Research On The Method Of Discretization And Numeric Algorithm For Elasto-Plastic About FM-BEM

In this paper, we study 3D fast multipole boundary element method (FM-BEM) for potential problems and 3D FM-BEM for elastic problems, the singular integrals in 3D FM-BEM for potential problems and elastic problems can be dealt with. Mathematical theory of numerical computation was studied for the elasto-plastic FM-BEM. Some computational formulations were presented for the elasto-plastic FM-BEM. In spherical coordinate system, related formulations of third-order partial derivatives were obtained and converted into 27 ones with rectangular coordinates. Due to its high efficiency and low computing memory demanding, the above method makes the large-scale computing possible.The Paper includes five chapters. Chapter 1 is introduction, which summarizes the development of BEM, Fast multipole method (FMM), and FM -BEM, then presented the source, significance of the task and the major work of the paper.In chapter 2, we introduce the fast multipole expansion and the fast multipole boundary element method basic theory knowledge, and it establishes the foundation of the fast multipole expansion method fuses with BEM form and the followlling to study FM-BEM; also we illustrate the key combinational point that between FMM and BEM simply.In chapter 3, discrete formulations of the BIE for the 3D potential problem FM-BEM is given, and the method of solving the singularity in 3D potential FM-BEM can be obtain . Also, we get the new discrete formulations without singularity for potential problem.In chapter 4, discrete formulations of the BIE for the 3D elastic problem FM-BEM is given, and the method of solving the singularity in 3D elastic FM-BEM can be obtain . Also, we get the new discrete formulations without singularity for elastic problem.In chapter 5, mathematical theory of numerical computation was studied for the elasto-plastic FM-BEM. Some computational formulations were presented for the elasto-plastic FM-BEM. In spherical coordinate system, related formulations of third-order partial derivatives are obtained and Converted into 27 ones with rectangular coordinates. These numerical formulations established strong mathematical foundation for the FM-BEM solution of elasto-plastic and plastic problems in the rolling engineering field and in other fields.