LIU Dong-sheng, Charles H-T WANG. Variational Principle for a Special Cosserat Rod[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1091-1099. doi: 10.3879/j.issn.1000-0887.2009.09.011
Citation: LIU Dong-sheng, Charles H-T WANG. Variational Principle for a Special Cosserat Rod[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1091-1099. doi: 10.3879/j.issn.1000-0887.2009.09.011

Variational Principle for a Special Cosserat Rod

doi: 10.3879/j.issn.1000-0887.2009.09.011
  • Received Date: 2009-03-16
  • Rev Recd Date: 2009-08-12
  • Publish Date: 2009-09-15
  • Based on the Cosserat theory,the nonlinear models of a rod in 3-dimensional space was described.Using pseudo-rigid body method and variational principle the equations of motion of Cosserat rod including shear deformation were obtained.
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  • [1]
    Love A E H.A Treatise on the Mathematical Theory of Elasticity[M].4th Ed.New York:Cambridge University Press,1994.
    [2]
    Faulkner M G,Steigmann D J.Controllable deformations of elastic spatial rods[J].Acta Mechanica,1993,101(1):31-43. doi: 10.1007/BF01175595
    [3]
    Steigmann D J,Faulkner M G.Variational theory for spatial rods[J].Journal of Elasticity,1993,33(1):1-26. doi: 10.1007/BF00042633
    [4]
    Cohen H,Muncaster R G.Theory of Pseudo-Rigid Bodies[M].Berlin:Springer,1984.
    [5]
    Papadopoulos P.On the class of higher-order pseudo-rigid bodies[J].Math Mech Solids,2001,6(6):631-640. doi: 10.1177/108128650100600604
    [6]
    Green A E,Naghdi P M,Wenner M L.On the theory of rods I:derivations from the three-dimensional equations[J].Proc Royal Soc London A,1974,337(1611):451-483. doi: 10.1098/rspa.1974.0061
    [7]
    Green A E,Naghdi P M,Wenner M L.On the theory of rods II:developments by direct approach[J].Proc Royal Soc London A,1974,337(1611):485-507. doi: 10.1098/rspa.1974.0062
    [8]
    Naghdi P M,Rubin M B.Constrained theories of rods[J].J Elast,1984,14(4):343-361. doi: 10.1007/BF00125605
    [9]
    Rubin M B.An intrinsic formulation for nonlinear elastic rod[J].Int J Solids Struct,1997,34(31/32):4191-4212. doi: 10.1016/S0020-7683(96)00158-8
    [10]
    Rubin M B.Numerical solution procedures for nonlinear on elastic rods using the theory of a Cosserat point[J].Int J Solids Struct,2001,38(24/25):4395-4437. doi: 10.1016/S0020-7683(00)00271-7
    [11]
    Zhang H W,Wang H,Chen B S,et al.Parametric variational principle based on elastic-plastic analysis of cosserat continuum[J].Acta Mechanica Solida Sinica,2007,20(1):65-74.
    [12]
    Zhang H W,Wang H,Chen B S,et al.Analysis of Cosserat materials with Voronoi cell finite element method and parametric variational principle[J].Comput Methods Appl Mech Engrg,2008,197(6/8):741-755. doi: 10.1016/j.cma.2007.09.003
    [13]
    Neff P.A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations[J].International Journal of Engineering Science,2006,44(8/9):574-594. doi: 10.1016/j.ijengsci.2006.04.002
    [14]
    Sansour C,Skatulla S.A non-linear Cosserat continuum-based formulation and moving least square approximations in computations of size-scale effects in elasticity[J].Computational Materials Science,2008,41(4):589-601. doi: 10.1016/j.commatsci.2007.05.024
    [15]
    Sansour C,Skatulla S.A strain gradient generalized continuum approach for modelling elastic scale effects[J].Comput Methods Appl Mech Engrg,2009,198(15/16):1401-1412. doi: 10.1016/j.cma.2008.12.031
    [16]
    Cao D Q,Liu D,Wang C.Three-dimensional nonlinear dynamics of slender structures:Cosserat rod element approach[J].Int J Solids Struct,2006,43(3/4):760-783. doi: 10.1016/j.ijsolstr.2005.03.059
    [17]
    Liu D,Cao D Q,Rosing R,et al.Finite element formulation of slender structures with shear deformation based on the Cosserat theory[J].Int J Solids Struct,2007,44(24):7785-7802. doi: 10.1016/j.ijsolstr.2007.05.011
    [18]
    Wang C,Liu D,Rosing R,et al.Construction of nonlinear dynamic MEMS component models using Cosserat theory[J].Analog Integrated Circuits and Signal Processing,2004,40(2):117-130. doi: 10.1023/B:ALOG.0000032593.34671.fa
    [19]
    Antman S S.Nonlinear Problems of Elasticity[M].New York:Springer,1995.
    [20]
    Sattinger D H,Weaver O L.Lie Groups and Algebras With Applications to Physics,Geometry,and Mechanics[M].New York:Springer-Verlag,1993.
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