An Improved Explicit-Implicit Precise Integration Method for Nonlinear Dynamic Analysis of Structures

Abstract

In this paper, an improved explicit-implicit precise integration method (EIPIM) is proposed for nonlinear dynamic analysis of structures based on the refined precise integration method (RPIM). The RPIM may face a numerical instability problem when using large time steps while the proposed EIPIM uses an explicit predictor-implicit corrector scheme to provide more stable and accurate results and allow for large time steps. When using EIPIM, the unknown displacements at the sta rting point are predicted by an explicit function, and the trial displacements at the second step are corrected by the implicit Lagrange interpolation method. In terms of numerical stability and precision, eight explicit formulas have been evaluated to develop a better predictor for EIPIM, i.e., two third-order, four fourth-order and two fifth-order functions. Four examples involving both linear and nonlinear problems illustrate the high stability and numerical efficiency of the proposed method. It is found that the explicit predictors EIPIM_O31 and EIPIM_O41 show good performance and are recommended for nonlinear dynamic analysis.