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Volumn 20, Issue 1, 2008, Pages 51-68

A comparison of finite elements for nonlinear beams: The absolute nodal coordinate and geometrically exact formulations

Author keywords

Absolute nodal coordinate; Finite element; Flexible multibody; Geometrically exact; Nonlinear beam

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; NUMERICAL METHODS; ONTOLOGY;

EID: 45849119062     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-008-9105-7     Document Type: Article
Times cited : (118)

References (46)
  • 3
    • 0026404435 scopus 로고
    • Dynamics of flexible multibody systems using Cartesian co-ordinates and large displacement theory
    • Avello, A., García de Jalón, J.: Dynamics of flexible multibody systems using Cartesian co-ordinates and large displacement theory. Int. J. Numer. Methods Eng. 32, 1543-1563 (1991)
    • (1991) Int. J. Numer. Methods Eng. , vol.32 , pp. 1543-1563
    • Avello, A.1    Jalón De J.García2
  • 5
    • 0018295243 scopus 로고
    • Large displacement analysis of three-dimensional beam structures
    • Bathe, K.J., Belourchi, S.: Large displacement analysis of three-dimensional beam structures. Int. J. Numer. Methods Eng. 14, 961-986 (1979)
    • (1979) Int. J. Numer. Methods Eng. , vol.14 , pp. 961-986
    • Bathe, K.J.1    Belourchi, S.2
  • 6
  • 7
    • 0032024870 scopus 로고    scopus 로고
    • On the parametrization of finite rotations in computational mechanics. A clarification of concepts with application to smooth shells
    • Betsch, P., Menzel, A., Stein, E.: On the parametrization of finite rotations in computational mechanics. A clarification of concepts with application to smooth shells. Comput. Methods Appl. Mech. Eng. 155, 273-305 (1998)
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.155 , pp. 273-305
    • Betsch, P.1    Menzel, A.2    Stein, E.3
  • 8
    • 0037199848 scopus 로고    scopus 로고
    • Frame-indifferent beam element based upon the geometrically exact beam theory
    • Betsch, P., Steinmann, P.: Frame-indifferent beam element based upon the geometrically exact beam theory. Int. J. Numer. Methods Eng. 54, 1775-1788 (2002)
    • (2002) Int. J. Numer. Methods Eng. , vol.54 , pp. 1775-1788
    • Betsch, P.1    Steinmann, P.2
  • 9
    • 0038495088 scopus 로고    scopus 로고
    • Constrained dynamics of geometrically exact beams
    • Betsch, P., Steinmann, P.: Constrained dynamics of geometrically exact beams. Comput. Mech. 31, 49-59 (2003)
    • (2003) Comput. Mech. , vol.31 , pp. 49-59
    • Betsch, P.1    Steinmann, P.2
  • 12
    • 0024116484 scopus 로고
    • A beam finite element nonlinear theory with finite rotations
    • Cardona, A., Geradin, M.: A beam finite element nonlinear theory with finite rotations. Int. J. Numer. Methods Eng. 26, 2403-2434 (1988)
    • (1988) Int. J. Numer. Methods Eng. , vol.26 , pp. 2403-2434
    • Cardona, A.1    Geradin, M.2
  • 14
    • 33746451257 scopus 로고    scopus 로고
    • Objectivity of strain measures in geometrically exact 3D beam theory and its finite element implementation
    • Crisfield, M.A., Jelenić, U.: Objectivity of strain measures in geometrically exact 3D beam theory and its finite element implementation. Proc. R. Soc. Lond. Ser. A 455, 1125-1147 (1999)
    • (1999) Proc. R. Soc. Lond. Ser. A , vol.455 , pp. 1125-1147
    • Crisfield, M.A.1    Jelenić, U.2
  • 16
    • 33751575445 scopus 로고
    • Exact theory of stress and strain in rods and shells
    • Ericksen, J.L., Truesdell, C.: Exact theory of stress and strain in rods and shells. Arch. Ration. Mech. Anal. 1, 195-323 (1958)
