A classical time integration method applied for solution of nonlinear equations of a double-layer tensegrity
The paper aims to investigate the nonlinear geometrical behavior of a tensegrity structure subject to dynamic loading in the time domain. The geometric nonlinearity is considered here with the aid of a simple set of equations, based on the Finite Element Method, but using nodal positions rather than...
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| Vydané v: | Journal of the Brazilian Society of Mechanical Sciences and Engineering Ročník 35; číslo 1; s. 41 - 50 |
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| Jazyk: | English |
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01.03.2013
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| Abstract | The paper aims to investigate the nonlinear geometrical behavior of a tensegrity structure subject to dynamic loading in the time domain. The geometric nonlinearity is considered here with the aid of a simple set of equations, based on the Finite Element Method, but using nodal positions rather than nodal displacements as variables. The finite element strains are evaluated directly from the proposed position concept, using a coordinate system fixed in space. The performance of two transient direct integration algorithms was implemented, one explicit and another implicit, considering the eventual inclusion of a numerical damping in the positional formulation. The algorithmic numerical damping is especially interesting for analyses during long time periods or for unstable slender structures. The dynamical behavior of a double-layer tensegrity system is analyzed using the time integration algorithms developed in the paper. Results point to the importance of the numerical damping in the analysis and the mechanical behavior dependence of the initial strain level prescribed in the cables. The development of classical time integration schemes for the positional formulation is original and the application for the double-layer tensegrity proves the accuracy of the method. |
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| AbstractList | The paper aims to investigate the nonlinear geometrical behavior of a tensegrity structure subject to dynamic loading in the time domain. The geometric nonlinearity is considered here with the aid of a simple set of equations, based on the Finite Element Method, but using nodal positions rather than nodal displacements as variables. The finite element strains are evaluated directly from the proposed position concept, using a coordinate system fixed in space. The performance of two transient direct integration algorithms was implemented, one explicit and another implicit, considering the eventual inclusion of a numerical damping in the positional formulation. The algorithmic numerical damping is especially interesting for analyses during long time periods or for unstable slender structures. The dynamical behavior of a double-layer tensegrity system is analyzed using the time integration algorithms developed in the paper. Results point to the importance of the numerical damping in the analysis and the mechanical behavior dependence of the initial strain level prescribed in the cables. The development of classical time integration schemes for the positional formulation is original and the application for the double-layer tensegrity proves the accuracy of the method. |
| Author | Barros, Felício Bruzzi Greco, Marcelo Ferreira, Ivone Passos |
| Author_xml | – sequence: 1 givenname: Marcelo surname: Greco fullname: Greco, Marcelo email: mgreco@dees.ufmg.br organization: Graduate Program in Structural Engineering, Department of Structural Engineering, Federal University of Minas Gerais – sequence: 2 givenname: Ivone Passos surname: Ferreira fullname: Ferreira, Ivone Passos organization: Graduate Program in Structural Engineering, Department of Structural Engineering, Federal University of Minas Gerais – sequence: 3 givenname: Felício Bruzzi surname: Barros fullname: Barros, Felício Bruzzi organization: Graduate Program in Structural Engineering, Department of Structural Engineering, Federal University of Minas Gerais |
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| Cites_doi | 10.1002/eqe.4290050306 10.1061/(ASCE)0893-1321(1998)11:2(37) 10.1016/S0020-7683(00)00233-X 10.1260/026635106780866015 10.1061/(ASCE)0733-9445(1991)117:6(1660) 10.1016/S0045-7949(03)00291-8 10.1260/0266351011495322 10.1061/(ASCE)0733-9445(2004)130:10(1454) 10.1260/026635102760123051 10.1061/40722(153)42 10.1016/j.compstruc.2004.05.008 10.1016/j.finel.2009.05.005 10.1016/j.finel.2006.04.007 10.1016/S0141-0296(01)00130-4 10.1007/s11071-007-9328-9 10.1016/j.mechmachtheory.2008.06.008 10.1260/026635103769518198 10.1061/(ASCE)0893-1321(2001)14:3(85) |
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| Keywords | Positional formulation Time integration algorithm Tensegrity structures Dynamics Nonlinear analysis |
