Improved Virtual Boundary Element Method

Based on the traditional virtual boundary element method based on single layer potential and superposition principle,the choice of virtual boundary position will be limited when solving some finite domain problems.There may be no solution when solving some infinite domain problems.In this paper,the shortcomings of the traditional virtual boundary element method are proved theoretically and verified by numerical examples.On this basis,the traditional virtual boundary element formula based on single layer potential and superposition principle is improved,and numerical examples are verified.In addition,an improved virtual boundary element method based on single layer potential and superposition principle is proposed,which avoids the deficiency of traditional virtual boundary element method.It is worth mentioning that this method is suitable for solving any boundary value problem.The formula of virtual boundary element formula based on single layer potential and superposition principle is that the formula of finite field problem and infinite domain problem has different forms.In Chapter 6,we study the virtual boundary element method for three-dimensional potentials and elastic thin bodies and coating problems.The specific work is:In the first chapter,the boundary element method and the virtual boundary element method are introduced,and the history of the virtual boundary element and the research status are discussed.The third and fourth chapters use the improved virtual boundary element method to study the two-dimensional potential problem respectively,and give numerical examples.The fifth chapter is to explore the plane elasticity problem by the improved virtual boundary element method.In chapter 6,the problem of three-dimensional elastic thin body and coating structure is explored by virtual boundary element method.