Development of composite sub-step explicit dissipative algorithms with truly self-starting property
This paper focuses mainly on the development of composite sub-step explicit algorithms for solving nonlinear dynamic problems. The proposed explicit algorithms are required to achieve the truly self-starting property, so avoiding computing the initial acceleration vector, and the controllable numeri...
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| Published in: | Nonlinear dynamics Vol. 103; no. 2; pp. 1911 - 1936 |
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| Language: | English |
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01.01.2021
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| ISSN: | 0924-090X, 1573-269X |
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| Abstract | This paper focuses mainly on the development of composite sub-step explicit algorithms for solving nonlinear dynamic problems. The proposed explicit algorithms are required to achieve the truly self-starting property, so avoiding computing the initial acceleration vector, and the controllable numerical dissipation at the bifurcation point, so eliminating spurious high-frequency components. With these two requirements, the single and two sub-step explicit algorithms with truly self-starting property and dissipation control are developed and analyzed. The present single sub-step algorithm shares the same spectral accuracy as the known Tchamwa–Wielgosz scheme, but the former possesses some advantages for solving wave propagation problems. The present two sub-step algorithm provides a larger stability limit, twice than those of single step schemes, due to explicit solutions of linear systems twice within each time increment. Numerical examples are also simulated to show numerical performance and superiority of two novel explicit methods over other explicit schemes. |
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| AbstractList | This paper focuses mainly on the development of composite sub-step explicit algorithms for solving nonlinear dynamic problems. The proposed explicit algorithms are required to achieve the truly self-starting property, so avoiding computing the initial acceleration vector, and the controllable numerical dissipation at the bifurcation point, so eliminating spurious high-frequency components. With these two requirements, the single and two sub-step explicit algorithms with truly self-starting property and dissipation control are developed and analyzed. The present single sub-step algorithm shares the same spectral accuracy as the known Tchamwa–Wielgosz scheme, but the former possesses some advantages for solving wave propagation problems. The present two sub-step algorithm provides a larger stability limit, twice than those of single step schemes, due to explicit solutions of linear systems twice within each time increment. Numerical examples are also simulated to show numerical performance and superiority of two novel explicit methods over other explicit schemes. |
| Author | Li, Jinze Yu, Kaiping |
| Author_xml | – sequence: 1 givenname: Jinze orcidid: 0000-0003-2563-1223 surname: Li fullname: Li, Jinze organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology – sequence: 2 givenname: Kaiping orcidid: 0000-0002-7722-0138 surname: Yu fullname: Yu, Kaiping email: kaipingyu1968@gmail.com organization: Department of Astronautic Science and Mechanics, Harbin Institute of Technology |
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| Keywords | Structural dynamics Truly self-starting Composite sub-step Explicit integration Controllable dissipation |
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| References_xml | – reference: WilsonELFarhoomandIBatheKJNonlinear dynamic analysis of complex structuresEarthq. Eng. Struct. Dyn.197213241252 – reference: LiJYuKA novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamicsArch. Appl. Mech.201990737772 – reference: HeHTangHYuKLiJYangNZhangXNonlinear aeroelastic analysis of the folding fin with freeplay under thermal environmentChin. J. Aeronaut.202033923572371 – reference: WenWDengSWangNDuanSFangDAn improved sub-step time-marching procedure for linear and nonlinear dynamics with high-order accuracy and high-efficient energy conservationAppl. Math. Model.202190781004155263 – reference: KimWAn improved implicit method with dissipation control capability: the simple generalized composite time integration algorithmAppl. Math. Model.2020819109304065729 – reference: Rezaiee-PajandMKarimi-RadMAn accurate predictor–corrector time integration method for structural dynamicsInt. J. Steel Struct.201717310331047 – reference: MaheoLRioGGrolleauVOn the use of some numerical damping methods of spurious oscillations in the case of elastic wave propagationMech. Res. Commun.201138281881272.74234 – reference: ChangSYA dual family of dissipative structure-dependent integration methods for structural nonlinear dynamicsNonlinear Dyn.2019981703734 – reference: LiJYuKAn alternative to the Bathe algorithmAppl. Math. Model.201969255272389506007186525 – reference: KimWReddyJNNovel explicit time integration schemes for efficient transient analyses of structural problemsInt. J. Mech. Sci.2020172105429 – reference: TammaKKNamburuRRA robust self-starting explicit computational methodology for structural dynamic applications: architecture and RepresentationsInt. J. Numer. Methods Eng.199029714411454 – reference: HilberHMHughesTJRCollocation, dissipation and ‘overshoot’ for time integration schemes in structural dynamicsEarthq. Eng. Struct. Dyn.19786199117 – reference: KimWA new family of two-stage explicit time integration methods with dissipation control capability for structural dynamicsEng. Struct.2019195358372 – reference: ChangSYDissipative, noniterative integration algorithms with unconditional stability for mildly nonlinear structural dynamic problemsNonlinear Dyn.201579216251649 – reference: HughesTJRLiuWKImplicit–explicit finite elements in transient analysis: implementation and numerical examplesJ. Appl. Mech.19784523753780392.73077 – reference: SoaresDJrAn enhanced explicit time-marching technique for wave propagation analysis considering adaptive time integratorsComput. Methods Appl. Mech. Eng.202036311288240648101436.74030 – reference: NohGBatheKJThe Bathe time integration method with controllable spectral radius: the ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _\infty $$\end{document}-Bathe methodComput. Struct.2019212299310 – reference: NamburuRRTammaKKA generalized γs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma _s$$\end{document}-family of self-starting algorithms for computational structural dynamicsAIAA J.199210.2514/6.1992-2330 – reference: HeHYuKTangHLiJZhouQZhangXVibration experiment and nonlinear modelling research on the folding fin with freeplayChin. J. Theor. Appl. Mech.201951923572371 – reference: NohGBatheKJAn explicit time integration scheme for the analysis of wave propagationsComput. Struct.2013129178193 – reference: SoaresDJrA simple and effective new family of time marching procedures for dynamicsComput. Methods Appl. Mech. Eng.20142831138116632838041425.65077 – reference: LiJYuKHeHA second-order accurate three sub-step composite algorithm for structural dynamicsAppl. Math. Model.20207713911412402869307193034 – reference: LiJYuKLiXA novel family of controllably dissipative composite integration algorithms for structural dynamic analysisNonlinear Dyn.201996424752507 – reference: BorstRDCrisfieldMRemmersJVerhooselCNonlinear Finite Element Analysis of Solids and Structures. 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| SubjectTerms | Algorithms Automotive Engineering Classical Mechanics Control Dynamical Systems Engineering Linear systems Mechanical Engineering Nonlinear dynamics Numerical dissipation Original Paper Stability Vibration Wave propagation |
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| Title | Development of composite sub-step explicit dissipative algorithms with truly self-starting property |
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