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| References_xml | – reference: HanaorALiaoMDouble-layer tensegrity grids: static loading responseJ Struct Eng19911171660167410.1061/(ASCE)0733-9445(1991)117:6(1660) – reference: MoussaBKahlaNBPonsJCEvolution of natural frequencies in tensegrity systems: a case studyInt J Space Struct200116577310.1260/0266351011495322 – reference: KahlaNBMoussaBEffect of a cable rupture on tensegrity systemsInt J Space Struct200217516510.1260/026635102760123051 – reference: OppenheimIJWilliamsWOVibration and damping in three-bar tensegrity structureJ Aerosp Eng200114859110.1061/(ASCE)0893-1321(2001)14:3(85) – reference: GrecoMGesualdoFARVenturiniWSCodaHBNonlinear positional formulation for space truss analysisFinite Elem Anal Des20064210791086224543010.1016/j.finel.2006.04.007 – reference: HilberHMHughesTJRTaylorRImproved numerical dissipation for time integration algorithms in structural dynamicsEarthq Eng Struct Dyn1977528329210.1002/eqe.4290050306 – reference: SultanCCorlessMSkeltonRELinear dynamic of tensegrity structuresEng Struct20022467168510.1016/S0141-0296(01)00130-4 – reference: DjouadiSMotroRPonsJCCrosnierBActive control of tensegrity systemsJ Aerosp Eng199811374410.1061/(ASCE)0893-1321(1998)11:2(37) – reference: HusseinBNegrutDShabanaAAImplicit and explicit integration in the solution of the absolute nodal coordinate differential-algebraic equationsNonlinear Dyn2008214283296244901810.1007/s11071-007-9328-9 – reference: GrecoMFerreiraIPLogarithmic strain measure applied to the nonlinear positional formulation for space truss analysisFinite Elem Anal Design20094563263910.1016/j.finel.2009.05.005 – reference: TokluYCNonlinear analysis of trusses through energy minimizationComput Struct2004821581158910.1016/j.compstruc.2004.05.008 – reference: Smith IFC (2004) An active structure that adapts and learns. In: Proceedings of the 9th biennial ASCE Aerospace Division International Conference on Engineering, Construction, and Operations in Challenging Environments, Houston – reference: MurakamiHStatic and dynamic analysis of tensegrity structures. Part II. Quasi-static analysisInt J Solids Struct2001383615362910.1016/S0020-7683(00)00233-X – reference: TurJMMJuanSHTensegrity frameworks: dynamic analysis review and open problemsMech Mach Theory2009441180538098510.1016/j.mechmachtheory.2008.06.008 – reference: DubéJFAngellierNCorrelation between eigenmodes and the selfstress state identification of a tensegrity gridInt J Space Struct20062122323210.1260/026635106780866015 – reference: LazzariMVitalianiRVMajowieckiMSaettaADynamic behavior of a tensegrity system subjected to follower wind loadingComput Struct2003812199221710.1016/S0045-7949(03)00291-8 – reference: MotroRRaducanuVTensegrity systemsInt J Space Struct200318778410.1260/026635103769518198 – reference: ArgyrisJMlejnekHPDynamics of structures: texts on computational mechanics1991AmsterdamNorth-holland0792.73001 – reference: FestESheaKSmithIFCActive tensegrity structureJ Struct Eng20041301454146510.1061/(ASCE)0733-9445(2004)130:10(1454) – volume: 5 start-page: 283 year: 1977 ident: 9_CR8 publication-title: Earthq Eng Struct Dyn doi: 10.1002/eqe.4290050306 – volume: 11 start-page: 37 year: 1998 ident: 9_CR2 publication-title: J Aerosp Eng doi: 10.1061/(ASCE)0893-1321(1998)11:2(37) – volume: 38 start-page: 3615 year: 2001 ident: 9_CR14 publication-title: Int J Solids Struct doi: 10.1016/S0020-7683(00)00233-X – volume: 21 start-page: 223 year: 2006 ident: 9_CR3 publication-title: Int J Space Struct doi: 10.1260/026635106780866015 – volume: 117 start-page: 1660 year: 1991 ident: 9_CR7 publication-title: J Struct Eng doi: 10.1061/(ASCE)0733-9445(1991)117:6(1660) – volume: 81 start-page: 2199 year: 2003 ident: 9_CR11 publication-title: Comput Struct doi: 10.1016/S0045-7949(03)00291-8 – volume-title: Dynamics of structures: texts on computational mechanics year: 1991 ident: 9_CR1 – volume: 16 start-page: 57 year: 2001 ident: 9_CR13 publication-title: Int J Space Struct doi: 10.1260/0266351011495322 – volume: 130 start-page: 1454 year: 2004 ident: 9_CR4 publication-title: J Struct Eng doi: 10.1061/(ASCE)0733-9445(2004)130:10(1454) – volume: 17 start-page: 51 year: 2002 ident: 9_CR10 publication-title: Int J Space Struct doi: 10.1260/026635102760123051 – ident: 9_CR16 doi: 10.1061/40722(153)42 – volume: 82 start-page: 1581 year: 2004 ident: 9_CR18 publication-title: Comput Struct doi: 10.1016/j.compstruc.2004.05.008 – volume: 45 start-page: 632 year: 2009 ident: 9_CR5 publication-title: Finite Elem Anal Design doi: 10.1016/j.finel.2009.05.005 – volume: 42 start-page: 1079 year: 2006 ident: 9_CR6 publication-title: Finite Elem Anal Des doi: 10.1016/j.finel.2006.04.007 – volume: 24 start-page: 671 year: 2002 ident: 9_CR17 publication-title: Eng Struct doi: 10.1016/S0141-0296(01)00130-4 – volume: 214 start-page: 283 year: 2008 ident: 9_CR9 publication-title: Nonlinear Dyn doi: 10.1007/s11071-007-9328-9 – volume: 44 start-page: 1 year: 2009 ident: 9_CR19 publication-title: Mech Mach Theory doi: 10.1016/j.mechmachtheory.2008.06.008 – volume: 18 start-page: 77 year: 2003 ident: 9_CR12 publication-title: Int J Space Struct doi: 10.1260/026635103769518198 – volume: 14 start-page: 85 year: 2001 ident: 9_CR15 publication-title: J Aerosp Eng doi: 10.1061/(ASCE)0893-1321(2001)14:3(85) |
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| Title | A classical time integration method applied for solution of nonlinear equations of a double-layer tensegrity |
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