A computational model for multiple collisions of rigid bodies: An extension of A-CD2 method

Roberto León, Luis Salinas, Claudio E. Torres

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The A-CD2 method gives a mechanical description for instantaneous collisions between rigid bodies. This method considers a solid that moves with constant velocity in the intervals [t1, tc[ and ]tc, t2]. The contact points at tc are computed with the current position and the new velocities, due to the collision at tc, are calculated by means of a constrained optimization problem. Several applications have used this method. When the solid is governed by a torque free motion, the velocities are not necessarily constants, because depend on the moments of inertia. This behavior is not included in the ACD2 method, since constant velocities are considered. An extension includes the use of the Euler equations for modeling the angular velocities, when the body is torque free. Therefore, non constant angular velocities are obtained when the moments of inertia are different. An important result is the reduction in the computational complexity of the original algorithm, from O(N2) to O(N), mainly due to the contact detection stage. This reduction allows to handle problem 20 times larger than the original. Numerical simulations for granular layers motion are presented.

Original languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publicationSolids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
EditorsRoger Owen, Rene de Borst, Jason Reese, Chris Pearce
PublisherInternational Centre for Numerical Methods in Engineering, CIMNE
Pages1896-1905
Number of pages10
ISBN (Electronic)9788494731167
Publication statusPublished - 1 Jan 2020
Event6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018

Publication series

NameProceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

Conference

Conference6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
CountryUnited Kingdom
CityGlasgow
Period11/06/1815/06/18

Keywords

  • Computational complexity
  • Contact detection
  • Rigid body collision

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Mechanics of Materials
  • Mechanical Engineering

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  • Cite this

    León, R., Salinas, L., & Torres, C. E. (2020). A computational model for multiple collisions of rigid bodies: An extension of A-CD2 method. In R. Owen, R. de Borst, J. Reese, & C. Pearce (Eds.), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 (pp. 1896-1905). (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018). International Centre for Numerical Methods in Engineering, CIMNE.