    • (1958) Arch. Ration. Mech. Anal. , vol.1 , pp. 195-323
    • Ericksen, J.L.1    Truesdell, C.2
  • 17
    • 33845401878 scopus 로고    scopus 로고
    • Analysis of stress and strain in the absolute nodal coordinate formulation
    • 4
    • Gerstmayr, J., Matikainen, M.K.: Analysis of stress and strain in the absolute nodal coordinate formulation. Mech. Des. Struct. Mach. 34(4), 409-430 (2006)
    • (2006) Mech. Des. Struct. Mach. , vol.34 , pp. 409-430
    • Gerstmayr, J.1    Matikainen, M.K.2
  • 18
    • 77955655302 scopus 로고    scopus 로고
    • Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation
    • García Orden, J.C., Goicolea, J.M., Cuadrado, J. (eds.) Madrid, Spain, 21-24 June
    • Gerstmayr, J., Shabana, A.A.: Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation. In: García Orden, J.C., Goicolea, J.M., Cuadrado, J. (eds.) Multibody Dynamics 2005. ECCOMAS Thematic Conference, Madrid, Spain, 21-24 June 2005
    • (2005) Multibody Dynamics 2005. ECCOMAS Thematic Conference
    • Gerstmayr, J.1    Shabana, A.A.2
  • 19
    • 33745913632 scopus 로고    scopus 로고
    • Analysis of thin beams and cables using the absolute nodal coordinate formulation
    • 1-2
    • Gerstmayr, J., Shabana, A.A.: Analysis of thin beams and cables using the absolute nodal coordinate formulation. Nonlinear Dyn. 45(1-2), 109-130 (2006)
    • (2006) Nonlinear Dyn. , vol.45 , pp. 109-130
    • Gerstmayr, J.1    Shabana, A.A.2
  • 21
    • 0000715308 scopus 로고
    • On the theory of rods i derivations from the three dimensional equations
    • Green, A.E., Naghdi, P.M., Wenner, M.L.: On the theory of rods I derivations from the three dimensional equations. Proc. R. Soc. Lond. Ser. A 337, 451-483 (1974)
    • (1974) Proc. R. Soc. Lond. Ser. A , vol.337 , pp. 451-483
    • Green, A.E.1    Naghdi, P.M.2    Wenner, M.L.3
  • 22
  • 24
    • 0029291922 scopus 로고
    • On finite element implementations of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
    • Ibrahimbegovic, A.: On finite element implementations of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elements. Comput. Methods Appl. Mech. Eng. 122, 11-26 (1995)
    • (1995) Comput. Methods Appl. Mech. Eng. , vol.122 , pp. 11-26
    • Ibrahimbegovic, A.1
  • 25
    • 0032026641 scopus 로고    scopus 로고
    • Finite rotations in dynamics of beams and implicit time-stepping algorithms
    • 5
    • Ibrahimbegovic, A., Al Mikdad, M.: Finite rotations in dynamics of beams and implicit time-stepping algorithms. Int. J. Numer. Methods Eng. 41(5), 781-814 (1998)
    • (1998) Int. J. Numer. Methods Eng. , vol.41 , pp. 781-814
    • Ibrahimbegovic, A.1    Al Mikdad, M.2
  • 26
    • 0032299057 scopus 로고    scopus 로고
    • Interpolation of rotational variables in nonlinear dynamics of 3D beams
    • Jelenić, G., Crisfield, M.A.: Interpolation of rotational variables in nonlinear dynamics of 3D beams. Int. J. Numer. Methods Eng. 43, 1193-1222 (1998)
    • (1998) Int. J. Numer. Methods Eng. , vol.43 , pp. 1193-1222
    • Jelenić, G.1    Crisfield, M.A.2
  • 27
    • 0032647649 scopus 로고    scopus 로고
    • Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
    • Jelenić, G., Crisfield, M.A.: Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics. Comput. Methods Appl. Mech. Eng. 171, 141-171 (1999)
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.171 , pp. 141-171
    • Jelenić, G.1    Crisfield, M.A.2
  • 28
    • 0036298788 scopus 로고    scopus 로고
    • Using finite strain 3D-material models in beam and shell elements
