Variational approaches for dynamics and time-finite-elements: numerical studies
Variational approaches for dynamics and time-finite-elements: numerical studies
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动力学和时间有限元的变分方法：数值研究
DOI：
10.1007/bf00370057
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
S. Atluri
中科院分区：
文献类型：
--
作者：
M. Borri;F. Mello;S. Atluri
本文提出了动力学问题的一般变分公式，这是很容易实现的数值。发展提出了非常普遍的弱制定所产生的线性和角动量平衡的考虑，以及众所周知的变分priciples之间的关系。二域和三域混合形式是从一般的弱形式发展而来的。大的旋转运动的变分原理线性化，并在时间有限元框架中实现，与相应的“切线”运营商推导出适当的表达式。为了证明各种公式的有效性，考虑了自由刚体运动的特殊情况。原始配方示出具有不稳定的数值行为，而混合配方表现出物理稳定的行为。本文提出的配方形成的基础上，继续调查约束动力系统和多刚体系统，这将在随后的论文中报道。
This paper presents general variational formulations for dynamical problems, which are easily implemented numerically. The development presents the relationship between the very general weak formulation arising from linear and angular momentum balance considerations, and well known variational priciples. Two and three field mixed forms are developed from the general weak form. The variational principles governing large rotational motions are linearized and implemented in a time finite element framework, with appropriate expressions for the relevant “tangent” operators being derived. In order to demonstrate the validity of the various formulations, the special case of free rigid body motion is considered. The primal formulation is shown to have unstable numerical behavior, while the mixed formulation exhibits physically stable behavior. The formulations presented in this paper form the basis for continuing investigations into constrained dynamical systems and multi-rigid-body systems, which will be reported in subsequent papers.