Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Aspects of Impact of Planar Deformable Bodies as Linear Complementarity Problems

Aspects of Impact of Planar Deformable Bodies as Linear Complementarity Problems This paper extends the linear complementarity problem formulation of (7) and (8) for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in (7). Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Multidiscipline Modeling in Materials and Structures Emerald Publishing

Aspects of Impact of Planar Deformable Bodies as Linear Complementarity Problems

Loading next page...
 
/lp/emerald-publishing/aspects-of-impact-of-planar-deformable-bodies-as-linear-Eg8bJEP0rt
Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
1573-6105
DOI
10.1163/157361108785963046
Publisher site
See Article on Publisher Site

Abstract

This paper extends the linear complementarity problem formulation of (7) and (8) for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in (7). Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.

Journal

Multidiscipline Modeling in Materials and StructuresEmerald Publishing

Published: Jan 1, 2008

Keywords: Impact; Planar deformable bodies; Complementarity problem; Multibody systems

There are no references for this article.