Lie Group Modeling of Nonlinear Helical Beam Elements
Lie Group Modeling of Nonlinear Helical Beam Elements
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非线性螺旋梁单元的李群建模
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Müller
中科院分区：
文献类型：
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作者：
R. Jödicke;U. Jungnickel;A. Müller
基于SE（3）群理论，提出了一种粘弹性梁模型。我们将杆上的有限框架之间的梁离散化，并将这些框架的构型视为SE（3）李群的元素。两个相邻的框架由梁连接。假设曲率和应变在它们之间的轨迹上是恒定的。如果梁的挠度曲线被建模为螺旋线，则所得到的梁模型对于大的弯曲变形是几何精确的。离散梁单元的刚度矩阵由潜在的拉伸能和剪切能以及潜在的弯曲能和扭转能得到。通过与SO（3）× RP3变体的比较，证明了该SE（3）模型在平移弹性坐标和平移力方面的优势。
A viscoelastic beam model is presented based on SE(3) group theory. We discretize a rod with beams between finite frames on the rod and regard the configurations of these frames as elements of the SE(3) Lie group. Two subsequent frames are connected by a beam. The curvatures and strains are assumed to be constant on the trajectory between them. If the deflection curve of the beam is modeled as a helix, the resulting beam model is geometrical exact for large bending deformations. The stiffness matrices of the discrete beam elements result from the potential extensional and shearing energy as well as from the potential bending and torsion energy. The benefit of this SE(3) modeling for translational elastic coordinates and for translational forces in comparison to an SO(3) × ℝ3 variant is demonstrated.Copyright © 2014 by ASME