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An identical second‐order single step explicit integration algorithm with dissipation control for structural dynamics
Author(s) -
Li Jinze,
Yu Kaiping,
Li Xiangyang
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6574
Subject(s) - dissipation , simple (philosophy) , algorithm , mathematics , bifurcation , point (geometry) , function (biology) , computer science , nonlinear system , geometry , physics , thermodynamics , philosophy , epistemology , quantum mechanics , evolutionary biology , biology
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 ofρ 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.