Repairing,Defeaturing And Meshing Algorithms For CAD Models With The Hybrid Surface B-rep

To facilitate a numerical simulation, one needs to first prepare a geometry model and then discretise this model into a mesh. These two steps together are called the pre-processing of the simulation. For a simulation with complex configurations, both steps are major performance bottlenecks because of intensive manual interactions. Recent advances of automatic mesh generation technologies relieve the burden of mesh generation to some extent. However, in many cases, creating qualified geometry inputs for mesh generation remains an outstanding challenge.Most analysis models come from Computer Aided Design (CAD) systems. The original CAD models rarely meet the requirement of mesh generation and they need to be processed following a two-step procedure. Firstly, a CAD model is often contaminated by geometry errors, which if not rectified may collapse or invalidate the meshing procedure. Therefore, a repairing procedure is required to clean the CAD model and remove such geometry errors. Secondly, the input CAD model may contain many details for manufacturing or other purposes, but the meshing algorithm may fail to recognise them and generate badly shaped elements under larger mesh sizes than the geometry scales of the fine details. Even if the meshing algorithm captures these details and generates a mesh with acceptable quality, the total element number may increase massively due to small element sizes defined around the details. Therefore, a defeaturing step is indispensable to remove the details with minor analysis significance and ensure the output mesh can define a cost-effective analysis model.Mesh generation starts from surface meshing. In most cases, the subsequent volume meshing relies on the surface mesh only and does not access the CAD model. Therefore, to some extent, the most important step of geometry preparation is to define a clean and defeatured surface model.In the CAD and Computer Graphics (CG) communities, many methods have been proposed to depict a surface. However, the continuous representation based on NURBS, Bezier and Coons patches and the discrete representation based on triangular facets presently dominate in the community of Computer Aided Engineering (CAE). Accordingly, techniques for surface repairing and defeaturing can be categorised into two groups:those applied directly to the continuous model and those to the discrete model.Geometry computations defined on a discrete model are very efficient because the edges and facets that depict the surface have linear equations. In contrast, a continuous surface has a high-order irreversible parametric representation. Many computations define on it depend on numerically instable iterative procedures, hence more time-consuming and less reliable. Nevertheless, the continuous surface has its own strengths. Firstly, the design of most industry products is based on continuous surfaces. If the computational mesh is defined on a discrete model, the simulation accuracy may degrade due to the geometry inaccuracy of the mesh. Secondly, the continuous surface is usually organised with a boundary representation (B-rep). Many efficient defeaturing and meshing algorithms have been developed by utilising the topology entities of the B-rep. These algorithms cannot be applied on a pure discrete model that is internally organised with some edge-based data structures.In this study, we propose a new data structure namely the hybrid surface B-rep. It combines the continuous and discrete representations of surfaces. Each topology entity of the surface B-rep has a dual geometry representation in default. In addition, the mappings are maintained between the topology entities (faces, curves and points) of the B-rep and their counterparts (facets, edges and vertices) on the discrete model. The primary motivation of developing this data structure is to enrich our choices of geometry repairing, geometry defeaturing and mesh generation algorithms to serve different application purposes better. Upon this data structure, we can combine different types of algorithms in one pre-processing workflow. By contrast, most of the existing pre-processing approaches are solely based on either the discrete or the continuous model. As a result, they can only employ one type of geometry repairing, geometry defeaturing and mesh generation algorithms.More specifically, the contributions of this thesis are listed as follow.Firstly, a hybrid surface B-rep is proposed to enable the development of new algorithms that can take advantage of the prevailing geometry repairing and defeaturing algorithms for continuous and discrete surface models. This B-rep is further extended by incorporating virtual topologies to enable the virtual operations based defeaturing algorithms. Furthermore, a light-weight CAD engine is developed based on the proposed B-rep data structure. By introducing this engine as the integration middleware, a three-layer scheme is implemented to integrate our in-house CAE software High End Digital Prototyping (HEDP) with mainstream CAD software.Secondly, a novel topology generation algorithm is proposed to process CAD models with small gaps and overlaps on surface boundaries. Given a continuous surface model, its discrete representation is generated first. The dual relation of the continuous and discrete models is represented in a hybrid surface B-rep. Next, the small intersections and gaps in surface boundaries are repaired on the discrete model. Based on the dual relation of the discrete and continuous models, the lost topologies in the B-rep due to geometric errors are generated automatically. In all of the steps, geometry computations mainly occur on the discrete model. They are more reliable and efficient than their counterparts on the continuous model. More importantly, although the geometry of the continuous model remains unchanged from the very beginning, the repaired model has a valid B-rep, which enables the development of efficient defeaturing and meshing algorithms that need access the topology entities of a valid B-rep.Thirdly, to remove the surface features that prevent the generation of high-quality meshes, an automatic defeaturing approach is proposed with the aid of the hybrid surface B-rep. Four types of surface features, i.e. short edges, tiny surfaces, proximities and unsmoothed surface boundaries, are recognized, among which short edges are suppressed by edge clustering, and other features are suppressed by surface clustering. Meanwhile, virtual operations are employed in both edge and surface clustering. Meanwhile, a novel algorithm is proposed to mesh the virtual surfaces formed in the surface defeaturing step. Here, a virtual surface refers to a combination of neighboring surfaces. Since the virtual surface has no unified parametric space, the existing parametric surface meshing algorithm cannot be employed for it directly. Instead, an indirect algorithm is employed to mesh the virtual surface in this study, which firstly meshes the discrete representation of the virtual surface by reparameterising the discrete surface, and then projects the mesh points onto the continuous surface. In the second step, the hybrid surface B-rep plays a key role by providing the necessary dual relation of the continuous and discrete surfaces.