Convergence of the generalized-α scheme for constrained mechanical systems

By Martin Arnold, O. Bruls. 2007

446 citations recorded by the source corpus.

Abstract A variant of the generalized-α scheme is proposed for constrained mechanical systems represented by index-3 DAEs. Based on the analogy with linear multistep methods, an elegant convergence analysis is developed for this algorithm. Second-order convergence is demonstrated both for the generalized coordinates and the Lagrange multipliers, and those theoretical results are illustrated by numerical tests.

Subfields: Computational Mechanics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/734773be411c2c4d611f3ffc3ab214eb62c4b821

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In Computational Mechanics

1. K. Luo
2. Cheng Liu
3. Liping Chen
4. Haiyan Hu
5. Jingzhou Yang
6. Qiang Tian
7. Yunqing Zhang

In Control and Systems Engineering

1. Qiang Tian
2. Haiyan Hu
3. Cheng Liu
4. Yunqing Zhang
5. K. Luo
6. Liping Chen
7. Jingzhou Yang
8. Paulo Flores

In Numerical Analysis

1. K. Luo
2. Cheng Liu
3. Liping Chen
4. Haiyan Hu
5. Jingzhou Yang
6. Qiang Tian
7. Yunqing Zhang

Citations in the corpus

• Simulation of planar flexible multibody systems with clearance and lubricated revolute joints (2010, methodology): “Based on the generalized-α method, Arnold and Bruls [ 52 ] proposed a computational scheme.”
• Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation (2016, methodology): “In the present study, the generalized-alpha algorithm [24,25] is used so as to achieve an optimal combination of accuracy at the low-frequency range and numerical damping at the high-frequency range.”
• A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints (2013, unknown): “An extended analysis on the global convergence can be found in [6].”
• On the Use of Lie Group Time Integrators in Multibody Dynamics (2010, unknown): “This method is also able to solve dynamic problems with kinematic constraints, as shown by Cardona and G´eradin [9] and Arnold and Br¨uls [13].”
• Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme (2014, unknown): “According to [21], the generalized-α method combines the equations of motion at time step n + 1 with some difference equations.”