有约束条件的 Cosserat-rod 模型半显式时间积分的李群局部坐标

IF 2.6 2区 工程技术 Q2 MECHANICS Multibody System Dynamics Pub Date : 2024-06-20 DOI:10.1007/s11044-024-10002-8
Denise Tumiotto, Martin Arnold
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引用次数: 0

摘要

显式 Runge-Kutta 方法是系统动力学中处理非刚性问题的时间积分方法的黄金标准,因为它们将每个时间步的小数值计算量与高精度、误差控制和直接实施相结合。在分析梁动力学时,我们将它们与李群环境下的局部坐标方法相结合,以解决大旋转问题。在对几何精确的梁模型进行粗网格离散化时,通过内部约束强制执行刚性剪切力和非伸缩性条件。由此产生的非刚性约束系统由半显式方法处理,该方法依赖于速度级的约束,避免了各种牛顿-拉夫逊迭代。我们构建了阶数高达五阶的半显 Runge-Kutta Lie 组方法,该方法配备了自适应步长策略,使用嵌入式 Runge-Kutta 对进行误差估计。这些方法成功地测试了柔性梁的卷起机动和经典的飞行意大利面条基准。
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Local coordinates on Lie groups for half-explicit time integration of Cosserat-rod models with constraints

Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse-grid discretization of a geometrically exact beam model. The resulting nonstiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton–Raphson iteration. We construct half-explicit Runge–Kutta Lie group methods of order up to five that are equipped with an adaptive step-size strategy using embedded Runge–Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying-spaghetti benchmark.

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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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