A truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamics

In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-startin...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Nonlinear dynamics Ročník 102; číslo 4; s. 2503 - 2530
Hlavní autoři:	Li, Jinze, Yu, Kaiping
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Dordrecht Springer Netherlands 01.12.2020 Springer Nature B.V
Témata:	Algorithms Automotive Engineering Classical Mechanics Control Dynamical Systems Engineering Mechanical Engineering Nonlinear control Nonlinear dynamics Original Paper Parameters Stability Vibration Structural dynamics Two sub-step scheme Truly self-starting Implicit integration algorithm Controllable dissipation
ISSN:	0924-090X, 1573-269X
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters ( γ and ρ ∞ ). The classical dissipative parameter ρ ∞ determines numerical dissipations in the high-frequency while γ adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot.
AbstractList	In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters (γ and ρ∞). The classical dissipative parameter ρ∞ determines numerical dissipations in the high-frequency while γ adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot. In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters ( γ and ρ ∞ ). The classical dissipative parameter ρ ∞ determines numerical dissipations in the high-frequency while γ adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot.
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
BookMark	eNp9kEtLQzEQhYMo2Kp_wFXAdXSS2_vIUsQXFNwodBemuUmN3CY1SZH-e2OvILjoahZzvjNzzpQc--ANIZccrjlAe5M4h5YzEMCg4cBZd0QmvG4rJhq5OCYTkGLGQMLilExT-gCASkA3IeGW5rgddjSZwbKUMWbnV9StN4PTLlOLa1e2wVLns1lFzC54isMqRJff14l-lUF7l5LbjDsdfI5hoDZEWr4cnDcYab_zxUmnc3JicUjm4neekbeH-9e7JzZ_eXy-u50zXXGZ2cw2s75fAgoheNsvbYXS1sA7bRo0DfAaZSu0XLYSddfU2KPm2GFXmKavl9UZuRp9NzF8bk3K6iNsoy8nlZi1lSjhZV1U3ajSMaQUjVUl8z5GjugGxUH91KvGelWpV-3rVV1BxT90E90a4-4wVI1QKmK_MvHvqwPUN4a5klY
CitedBy_id	crossref_primary_10_1002_nme_7639 crossref_primary_10_1016_j_cma_2021_114274 crossref_primary_10_1016_j_istruc_2025_109232 crossref_primary_10_1002_nme_7291 crossref_primary_10_1007_s00419_024_02637_y crossref_primary_10_1016_j_euromechsol_2022_104829 crossref_primary_10_1016_j_apm_2022_10_012 crossref_primary_10_1007_s00419_022_02286_z crossref_primary_10_1007_s11071_021_06202_y crossref_primary_10_1016_j_cma_2022_114945 crossref_primary_10_1016_j_compstruc_2022_106921
Cites_doi	10.1002/nme.1620151011 10.1002/eqe.4290010305 10.1016/j.cja.2020.05.005 10.1016/0045-7949(89)90315-5 10.1002/nme.1620372303 10.1016/j.compstruc.2018.03.006 10.1016/j.compstruc.2013.02.006 10.1002/eqe.4290150710 10.1016/j.cma.2014.08.007 10.1016/0045-7825(76)90008-6 10.1016/j.jcp.2009.12.028 10.1007/s00419-019-01637-7 10.1016/j.compstruc.2018.11.001 10.1061/JMCEA3.0000098 10.1016/j.apm.2019.11.033 10.1002/cnm.1630040211 10.1002/9781119965893 10.2514/6.1992-2330 10.1016/j.compstruc.2018.10.008 10.1002/nme.5329 10.1016/j.compstruc.2006.09.004 10.1016/j.compstruc.2019.05.015 10.1016/j.compstruc.2013.07.001 10.1007/s11071-019-04936-4 10.1007/s11071-014-1765-7 10.1115/1.2900803 10.1016/j.apm.2015.10.027 10.1115/1.3423600 10.1002/eqe.4290050306 10.1002/nme.6064 10.1016/j.apm.2018.12.027 10.1016/0045-7949(89)90314-3 10.1002/9781118375938 10.1016/j.apm.2019.08.022 10.1016/j.compstruc.2005.08.001 10.1002/nme.873 10.1002/nme.4715 10.1002/eqe.4290060111 10.1155/2018/1985907
ContentType	Journal Article
Copyright	Springer Nature B.V. 2020 Springer Nature B.V. 2020.
