research-article

Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics

Author:

Per LötstedtAuthors Info & Claims

SIAM Journal on Scientific and Statistical Computing, Volume 5, Issue 2

Pages 370 - 393

https://doi.org/10.1137/0905028

Published: 01 June 1984 Publication History

Abstract

A numerical method is given for the solution of a system of ordinary differential equations and algebraic, unilateral constraints. The equations govern the motion of a mechanical system of rigid bodies, where contacts between the bodies are created and disappear in the time interval of interest. The ordinary differential equations are discretized by linear multistep methods. In order to satisfy the constraints, a quadratic programming problem is solved at each time step. The fact that the variation of the objective function is small from step to step is utilized to save computing time. A discrete friction model, based on Coulomb’s law of friction and suitable for efficient computation, is proposed for planar problems where dry friction cannot be neglected. The normal forces and the friction forces are the optimal solution to a quadratic programming problem. The methods are tested on four model problems. A data structure and possible generalizations are discussed.

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Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics

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Published In

cover image SIAM Journal on Scientific and Statistical Computing

SIAM Journal on Scientific and Statistical Computing Volume 5, Issue 2

Jun 1984

242 pages

ISSN:0196-5204

DOI:10.1137/sijcd4.1984.5.issue-2

Issue’s Table of Contents

Copyright © 1984 Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 June 1984

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Cited By

Truong NYuksel CWatcharopas CLevine JKirby R(2022)Particle Merging-and-SplittingIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.309377628:12(4546-4557)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1109/TVCG.2021.3093776
Bravo M DRengifo Rodas C(2021)Design of a Dynamic Simulator for a Biped RobotModelling and Simulation in Engineering10.1155/2021/55391232021Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1155/2021/5539123
Ferguson ZLi MSchneider TGil-Ureta FLanglois TJiang CZorin DKaufman DPanozzo D(2021)Intersection-free rigid body dynamicsACM Transactions on Graphics10.1145/3450626.345980240:4(1-16)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1145/3450626.3459802
Li SZhang TWang GSun HManocha D(2017)Multi-contact frictional rigid dynamics using impulse decomposition2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS.2017.8206547(6420-6427)Online publication date: 24-Sep-2017
https://dl.acm.org/doi/10.1109/IROS.2017.8206547
Mohtat AKövecses J(2016)Dynamic constraint-based rendering of contacts in haptics2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC)10.1109/SMC.2016.7844966(004657-004662)Online publication date: 9-Oct-2016
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Harmon DPanozzo DSorkine OZorin D(2011)Interference-aware geometric modelingProceedings of the 2011 SIGGRAPH Asia Conference10.1145/2024156.2024171(1-10)Online publication date: 12-Dec-2011
https://dl.acm.org/doi/10.1145/2024156.2024171
Kaufman DSueda SJames DPai D(2008)Staggered projections for frictional contact in multibody systemsACM SIGGRAPH Asia 2008 papers10.1145/1457515.1409117(1-11)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1145/1457515.1409117
Baraff DSchweitzer DGlassner AKeeler M(1994)Fast contact force computation for nonpenetrating rigid bodiesProceedings of the 21st annual conference on Computer graphics and interactive techniques10.1145/192161.192168(23-34)Online publication date: 24-Jul-1994
https://dl.acm.org/doi/10.1145/192161.192168
Moré JToraldo G(1991)On the Solution of Large Quadratic Programming Problems with Bound ConstraintsSIAM Journal on Optimization10.1137/08010081:1(93-113)Online publication date: 1-Feb-1991
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