Analysis Of Boundary Layer Effect Of Anisotropic Problem By Boundary Element Method

Anistropic materials are applied widely in machining field and in cutting edge technology about national defense. Boundary element method, an important numerical method, is playing a more and more important role in numerical simulation and engineering simulation.However, traditional boundary element method has to confront with a hard problem which needs to calculate singular integral and nearly singular integral, especially about the latter, and limits, to a large extent, application of boundary element method in engineering problems. In this thesis, nearly singular integral is discussed and the root cause is analysized, nonlinear varialble substitutions method is introduced, which increases calculation accuracy and broadens the range of application in actual situations.The tasks the thesis finishes are:In the first chapter, the development of boundary element method, and especially caclation method about singular integral and nearly singular integral are summarized.In the second chapter, the root reasons are analysized and efficient nonlinear variable substitutions are introduced in order to eliminate nearly singular integral about kernel function.In the third chapter, discrete scheme about boundary element method is discussed in detail by giving two examples, two-demensioanal anisotropy potential problems and orthogonal anisotrop orthotropic elastic problems. Moreover, to solve boundary layer effect problem, physical parameters near boundary points are calculated accurately through the algorithm.