Basic Research On Numerical Stimulation Of Flow By Stretch Along A Curved Line

Since the 40's in 20th century, the advent of new material and the use of new product technology have challenged the traditional study in mechanics. In the same time, the development of computer has provided a chance to advance for nonlinear continuum mechanics. This paper is under the above circumstance, which associates the new material mechanics and the mechanics of new product technology, it also make use of the computer technology to solve the nonlinear problems. The paper researches the stimulation principle and method of the fluid-solid material flow by stretch along a curved line. The problem exists typically in polymer product and continuing cast. Because of the importance of the industry, the paper is valuable in engineering. The paper also discusses multi-field, multi-phase, multi-state and computer technology, so the paper is also valuable in study. In chapter 1, the background, the history and the study status of model of 'flow of fluid-solid material along a curved line by stretch' are provided. In chapter 2, a three dimensional model is derived from the continuum mechanics. The most important part is a constitutive equation including the character of both fluid and solid, which is convenient for stimulation and concludes both fluid property and sold property. The constitutive equation is a Euler form to a reference which has initial stresses (or residual stresses), The constitutive equation also refers to a motion of constant velocity along a straight line. In chapter 3, some theories of approximation are given from the point of mathematics and from physics. In chapter 4, a numerical method for the model of 'flow of fluid-solid material along a curved line by stretch' is derived from details. The concept of finite flow-element is firstly set up. The paper depicts the elasticity with Euler form and associates the form with depiction of behavior of fluid. The method takes the velocity as basic variables and then derives the left-deformation tensor from the velocity in order to deal with the time-independent motion. At last in this chapter the equations of the finite flow-element are set up from the principle of the virtual work. The numerical method is called finite flow-element method. In chapter 5, Some applications of the theory of the model of 'flow of fluid-solid material along a curved line by stretch' are discussed. The most important parts of thischapter include the curvature separation method of small parameter, the area modification method by mass conversation and the flow curve iteration method based on the general force governing equations. The flow curve iteration method is meaningful to the production. In chapter 6, a conclusion of the paper and the prospects of the continuing study are given.