Copyright_xml	– notice: Springer Nature B.V. 2020 – notice: Springer Nature B.V. 2020.
DBID	AAYXX CITATION 8FE 8FG ABJCF AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS
DOI	10.1007/s11071-020-06101-8
DatabaseName	CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland ProQuest Central Technology collection ProQuest One Community College ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection
DatabaseTitle	CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (New) Engineering Collection ProQuest One Academic (New)
DatabaseTitleList	Engineering Database
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering
EISSN	1573-269X
EndPage	2530
ExternalDocumentID	10_1007_s11071_020_06101_8
GrantInformation_xml	– fundername: National Natural Science Foundation of China grantid: 11372084 funderid: http://dx.doi.org/10.13039/501100001809
GroupedDBID	-5B -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 28- 29N 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARCEE ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW L6V LAK LLZTM M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9T PF0 PT4 PT5 PTHSS QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SCV SDH SDM SEG SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z83 Z86 Z88 Z8M Z8N Z8R Z8S Z8T Z8W Z8Z Z92 ZMTXR _50 ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB DWQXO PKEHL PQEST PQQKQ PQUKI PRINS
ID	FETCH-LOGICAL-c319t-4f64ddb0a22217dbf3a9f5018ce6ae6015a972c9b79ac865adac1a8a8db06d5b3
IEDL.DBID	RSV
ISICitedReferencesCount	15
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000592562400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0924-090X
IngestDate	Wed Nov 05 00:44:35 EST 2025 Sat Nov 29 03:06:27 EST 2025 Tue Nov 18 22:06:50 EST 2025 Fri Feb 21 02:32:35 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Keywords	Structural dynamics Two sub-step scheme Truly self-starting Implicit integration algorithm Controllable dissipation
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c319t-4f64ddb0a22217dbf3a9f5018ce6ae6015a972c9b79ac865adac1a8a8db06d5b3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-2563-1223 0000-0002-7722-0138
PQID	2473220895
PQPubID	2043746
PageCount	28
ParticipantIDs	proquest_journals_2473220895 crossref_citationtrail_10_1007_s11071_020_06101_8 crossref_primary_10_1007_s11071_020_06101_8 springer_journals_10_1007_s11071_020_06101_8
PublicationCentury	2000
PublicationDate	20201200 2020-12-00 20201201
PublicationDateYYYYMMDD	2020-12-01
PublicationDate_xml	– month: 12 year: 2020 text: 20201200
PublicationDecade	2020
PublicationPlace	Dordrecht
PublicationPlace_xml	– name: Dordrecht
PublicationSubtitle	An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems
PublicationTitle	Nonlinear dynamics
PublicationTitleAbbrev	Nonlinear Dyn
PublicationYear	2020
Publisher	Springer Netherlands Springer Nature B.V
Publisher_xml	– name: Springer Netherlands – name: Springer Nature B.V
References	LiJYuKA novel family of composite sub-step algorithms with desired numerical dissipations for structural dynamicsArch. Appl. Mech.201990737772 SubbarajKDokainishMAA survey of direct time-integration methods in computational structural dynamics-II. implicit methods.Comput. Struct.19893261387140110179860702.73073 NickellRNonlinear dynamics by mode superpositionComput. Methods Appl. Mech. Eng.1976711071294554900316.73068 ZhouXTammaKKDesign, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamicsInt. J. Numer. Methods Eng.200459559766820316201068.74616 BenítezJMMontánsFJThe value of numerical amplification matrices in time integration methodsComput. Struct.20131285243250 MalakiyehMMShojaeeSBatheKJThe Bathe time integration method revisited for prescribing desired numerical dissipationComput. Struct.2019212289298 