细长杆的Cosserat动力学模型和变分原理

刘东生; 查尔斯·王

doi:10.3879/j.issn.1000-0887.2009.09.011

细长杆的Cosserat动力学模型和变分原理

doi: 10.3879/j.issn.1000-0887.2009.09.011

刘东生¹,
查尔斯·王²

1.
南京理工大学应用数学系,南京 210094;2.阿伯丁大学工程和物理科学学院,阿伯丁,英国

基金项目: 教育部留学回国人员科研启动基金资助项目

详细信息

作者简介:
刘东生(1962- ),男,江苏泰州人,教授,博士(联系人.E-mail:lds1@mail.njust.edu.cn).

中图分类号: O33;O343.5
计量
- 文章访问数: 2456
- HTML全文浏览量: 129
- PDF下载量: 1135
- 被引次数: 0
出版历程
- 收稿日期: 2009-03-16
- 修回日期: 2009-08-12
- 刊出日期: 2009-09-15

Variational Principle for a Special Cosserat Rod

LIU Dong-sheng¹,
Charles H-T WANG²

1.
Applied Mathematics Department, Nanjing University of Science and Technology, Nanjing 210094, P. R. China;

摘要

摘要: 利用Cosserat理论建立了细长杆的三维非线性动力学模型．借助伪刚体法和变分原理得到了Cosserat杆的包括各种形变的三维空间运动方程．
- 细长杆 /
- 变分原理 /
- Cosserat理论
Abstract: 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.
- rod /
- variational principle /
- Cosserat theory

HTML全文

参考文献(20)

[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.