Finite Element Method on Contact Problem of Non-newtonian Fluid Material

Abstract

Abstract-In this paper, we use finite element method to study contact problem of non-Newtonian fluid material. We focus on Cauchy equation which describes the velocity changes in the flow field. The space domain is discrete by Lagrange interpolation function with 16-point bicubic elements. The time domain is discrete by two schemes: two-step Adams explicit scheme and Crank-Nicolson scheme. We study the convergence. In numerical experiments, the error of the equation is shown by comparing the numerical solutions with the exact solutions.Keywords-non-Newtonian fluid; finite element method; contact problem; two-step Adams explicit scheme I.INTRODUCTION With the continuous development of network and modern communication technology, the concept of the networked intelligent sensor based on the technology of wireless produced. In some special goods transport, environmental parameters have higher requirements for container. Wireless sensor network (WSN) is a good way to monitoring parameters. We apply WSN to warehouse management. Three dimensional space deployment of the wireless sensor network nodes is one of the big problems in the research. One of the effective node deployment plan, is to perform finite element meshes based on cube or sphere on the certain storage space.Under the condition of high speed collision, the solid material can cause enormous deformation in such a short time. Thus, we can agree that it also has fluid property. Socalled non-Newtonian fluid is a fluid whose shear stress and shear rate cannot always keep a linear relationship, such as blood, toothpaste, oil paint and slurry. Different rheological properties of different type of non-Newtonian fluid will appear under the changes of shear rate. For example, Bingham plastic body exists yield stress. Besides, dilatants fluid has shear thickening properties. With the continuous development of materials science and related research technology, the applications of non-Newtonian fluid material field are deepening.In the research of non-Newtonian fluid material, we always use coupled PDE equations. The standard P-T/T equation is the best estimates for the stress over-shoot. Cauchy conservation equation may be used to calculate the large deformation resulting from stress (shear thinning). It can be used to describe the velocity and the stress distribution in the contract problem.In this paper, we focus on the Cauchy equation which describes the velocity changes in the flow field.