Modeling Spatial Motion of 3D Deformable Multibody Systems with Nonlinearities
- 122 Downloads
A computational strategy for modeling spatial motion of systems of flexible spatial bodies is presented. A new integral formulation of constraints is used in the context of the floating frame of reference approach. We discuss techniques to linearize the equations of motion both with respect to the kinematical coupling between the deformation and rigid body degrees of freedom and with respect to the geometrical nonlinearities (inclusion of stiffening terms). The plastic behavior of bodies is treated by means of plastic multipliers found as the result of fixed-point type iterations within a time step. The time integration is based on implicit Runge Kutta schemes with arbitrary order and of the RadauIIA type. The numerical results show efficiency of the developed techniques.
Keywordsconstraint linearization integral constraints geometrical stiffening elasto-plasticity
Unable to display preview. Download preview PDF.
- 2.Düster, A., High order finite elements for three-dimensional, thin-walled nonlinear continua. Aachen: Shaker Verlag, 2002.Google Scholar
- 3.Eich-Soellner, E. and Führer, C., Numerical methods in multibody dynamics, B.G. Teubner, Stuttgart, 1998.Google Scholar
- 7.Kübler, L., Eberhard. P. and Geisler, J., ‘Flexible multibody systems with large deformations using absolute nodal coordinates for isoparametric solid brick elements’, Proceedings of DETC’03, Chicago, Illinois, USA, 2003.Google Scholar
- 8.Ryu, J., Kim, S.S. and Kim, S.S., ‘A general approach to stress stiffening effects on flexible multibody dynamic systems’, Mechanics of Structures and Machines 22(2), 1994, 157–180.Google Scholar
- 11.Sharf, I., ‘A survey of geometric stiffening in multibody dynamics formulations, Wave motion, intelligent structures and nonlinear mechanics’, Ser. Stab. Vib. Control Struct. 1, 1995, 239–279, World Sci. Publishing, River Edge, NJ.Google Scholar
- 13.Truesdell, C., Rational Thermodynamics, McGraw-Hill, 1969.Google Scholar
- 14.Truesdell, C. and Noll, W., The Non-linear Field Theories of Mechanics, In: Encyclopedia of Physics III/1, Springer, Berlin, 1996.Google Scholar
- 15.Vetyukov, Yu, ‘Consistent approximation for the strain energy of a 3D elastic body adequate for the stress stiffening effect’, To appear in International Journal of Structural Stability and Dynamics, 4(2), 2004.Google Scholar
- 17.Vetyukov, Yu., Gerstmayr, J. and Irschik, H., ‘Fixed-point type iterations in numerical simulations for static and dynamic elastoplasticity’, PAMM. Proc. Appl. Math. Mech. 3, 318–319.Google Scholar
- 18.Vetyukov, Yu., Gerstmayr, J. and Irschik, H., ‘The comparative analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2D elastic pendulum’, J. Computers and Structures, accepted for publication.Google Scholar