Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T07:06:13.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of Non-Physical Chosen Parameters on Impact Dynamics of Discretized Elastic Bodies

Published online by Cambridge University Press:  09 October 2017

J. Y. Wang ,
Z. Y. Liu  and
J. Z. Hong
J. Y. Wang
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai, China
Z. Y. Liu*
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai, China
J. Z. Hong
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai, China
*
*Corresponding author ([email protected])
Get access

Abstract

In the dynamic analysis of discretized elastic bodies with contacts/impacts, the common formulations to model contact force include the penalty method and the Lagrangian method, which are different in the constraint imposition strategies. Traditionally, the Lagrangian method is thought to be less efficient due to additional multipliers and numerical complexity, however, the viewpoint is challenged in this paper. The goal of this paper is to investigate how numerical efficiency and accuracy using the two different methods are influenced by some non-physical chosen parameters such as stiffness coefficient, time step size and spatial discretization. An experimental sphere-rod impact problem and a multi-point impact problem are solved to evaluate certain numerical intricacies of the two implementations. The results show that in dealing with normal impact problems, the choice of penalty factor and time step size using the penalty method is not an omissible act to obtain accuracy and stability, while there are no such manually-defined parameters using the Lagrangian method. Moreover, there seems to be a clear advantage of the Lagrangian method in which much less mesh elements are needed to achieve the same accuracy compared to those of the penalty method.

Keywords

Non-physical chosen parametersPenalty methodLagrangian methodEfficiency and accuracy
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 2 , April 2019 , pp. 167 - 177
Copyright
© The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Wehage, R. A. and Haug, E. J., “Dynamic Analysis of Mechanical Systems with Intermittent Motion,” Journal of Mechanical Design, 104, pp. 778–784 (1982).Google Scholar
Glocker, C., “On Frictionless Impact Models in Rigid-Body Systems,” Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 359, pp. 2385–2404 (2001).Google Scholar
Stronge, W. J., Impact Mechanics, Cambridge University Press, Cambridge (2000).Google Scholar
Djerassi, S., “Collision with Friction; Part A: Newton’s Hypothesis,” Multibody System Dynamics, 21, pp. 37–54 (2009).Google Scholar
Wang, J., Liu, C. and Zhao, Z., “Non-Smooth Dynamics of a 3D Rigid Body on a Vibrating Plate,” Multibody System Dynamics, 32, pp. 217–239 (2014).Google Scholar
Goldsmith, W., Impact: The Theory and Physical Behavior of Colliding Solids, Edward Arnold, London (1960).Google Scholar
Hunt, K. H. and Crossley, F. R. E., “Coefficient of Restitution Interpreted as Damping in Vibro-Impact,” Journal of Applied Mechanics, 42, pp. 440–445 (1975).Google Scholar
Lankarani, H. M. and Nikravesh, P. E., “Continuous Contact Force Models for Impact Analysis in Multibody Systems,” Nonlinear Dynamics, 5, pp. 193–207 (1994).Google Scholar
Tian, Q., Zhang, Y., Chen, L. and Flores, P., “Dynamics of Spatial Flexible Multibody Systems with Clearance and Lubricated Spherical Joints,” Computers & Structures, 87, pp. 913–929 (2009).Google Scholar
Wriggers, P., Computational Contact Mechanics, Springer Verlag, Berlin Heidelberg (2006).Google Scholar
Choi, J., Ryu, H. S., Kim, C. W. and Choi, J. H., “An Efficient and Robust Contact Algorithm for a Compliant Contact Force Model between Bodies of Complex Geometry,” Multibody System Dynamics, 23, pp. 99–120 (2010).Google Scholar
Zhang, J. and Wang, Q., “Modeling and Simulation of a Frictional Translational Joint with a Flexible Slider and Clearance,” Multibody System Dynamics, 38, pp. 367–389 (2016).Google Scholar
Tur, M., Fuenmayor, F. J. and Wriggers, P., “A Mortar-Based Frictional Contact Formulation for Large Deformations Using Lagrange Multipliers,” Computer Methods in Applied Mechanics & Engineering, 198, pp. 2860–2873 (2009).Google Scholar
Hartmann, S., Weyler, R., Oliver, J., Cante, J. C. and Hernández, J., “A 3D Frictionless Contact Domain Method for Large Deformation Problems,” Computer Modeling in Engineering & Sciences, 55, pp. 211–269 (2010).Google Scholar
Chen, P., Liu, J. and Hong, J., “Contact-Impact Formulation for Multi-Body Systems Using Component Mode Synthesis,” Acta Mechanica Sinica, 29, pp. 437–442 (2013)Google Scholar
Duan, Y., Zhang, D. and Hong, J., “Partition Method for Impact Dynamics of Flexible Multibody Systems Based on Contact Constraint,” Applied Mathematics and Mechanics, 34, pp. 1393–1404 (2013).Google Scholar
Brenan, K. E., Campbell, S. L. and Petzold, L. R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia (1996).Google Scholar
Weyler, R., Oliver, J., Sain, T. and Cante, J. C., “On the Contact Domain Method: A Comparison of Penalty and Lagrange Multiplier Implementations,” Computer Methods in Applied Mechanics and Engineering, 205–208, pp. 68–82 (2012).Google Scholar
Taylor, R. L. and Papadopoulos, P., “On a Finite Element Method for Dynamic Contact/Impact Problems,” International Journal for Numerical Methods in Engineering, 36, pp. 2123–2140 (1993).Google Scholar
Ambrosio, J., Pombo, J., Rauter, F. and Pereira, M., “A Memory Based Communication in the Co-Simulation of Multibody and Finite Element Codes for Pantograph-Catenary Interaction Simulation,” Multibody Dynamics, 12, pp. 231–252 (2009).Google Scholar
Seifried, R., Schiehlen, W. and Eberhard, P., “Numerical and Experimental Evaluation of the Co-Efficient of Restitution for Repeated Impacts,” International Journal of Impact Engineering, 32, pp. 508–524 (2005).Google Scholar
Laursen, T. A., Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis, Springer Verlag, Berlin Heidelberg (2002).Google Scholar
Hallquist, J. O., LS-DYNA Theory Manual, Livermore Software Technology Corporation, California (2006).Google Scholar
Heinstein, M. W., Mello, F. J., Attaway, S. W. and Laursen, T. A., “Contact-Impact Modeling in Explicit Transient Dynamics,” Computer Methods in Applied Mechanics and Engineering, 187, pp. 621–640 (2000).Google Scholar
Seifried, R., Hu, B. and Eberhard, P., “Numerical and Experimental Investigation of Radial Impacts on a Half-Circular Plate,” Multibody System Dynamics, 9, pp. 265–281 (2003).Google Scholar