Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
권호 표지

Formulations of Linear and Nonlinear Finite Element for Dynamic Flexible Beam

유연보의 동역학 해석에 대한 선형 및 비선형 유한요소 정식화

  • 윤성호 (금오공과대학교, 기계공학부(자동차))
  • Published : 2006.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements using CO elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. In the final formulation are presented Coriolis and Gyroscopic forces as well as linear and nonlinear stiffnesses effects for the forthcoming numerical computation.

Keywords

References

  1. Bathe, K. J., 'Finite Element Procedures,' Prentice-Hall Inc., pp.148-212 and pp. 768-784, 1996
  2. Reddy, J. N., 'Finite Element Method,' 2nd ed., McGraw-Hill Inc., pp.143-166, 1993
  3. Meriam, J. L., Kraige, L. G., 'Engineering Mechanics Dynamics,' 4th ed., John Wiley & Sons Inc., p.395 and p.581, 1998
  4. Yoo, H. H., Ryan, R. R. and Scott, R. A., 'Dynamics of Flexible Beams Undergoing Overall Motions,' Journal of Sound and Vibration, Vol. 181, No.2, 1995, pp.261-278 https://doi.org/10.1006/jsvi.1995.0139
  5. Geradin, M. and Cardona, A., 'Flexible Multibody Dynamics,' John Wiley & Sons Ltd., pp.44-65, and pp.67-88, 2000
  6. Kim, C. B. and Back, Y G., 'Dynamic Analysis of a Flexible Body in Multibody System Using DADS and MSC/NASTRAN,' J. of the KSPE, Vol. 18, No.2, pp.63-71, 2001
  7. Pal, P. F. and Palazotto, A. N., 'Large Deformation analysis of flexible beams,' International J. of Solids and Structures, Vol. 33, pp.1335-1353, 1996 https://doi.org/10.1016/0020-7683(95)00090-9
  8. Liu, J. Y. and Hong, J. Z., 'Geometric Stiffening of Flexible Link System with Large Overall Motion,' J. of Computers & Structures, Vol. 81, pp.2829-2841, 2003 https://doi.org/10.1016/j.compstruc.2003.07.001
  9. Golo, G. V., Talasila, A. J. and Schaft V. D., 'A Hamiltonian Formulation of the Timoshenko Beam Model,' Proc. of Mechatronics 2002, University of Twente, The Netherlands, pp.24-26, 2002
  10. Geradin, M. and Cardona, A., 'Flexible Multibody Dynamics,' John Wiley & Sons Ltd., pp.144-150, 2000
  11. Baazant, Z. P., 'Finite Strain Generalization of Small Strain Constitutive Relations for Any Finite Strain Tensor and Additive Volumetric-deviatoric split,' International J. of Solids and Structures, Vol. 33, pp.2887 - 2897, 1996 https://doi.org/10.1016/0020-7683(96)00002-9
  12. Fung, R. F. and Chang, H. C., 'Dynamics Modelling of a Non-linearly Constrained Flexible Manipulator with a Tip Mass by Hamilton's Principle,' J. of Sound and Vibration, Vol. 216, pp.751-769, 1998 https://doi.org/10.1006/jsvi.1998.1718
  13. Kim, C., Kim, T. G., Shin, D. S. and Lee, S. B., 'Numerical Methods for Engineers,' Korean McGraw-Hill, pp.153-158, 2001