ChangSYDissipative, noniterative integration algorithms with unconditional stability for mildly nonlinear structural dynamic problemsNonlinear Dyn.201579216251649 ShimadaMHoitinkATammaKKThe fundamentals underlying the computations of acceleration for general dynamic applications: issues and noteworthy perspectivesCMES Comput. Model. Eng. Sci.20151042133158 de BorstRCrisfieldMANon-Linear Finite Element Analysis of Solids and Structures2012New YorkWiley Series in Computational Mechanics. Wiley1300.74002 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 HarJTammaKKAdvances in Computational Dynamics of Particles, Materials and Structures2012New YorkWiley1248.74001 LiJYuKNoniterative integration algorithms with controllable numerical dissipations for structural dynamicsInt. J. Comput. Methods20181531850111398522307086729 FernandesWLVasconcellosDBGrecoMDynamic instability in shallow arches under transversal forces and plane frames with semirigid connectionsMath. Probl. Eng.20182018114382524110.1155/2018/19859071426.74181 NewmarkNMA method of computation for structural dynamicsJ. Eng. Mech. Div.19598536794 LiJYuKAn alternative to the Bathe algorithmAppl. Math. Modell.201969255272389506007186525 BatheKJFinite Element Procedures20142Englewood CliffsPrentice-Hall1326.65002 ShaoHCaiCA three parameters algorithm for numerical integration of structural dynamic equationsChin. J. Appl. Mech.1988547681 ChungJHulbertGMA time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} methodJ. Appl. Mech.199360237137512239710775.73337 ZhangHMXingYFOptimization of a class of composite method for structural dynamicsComput. Struct.20182026073 Namburu, R.R., Tamma, K.K.: A 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 dynamics. In: AIAA Journal (1992) ButcherJCThe Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods1987New JerseyJohn Wiley and Sons0616.65072 HilberHMHughesTJRTaylorRLImproved numerical dissipation for time integration algorithms in structural dynamicsEarthq. Eng. Struct. Dyn.197753283292 NohGBatheKJFor direct time integrations: a comparison of the Newmark and 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 schemesComput. Struct.2019225106079 LiJYuKHeHA second-order accurate three sub-step composite algorithm for structural dynamicsAppl. Math. Modell.20207713911412402869307193034 LiJLiXYuKEnhanced studies on the composite sub-step algorithm for structural dynamics: the Bathe-like algorithmAppl. Math. Modell.2020803364404269107193114 WoodWLOduorMEStability properties of some algorithms for the solution of nonlinear dynamic vibration equationsCommun. Appl. Numer. Methods1988422052120643.65044 ShimadaMMasuriSTammaKKA novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systemsInt. J. Numer. Methods Eng.20151023–48678911352.65371 SoaresDJrA simple and effective new family of time marching procedures for dynamicsComput. Methods Appl. Mech. Eng.20142831138116632838041425.65077 WoodWBossakMZienkiewiczOAn alpha modification of Newmark’s methodInt. J. Numer. Methods Eng.19801510156215665953730441.73106 NohGHamSBatheKJPerformance of an implicit time integration scheme in the analysis of wave propagationsComput. Struct.201312393105 ChungJLeeJMA new family of explicit time integration methods for linear and non-linear structural dynamicsInt. J. Numer. Methods Eng.199437233961397613111450814.73074 HughesTJRThe Finite Element Method: Linear Static and Dynamic Finite Element Analysis2000DoverDover Publications, Dover Civil and Mechanical Engineering1191.74002 BatheKJBaigMMIOn a composite implicit time integration procedure for nonlinear dynamicsComput. Struct.20058331–32251325242174999 WilsonELFarhoomandIBatheKJNonlinear dynamic analysis of complex structuresEarthq. Eng. Struct. Dyn.197213241252 