smaller than that of the Newmark method in the stability interval. The EAIM2 and the EAIM3 possess the lowest computation efforts at the same accuracy level in the above-mentioned integration methods.