An Element Implementation Of The Boundary Face Method And Its Application In Analysis Of Complex Structures

The seamless integration of CAD and CAE is a hot research field in mechanical engineering. It has long been recongnized that the finite element method (FEM) is the most basic CAE technique. In this method, the CAE model is generated from a related CAD model by meshing tools. These two models are treated as separated modules, namely, the former is a discrete model represented by elements approximatively, while the later is a continuous model with mathematical representation. Although the CAE techniques were incorporated into the most of CAD packages, the integration of their models has not been completed in essence. Therefore, this dissertation conducts some useful researches and trials on the seamless integration of CAD and CAE in terms of theories and programming techniques on the boundary face method (BFM). Firstly, an element implementation of the BFM is proposed by using surface elements, which are located in the parametric space of a surface, resulting in the method seamlessly interacting with the boundary representation (B-rep) data. This data is used in most CAD modeling. On the other hand, design and analysis are tightly integrated into a completely unified framework by solving some related key problems. As a result, the following studies are carried out in this dissertation.(1) The BFM is implemented by using surface elements. The first implementation of the BFM is considered as a meshless method, in which the moving least-squares approximation (MLS) is employed. However, the MLS needs to perform a lot of matrix operations, thus with less efficiency. In addition, the accuracy for the MLS is dependent on the quality of the distribution of discrete nodes. For complex structures, these discrete nodes are constructed elaborately by existing background mesh. Therefore, the polynomial approximation directly based on the elements may be a better option than MLS for the BFM used in analysis of the problems with complex structures. The new implementation is much like the boundary element method (BEM), because the boundary integral equation (BIE) and elements are commonly used in both methods. However, in our implementation, surface elements are represented by parametric coordinates, which is exactly with the representation of the surface in the computer graphics. Surface elements are used only for boundary integration and variable approximation, but not for geometry approximation. The geometric data in integration elements, such as the physical coordinates and out normals, are calculated accurately from the formula of a parametric surface. As all surfaces are represented by parametric forms in the B-rep data, the computational model used in BFM can be directly based on the CAD model by using the surface elements, thus the BFM can seamlessly interact with CAD software.(2) To deal with thin structures based on three-dimension theory effectively, a novel no-linear distance transformation is proposed to compute nearly singular integrals. This uniform transformation can accurately calculate the integrals with near weak and strong singularities over different types of surface elements, such as triangular elements and quadrilateral elements with planar or curved shapes. A new local coordinate system is introduced here firstly. Its implementation is simpler than that of the polar system because the coordinate variables of the new system are limited into a fixed span. Thus, there is no need to calculate their spans over different triangular patches. The accuracy of the new method is much less sensitive to the position of the projection point than the conventional method. This is to say, our method can still obtain accurate results even if a projection point is a little far away from the ideal projection point.(3) Using C++codes, the program for automatically generating surface mesh over the solid boundary is developed. Some special C++classes are designed to performing different tasks needed in overall mesh generation, such as mesh data management, curve discretization, nodal spacing control and the implementation of any meshing method. The advancing front method (AFM) is improved and extended to application to the closed surface mesh generation as well as surface mesh with hard points or hard lines. A tool for mesh data management is developed using the standard template library (STL) in Visual C++. This tool can very efficiently handle many types of storages and queries of the mesh entities as well as their connectivity relationships. Another tool for organizing the data containing a large number of fronts in the AFM is also developed. The data, including nodes and fronts, can be update and queried quickly by this tool.(4) A kernel program framework for the element implementation of the BFM is developed and also integrated into the Unigraphics (UG) modeling system successfully. In the system, a large number of numerical examples are taken. The examples show that our method has high convergence rate and obtains high accurate results. Comparing with the conventional BEM, the BFM can provide more accurate results than the BEM, especially in the case where mesh is very coarse. Comparing with the EFM, the BFM with a smaller number of the elements can keep results with the same level of displacement accuracy with the EFM, but provides more accurate stresses than that of the EFM. In addition, our method analyzes the complicated structures with small configurations in a simply way. The problems with thin and super-thin structures of uniform or variable thickness are also solved effectively based on three-dimensional potential or elastic theory.(5) For the purpose of analysis of complex structures including small open-ended holes with better efficiency, a new tube surface element is proposed, which is located in the parametric space of a tube surface. The slender tubular hole can be represented with a small number of these elements while keeps the exact geometry. In each tube element, the field variables are interpolated by the trigonometric functions along the circumference together with a linear or quadratic polynomial functions along the longitudinal direction. To model the end faces that are intersected by the tubular holes, a special triangular element with negative parts is proposed. Using these two special types of elements, both modeling effort and computational requirements (such as memory and time) are saved substantially.