    • 8
    • Klinkel, S., Govindjee, S.: Using finite strain 3D-material models in beam and shell elements. Eng. Comput. 19(8), 902-921 (2002)
    • (2002) Eng. Comput. , vol.19 , pp. 902-921
    • Klinkel, S.1    Govindjee, S.2
  • 29
    • 37049026197 scopus 로고    scopus 로고
    • A nonlinear beam element formulation in the framework of an energy preserving time integration scheme for constrained multibody systems dynamics
    • Lens, E.V., Cardona, A.: A nonlinear beam element formulation in the framework of an energy preserving time integration scheme for constrained multibody systems dynamics. Comput. Struct. 86, 47-63 (2008)
    • (2008) Comput. Struct. , vol.86 , pp. 47-63
    • Lens, E.V.1    Cardona, A.2
  • 30
    • 39749110538 scopus 로고    scopus 로고
    • Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: A comparative study
    • doi:10.1007/s11044-007-9070-6
    • Maqueda, L.G., Bauchau, O.A., Shabana, A.A.: Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study. Multibody Syst. Dyn. (2007). doi:10.1007/s11044-007-9070-6
    • (2007) Multibody Syst. Dyn.
    • Maqueda, L.G.1    Bauchau, O.A.2    Shabana, A.A.3
  • 31
    • 0000314657 scopus 로고
    • A one-dimensional finite strain beam theory: The plane problem
    • Reissner, E.: A one-dimensional finite strain beam theory: the plane problem. J. Appl. Math. Phys. (ZAMP) 23, 795-804 (1972)
    • (1972) J. Appl. Math. Phys. (ZAMP) , vol.23 , pp. 795-804
    • Reissner, E.1
  • 32
    • 5444266729 scopus 로고    scopus 로고
    • The interpolation of rotations and its application to finite element models of geometrically exact rods
    • 2
    • Romero, I.: The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput. Mech. 34(2), 121-133 (2004)
    • (2004) Comput. Mech. , vol.34 , pp. 121-133
    • Romero, I.1
  • 33
    • 0037199851 scopus 로고    scopus 로고
    • An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics
    • 12
    • Romero, I., Armero, F.: An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics. Int. J. Numer. Methods Eng. 54(12), 1683-1716 (2002)
    • (2002) Int. J. Numer. Methods Eng. , vol.54 , pp. 1683-1716
    • Romero, I.1    Armero, F.2
  • 34
    • 0037818736 scopus 로고    scopus 로고
    • Multiplicative updating of the rotation tensor in the finite element analysis of rods and shells-a path independent approach
    • Sansour, C., Wagner, W.: Multiplicative updating of the rotation tensor in the finite element analysis of rods and shells-a path independent approach. Comput. Mech. 31, 153-162 (2003)
    • (2003) Comput. Mech. , vol.31 , pp. 153-162
    • Sansour, C.1    Wagner, W.2
  • 35
    • 33244462428 scopus 로고    scopus 로고
    • Comparison of three-dimensional flexible beam elements for dynamic analysis: Finite element method and absolute nodal coordinate formulation
    • Long Beach, CA, Sept.
    • Schwab, A.L., Meijaard, J.P.: Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: IDETC/CIE 2005 ASME International Design Engineering Technical Conferences, Long Beach, CA, Sept. 2005
    • (2005) IDETC/CIE 2005 ASME International Design Engineering Technical Conferences
    • Schwab, A.L.1    Meijaard, J.P.2
  • 36
    • 0038205727 scopus 로고    scopus 로고
    • Use of the finite element absolute nodal coordinate formulation in modeling slope discontinuity
    • Shabana, A.A., Mikkola, A.M.: Use of the finite element absolute nodal coordinate formulation in modeling slope discontinuity. Trans. Am. Soc. Mech. Eng. J. Mech. Des. 125, 342-350 (2003)
    • (2003) Trans. Am. Soc. Mech. Eng. J. Mech. Des. , vol.125 , pp. 342-350
