Research On The Theory Methods For The Fast Algorithm In The Boundary Element Method For The Elasticity And Elasto-Plas Ticity Contact With Friction

In this paper, it is considered of the three-dimensional rolling theory of the precision band of the elastic deformation, which came forth in 1982. And clarified of the landscape orientation distribution characteristic of the rolling pressure obtained by experiments, namely it shows "parabola type" "hollowware bottom type" or even "cat-ear type" of the landscape orientation distribution of the rolling pressure with the increasing of the ratio of the width and thickness. In the late ten years, the consideration of the Boundary Element Method model for the precision band coupling contact has been based on the three-dimensional elasto-plasticity frictional contact Boundary Element Method. Then it is given the quantitative description of the landscape orientation distribution of the "parabola type" and "hollowware bottom type" rolling pressure. In this paper, existence and uniqueness of the solution is proved for the three-dimensional elasto-plasticity frictional contact Boundary Element Method, and the fast computational model is set up for the strip steel contact Boundary Element Method considering the elastic deformation of the roller. As the same time, it is given the quantitative description of the landscape orientation distribution of the "cat-ear type" rolling pressure with the ratio of the width and thickness being 200.This paper is divided into five chapters. In Chapter one, the part of introduction, it is summarized of the steel and rolling production technology and the trends of the theoretical development in the twenty-first century; it is viewed vertically of the history of the development of the Boundary Element Method for the elastic contact problem, the Adaptive Boundary Element Method, the Boundary Element Method for the elasto-plasticity contact problem, network parallel algorithm for the elasto-plasticity contact problem with friction, existence and uniqueness of the solution for the contact problem with friction etc; it is viewed across of the trends of the rolling theory on the coupling deformation of the band and roller and the problems that exist; it is described of the source, the objective, the research contents and the significance. In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution. And it is proved of existence and uniqueness of the solution to the condensation matrix for the three-dimensional elasto-plasticity contact problem with friction, which settles the mathematical basis for the three-dimensional elasto-plasticity frictional contact Boundary Element Method. In Chapter three, it is given of the integrated format such as the control equation and the constructive equation for the three-dimensional elasto-plasticity frictional contact problem with fixed solution, of the discretization format, and of the determination condition format for the frictional contact based on Kuhn linear friction and the law of plasticity flow, and given of the fast network parallel algorithm on the FORTRAN language flat with many computers. In Chapter four, it is finished of the analysis of the stress field such as three-dimensional deformation of the strip steel, rolling pressure, frictional force in the rolling direction and landscape orientation, and of the consideration and the contrastive discussion of the basic phenomena and character in rolling, using the contact and coupling model of the strip steel and roller based on the three-dimensional elasto-plasticity frictional contact boundary element fast condensation and the network parallel algorithm with seven computers, under nine groups of rolling condition. In Chapter five, o...