Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation

There has been a growing attention to efficient simulations of multibody systems, which is apparently seen in many areas of computer-aided engineering and design both in academia and in industry. The need for efficient or real-time simulations requires high-fidelity techniques and formulations that...

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Vydáno v:Nonlinear dynamics Ročník 95; číslo 1; s. 727 - 747
Hlavní autoři: Malczyk, Paweł, Frączek, Janusz, González, Francisco, Cuadrado, Javier
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.01.2019
Springer Nature B.V
Témata:
Acceleration
Accuracy
Algorithms
Automotive Engineering
CAE
Classical Mechanics
Closed loops
Computer aided engineering
Computer memory
Computer simulation
Computing time
Control
Dynamical Systems
Engineering
Formulations
Iterative methods
Kinematics
Mechanical Engineering
Microprocessors
Multibody systems
Nonlinear equations
Original Paper
Parallel processing
Real time
Simulation
System dynamics
Topology
Vibration
Mass-orthogonal projections
Parallel computing
Long chain simulations
Real-time simulations
Divide-and-conquer algorithm
Trapezoidal rule
Multibody dynamics
ISSN:0924-090X, 1573-269X
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Popis
Shrnutí:There has been a growing attention to efficient simulations of multibody systems, which is apparently seen in many areas of computer-aided engineering and design both in academia and in industry. The need for efficient or real-time simulations requires high-fidelity techniques and formulations that should significantly minimize computational time. Parallel computing is one of the approaches to achieve this objective. This paper presents a novel index-3 divide-and-conquer algorithm for efficient multibody dynamics simulations that elegantly handles multibody systems in generalized topologies through the application of the augmented Lagrangian method. The proposed algorithm exploits a redundant set of absolute coordinates. The trapezoidal integration rule is embedded into the formulation and a set of nonlinear equations need to be solved every time instant. Consequently, the Newton–Raphson iterative scheme is applied to find the system coordinates and joint constraint loads in an efficient and highly parallelizable manner. Two divide-and-conquer-based mass-orthogonal projections are performed then to circumvent the effect of constraint violation errors at the velocity and acceleration level. Sample open- and closed-loop multibody system test cases are investigated in the paper to confirm the validity of the approach. Challenging simulations of multibody systems featuring long kinematic chains are also performed in the work to demonstrate the robustness of the algorithm. The details of OpenMP-based parallel implementation on an eight-core shared memory computer are presented in the text and the parallel performance results are extensively discussed. Significant speedups are obtained for the simulations of small- to large-scale multibody open-loop systems. The mentioned features make the proposed algorithm a good general purpose approach for high-fidelity, efficient or real-time multibody dynamics simulations.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4593-3