Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems

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

Abstract

This paper presents the mathematical framework for the efficient construction of the equations of motion of complex multibody problems when uncertainty exists in the systems' parameters and/or inputs. Herein, uncertainty is prorogated through the system dynamics by using the method of polynomial chaos expansion (PCE). In this scheme, states of the system are projected onto the space of appropriate orthogonal base functions. Furthermore, the method of Divide-and-Conquer Algorithm (DCA) is extended to construct the equations of motion of the resulting non-deterministic system. In this scheme, the mathematical formulation to generate the projected handle equations of motion of the bodies and the projected constraint equations of the connecting joints are constructed in terms of the PCE. Finally, these projected equations are used to perform the assembly and disassembly passes to form and solve the equations of motion. The proposed method is highly parallelizable and scales down the computational complexity as a linear and logarithmic function of the state variables in serial and parallel implementations, respectively.

Original languageEnglish (US)
Title of host publicationProceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015
PublisherInternational Center for Numerical Methods in Engineering
Pages196-207
Number of pages12
ISBN (Electronic)9788494424403
StatePublished - 2015
Event2015 ECCOMAS Thematic Conference on Multibody Dynamics, Multibody Dynamics 2015 - Barcelona, Spain
Duration: Jun 29 2015Jul 2 2015

Other

Other2015 ECCOMAS Thematic Conference on Multibody Dynamics, Multibody Dynamics 2015
CountrySpain
CityBarcelona
Period6/29/157/2/15

Fingerprint

Equations of motion
Chaos theory
Polynomials
Computational complexity
Dynamical systems
Uncertainty

Keywords

  • Divide-and-conquer algorithm
  • Multibody dynamics
  • Polynomial chaos expansion
  • Uncertainty quantification

ASJC Scopus subject areas

  • Automotive Engineering
  • Mechanical Engineering
  • Control and Systems Engineering

Cite this

Poursina, M. (2015). Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems. In Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015 (pp. 196-207). International Center for Numerical Methods in Engineering.

Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems. / Poursina, Mohammad.

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015. International Center for Numerical Methods in Engineering, 2015. p. 196-207.

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

Poursina, M 2015, Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems. in Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015. International Center for Numerical Methods in Engineering, pp. 196-207, 2015 ECCOMAS Thematic Conference on Multibody Dynamics, Multibody Dynamics 2015, Barcelona, Spain, 6/29/15.
Poursina M. Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems. In Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015. International Center for Numerical Methods in Engineering. 2015. p. 196-207
Poursina, Mohammad. / Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems. Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015. International Center for Numerical Methods in Engineering, 2015. pp. 196-207
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