The Study Of Virtual Boundary Element Method In 3D Thin Body Problems

The aim of this paper is to study the application of Virtual Boundary Element Method(VBEM)in the 3D thin body problems.The application of coating structure and thin-body structure have found an increasingly wide utilization in project,but numerical analysis is a difficult problem in the field of scientific computing domain.It is very difficult and time-consuming to estimate the integrals by the conventional boundary element when we analysis anisotropic thin-body structure involving singular and nearly singular integrals.VBEM is a nonsingular boundary element method,which can avoid dealing with nearly singular integrals successfully.It has been widely used in scientific and technical computation,while the study on the 2D coating structure and 3D thin body structure is still not enough.In this paper,an efficient analytical method is developed in VBEM for 3D thin body problems in both potential and elasticity problem are also presented.Also VBEM for 2-D thin walled structures in potential problems are researched sketchily.What's more,the study of anisotropic thin-body structure extends the application field of VBEM,which opens a new approach to deal with the anisotropic thin-body structure,as well as VBEM.Based on the virtual boundary element method,since the calculation of singular and nearly singular integrals is avoid,very promising results are obtained when the thickness of thin-body structure is in the nano-scales.In addition,this method is high efficient and simple for program design.specific work is as follows:An overview of the developing statuas and the existing problems of VBEM are presented in chapter one;In the second chapter and third chapter,the 3D thin body problems in potential and elasticity are researched by VBEM respectively,Besides,arc and elliptical elements for VBEM are developed.In the forth chapter,VBEM is used for dealing with 3D thin body problems;In the fifth chapter,2D coating structure problems in potential are researched by VBEM sketchily.Results of practical examples display the advantages of the method,which extends the application field of VBEM.