SoaresDJrA simple and effective single-step time marching technique based on adaptive time integratorsInt. J. Numer. Methods Eng.2016109134413683602565 BatheKJConserving energy and momentum in nonlinear dynamics: A simple implicit time integration schemeComputers & Structures2007857–84374452303506 HulbertGMHughesTJRAn error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamicsEarthq. Eng. Struct. Dyn.1987157901910 LiJYuKLiXA novel family of controllably dissipative composite integration algorithms for structural dynamic analysisNonlinear Dyn.201996424752507 HeHTangHYuKLiJYangNZhangXNonlinear aeroelastic analysis of the folding fin with freeplay under thermal environmentChin. J. Aeronaut.202033923572371 DokainishMASubbarajKA survey of direct time-integration methods in computational structural dynamics-I. explicit methods.Comput. Struct.19893261371138610179850702.73072 HilberHMHughesTJRCollocation, dissipation and ‘overshoot’ for time integration schemes in structural dynamicsEarthq. Eng. Struct. Dyn.19786199117 DongSBDF-like methods for nonlinear dynamic analysisJ. Comput. Phys.201022983019304525958061307.74069 ParkKCAn improved stiffly stable method for direct integration of nonlinear structural dynamic equationsJ. Appl. Mech.19754224644703759150342.65046 SoaresDAn implicit family of time marching procedures with adaptive dissipation controlAppl. Math. Modell.201640433253341345453007159254 SoaresDJrA model/solution-adaptive explicit-implicit time marching technique for wave propagation analysisInt. J. Numer. Methods Eng.20191195906173988562 J Li (6101_CR37) 2018; 15 W Wood (6101_CR13) 1980; 15 R de Borst (6101_CR12) 2012 K Subbaraj (6101_CR11) 1989; 32 J Li (6101_CR33) 2019; 96 D Soares Jr (6101_CR20) 2014; 283 X Zhou (6101_CR36) 2004; 59 JM Benítez (6101_CR18) 2013; 128 J Li (6101_CR31) 2020; 80 MA Dokainish (6101_CR10) 1989; 32 J Chung (6101_CR45) 1994; 37 GM Hulbert (6101_CR16) 1987; 15 6101_CR19 D Soares Jr (6101_CR23) 2019; 119 M Shimada (6101_CR15) 2015; 102 J Har (6101_CR7) 2012 J Li (6101_CR28) 2019; 90 EL Wilson (6101_CR5) 1972; 1 KJ Bathe (6101_CR2) 2014 NM Newmark (6101_CR4) 1959; 85 J Li (6101_CR40) 2020; 77 WL Fernandes (6101_CR43) 2018; 2018 R Nickell (6101_CR42) 1976; 7 G Noh (6101_CR32) 2013; 123 MM Malakiyeh (6101_CR29) 2019; 212 SY Chang (6101_CR34) 2015; 79 G Noh (6101_CR39) 2019; 225 H He (6101_CR44) 2020; 33 M Shimada (6101_CR17) 2015; 104 KJ Bathe (6101_CR25) 2007; 85 KC Park (6101_CR6) 1975; 42 TJR Hughes (6101_CR1) 2000 HM Hilber (6101_CR14) 1977; 5 G Noh (6101_CR30) 2019; 212 J Chung (6101_CR9) 1993; 60 S Dong (6101_CR27) 2010; 229 D Soares (6101_CR21) 2016; 40 H Shao (6101_CR8) 1988; 5 J Li (6101_CR26) 2019; 69 KJ Bathe (6101_CR24) 2005; 83 HM Hilber (6101_CR35) 1978; 6 HM Zhang (6101_CR38) 2018; 202 JC Butcher (6101_CR3) 1987 D Soares Jr (6101_CR22) 2016; 109 WL Wood (6101_CR41) 1988; 4
References_xml	– reference: BatheKJConserving energy and momentum in nonlinear dynamics: A simple implicit time integration schemeComputers & Structures2007857–84374452303506 – 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: HulbertGMHughesTJRAn error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamicsEarthq. Eng. Struct. Dyn.1987157901910 – reference: ShimadaMMasuriSTammaKKA novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systemsInt. J. Numer. Methods Eng.20151023–48678911352.65371 – reference: MalakiyehMMShojaeeSBatheKJThe Bathe time integration method revisited for prescribing desired numerical dissipationComput. Struct.2019212289298 – reference: HilberHMHughesTJRCollocation, dissipation and ‘overshoot’ for time integration schemes in structural dynamicsEarthq. Eng. Struct. Dyn.19786199117 – reference: ChangSYDissipative, noniterative integration algorithms with