| The aim of this paper is to study the application of Virture Boundary Element Method(VBEM) in the thin body problems. Compared with Traditional Boundary Element Methodm, VBEM is a nonsingular boundary element method, which can avoid dealing with singluar and nearly singular integrals successfully. It has been widely used in the research on common structure and the solution caculated by this method is very well. However, the study on ordinary thin body can be counted on one hand. This paper provides a new approach to deal with 2D thin body in potential problems and also extends the application field of VBEM. For VBEM, the choice of distance between virtual boundary and real boundary is a key problem and may greatly affect the accuracy and reliability of the results. Numerical experiments show that fairly high accuracy of numerical results can be achieved by utilizing the formula of distance between virtual and real boundary, even when the structure is narrowed down to the thickness to length ratio in the micro (1E-6) or nano (1E-9) scales, which sufficiently indicates that VBEM is suit for solving 2D thin body problems. What’s more, this method is high efficient and simple for programm design.The specific work is as follows:The developing statuas and the existing problems of VBEM are summarized entirely in chapter one.In the second and third chapter,2D thin body problems in potential and elasticity are researched by VBEM respectively. Moreover, the formula of distance between virtual and real boundary is tesed by many numerical examples. Arc and elliptical elements for VBEM are developed in the end.The 3D thin body problems in potential and elastic problems are studied by VBEM in the fourth chapter. Besides, spherical element is proposed.In the fifth chapter, VBEM is used for dealing with 3D thin body problems in anisotropic theory, which extends the application field of VBEM. |
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