Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Recently, a finite element formulation, called the absolute nodal coordinate formulation (ANCF), was proposed for the large rotation and deformation analysis of flexible bodies. In this formulation, absolute position and slope coordinates are used to define the finite element configuration. Infinitesimal or finite rotations are not used as nodal coordinates. The ANCF finite elements have many unique features that distinguish them from other existing finite element methods used in the dynamic analysis of the flexible multibody systems. In such systems, there appears the necessity of solving systems of differential-algebraic equations (DAEs) of index 3. Accurate solving of the DAEs is a non-trivial problem. However, in the literature about the ANCF one can hardly find any detailed information about the procedures that are used to solve the DAEs. Therefore, the current paper is devoted to the analysis of selected DAE solvers, which are applied to simulations of simple mechanisms.
Czasopismo
Rocznik
Tom
Strony
75--83
Opis fizyczny
Bibliogr. 16 poz., Wykr.
Twórcy
autor
autor
- The Institute of Aeronautics and Applied Mechanics, The Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, ul. Nowowiejska 24, 00-665 Warsaw, Poland, gorzech@meil.pw.edu.pl
Bibliografia
- 1. Bathe K. J. (1996), Finite Element Procedures, Prentice Hall, New Jersay.
- 2. Brenan K. E., Campbell S. L., Petzold L. R. (1996), Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia.
- 3. Frączek J. (2002), Modelowanie mechanizmów przestrzennych metodą układów wieloczłonowych, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa.
- 4. Frączek J., Malczyk P., Parallel Divide and Conquer Algorithm for Constrained Multibody System Dynamics based on Augmented Lagrangian Method with Projections-based Error Correction, Nonlinear Dynamics, DOI: 10.1007/s11071-012-0503-22012, to be printed.
- 5. Gear C. W., Leimkuhler B., Gupta G. K. (1985), Automatic integration of Euler-Lagrange equations with constraints, Journal of Computational and Applied Mathematics, Vol. 12-13, No. 0, 77-90.
- 6. Gerstmayr J., Matikainen M., Mikkola A. (2008), A geometrically exact beam element based on the absolute nodal coordinate formulation, Multibody System Dynamics, Vol. 20, No. 4, 359-384.
- 7. Gerstmayr J., Shabana A. A. (2006), Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation, Nonlinear Dynamics, Vol. 45, No. 1, 109-130.
- 8. Hairer E., Wanner G. (1996), Solving oridinary differential equations II. Stiff and differential-algebraic problems, Springer-Verlag, Berlin.
- 9. Haug E. J. (1989), Computer-Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic Methods, Allyn and Bacon, Massachusetts.
- 10. Hussein B., Negrut D., Shabana A. A. (2008), Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations, Nonlinear Dynamics, Vol. 54, No. 4, 283-296.
- 11. Iavernaro F., Mazzia F. (1998), Solving ordinary differential equations by generalized Adams methods: properties and implementation techniques, Applied Numerical Mathematics, Vol. 28, No. 2-4, 107-126.
- 12. Nikravesh P. E. (1988), Computer-Aided Analysis of Mechanical Systems, Prentice Hall, New Jersey.
- 13. Shabana A. A. (1997), Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation, Multibody System Dynamics, Vol. 1, No. 3, 339-348.
- 14. Shabana A. A. (2003), Dynamics of Multibody Systems, Cambridge University Press, Cambridge.
- 15. Shabana A. A. (2008), Computational Continuum Mechanics, Cambridge University Press, Cambridge.
- 16. Shabana A. A., Yakoub R. Y. (2001), Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Part I and II, Journal of Mechanical Design, Vol. 123, No. 4, 606-621.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0068-0019