预应力曲杆的Cosserat动力学模型

Dynamic modeling of pre-stressed curved Cosserat rods

为了更方便地使用Cosserat杆模型对各种细长结构进行动力学建模,在该杆模型的框架下通过引入描述固连在杆横截面随其一起运动的初始变形、初始横截面转动以及横截面间的初始接触力和力矩等变量,建立了考虑预应力的细长曲杆的Cosserat动力学模型.在得到的模型的框架下,基于相应的物理假设,从数学演绎的角度推导了桥梁建设中广泛应用的具有初始垂度的拉索以及圆拱梁的动力学方程,结果与文献中采用其他方法得到的相应的动力学方程一致.由于Cosserat理论采用了精确的几何构形,这里导出的细长预应力曲杆动力学模型不仅保留了所有的几何非线性特征,而且具有很好的普适性,通过它可以容易地导出实际工程问题中细长结构的非线性动力学模型.

To dynamically model slender structures conveniently by Cosserat rod theory, the dynamic equations for pre-stressed curved Cosserat rods are established within the framework of this rod theory by defining variables to describe their initial configurations, their pre-stresses and their initial deformations, which move along with their cross sections. Based on their corresponding specific assumptions, the dynamic equations for a cable with initial sag and a circular arch beam, which have wide applications in bridge structures, are explored within the framework of pre-stressed curved Cosserat rods, respectively. The results are in agreement with their corresponding equations obtained by other methods in references. Since the Cosserat theory is geometrically exact, the dynamic equations for pre-stressed curved Cosserat rods derived here are not only retaining all geometric nonlinear characteristics but also of universality, which can be effectively and efficiently exploited to nonlinear dynamically model for slender structures in practical engineering situations.