unconditional stability for mildly nonlinear structural dynamic problemsNonlinear Dyn.201579216251649 – reference: NickellRNonlinear dynamics by mode superpositionComput. Methods Appl. Mech. Eng.1976711071294554900316.73068 – 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: SoaresDJrA model/solution-adaptive explicit-implicit time marching technique for wave propagation analysisInt. J. Numer. Methods Eng.20191195906173988562 – 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. Modell.20207713911412402869307193034 – reference: NohGBatheKJFor direct time integrations: a comparison of the Newmark and 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 schemesComput. Struct.2019225106079 – reference: LiJLiXYuKEnhanced studies on the composite sub-step algorithm for structural dynamics: the Bathe-like algorithmAppl. Math. Modell.2020803364404269107193114 – reference: LiJYuKLiXA novel family of controllably dissipative composite integration algorithms for structural dynamic analysisNonlinear Dyn.201996424752507 – reference: SubbarajKDokainishMAA survey of direct time-integration methods in computational structural dynamics-II. implicit methods.Comput. Struct.19893261387140110179860702.73073 – reference: HilberHMHughesTJRTaylorRLImproved numerical dissipation for time integration algorithms in structural dynamicsEarthq. Eng. Struct. Dyn.197753283292 – reference: FernandesWLVasconcellosDBGrecoMDynamic instability in shallow arches under transversal forces and plane frames with semirigid connectionsMath. Probl. Eng.20182018114382524110.1155/2018/19859071426.74181 – reference: de BorstRCrisfieldMANon-Linear Finite Element Analysis of Solids and Structures2012New YorkWiley Series in Computational Mechanics. Wiley1300.74002 – reference: Namburu, R.R., Tamma, K.K.: A 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 dynamics. In: AIAA Journal (1992) – reference: WoodWBossakMZienkiewiczOAn alpha modification of Newmark’s methodInt. J. Numer. Methods Eng.19801510156215665953730441.73106 – reference: BatheKJFinite Element Procedures20142Englewood CliffsPrentice-Hall1326.65002 – reference: BenítezJMMontánsFJThe value of numerical amplification matrices in time integration methodsComput. Struct.20131285243250 – reference: WoodWLOduorMEStability properties of some algorithms for the solution of nonlinear dynamic vibration equationsCommun. Appl. Numer. Methods1988422052120643.65044 – reference: DokainishMASubbarajKA survey of direct time-integration methods in computational structural dynamics-I. explicit methods.Comput. Struct.19893261371138610179850702.73072 – reference: SoaresDJrA simple and effective single-step time marching technique based on adaptive time integratorsInt. J. Numer. Methods Eng.2016109134413683602565 – reference: ShimadaMHoitinkATammaKKThe fundamentals underlying the computations of acceleration for general dynamic applications: issues and noteworthy perspectivesCMES Comput. Model. Eng. Sci.20151042133158 – reference: LiJYuKAn alternative to the Bathe algorithmAppl. Math. Modell.201969255272389506007186525 – reference: HarJTammaKKAdvances in Computational Dynamics of Particles, Materials and Structures2012New YorkWiley1248.74001 – reference: ShaoHCaiCA three parameters algorithm for numerical integration of structural dynamic equationsChin. J. Appl. Mech.1988547681 – reference: ParkKCAn improved stiffly stable method for direct integration of nonlinear structural dynamic equationsJ. Appl. Mech.19754224644703759150342.65046 – reference: ZhouXTammaKKDesign, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamicsInt. J. Numer. Methods Eng.200459559766820316201068.74616 – reference: LiJYuKNoniterative integration algorithms with controllable numerical dissipations for structural