In this paper, an advanced algorithm is presented to efficiently form and solve the equations of motion of multibody problems involving uncertainty in the system parameters and/or excitations. Uncertainty is introduced to the system through the application of polynomial chaos expansion (PCE). In this scheme, states of the system, nondeterministic parameters, and constraint loads are projected onto the space of specific orthogonal base functions through modal values. Computational complexity of traditional methods of forming and solving the resulting governing equations drastically grows as a cubic function of the size of the nondeterministic system which is significantly larger than the original deterministic multibody problem. In this paper, the divide-and-conquer algorithm (DCA) will be extended to form and solve the nondeterministic governing equations of motion avoiding the construction of the mass and Jacobian matrices of the entire system. In this strategy, stochastic governing equations of motion of each individual body as well as those associated with kinematic constraints at connecting joints are developed in terms of base functions and modal terms. Then using the divide-and-conquer scheme, the entire system is swept in the assembly and disassembly passes to recursively form and solve nondeterministic equations of motion for modal values of spatial accelerations and constraint loads. In serial and parallel implementations, computational complexity of the method is expected to, respectively, increase as a linear and logarithmic function of the size.
Skip Nav Destination
Article navigation
Research-Article
Extended Divide-and-Conquer Algorithm for Uncertainty Analysis of Multibody Systems in Polynomial Chaos Expansion Framework
Mohammad Poursina
Mohammad Poursina
Assistant Professor
Mem. ASME
Department of Aerospace
and Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721
e-mail: poursina@email.arizona.edu
Mem. ASME
Department of Aerospace
and Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721
e-mail: poursina@email.arizona.edu
Search for other works by this author on:
Mohammad Poursina
Assistant Professor
Mem. ASME
Department of Aerospace
and Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721
e-mail: poursina@email.arizona.edu
Mem. ASME
Department of Aerospace
and Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721
e-mail: poursina@email.arizona.edu
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 24, 2014; final manuscript received September 3, 2015; published online November 16, 2015. Assoc. Editor: Dan Negrut.
J. Comput. Nonlinear Dynam. May 2016, 11(3): 031015 (9 pages)
Published Online: November 16, 2015
Article history
Received:
September 24, 2014
Revised:
September 3, 2015
Citation
Poursina, M. (November 16, 2015). "Extended Divide-and-Conquer Algorithm for Uncertainty Analysis of Multibody Systems in Polynomial Chaos Expansion Framework." ASME. J. Comput. Nonlinear Dynam. May 2016; 11(3): 031015. https://doi.org/10.1115/1.4031573
Download citation file:
Get Email Alerts
Cited By
A comparative analysis among dynamics modelling approaches for space manipulator systems
J. Comput. Nonlinear Dynam
An Efficient Analysis of Amplitude and Phase Dynamics in Networked MEMS-Colpitts Oscillators
J. Comput. Nonlinear Dynam
Data-Driven Modeling of Tire–Soil Interaction With Proper Orthogonal Decomposition-Based Model Order Reduction
J. Comput. Nonlinear Dynam (December 2024)
Related Articles
Comparison of Semirecursive and Subsystem Synthesis Algorithms for the Efficient Simulation of Multibody Systems
J. Comput. Nonlinear Dynam (January,2017)
Special Issue: Geometric Methods and Formulations
J. Comput. Nonlinear Dynam (March,2017)
An Ordinary Differential Equation Formulation for Multibody Dynamics: Nonholonomic Constraints
J. Comput. Inf. Sci. Eng (March,2017)
Uncertainty Quantification of NO x Emission Due to Operating Conditions and Chemical Kinetic Parameters in a Premixed Burner
J. Eng. Gas Turbines Power (December,2018)
Related Proceedings Papers
Related Chapters
The Applications of the Cloud Theory in the Spatial DMKD
International Conference on Electronics, Information and Communication Engineering (EICE 2012)
Updates, Revisions and Corrections to this Book
Supplement to Fluid Mechanics, Water Hammer, Dynamic Stresses, and Piping Design
A New Chaos Based Image Encryption Algorithm
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)