On the parametrization of finite rotations in computational mechanics - A classification of concepts with application to smooth shells
On the parametrization of finite rotations in computational mechanics - A classification of concepts with application to smooth shells
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DOI：
10.1016/s0045-7825(97)00158-8
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发表时间：
1998-03-30
影响因子：
7.2
通讯作者：
Stein, E
中科院分区：
文献类型：
--
作者：
Betsch, P;Menzel, A;Stein, E
本文讨论了大旋转的计算处理，并应用于光滑壳的有限元离散。对基于各种旋转参数化的公式进行了回顾，并根据其更新结构对其进行了分类：类别（II）基于总旋转自由度，导致可加性更新结构，而类别(I)依赖于线性化旋转自由度，导致可乘性更新结构。在此分类的基础上，开发了新的配方。其中，在（II）类中应用的Rodrigues公式具有旋转矢量两个分量的加性更新结构，在(I)类中应用的两个连续初等旋转（在欧拉角意义上）产生无奇点的公式。数值算例证实，在第（II）类中应用的每个旋转参数化都会导致奇点，而在第(I)类中应用则可以计算不受大小限制的整体旋转，而不存在任何奇点。(C) 1998 Elsevier Science S.A.
This paper concerns the computational treatment of large rotations with application to the finite element discretisation of smooth shells. Formulations based on various rotational parametrizations are reviewed and classified with respect to their update structure: category (II) is based on total rotational degrees of freedom leading to an additive update structure, whereas category (I) relies on linearized rotational degrees of freedom leading to a multiplicative update structure. Based on this classification, new formulations are developed. Among them are the Rodrigues formula applied within category (II) with additive update structure for the two components of the rotation vector and two successive elementary rotations (in the sense of Euler angles) applied within category (I) yielding a singularity-free formulation. The numerical examples confirm that every rotational parametrization when applied within category (II) leads to singularities, whereas the application within category (I) enables the calculation of overall rotations unrestricted in size without any singularity. (C) 1998 Elsevier Science S.A.