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首页> 外文期刊>Multibody System Dynamics >The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics
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The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

机译：离散零空间方法用于受约束机械系统的能量一致集成。第三部分：灵活的多体动力学

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摘要

In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367–391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy–momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method.
机译：在当前的工作中，由Betsch和Steinmann开发的用于计算刚体和非线性梁的统一框架（Multibody Syst。Dyn。8，367-391，2002）扩展到了非线性壳的领域。特别是，提出了一种特殊的壳约束公式，该公式导致了以一组微分代数方程（DAE）为特征的半离散运动方程。 DAE提供了对刚体，半离散梁和壳体以及因此而来的灵活多体系统的统一描述。约束可以分为两类：（i）与约束的刚度假设紧密相关的内部约束，以及（ii）与多实体框架中的关节存在有关的外部约束。因此，本方法在整个时间离散化过程中都避免使用旋转变量，从而简化了用于灵活多体动力学的能量动量方法的设计。在离散化完成之后，通过消除约束力来减小离散系统的尺寸。数值示例处理空间曲柄曲柄机制和相交的壳说明了该方法的性能。

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