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Institute of Engineering and Computational Mechanics

## Linear Complementarity Problems for Continual Contact of Deformable Bodies

### Project Description

With increasing importance of the simulation of multibody systems in industry and engineering, there are more and more applications which deal with contact problems and make it an essential and very demanding topic in multibody dynamics. Therefore, many investigations focus on this topic and many theoretical and mathematical methods are developed for this purpose. Linear complementarity problems resulting from one of these methods were frequently used for contact modeling of rigid bodies. In this approach the contact problem of rigid bodies is formulated in a complementarity form for the cases of continual contact and impact.

Descriptions leading to Linear Complementarity Problems (LCPs) are well established in the contact modeling of rigid multibody systems and have a very strong mathematical basis [1]. These approaches yield exact solutions for contact problems consisting of contact (force/ acceleration level) and impact (impulse/ velocity level). By utilizing these methods, also frictional contact can be handled appropriately.

In applications where the flexibility of contacting bodies is not negligible, rigid bodies contact can not be used anymore and the deformability of contacting bodies must be taken into account. Therefore, in this work, it has been tried to reformulate this method in order to be able to consider the deformation of contacting bodies.

In this formulation, deformable bodies are modeled based on the moving frame of reference approach with modal coordinates which is frequently used for the simulation of flexible multibody systems. The linear complementarity equations are solved by the PATH solver [2] which is an algorithm for mixed complementarity problems.

[1] F. Pfeiffer and C. Glocker: Multibody Dynamics with Unilateral Contacts. J. Wiley & Sons, New York, 1996.

[2] P.S. Dirske and M.C. Ferris: The PATH Solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, Vol. 5, 123--156, 1995.

### Examples

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