### 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 language | English (US) |
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Title of host publication | Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015 |

Publisher | International Center for Numerical Methods in Engineering |

Pages | 196-207 |

Number of pages | 12 |

ISBN (Electronic) | 9788494424403 |

State | Published - 2015 |

Event | 2015 ECCOMAS Thematic Conference on Multibody Dynamics, Multibody Dynamics 2015 - Barcelona, Spain Duration: Jun 29 2015 → Jul 2 2015 |

### Other

Other | 2015 ECCOMAS Thematic Conference on Multibody Dynamics, Multibody Dynamics 2015 |
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Country | Spain |

City | Barcelona |

Period | 6/29/15 → 7/2/15 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Generalization of the Divide-and-Conquer Algorithm for the uncertainty quantification of multibody systems

AU - Poursina, Mohammad

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Divide-and-conquer algorithm

KW - Multibody dynamics

KW - Polynomial chaos expansion

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=84979519259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979519259&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84979519259

SP - 196

EP - 207

BT - Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015, Multibody Dynamics 2015

PB - International Center for Numerical Methods in Engineering

ER -