DOI QR코드

DOI QR Code

A Relative Nodal Displacement Method for Element Nonlinear Analysis

상대 절점 변위를 이용한 비선형 유한 요소 해석법

  • Published : 2005.04.01

Abstract

Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian furmulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacement sand traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large deformations are analyzed to demonstrate the efficiency and validity of the proposed method.

Keywords

Relative Nodal Displacement;Moving Reference Frame;Topology Analysis; Finite Element Method;Large Deformation;Truss Structure

References

  1. El Damatty, A. A., Korol, R. M. and Mirza, F. A., 1997, 'Large Displacement Extension of Consistent Shell Element for Static and Dynamic Analysis,' Computers & Structures, Vol. 62, No, 6, pp, 943-960 https://doi.org/10.1016/S0045-7949(96)00303-3
  2. Mayo, J. and Dominquez, J., 1997, 'A Finite Element Geometrically Nonlinear Dynamic Formulation of Flexible Multibody Systems using a New Displacements Representation,' J. Vibration and Acoustics, Vol. 119, pp. 573-580 https://doi.org/10.1115/1.2889764
  3. Dhatt, G. and Touzot, G., 1984, The Finite Element Method Displayed, John Wiley & Sons
  4. Bathe, K. J., 1996, Finite Element Procedures, Prentice-Hall
  5. Avello, A., Garcia De Jolon J. and Bayo, E., 1991, 'Dynamics of Flexible Multibody Systems using Cartesian Co-ordinates and Large Displacement Theory,' Int. J. Numer. Methods Eng., Vol. 32, No. 8, pp. 1543-1564 https://doi.org/10.1002/nme.1620320804
  6. Shabana, A. A., 1996, 'An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,' Technical Report MBS 96-1-UIC, Department of Mechanical Engineering, University of Illionois at Chicago
  7. Shabana, A. A. and Christensen, A., 1997, 'Three Dimensional Absolute Nodal Coordinate Formulation: Plate Problem,' Int. J. Numer. Methods Eng., Vol. 40, No. 15,pp. 2275-2790 https://doi.org/10.1002/(SICI)1097-0207(19970815)40:15<2775::AID-NME189>3.0.CO;2-#
  8. Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd edition, Cambridge University Press
  9. Takahashi, Y. and Shimizu, N., 1999, 'Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams,' Proceedings of the ASME Design Engineering Technical Conferences
  10. Kim, K. S., Kim, K. S. and Yoo, W. S., 2000, 'Analysis of Large Deformation in Elastic Multibody Systems Using Absolute Nodal Coordinates' KSAE Autumn Conference, pp, 80-86
  11. Featherstone, R., 1983, 'The Calculation of Robot Dynamics Using Articulated-Body Inertias,' Int. J. Roboics Res., Vol. 2, pp. 13-30 https://doi.org/10.1177/027836498300200102
  12. Bae, D. S. and Haug, E. J., 1987, 'A Recursive Formulation for Constrained Mechanical System Dynamics: Part I. Open Loop Systems,' Mech. Struct. and Machines, Vol. 15, No.3, pp. 359-382 https://doi.org/10.1080/08905458708905124
  13. Bae, D. S. and Haug, E. J., 1987, 'A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems,' Mech. Struct. and Machines, Vol. 15, No.4, pp. 481-506 https://doi.org/10.1080/08905458708905130
  14. Lin, T. C. and Yae, K. H., 1994, 'Recursive Linearization of Multibody Dynamics and Application to Control Design,' J. of mechanical design, Vol. 116, pp. 445-451 https://doi.org/10.1115/1.2919399
  15. Bae, D. S., Han, J. M., Choi, J. H. and Yang, S. M., 2001, 'A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics,' Int. J. Numer. Meth. Engng, Vol. 50, pp. 1841-1859 https://doi.org/10.1002/nme.97
  16. Ryu, H. S., Bae, D. S., Choi, J. H. and A. Shabana, A.A., 2001, 'A Compliant Track Model For High Speed, High Mobility Tracked Vehicle,' Int. J. Number. Meth. Engng, Vol 50, pp. 1841-1859 https://doi.org/10.1002/1097-0207(20000810)48:10<1481::AID-NME959>3.0.CO;2-P
  17. Bae, D. S., Cho, H. J., Lee, S. H. and Moon, W. K., 2001, 'Recursive Formulas for Design Sensitivity Analysis of Mechanical Systems,' Comput. Methods Appl. Mech. Engrg., Vol. 190, pp. 3865-3879 https://doi.org/10.1016/S0045-7825(00)00303-0
  18. Haug, E. J., 1989, Computer-Aided Kinematics and Dynamics of Mechanical Systems: Volume I. Basic Methods, Allyn and Bacon
  19. Crisfield, M. A., 1997, Non-Linear Finite Element Analysis of Solids and Structures, Wiley