    • Shabana, A.A.1    Mikkola, A.M.2
  • 37
    • 13644283164 scopus 로고    scopus 로고
    • Three dimensional absolute nodal coordinate formulation for beam elements: Theory
    • 4
    • Shabana, A.A., Yakoub, R.Y.: Three dimensional absolute nodal coordinate formulation for beam elements: theory. ASME J. Mech. Des. 123(4), 606-613 (2001)
    • (2001) ASME J. Mech. Des. , vol.123 , pp. 606-613
    • Shabana, A.A.1    Yakoub, R.Y.2
  • 38
    • 0022060633 scopus 로고
    • A finite strain beam formulation. Part I. the three-dimensional dynamic problem
    • Simo, J.C.: A finite strain beam formulation. Part I. The three-dimensional dynamic problem. Comput. Methods Appl. Mech. Eng. 49, 55-70 (1985)
    • (1985) Comput. Methods Appl. Mech. Eng. , vol.49 , pp. 55-70
    • Simo, J.C.1
  • 39
    • 0029305275 scopus 로고
    • Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms
    • 9
    • Simo, J.C., Tarnow, N., Doblaré, M.: Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms. Int. J. Numer. Methods Eng. 38(9), 1431-1473 (1995)
    • (1995) Int. J. Numer. Methods Eng. , vol.38 , pp. 1431-1473
    • Simo, J.C.1    Tarnow, N.2    Doblaré, M.3
  • 40
    • 0022874575 scopus 로고
    • On the dynamics of flexible beams under large overall motions-the plane case II
    • 4
    • Simo, J.C., Vu-Quoc, L.: On the dynamics of flexible beams under large overall motions-the plane case II. Trans. Am. Soc. Mech. Eng. J. Appl. Mech. 53(4), 855-63 (1986)
    • (1986) Trans. Am. Soc. Mech. Eng. J. Appl. Mech. , vol.53 , pp. 855-63
    • Simo, J.C.1    Vu-Quoc, L.2
  • 41
    • 0022792209 scopus 로고
    • A three-dimensional finite-strain rod model Part II: Computational aspects
    • Simo, J.C., Vu-Quoc, L.: A three-dimensional finite-strain rod model Part II: Computational aspects. Comput. Methods Appl. Mech. Eng. 58, 79-116 (1986)
    • (1986) Comput. Methods Appl. Mech. Eng. , vol.58 , pp. 79-116
    • Simo, J.C.1    Vu-Quoc, L.2
  • 42
    • 0023964748 scopus 로고
    • On the dynamics in space of rods undergoing large motions-a geometrically exact approach
    • 2
    • Simo, J.C., Vu-Quoc, L.: On the dynamics in space of rods undergoing large motions-a geometrically exact approach. Comput. Methods Appl. Mech. Eng. 66(2), 125-161 (1988)
    • (1988) Comput. Methods Appl. Mech. Eng. , vol.66 , pp. 125-161
    • Simo, J.C.1    Vu-Quoc, L.2
  • 43
    • 0033339258 scopus 로고    scopus 로고
    • Statically and kinematically exact nonlinear theory of rods and its numerical verification
    • Smoleński, W.M.: Statically and kinematically exact nonlinear theory of rods and its numerical verification. Comput. Methods Appl. Mech. Eng. 178, 89-113 (1999)
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.178 , pp. 89-113
    • Smoleński, W.M.1
  • 44
    • 1442283386 scopus 로고    scopus 로고
    • Description of elastic forces in absolute nodal coordinate formulation
    • Sopanen, J.T., Mikkola, A.M.: Description of elastic forces in absolute nodal coordinate formulation. Nonlinear Dyn. 34, 53-74 (2003)
    • (2003) Nonlinear Dyn. , vol.34 , pp. 53-74
    • Sopanen, J.T.1    Mikkola, A.M.2
  • 45
    • 13644282674 scopus 로고    scopus 로고
    • Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications
    • 4
    • Yacoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. Am. Soc. Mech. Eng. J. Mech. Eng. 123(4), 614-621 (2001)
    • (2001) Am. Soc. Mech. Eng. J. Mech. Eng. , vol.123 , pp. 614-621
    • Yacoub, R.Y.1    Shabana, A.A.2


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