Finite element formulation of slender structures with shear deformation based on the Cosserat theory

International Journal of Solids and Structures

Volumn 44, Issue 24, 2007, Pages 7785-7802

  Liu, Dongsheng ^a   Cao, D Q ^b   Rosing, Richard ^a   Wang, Charles H T ^c   Richardson, Andrew ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

Cosserat rod element; Cosserat theory; Nonlinear dynamics; Slender structure

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; DYNAMICS; MATHEMATICAL MODELS; PROBLEM SOLVING; SHEAR DEFORMATION; TORSIONAL STRESS;

COSSERAT ROD ELEMENT; COSSERAT THEORY; SLENDER STRUCTURE;

FINITE ELEMENT METHOD;

EID: 35148848747     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.05.011     Document Type: Article

References (18)

1. ANSYS University Intermediate v8.0, http://www.ansys.com.
2. Antman S.S. Nonlinear Problems of Elasticity, Applied Mathematical Sciences vol.107 (1995), Springer, New York
3. Arfken G. Mathematical Methods for Physicists (1985), Academic Press Inc., San Fiego
4. Argyris J.H., Dunne P.C., Malejannakis G., and Scharpf D.W. On large displacements-small strain analysis of structures with rotational degree of freedom. Computer Methods in Applied Mechanics and Engineering 14 (1978) 99-135
5. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2002), Wiley, Chichester
6. Cao D.Q., Liu D., and Wang C. Nonlinear dynamic modelling for MEMS components via the Cosserat rod element approach. Journal of Micromechanics and Microengineering 15 (2005) 1335-1343
7. Cao D.Q., Liu D., and Wang C. Three dimensional nonlinear dynamics of slender structures: Cosserat rod element approach. International Journal of Solids and Structures 43 (2006) 760-783
8. Cardona A., and Geradin M. A beam finite element non-linear theory with finite rotations. International Journal for Numerical Methods in Engineering 26 (1988) 2403-2438
9. Dolphin Integration, SMASH, http://www.dolphin.fr/medal/smash/smash_overview.html.
10. Dutta A., and White D.W. Large displacement formulation of a three-dimensional beam element with cross-sectional warping. Computers and Structures 45 (1992) 9-24
11. Gould T., and Wang C. MEMS beams with defects: a model of non-ideal rods using Cosserat approach for component level modelling. Journal of Micromechanics and Microengineering 15 (2005) 76-80
12. The Institute of Electrical and Electronic Engineers, Inc., 1999. IEEE Standard VHDL Analog and Mixed-Signal Extensions, IEEE-SA Standards Board, 0-7381-1640-8.
13. Jones A., Gray A., and Hutton R. Manifolds and Mechanics (1987), Combridge University Press, Camberidge
14. Przemieniecki J.S. Theory of Matrix Structural Analysis (1968), McGraw-Hill Book Company, New York
15. Rosing, R., Liu, D., De Masi, B., Wittler, O., Richardson, A., 2006. Verification of correct operation of a MEMS device over its temperature range, through modelling and simulation. In: Proceedings of the 12th IEEE International Mixed Signal Testing Workshop, 21-23 June 2006, Edinburgh, UK, pp. 115-120.
16. Shabana A.A. Dynamics of Multibody Systems. 2nd ed. (1998), Combridge University Press, Camberidge
17. Stuelpnagel J. On the parametrization of the three-dimensional rotation group. SIAM Review 6 (1964) 422-430
18. Wang C., Liu D., Rosing R., Richardson A., and Masi B.D. Construction of nonlinear dynamic MEMS component models using Cosserat theory. Analog Integrated Circuits and Signal Processing 40 (2004) 117-130