dynamicsInt. J. Comput. Methods20181531850111398522307086729 – reference: NewmarkNMA method of computation for structural dynamicsJ. Eng. Mech. Div.19598536794 – reference: ButcherJCThe Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods1987New JerseyJohn Wiley and Sons0616.65072 – reference: ChungJHulbertGMA time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} methodJ. Appl. Mech.199360237137512239710775.73337 – reference: ZhangHMXingYFOptimization of a class of composite method for structural dynamicsComput. Struct.20182026073 – reference: ChungJLeeJMA new family of explicit time integration methods for linear and non-linear structural dynamicsInt. J. Numer. Methods Eng.199437233961397613111450814.73074 – reference: NohGHamSBatheKJPerformance of an implicit time integration scheme in the analysis of wave propagationsComput. Struct.201312393105 – reference: SoaresDAn implicit family of time marching procedures with adaptive dissipation controlAppl. Math. Modell.201640433253341345453007159254 – reference: DongSBDF-like methods for nonlinear dynamic analysisJ. Comput. Phys.201022983019304525958061307.74069 – reference: HughesTJRThe Finite Element Method: Linear Static and Dynamic Finite Element Analysis2000DoverDover Publications, Dover Civil and Mechanical Engineering1191.74002 – reference: BatheKJBaigMMIOn a composite implicit time integration procedure for nonlinear dynamicsComput. Struct.20058331–32251325242174999 – volume: 15 start-page: 1562 issue: 10 year: 1980 ident: 6101_CR13 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620151011 – volume: 1 start-page: 241 issue: 3 year: 1972 ident: 6101_CR5 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290010305 – volume: 33 start-page: 2357 issue: 9 year: 2020 ident: 6101_CR44 publication-title: Chin. J. Aeronaut. doi: 10.1016/j.cja.2020.05.005 – volume: 32 start-page: 1387 issue: 6 year: 1989 ident: 6101_CR11 publication-title: Comput. Struct. doi: 10.1016/0045-7949(89)90315-5 – volume: 37 start-page: 3961 issue: 23 year: 1994 ident: 6101_CR45 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620372303 – volume: 202 start-page: 60 year: 2018 ident: 6101_CR38 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.03.006 – volume: 123 start-page: 93 year: 2013 ident: 6101_CR32 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2013.02.006 – volume: 104 start-page: 133 issue: 2 year: 2015 ident: 6101_CR17 publication-title: CMES Comput. Model. Eng. Sci. – volume: 15 start-page: 901 issue: 7 year: 1987 ident: 6101_CR16 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290150710 – volume: 283 start-page: 1138 year: 2014 ident: 6101_CR20 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2014.08.007 – volume: 7 start-page: 107 issue: 1 year: 1976 ident: 6101_CR42 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/0045-7825(76)90008-6 – volume-title: Finite Element Procedures year: 2014 ident: 6101_CR2 – volume: 229 start-page: 3019 issue: 8 year: 2010 ident: 6101_CR27 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.12.028 – volume: 90 start-page: 737 year: 2019 ident: 6101_CR28 publication-title: Arch. Appl. Mech. doi: 10.1007/s00419-019-01637-7 – volume: 5 start-page: 76 issue: 4 year: 1988 ident: 6101_CR8 publication-title: Chin. J. Appl. Mech. – volume: 212 start-page: 299 year: 2019 ident: 6101_CR30 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.11.001 – volume: 85 start-page: 67 issue: 3 year: 1959 ident: 6101_CR4 publication-title: J. Eng. Mech. Div. doi: 10.1061/JMCEA3.0000098 – volume: 80 start-page: 33 year: 2020 ident: 6101_CR31 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2019.11.033 – volume: 4 start-page: 205 issue: 2 year: 1988 ident: 6101_CR41 publication-title: Commun. Appl. Numer. Methods doi: 