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Coupled principles for computational frictional contact mechanics
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Coupled principles for computational frictional contact mechanics
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ETD_1753
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052252
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eng
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theses
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Computer Science
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Contact mechanics--Mathematical models
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Friction
Abstract
Methods for simulating frictional contact response are in high demand in robotics, graphics, biomechanics, structural engineering, and many other fields where the accurate modeling of interactions between solids are required. While techniques for accurately simulating structures and continua have advanced rapidly, methods for simulating the contact between solids have lagged behind. This thesis addresses the difficulties encountered in designing robust, accurate, and efficient computational methods for simulating frictional contact dynamics. We focus on understanding the fundamental sources of difficulty in frictional contact modeling, elucidating existing structures that can be leveraged to minimize them, and designing robust, accurate and efficient algorithms to simulate challenging frictional contact problems.
In this thesis a Coupled Principles formulation of discrete, time-continuous frictional contact is developed in depth. This is then applied as the basis for deriving novel, time-discrete, variational integrators that pose the discrete frictional contact problem as a system of coupled minimizations. Solutions to these systems are given by points that are optimal for both of the minimizations and avoid known issues with existing variational integration approaches for friction and contact. We then consider a specific two-step variant of these variational schemes that generalizes the popular Stewart-Trinkle model for frictional contact simulation. This is taken as a starting point for investigating the sources of difficulties found in solving these types of methods. We show that existing solution algorithms that have generally been presumed suitable for solving the contact-related optimization problems posed by these methods, fail entirely for many important examples of frictional contact and then address these limitations with our Staggered Projections algorithm. Applying a fixed-point scheme, derived from the Coupled Principles Formulation, we show that Staggered Projections efficiently obtains accurate solutions to optimization problems for many frictional contact problems that were previously impractical to solve. Finally, we also offer a detailed convergence analysis of the Staggered Projections algorithm, as well as simulations and instrumented examples that capture convincing and accurate frictional contact behaviors for both rigid and large deformation models.
In this thesis a Coupled Principles formulation of discrete, time-continuous frictional contact is developed in depth. This is then applied as the basis for deriving novel, time-discrete, variational integrators that pose the discrete frictional contact problem as a system of coupled minimizations. Solutions to these systems are given by points that are optimal for both of the minimizations and avoid known issues with existing variational integration approaches for friction and contact. We then consider a specific two-step variant of these variational schemes that generalizes the popular Stewart-Trinkle model for frictional contact simulation. This is taken as a starting point for investigating the sources of difficulties found in solving these types of methods. We show that existing solution algorithms that have generally been presumed suitable for solving the contact-related optimization problems posed by these methods, fail entirely for many important examples of frictional contact and then address these limitations with our Staggered Projections algorithm. Applying a fixed-point scheme, derived from the Coupled Principles Formulation, we show that Staggered Projections efficiently obtains accurate solutions to optimization problems for many frictional contact problems that were previously impractical to solve. Finally, we also offer a detailed convergence analysis of the Staggered Projections algorithm, as well as simulations and instrumented examples that capture convincing and accurate frictional contact behaviors for both rigid and large deformation models.
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electronic resource
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xxi, 140 p. : ill.
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Ph.D.
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Includes bibliographical references (p. 132-139)
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by Danny M. Kaufman
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Kaufman
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Daniel M.
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1972-
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Daniel M. Kaufman
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Dinesh
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Dinesh K Pai
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Steiger
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William
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William Steiger
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Richter
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Gerard
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Gerard Richter
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Kumar
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Vijay
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Vijay Kumar
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Rutgers University
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Graduate School - New Brunswick
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2009
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2009-05
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xx
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Rutgers University Electronic Theses and Dissertations
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doi:10.7282/T3VD6ZKG
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ETD doctoral
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Open
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Daniel
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2009-04-16 17:08:49
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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365 days
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