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A linear programming-based algorithm for the signed separation of (non-smooth) convex bodies

Johnson, G. and Ortiz, M. and Leyendecker, S. (2012) A linear programming-based algorithm for the signed separation of (non-smooth) convex bodies. Computer Methods in Applied Mechanics and Engineering, 233-236 . pp. 49-67. ISSN 0045-7825. http://resolver.caltech.edu/CaltechAUTHORS:20121107-081815613

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Abstract

A subdifferentiable global contact detection algorithm, the Supporting Separating Hyperplane (SSH) algorithm, based on the signed distance between supporting hyperplanes of two convex sets is developed. It is shown that for polyhedral sets, the SSH algorithm may be evaluated as a linear program, and that this linear program is always feasible and always subdifferentiable with respect to the configuration variables, which define the constraint matrix. This is true regardless of whether the program is primal degenerate, dual degenerate, or both. The subgradient of the SSH linear program always lies in the normal cone of the closest admissible configuration to an inadmissible contact configuration. In particular if a contact surface exists, the subgradient of the SSH linear program is orthogonal to the contact surface, as required of contact reactions. This property of the algorithm is particularly important in modeling stiff systems, rigid bodies, and tightly packed or jammed systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.cma.2012.04.006DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0045782512001260PublisherUNSPECIFIED
Additional Information:© 2012 Elsevier B.V. Received 13 August 2011. Received in revised form 6 March 2012. Accepted 4 April 2012. Available online 21 April 2012. The support of the W. M. Keck Foundation through Caltech’s Keck Institute for Space Studies is gratefully acknowledged.
Group:Keck Institute for Space Studies
Funders:
Funding AgencyGrant Number
W. M. Keck Foundation UNSPECIFIED
Caltech Keck Institute for Space Studies (KISS)UNSPECIFIED
Subject Keywords:Contact; Lagrangian dynamics; Linear programming; Non-smooth analysis
Record Number:CaltechAUTHORS:20121107-081815613
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20121107-081815613
Official Citation:G. Johnson, M. Ortiz, S. Leyendecker, A linear programming-based algorithm for the signed separation of (non-smooth) convex bodies, Computer Methods in Applied Mechanics and Engineering, Volumes 233–236, 1 August 2012, Pages 49-67, ISSN 0045-7825, 10.1016/j.cma.2012.04.006.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35318
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Nov 2012 19:17
Last Modified:23 Aug 2016 10:21

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