Elastic Rod Dynamics Model And Its Numerical Simulation

An elastic rod is an important mechanical model which has a wide range of applications in scientific and engineering problems such as the dynamical analysis of submarine cables and cable car, the simulation of hair and nets, and even the simulation of vine growth. In recent years, elastic rods have been an important tool to study the dynamical behavior of macromoleculars such as DNA, and great progress has been made in recent years.The main purpose of this thesis is constructing the dynamic models of an elastic rod and the numerical approaches in simulating its behavior in liquid, the main results are as follows:(1) A Hamilton-like equation is given to describe a slender elastic rod which is discussed. To make numerical treatment easier, quaternions are introduced and the equations are expressed in symplectic form. Symplectic runge-kutta method is then introduced to simulate an elastic rod. The multi-symplectic conservation law of the equation is derived. Then, multi-symplectic algorithm is employed to discretize the equation.The discrete multi-symplectic conservation law of the equation is certified.(2) A dynamical model of a Cosserat elastic rod is introduced. The model, described by quaternion, is easier to deal with in numerical simulation. The initial value problem is defined and the numerical example is given.(3) To simulate the movement of as a macromolecular in liquid, Browning motion has to be considered. So, in this paper, the effects of random forces and random moments to the moving rod are analyzed. A stochastic differential equation is introduced as the dynamical model to describe the random movements, and a numerical method is introduced to solve the problem.