A New Explicit Time Integration Scheme for Nonlinear Dynamic Analysis

Abstract

An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central di®erence method as a special case, while damping is shown to exert no e®ect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for speci¯c values of the parameters; (ii) the numerical dissipation contained can help¯lter out spurious high-frequency components; and (iii) the crucial lower modes are generally una®ected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central di®erence method.

On designing and developing single‐step second‐order implicit methods with dissipation control and zero‐order overshoots via subsidiary variables

“…Effective and accurate numerical simulations for various structural dynamic problems have attracted increasing attention and there are various types of integration algorithms developed based on different strategies. In general, these methods can be divided into explicit [1][2][3][4][5][6][7] and implicit [8][9][10][11][12][13] schemes, and both have their own advantages and disadvantages. This article focuses mainly on the development of implicit algorithms.…”

Improvement of Discrete-Mechanics-Type Time Integration Schemes by Utilizing Balance Relations in Integral form Together with Picard-Type Iterations

“…2 below, we introduce some explicit time-integration schemes from the literature, which then will be used in order to start the Picard-type iteration procedure. For other explicit time-integration schemes that could be used, the reader is referred to [9] and [10]. Here, we first shortly address two highly valuable explicit time-integration schemes, which were presented by Greenspan in [11], at which occasion he introduced the notion of discrete mechanics.…”

A Class of Synchronized Nonlinear Two-Dof Systems With Closed Form Solution

“…Studying nonlinear structural dynamic behavior and analysis from di erent theoretical and practical points of view started about a century ago [23][24][25] and have continued more intensively over the last decades [26][27][28][29][30][31][32][33][34][35][36][37][38] and, particularly, the last years [39][40][41][42][43].…”