The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics
The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics
复制标题
用于约束机械系统能量一致集成的离散零空间方法第三部分：灵活的多体动力学。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
P. Steinmann
中科院分区：
文献类型：
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作者：
S. Leyendecker;P. Betsch;P. Steinmann
摘要
在目前的工作中，统一的框架计算处理的刚体和非线性梁开发的Betsch和Steinmann（多体系统动力学。8，367-391，2002）被扩展到非线性壳的领域。特别是，提出了一种特定的约束制定的外壳，导致半离散的运动方程，其特征在于由一组微分代数方程（DAE）。DAE为刚体、半离散梁和壳以及柔性多体系统提供了统一的描述。约束可以分为两类：（i）内部约束，这是密切联系的机构的刚度假设，和（ii）外部约束有关的存在关节的多体框架。因此，本方法避免了在整个时间离散化中使用旋转变量，便于设计柔性多体动力学的能量-动量方法。在离散化完成后，通过消除约束力来进行离散系统的尺寸减小。空间曲柄滑块机构和相交壳体的数值例子说明了所提出的方法的性能。
Abstract
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.