Computer-aided Design And Engineering Analysis In The Numerical Manifold Method

Following a survey of classical numerical methods, this thesis puts forward a new numerical method—Patch Unit Method (PUM) based on elastics theory and the inner manifold structure of composite CAD surfaces. PUM inherits all the advantages of Finite element method (FEM), Boundary element method (BEM) and Element-free Galerkin method (EFGM), and avoids their limitations to some extent. PUM is a practical numerical method directly oriented to the CAD surface models. Algorithms concerning the calculations of PUM, such as the coupling of FEM-BEM, FEM-EFGM are also deduced in detail. In the end, a numerical example of PUM is given out and a comparison of the numerical results with ANSYS is performed, which shows that PUM is valid and reliable.The keynotes in the thesis are as follows:A manifold expression of a CAD surface model is presented. A CAD surface model is a piecewise composite surface, which is essentially a two-dimensional manifold in three-dimensional Euclidean space. So that a manifold expression of a CAD surface model is presented and analyzed according to the manifold's property of local analyticity and global connectivity.Patch Unit Method is raised out. Based on the fully analysis of the manifold structure of composite CAD surface models, PUM adopts a simple surface patch with its natural mathematical boundary as a computational unit, and regards the unit as an inner part and an outer part, then builds up relationship between the inner and outer via FE-BE/EFG-FE coupling, and the relationship among units by local FE coupling. Thus the total governing equation can be build up.Algorithms of FE-BE/EFG-FE coupling are given out. Using the weighted residual approach, the governing equations of FE-BE and FE-EFG coupling are deduced. This thesis also gives corresponding numerical examples, and the comparison of the numerical results with ANSYS shows the validity and reliability.