An identical second‐order single step explicit integration algorithm with dissipation control for structural dynamics. (7th December 2020)

• Record Type: Journal Article
• Authors: Li, Jinze; Yu, Kaiping; Li, Xiangyang
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 4(2021)
• Page Start: 1089
• Page End: 1132
• Publication Date: 2020-12-07
• Subjects: controllable dissipation -- direct time integration -- explicit algorithm -- explicit treatment -- single sub‐step; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6574
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: This article focuses mainly on the development of explicit integration algorithms for structural dynamics. Some known single‐step explicit schemes are first reviewed and their algorithmic parameters are uniformly given as a function of ρ b, denoting spectral radius at the bifurcation point. The simple review reveals that there are still some problems to be addressed. Then, a simple but general explicit integration algorithm (GSSE) is presented and analyzed. Besides, a truly self‐starting explicit algorithm and the true explicit form of generalized‐ α method are also given. The novel GSSE algorithm possesses very significant advantages in terms of accuracy and dissipation control. The GSSE method achieves not only controllable dissipation at the bifurcation point but also the identical second‐order accuracy of three primary variables. Numerical spectral analysis and examples are provided to clearly show the superiority of novel explicit methods over other single‐step explicit ones. Hence, the novel GSSE method is highly recommended to solving general dynamical problems.