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Technical Brief

Posing Multibody Dynamics With Friction and Contact as a Differential Complementarity Problem

[+] Author and Article Information
Dan Negrut

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706
e-mail: negrut@wisc.edu

Radu Serban

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706
e-mail: serban@wisc.edu

Alessandro Tasora

Dipartimento di Ingegneria Industriale,
University of Parma,
Parma 43121, Italy
e-mail: alessandro.tasora@unipr.it

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 14, 2017; final manuscript received July 17, 2017; published online October 31, 2017. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 13(1), 014503 (Oct 31, 2017) (6 pages) Paper No: CND-17-1068; doi: 10.1115/1.4037415 History: Received February 14, 2017; Revised July 17, 2017

This technical brief revisits the method outlined in Tasora and Anitescu 2011 [“A Matrix-Free Cone Complementarity Approach for Solving Large-Scale, Nonsmooth, Rigid Body Dynamics,” Comput. Methods Appl. Mech. Eng., 200(5–8), pp. 439–453], which was introduced to solve the rigid multibody dynamics problem in the presence of friction and contact. The discretized equations of motion obtained here are identical to the ones in Tasora and Anitescu 2011 [“A Matrix-Free Cone Complementarity Approach for Solving Large-Scale, Nonsmooth, Rigid Body Dynamics,” Comput. Methods Appl. Mech. Eng., 200(5–8), pp. 439–453]; what is different is the process of obtaining these equations. Instead of using maximum dissipation conditions as the basis for the Coulomb friction model, the approach detailed uses complementarity conditions that combine with contact unilateral constraints to augment the classical index-3 differential algebraic equations of multibody dynamics. The resulting set of differential, algebraic, and complementarity equations is relaxed after time discretization to a cone complementarity problem (CCP) whose solution represents the first-order optimality condition of a quadratic program with conic constraints. The method discussed herein has proven reliable in handling large frictional contact problems. Recently, it has been used with promising results in fluid–solid interaction applications. Alas, this solution is not perfect, and it is hoped that the detailed account provided herein will serve as a starting point for future improvements.

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References

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Tasora, A. , and Anitescu, M. , 2011, “ A Matrix-Free Cone Complementarity Approach for Solving Large-Scale, Nonsmooth, Rigid Body Dynamics,” Comput. Methods Appl. Mech. Eng., 200(5–8), pp. 439–453. [CrossRef]
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Kwarta, M. , and Negrut, D. , 2016, “ Using the Complementarity and Penalty Methods for Solving Frictional Contact Problems in Chrono: Validation for the Cone Penetrometer Test,” Simulation-Based Engineering Laboratory, University of Wisconsin-Madison, Madison, WI, Technical Report No. TR-2016-16. http://sbel.wisc.edu/documents/TR-2016-16.pdf
Kwarta, M. , and Negrut, D. , 2016, “ Using the Complementarity and Penalty Methods for Solving Frictional Contact Problems in Chrono: Validation for the Triaxial Test,” Simulation-Based Engineering Laboratory, University of Wisconsin-Madison, Madison, WI, Technical Report No. TR-2016-17.
Kwarta, M. , and Negrut, D. , 2016, “ Using the Complementarity and Penalty Methods for Solving Frictional Contact Problems in Chrono: Validation for the Shear-Test With Particle Image Velocimetry,” Simulation-Based Engineering Laboratory, University of Wisconsin-Madison, Madison, WI, Technical Report No. TR-2016-18.
Tasora, A. , Serban, R. , Mazhar, H. , Pazouki, A. , Melanz, D. , Fleischmann, J. , Taylor, M. , Sugiyama, H. , and Negrut, D. , 2016, “ Chrono: An Open Source Multi-Physics Dynamics Engine,” High Performance Computing in Science and Engineering (Lecture Notes in Computer Science), T. Kozubek , ed., Springer, Cham, Switzerland, pp. 19–49. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Bodies A and B in contact; a local reference frame {ni, ui, wi} is generated at the contact point based on contact detection information. The contact point is located in the centroidal and principal reference frames via the s¯i,A and s¯i,B vectors.

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