The Study On The Theory And Application Of Manifold Method

The manifold method(MM),a prosperous numerical method based on the finite cover,is a very flexible numerical analysis method which can uniformly deal with calculating problems of the widely used finite element method(FEM), discontinuous deformation analysis(DDA) and analytic method.The main works of this dissertation are to adopt the standard rectangle,the traditional finite elements and the overlapping sectors to construct the cover system in MM,and apply MM to the linear analysis of two-dimensional continuous bodys and the simutation of open crack propagation. First of all,the rectangular meshes are chosen as the cover system of MM. Some pivotal techniques in MM such as the implemetion of essential boundary conditions, the selection of weight functions, the computation method of high precision stress,the numerical integration of manifold element and the influence of the high-order displacement functions are discussed in detail.Because the standard rectangular meshes are uniformly used for complex bodys,this method has the advantages of easy implementing,applying and incorporating with the CAD technology. For the proposed theory and method,the objected oriented programming is introduced into the program designing in MM.By abstracting the finite cover system of MM as independent data classes,the design and implemention of the objects about MM are studied,in which the objects are managed by techniques of tree structure.For complex area with arbitrary shape,the cover system of MM have been automatically generated by using these objects and trees. By applying contour integral method and high-order displacement functions of MM,we obtain the accurate stress intensity factors of mixed-mode crack.Then, the open crack propagation of the mixed mode I and II is simulated by means of theories of linear elastic fracture mechanics.This provides a simple and effective numerical way for crack evolvement studying. In addition,based on the theory of manifold cover and moving least squares (MLS),an improved formulation of the element-free method(IEFM) is introduced. The proposed method can avoid the element meshing and simplify the construction of approximations in the field by using the discrete circle and sector covers.IEFM can also be regarded as a special form of MM.By close comparison with other meshless methods,IEFM has advantages of low computation cost,simple form and easy programming.