A Special Finite Element for Static and Dynamic Study of Mechanical Systems under Large Motion, Part 2
Keywords:
finite element method, large motion, mechanical systemsAbstract
In the first part of the paper the theory of the 3D dynamics of mechanical systems composed by elastic beams, structures and mechanisms, was studied. These systems are divided into so-called macro-elements and the movement equations of one macro-element were established. Only the Euler-Rodrigues parameters are used to describe the global motion of the system. In this second part of the paper a special finite element (SFET) having four degrees of freedom per node, the Euler-Rodrigues parameters, is described in details. The stiffness and mass matrices are expressed only in nodal Euler-Rodrigues parameters. The most important aspect of the proposed approach is that the exact equations, written for the deformed configuration, are solved. Therefore an extremely accurate and very fast convergent method results. To validate the SFET finite element finally several 2D and 3D, static and dynamic examples are presented and the accuracy of the results is discussed.
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References
[BAR 96] BARRACO A., Dynamique des systèmes mécaniques complexes, ENSAM, Centre
denseignement et de recherche de Paris, 1996.
[BAR 00] BARRACO A., Mécanique des structures, ENSAM, Centre denseignement et de
recherche de Paris, 2000.
[DVO 88] DVORKIN E. N., ONATE E., OLIVIER J., On A Non-linear Formulation for Curved
Timoshenko Beam Elements Considering Large Displacement/Rotation Increments, Int.
Journal for Numerical Methods in Engineering, Vol. 26, pp. 1597-1613, 1988.
[MUN 96] MUNTEANU M. Gh., DE BONA F., ZELENIKA S., An accurate non-linear analysis of
very large displacements of beam systems, Proceedings of the XXV AIAS National
Conference, International Conference on Material Engineering, Gallipoli - Lecce, pp. 59-
, 1996.
[MUN 00] MUNTEANU M. Gh., BARRACO A., CURTU I.., DE BONA F., Experimental Validation of
a Special Finite Element Type, Proceedings of the Danubia-Adria Symposium, Prague,
pp. 229-232, 2000.
[REI 73] REISSNER E., On one dimensional large displacement finite strain beam theory,
Studies Appl. Math. 52, pp. 87-95, 1973.
[SAJ 91] SAJE M., Finite Element Formulation of Finite Planar Deformation of Curved
Elastic Beams, Computers & Structures, Vol. 39, No 3/4, pp. 327-337, 1991.
[SHA 98] SHABANA A. A., HUSSIEN H. A., ESCALONA J. L., Application of the Absolute Nodal
Coordinate Formulation to Large Rotation and Large Deformation Problems, ASME,
Journal of Mechanical Design, Vol. 120, pp. 188-195, 1998.
[SIM 86] SIMO J.C., VU-QUOC L., On the dynamics of Flexible Beams Under Large Overall
Motions The Plane Case, Journal of Applied Mechanics, Vol 53, pp. 855-863, 1986.
[SIM 88] SIMO J.C., VU-QUOC L., On the dynamics in space of rods undergoing large motions
a geometric exact approach, Comput. Meth. Appl. Mech. Eng. 66, pp. 125-161, 1988.
[TAK 99] TAKAHASHI Y., SHIMIZU N., Study on Elastic Forces of the Absolute Nodal
Coordinate Formulation for Deformable Beams, Proceedings of the 1999 ASME Design
Engineering Technical Conferences September 12-15, Las Vegas, Nevada, 9 pp., 1999.
[TIM 61] TIMOSHENKO S. P., Theory of Elastic Stability, McGraw-Hill Book Company, New
York, 1961.
