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Augmented Time-Stepping by Step-Size Adjustment and Extrapolation

[+] Author Affiliations
Christian Studer, Christoph Glocker

ETH Zurich, Zurich, Switzerland

Paper No. DETC2007-34154, pp. 347-356; 10 pages
doi:10.1115/DETC2007-34154
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Time-stepping schemes are widely used when integrating non-smooth systems. In this paper we discuss an augmented time-stepping scheme which uses step-size adjustment and extrapolation. The time evolution of non-smooth systems can be divided in different smooth parts, which are separated by switching points. We deduce the time-stepping method of Moreau, which is a common order-one integration method for non-smooth systems. We formulate the method using contact inclusions, and show how these inclusions can be solved by a projection. We show how time-steps which contain a switching point can be detected by observing the projection behaviour, and propose a step-size adjustment, which treats these switching time-steps with a minimal step-size Δtmin . Time-steps in smooth parts of the motion are run with a larger step-size, and an extrapolation method, which is based on the time-stepping scheme, is used to increase the integration order. The presented method is suitable for mechanical systems with unilateral and frictional contacts. For simplicity, we deduce the method considering solely mechanical systems with one unilateral contact.

Copyright © 2007 by ASME
Topics: Motion

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