Abstract
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.
Highlights
1.1 BackgroundComputational efficiency has traditionally been a major concern of researchers developing algorithms for multibody dynamics simulations
HiL applications require specialized multibody formulations to decrease the turnaround time associated with the evaluation of multibody system dynamics
We propose a novel and generalized index3 divide and conquer formulation for multi-rigid body dynamics that elegantly handles redundant constraints and potential singular configurations that may appear in such simulations
Summary
Computational efficiency has traditionally been a major concern of researchers developing algorithms for multibody dynamics simulations. Considerable improvements in computer architectures have taken place during the last years, enabling the efficient simulation of larger and more complex mechanical systems. There are a large number of industry and academic applications that require efficient and accurate code execution. Some of these demand real-time performance, such as Hardware- and Human-in-theLoop (HiL) settings, e.g., simulators and test benches for physical components in the automotive industry. HiL applications require specialized multibody formulations to decrease the turnaround time associated with the evaluation of multibody system dynamics. The efficiency of multibody dynamics algorithms is determinant for the ability of these applications to meet their performance requirements
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