A 2D Corotational Beam Formulation Based On the Local Frame of Special Euclidean Group SE(2)

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL Journal of Computational and Nonlinear Dynamics Pub Date : 2023-03-06 DOI:10.1115/1.4057044
Pu You, Zhuyong Liu, Ziqi Ma
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Abstract

The corotational frame method is widely used in the simulation of flexible multibody dynamics. Its core idea is to separate the rigid motion from the flexible deformation so that it can make fully exploit a large number of excellent local finite elements. The essence of the conventional corotational frame method is the projection relationship between the element frame and the global frame. This paper explores another coordinate projection method for 2D corotational beam element. The projection relationship between the element frame and the local frame in the framework of Lie algebra se(2) has been proposed. Based on the description of SE(2), the formulation of corotational beam element and integration algorithm is presented. The local frame description greatly reduces the nonlinearity of the formula by eliminating the effect of the rigid body motion on the projection matrix, internal force and inertial force. Several examples of large deformation and or large rotation are performed, and it is found that the step-size convergence and iterative convergence of SE(2) description are improved compared with ℝ3 description. In additionMoreover, some examples are used given to verify that the frame invariance brought by SE(2)the coordinate transformation is valuable for improving computing efficiency. The presented transformation method can easily extend to other 2D corotational elements.
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基于特殊欧几里得群SE(2)局部框架的二维旋转梁公式
旋转框架法在柔性多体动力学仿真中得到了广泛的应用。其核心思想是将刚性运动与柔性变形分离,从而充分利用大量优秀的局部有限元。传统的旋转框架方法的本质是单元框架和整体框架之间的投影关系。本文探索了二维同向梁单元的另一种坐标投影方法。提出了李代数se(2)框架中单元框架与局部框架的投影关系。在SE(2)描述的基础上,提出了旋转梁单元的表达式和积分算法。局部框架描述通过消除刚体运动对投影矩阵、内力和惯性力的影响,大大降低了公式的非线性。通过对几个大变形和大旋转的算例分析,发现SE(2)描述的步长收敛性和迭代收敛性都比h(3)描述有所改善。此外,通过算例验证了SE(2)坐标变换带来的帧不变性对提高计算效率的价值。所提出的变换方法可以很容易地扩展到其他二维旋转元素。
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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