10.1002/cnm.1630040211 – volume-title: Advances in Computational Dynamics of Particles, Materials and Structures year: 2012 ident: 6101_CR7 doi: 10.1002/9781119965893 – ident: 6101_CR19 doi: 10.2514/6.1992-2330 – volume: 212 start-page: 289 year: 2019 ident: 6101_CR29 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2018.10.008 – volume: 109 start-page: 1344 year: 2016 ident: 6101_CR22 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.5329 – volume: 85 start-page: 437 issue: 7–8 year: 2007 ident: 6101_CR25 publication-title: Computers & Structures doi: 10.1016/j.compstruc.2006.09.004 – volume: 225 start-page: 106079 year: 2019 ident: 6101_CR39 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2019.05.015 – volume-title: The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods year: 1987 ident: 6101_CR3 – volume: 128 start-page: 243 issue: 5 year: 2013 ident: 6101_CR18 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2013.07.001 – volume: 96 start-page: 2475 issue: 4 year: 2019 ident: 6101_CR33 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-019-04936-4 – volume: 79 start-page: 1625 issue: 2 year: 2015 ident: 6101_CR34 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1765-7 – volume: 60 start-page: 371 issue: 2 year: 1993 ident: 6101_CR9 publication-title: J. Appl. Mech. doi: 10.1115/1.2900803 – volume: 40 start-page: 3325 issue: 4 year: 2016 ident: 6101_CR21 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2015.10.027 – volume: 42 start-page: 464 issue: 2 year: 1975 ident: 6101_CR6 publication-title: J. Appl. Mech. doi: 10.1115/1.3423600 – volume: 15 start-page: 1850111 issue: 3 year: 2018 ident: 6101_CR37 publication-title: Int. J. Comput. Methods – volume: 5 start-page: 283 issue: 3 year: 1977 ident: 6101_CR14 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290050306 – volume: 119 start-page: 590 year: 2019 ident: 6101_CR23 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.6064 – volume: 69 start-page: 255 year: 2019 ident: 6101_CR26 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2018.12.027 – volume: 32 start-page: 1371 issue: 6 year: 1989 ident: 6101_CR10 publication-title: Comput. Struct. doi: 10.1016/0045-7949(89)90314-3 – volume-title: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis year: 2000 ident: 6101_CR1 – volume-title: Non-Linear Finite Element Analysis of Solids and Structures year: 2012 ident: 6101_CR12 doi: 10.1002/9781118375938 – volume: 77 start-page: 1391 year: 2020 ident: 6101_CR40 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2019.08.022 – volume: 83 start-page: 2513 issue: 31–32 year: 2005 ident: 6101_CR24 publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2005.08.001 – volume: 59 start-page: 597 issue: 5 year: 2004 ident: 6101_CR36 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.873 – volume: 102 start-page: 867 issue: 3–4 year: 2015 ident: 6101_CR15 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.4715 – volume: 6 start-page: 99 issue: 1 year: 1978 ident: 6101_CR35 publication-title: Earthq. Eng. Struct. Dyn. doi: 10.1002/eqe.4290060111 – volume: 2018 start-page: 1 year: 2018 ident: 6101_CR43 publication-title: Math. Probl. Eng. doi: 10.1155/2018/1985907
SSID	ssj0003208
Score	2.3716826
Snippet	In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	2503
SubjectTerms	Algorithms Automotive Engineering Classical Mechanics Control Dynamical Systems Engineering Mechanical Engineering Nonlinear control Nonlinear dynamics Original Paper Parameters Stability Vibration
