Kinetic Aspects of Discrete Cosserat Rods
Kinetic Aspects of Discrete Cosserat Rods
复制标题
离散 Cosserat 棒的动力学方面
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Fabio Schneider
中科院分区：
文献类型：
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作者：
J. Linn;T. Hermansson;F. Andersson;Fabio Schneider
Cosserat杆理论为模拟细长柔性结构在局部小应变下的大空间变形提供了一个自洽的框架。基于几何有限差分的离散Cosserat杆模型保持了连续介质理论的基本性质。在拉格朗日力学的框架下，研究了交错网格上离散四元数Cosserat杆的运动学性质。假定超弹性本构行为，模型的欧拉-拉格朗日方程等价于力、力矩和惯性项的(半)离散平衡方程，该平衡方程是通过沿中心线的空间有限差分直接离散得到的。因此，能量最小化得到的平衡构型对应于准静态平衡方程的解。我们通过两个学术实例(欧拉弹性和基尔霍夫螺旋)来说明这一方法，并以汽车工业的一个使用案例(分析乘用车引擎室冷却软管的布局)来强调其在实际应用中的有效性。
The theory of Cosserat rods provides a self consistent framework for modeling large spatial deformations of slender flexible structures at small local strains. Discrete Cosserat rod models based on geometric finite differences preserve essential properties of the continuum theory. The present work investigates kinetic aspects of discrete quaternionic Cosserat rods defined on a staggered grid within the framework of Lagrangian mechanics. Assuming hyperelastic constitutive behaviour, the Euler–Lagrange equations of the model are shown to be equivalent to the (semi)discrete balance equations of forces, moments and inertial terms obtained from a direct discretization of the continuous balance equations via spatial finite differences along the centerline curve. Therefore, equilibrium configurations obtained by energy minimization correspond to solutions of the quasi-static balance equations. We illustrate this approach by two academic examples (Euler’s Elastica and Kirchhoff’s helix) and highlight its utility for practical applications with a use case from automotive industry (analysis of the layout of cooling hoses in the engine compartment of a passenger car).