An improved higher-order explicit time integration method with momentum corrector for linear and nonlinear dynamics

• Published in: Applied Mathematical Modelling 2021-10, Vol.98, p.287-308
• Main Authors: Liu, Tianhao, Huang, Fanglin, Wen, Weibin, Deng, Shanyao, Duan, Shengyu, Fang, Daining
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Control stability; Damping; Dynamic response; Dynamical systems; Elongation; Exact solutions; Explicit; Finite element method; Interpolation; Linear systems; Momentum; Momentum corrector; Nonlinear dynamics; Nonlinear systems; Numerical dissipation; Parameters; Structural dynamics; Time integration; Truncation errors
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.05.013

•The improved method achieves higher-order accuracy and controllable numerical dissipation.•The “momentum corrector” term is first introduced to improve accuracy.•High accuracy for nonlinear dynamics and discontinuous loads is illustrated. An improved explicit time integration method is proposed for linear and nonlinear dynamics. Its calculation procedure is obtained with cubic B-spline interpolation approximation and weighted residual method. In the formulation, a momentum corrector is used to improve actual computation accuracy, especially for some special discontinuous loads. Analytical solutions of the local truncation errors, algorithmic damping and period elongation have been deduced to obtain the influence of algorithmic parameters on these basis algorithmic properties. The proposed method possesses at least second-order accuracy and can achieve at most third-order accuracy for no physical damping case. With free algorithmic parameters, the proposed method has controllable stability and numerical dissipation. Some demonstrative numerical examples are tested to confirm high efficiency of the proposed method for a variety of dynamic problems such as, dynamic response analysis of linear systems under various representative applied loads, finite element analysis (FEA) for dynamic response of engineering structures, and nonlinear dynamic analysis for strong nonlinear system.