Study On Quadrilateral Mesh Generation For The Boundary Face Method And Their Implementation

The boundary face method (BFM), which is based on the boundary integral equation (BIE), inherits all advantages of the boundary element method (BEM) such as a lower computational scale of one order and abilities to solve problems on infinite domain and problems with singularities including crack propagation. In the BFM, the integration and variable approximation are both performed in the parametric space of the boundary surface. The geometric data such as coordinates, outward normals and Jacobians on integral points can be calculated directly from the parametric surface.In the conventional BEM, however, the geometric data are calculated through element interpolation,thus no geometric errors are introduced. The BFM is usually more accurate than the conventional BEM.In the implementation of the BFM, the grid generation is of great importance to the computation. The mesh in the BFM, however, is defined in the parametric space of the boundary surface. The mesh generation algorithm that is suitable for the BFM should be studied. In engineering applications, quadrilateral mesh has many advantages over the triangular mesh on both accuracy and efficiency. This paper studies the paving method, which is one of the quadrilateral mesh generation method, and its program application. The paving method is improved and extended to generate quadrilateral mesh on arbitrary surface. The improved method is implemented in the BFM to solve 3D potential problems and 3D elasticity problems.Contents of this paper are listed as follows:(1) According to the feature of the BFM and the general procedure of the paving method, a full study on the generation of the quadrilateral mesh on parametric surface has been done. The mesh generation in parametric space applying Riemann metric is emphasized. The original paving method has been improved. Moreover, mesh generation on closed surface has been studied.(2) The pre-process module for quadrilateral mesh in the BFM has been developed by using both language of the visual C++ and the secondary developing technology of the Uni-Graphics. Using the language of the visual C++, the program for quadrilateral mesh generation has been developed. Furthermore, the data management and critical problems in the mesh generation algorithm in the program has been discussed in details. By calling the functions that are available in the UG/Open API, data of the boundary represented solid model have been obtained and the final meshes have been displayed on the model.(3) BFM analyses have been performed with the mesh generated by the developed program. The quadrilateral mesh is generated in the parametric space of the boundary surface of the CAD solid models. The topology data of the original CAD geometric model are preserved. Thus the BFM has integrated CAD and CAE successfully. The BFM has been verified by numerical examples in which comparison between the numerical solution and the analytical solution was made. Furthermore, comparison study between the BFM and the finite element method (FEM) has been made to illustrate the advantages of the BFM.