SummonAdditionalLinks	– databaseName: ProQuest Central dbid: BENPR link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB509aAH3-L6IgdvWuwjTdOTqCieFhGFvZVJ2ujCurtuq-C_d9Kmrgp68VZokwa-yWRe-QbgyE9UwFVktZ8UHpex72GA9BQbbjRGHH1TN5tIej3Z76e3LuBWurLKVifWijofaxsjPw15QrLnyzQ-m7x4tmuUza66FhrzsGCZyngHFi6uerd3n7o4CuuedD55GTYi0XfXZprLc-T5kCsd2sYrJJie_H40zezNHynS-uS5Xv3vmtdgxdmc7LwRknWYK0YbsOrsT-Z2d7kBy1_ICTdhfM6q6evwnZXF0HhkRFq-gUc2qEvQBxVrQiNsbFhLOUEQMxw-0gqqp-eS2RAvs_l-V7XNXFk8IzuZjRqKDpyy_H1EM-lyCx6ur-4vbzzXnsHTtG8rjxvB81z5SCZGkOTKRJgayw-oC4EFOXoxpkmoU5WkqKWIMUcdoERJY0Qeq2gbOvSzYgdYpIROeaQMoiIREaj8RKAUiKEwQqguBC0ymXbc5baFxjCbsS5bNDNCM6vRzGQXjj_HTBrmjj-_3m8hzNwuLrMZfl04aYVg9vr32Xb_nm0PlkIrd3VVzD50CM3iABb1WzUop4dOhj8AsfX5lw priority: 102 providerName: ProQuest
Title	A truly self-starting implicit family of integration algorithms with dissipation control for nonlinear dynamics
URI	https://link.springer.com/article/10.1007/s11071-020-06101-8 https://www.proquest.com/docview/2473220895
Volume	102
WOSCitedRecordID	wos000592562400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-269X dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: M7S dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-269X dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLink Core Collection customDbUrl: eissn: 1573-269X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFH-o86AHv8X5MXLwpoV-pulRZcPTGE5lt_KSNnMwN1mr4H_vS5c6FRX0VmiSlrzvvJffAzh1Y-mFMjDaT3AnFJHroIf0FOlQKwxCdHXVbCLudsVgkPTspbCirnavU5KVpl5cdqNIhUJf3zRKIUZyxDI0yNwJI443_ft3_Rv4VR86lyILcwoxsFdlvl_jszla-Jhf0qKVtels_u8_t2DDepfsYs4O27CUT3Zg03qazMpxsQPrH2AId2F6wcrZ8_iVFflYO-QuGmSBIRtVxeajks0PQdhUsxpcgojJcDyczkblw2PBzGEuM5l9W5_NbAE8I4-YTeZgHDhj2euEVlLFHtx12rdX145txOAoktDSCTUPs0y6SM6EF2dSB5hogwSoco45hXQRJrGvEhknqASPMEPloUBBc3gWyWAfVuhj-QGwQHKVhIHUiJKYgaN0Y46CI_pccy6b4NX0SJVFKTfNMsbpAl_Z7G9K-5tW-5uKJpy9z3maY3T8Ovq4JnNq5bVI_TAmzeaKJGrCeU3WxeufVzv82_AjWPMNZ1T1MMewQtTNT2BVvZSjYtaCxmW727tpmQLUfqvi6jd8ifCl
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VggQcKBQQCwXmACeIyIfjOAeEKqBq1bJCokh7C2MnListu2UTQPun-I2MHacLSPTWA7dISSaK_WY8Mx6_AXgSFzoROnPWT8lIqDyOKCG-yq2whjJBsfXNJorxWE0m5fsN-DmchXFllYNN9Ia6XhiXI3-RioKxF6syf3X6NXJdo9zu6tBCo4fFYbP6wSFb-_LgDc_v0zTde3v8ej8KXQUiw3DrImGlqGsdE6-MSVFrm1FpHa2daSQ1HJ_kVBapKXVRklEyp5pMQooUvyPrXGcs9xJcFs76-1LBD2eWP0t9B7yYYxqX_5iEQzr9UT2OszhwT12bF1aDSP25EK692782ZP06t7f1v43QTbgRPGrc7VXgFmw0823YCt41BtvVbsP136gXb8NiF7vlt9kK22ZmI3aRHZvCCU59gf20wz7xgwuLA6EGAxhpdsJ_3H3-0qJLYKOrZgg16RiK_pGjAJz3BCS0xHo1Z0mmvQMfL2QQ7sImf6y5B5hpaUqRaUukWQEk6biQpCRRKq2UegTJgITKBGZ21yBkVq05pR16KkZP5dFTqRE8O3vntOclOffpnQEyVbBRbbXGywieD6Bb3_63tPvnS3sMV_eP3x1VRwfjwwdwLXWY9_U_O7DJM9s8hCvmezdtl4-89iB8umgw_gLzYFeZ
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9swED_WrJT1oVmzjabNOj30bTP1hyzLj6Vt2FgJgX2QN3OSrTaQJSF2B_3vd7LlJCvdYOzNYOlsdCfpPn8HcOYnKuAqsqefFB6Xse9hgPQUG240Rhx9UzebSEYjOZmk460q_jrbvQ1JNjUNFqVpXp0vc3O-KXwjq4XM4NA2TSGh8uQOPOe2aZC11798X5_FUVj3pPPJyrAeiYkrm3maxu9X00bffBQirW-eYff___klHDitk100YnIIz4p5D7pOA2Vuf5c92N-CJ3wFiwtWre5nD6wsZsYjNdIiDtyyaZ2EPq1Y4xxhC8Na0AliMsPZ7WI1re5-lMw6eZmN-Lu8beYS4xlpymzegHTgiuUPc6Kky9fwbXj99fKj5xo0eJp2buVxI3ieKx9JyQiSXJkIU2MRAnUhsCBTL8Y0CXWqkhS1FDHmqAOUKGmOyGMVvYEOfaw4AhYpoVMeKYOoSEgEKj8RKAViKIwQqg9By5tMO_Ry20Rjlm1wl-36ZrS-Wb2-mezD-_WcZYPd8dfRg5blmdvHZRbyhE48X6ZxHz60LN68_jO1438b_g72xlfD7ObT6PMJvAitkNQpMwPoEKOLt7Crf1bTcnVai_cvhaz52w
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+truly+self-starting+implicit+family+of+integration+algorithms+with+dissipation+control+for+nonlinear+dynamics&rft.jtitle=Nonlinear+dynamics&rft.au=Li%2C+Jinze&rft.au=Yu%2C+Kaiping&rft.date=2020-12-01&rft.pub=Springer+Netherlands&rft.issn=0924-090X&rft.eissn=1573-269X&rft.volume=102&rft.issue=4&rft.spage=2503&rft.epage=2530&rft_id=info:doi/10.1007%2Fs11071-020-06101-8&rft.externalDocID=10_1007_s11071_020_06101_8
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0924-090X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0924-090X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0924-090X&client=summon