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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 (zhuyongliu@sjtu.edu.cn)
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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 

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