The Optimization Solving Of Programming Multipole Boundary Element Method For The Problem Of 3D Elastic Contact With Friction

In the paper, we studied the multipole boundary element method for the problem of 3D elastic object contact with friction, introduce point to surface contact pattern with friction, and combine with mathematics programming new thought, establish the mathematics programming model for the 3D elastic object contact with friction. At the seam time, we introduce the optimization theory knowledge and the numerical technology, and conducte the research to the model solution, improve the computing efficiency for solving the contact problem with multipole boundary element method in the certain degreen, further to open up the direction of multipole boundary element method application in the large-scale project problem.The paper include five chapters, chapter 1 is the introduction,which summarizes the development of multipole boundary element method, optimization method, contact problem and the solution to the contact problem with friction, then present the source, significance of the task and the major work of the paper.In chapter 2, we introduce basic theory knowledge of the multipole expansion and the multipole boundary element method, and discusse the multipole expansion method's scope, this method renewed the traditional BEM theory and the computation structure. At the sametime, for the adaption of actual project computation question, we produce multipole boundary element method's under the rectangular coordinate system, and make the combination the multipole boundary element method's theory with practice well.In chapter 3, we introduce the basic theory of the optimization numerical technology. In view of the particularity which multipole boundary element method forms the matrix, we produces the equal problem of multipole boundary element method final forming the matix system of equation, using the conjugate direction method to solve the equal problem, and prove the existence uniqueness of its solution. Because the conjugate direction method has the merit of no need to save the iteration matrix, the faster convergence rate and quatratic termination, therefore, this method save the solution time greatly, and it is suitable for the large-scale project computation problem.In chapter 4, we introduce the basic correlation theory of mathematical programming, the contact problem and the detection model for point to surface contact pattern with friction, in combination with mathematics programming thought and multipole expension method, forms the optimization mathematics programming model for the point to surface contact with friction. This model's establishment avoive the non-linear problem for boundary condition, resovle the difficulty of the solution to contact problem with friction, it has the significant value for rolling project problem which contact surface has big slipping.In chapter 5, we introduce three solutions method to optimization mathematical programming model for the point to surface contact problem with friction, and make optimization computation example, and the mathematical theory of the multipole boundary element method for the 3D elastic contact problem with friction can be completed, the computing efficiency and precision can be improved.