超细长弹性杆的动力学模型及动力学方程解的存在性

Dynamic Model of Over Thin Elastic Rod and Existence of Solution of Dynamic Equation

在kirchhoff弹性杆理论框架下,考虑可以扭转、弯曲、剪切、拉伸并受到内力作用的弹性杆模型.在截面主轴坐标系下,建立了利用剪切拉伸向量描述的运动弹性杆的动力学模型;根据Doliwa和Santin提出的曲线运动方程的可解性理论,利用Lax方程可解性,分析了该动力学模型解的存在性,为对这一类动力学方程进行数值求解和数值模拟提供了理论依据.

Under the framework of Kirchhoff＇s elastic rod theory,the dynamic model of elastic rod under the action of reverse,curve,cut,stretching and inner force is considered.In the coordinate system of section＇s principal axis,according to the solvability theory of equation of curve motion advanced by Doliwa and Santin and using the solvability of Lax equation,the dynamic model of motion elastic rod described by cut and stretching vector is established,and the existence of solution of the dynamic model is analyzed,which provide theoretical basis for numerical solution and numerical simulation of this kind of dynamic equation.