Research On The Integration Of CAE And CAD Based On Boundary Face Method

Integration of CAD and CAE has become a hot research topic in the field of engineering and scientific computing. At present, the finite element method is widely used in the commercial CAE analysis software, and the analysis model is obtained from the related CAD by grid generati on module. The expression of CAD and CAE model is different, the former is a continuous parameter model, and the latter is an approximate discrete grid model. Therefore, although a lot of CAD softwares have been added the CAE analysis module, it’s not fundamentally achieve the integration between them. Boundary face method(BFM), which is based on the boundary integral equation(BIE), has many advantages, such as usually only require to discrete the surfaces of problem domain and can employ discontinuous el ement. In BFM, the numerical integration of the boundary and the interpolation of the field variables are all carried out in the two-dimensional parameter space of the boundary surface of the geometric model. Its geometry data are directly calculated by th e parametric surface expression, rather than by piecewise polynomial interpolation approaximation. Thus, the geometric error can be avoided in BFM, which is beneficial to achieve the seamless integration of CAD and CAE. In this dissertation, based on the BFM, a series of useful exploration is made on the realization and theory of integration of CAD and CAE. The main research work and achievements are as follows:(1) In order to realize automatic surface mesh generation of complex 3D entities, a program frame work of surface mesh generation using C++ language is developed. The framework is divided into six parts, including common geometry interface module, topology recovery, mesh size field, curve discretizing, mesh data management and mesh generation methods. A unified mesh data manager is designed to facilitate the adjustment maintenance and extension of the program. In this framework, various kinds of two-dimensional mesh generation methods can be easily added and implemented. The resulting mesh cells can b e converted into elements of analysis, and can be exported to other modules(such as body mesh generation module).(2) A Delaunay method coupled with the advancing front method for automatical surface triangular mesh generation is proposed. This method usi ng the advancing front method to generate surface internal point, and then inserts the point into the mesh using Delaunay kernel interpolation algorithm. A front recognition is proposed and applied, which is divided the front into active and non-active front. Only the front meet the requirements can be used to insert a new point. Adaptive surface mesh size field is created based on surface adjacent features, and it is used as the background mesh to specify mesh size distributions, which can better reflect t he shape proximity of surface. This method can generate high quality surface mesh, and can guarantee the convergence of the surface mesh generation. At the same time, the grid method is also realized, which greatly reduces the number of surface mesh genera tion for several types of surface features.(3) For the purpose of successful surface mesh generation of welded frame structure, due to the characteristics of the BFM, a geometric topology recovery approach based on continuous surface model is proposed. Th ree types of surface features, i.e. short edges, tiny surfaces and unsmoothed surface boundaries are removed from topology. All operations involved in the topology recovery are virtual operations, and don’t change the geometric definition of the original model. Meanwhile, a hybrid grid generation method based on the grid method is proposed. It uses different mesh generation methods for different sub regions, and merges the mesh of sub regions to get the final surface mesh. Compared with traditional mesh generation method, the number of surface mesh of welded frame structure is greatly reduced.(4) A general adaptive subdivision scheme is proposed for evaluation of weakly singular integrals and nearly singular integrals in the boundary integral equations. In our method, the element is subdivided into a number of patches through a sequence of spheres with decreasing radius. The patches obtained by our method are automatically refined as they approaching the source point. And during the process of generating patches, extra points merger operation are added to ensure that each patch is “good” in shape and size for standard Gaussian quadrature. Our method is applicable to any shape of element with arbitrary location of the source point inside or outside of the element. The calculation accuracy obtained using this method are significantly improved. Moreover, in the case of asking for the same level of calculation precision, this algorithm needs much less Gauss points, thus greatly improves the calculation efficiency.(5) In the implementation of multi-domain boundary face method, a domain number optimization algorithm is proposed to reduce the bandwidth of the overall assembled matrix. Due to the sparse structure of the matrix is directly related to the ordering of unknowns in the overall system of equations, a kind of ordering strategy is adopted to obtain an optimal blocks structure. The advantage of the algorithm is to make nonzero blocks of the overall assembled matrix are as close to the main diagonal as possible. In this algorithm, one or more level structures are generated by considering the freedom degrees and the connectivity of the domains. Then the bandwidth of these level structures is calculated for each successive structure. Finally, we renumber the domains according to the level structure of the smallest bandwidth. Numerical examples demonstrate that the time used for LU-decomposition of the overall matrix and the memory requirements for storing the matrix have been reduced significantly.