Generalized precise time domain integration method for nonlinear dynamic analysis

Aiming at the nonlinear dynamic state equation v • =H•v+f(v,t), the generalized precise time domain integration method for nonlinear dynamic analysis was proposed using the generalized precise integration method combined with the predictor-correction one. Firstly, in any time-subdomain, the variable v k at the current time moment was used to pre-estimate the variable to be solved v k+j/m (j=1,2,...,m) in the process of computation. Then the discrete nonlinear terms were expanded with Lagrange interpolation polynomial and taken as external loads, and the generalized precise integration method was used to directly solve the dynamic response of a nonlinear system. The proposed method was compared with four single-step methods, primary predictor-correction one and the predictor-corrector-symplectic time subdomain one. The numerical example results showed that the proposed method is easy to program and has a uniform computing format, higher accuracy, stability and efficiency; it can be applied in nonlinear dynamic response analysis of multi-DOF structural systems. © 2018, Editorial Office of Journal of Vibration and Shock. All right reserved.