基于混合曲面造型的CAD模型修复、特征简化与网络生成算法

发布时间：2018-04-30 16:07

本文选题：网格生成 + 修复　；参考：《浙江大学》2015年博士论文

【摘要】：前处理是复杂问题数值模拟的主要性能瓶颈,涉及大量人工干预,其效率严重依赖于用户经验。可靠高效的自动前处理算法是提高数值模拟效率和精度的关键。前处理研究主要包含2项内容：网格生成和面向网格生成的CAD模型处理。进一步细分,CAD模型处理包括模型修复和特征简化。模型修复算法负责将存在“错误”的“脏”几何转换为满足网格生成要求的“干净”几何；特征简化在模型修复之后进行,负责消除不必要的设计细节,以得到性价比更高的网格模型。自动网格生成的研究已取得很大进步。相比而言,自动CAD模型处理的研究虽也受到持续的关注,但其研究现状和实际需求仍有很大差距。数值模拟中,模型表面是几何错误和几何特征最为集中的区域,模型处理后紧接着生成曲面网格,且通常情形下,后续的体网格生成以曲面网格生成结果为输入,不再访问几何模型数据。基于这一考虑,本文的主要研究内容设定为面向曲面的CAD模型处理方法。曲面模型处理算法研究有2条平行的研究路线,一类基于连续曲面；另一类基于离散曲面。商业CAD系统构建的模型通常基于连续曲面,它数学表达严格,几何精度高,但定义在其上的几何计算通常是非线性的,数值稳定性差；离散曲面的基本元素为三角面片,相关几何计算是线性的,快速有效,但几何精度低。此外,离散曲面表征只涉及面片相邻等低层拓扑,应用于需高层拓扑支持的操作时,需构造连续曲面模型中常用的B-rep。本论文提出一类混合曲面造型方法,并系统性地研究了几类基于混合曲面造型的模型修复、特征简化和网格生成算法。相比单纯的基于连续曲面或离散曲面的方法,本论文所研究方法可兼顾两类方法长处,在底层系统设计、具体算法实现、网格生成质量等方面展现出独特的优势。将混合CAD造型方法应用于数值模拟前处理过程的思想对其它相关领域的研究有启发作用。具体地,本文在以下3点上做出了创新：(1)为兼顾基于连续曲面和离散曲面的模型修复和特征简化方法的优点,提出并实现了混合曲面造型；继而为支持仅改变模型拓扑、不改变模型几何定义的虚操作算法,引入虚拓扑,扩展B-rep的适用能力；最后基于上述增强的CAD模型表征方法,从软件工程的角度设计了一套分层的CAD/CAE系统集成方案,以屏蔽底层CAD数据来源和算法实现的多样性对上层CAE算法的影响。(2)基于混合曲面造型方法实现了连续曲面的自动拓扑生成算法,以处理曲面边界存在曲线交缠和细缝等缺陷的“脏”几何。几何计算在离散曲面上完成；拓扑计算先在离散曲面上完成,继而利用离散曲面和连续曲面之间的基本映射关系拓展到曲面B-rep。新算法不需要修改连续曲面的几何表征,修复后的模型满足后续特征简化和曲面网格生成算法的要求。(3)从高质量曲面网格生成的需求出发,基于混合曲面表征,提出了一类针对复杂组合参数曲面模型的自动特征简化算法,4类曲面特征的自动识别和简化。特征简化涉及到的所有操作均为虚操作,不涉及复杂的几何计算,可逆,且不改变模型的几何定义。针对“虚面”缺乏统一的连续曲面参数表达,无法直接复用已有网格生成算法的难题,提出了一类基于混合曲面造型的虚面网格生成算法。新算法先获得虚面离散模型的参数化表达；继而扩展连续曲面网格生成算法到任意参数曲面,实现离散曲面的网格化；最后基于离散模型和连续模型的映射关系,将定义在虚面离散模型上的曲面网格反映射回连续曲面。
[Abstract]:Preprocessing is the main performance bottleneck of numerical simulation of complex problems. It involves a large number of manual intervention, and its efficiency depends heavily on user experience. A reliable and efficient automatic preprocessing algorithm is the key to improve the efficiency and accuracy of numerical simulation. The preprocessing research mainly contains 2 Contents: grid generation and grid generated CAD model processing. One step subdivision, the CAD model processing includes model repair and feature simplification. The model repair algorithm is responsible for converting "dirty" geometry to "clean" geometry to meet the requirements of grid generation, and the feature is simplified after the model restoration, and it is responsible for eliminating unnecessary details to get a more cost-effective grid model. The research of automatic grid generation has made great progress. In comparison, the research of automatic CAD model processing has been paid more and more attention, but there is still a big gap between the research status and the actual demand. In numerical simulation, the model surface is the most concentrated area of geometric error and geometric feature, and the surface grid is generated after the model is processed. In general, the following body grid is generated with the result of surface mesh generation as input and no longer access to the geometric model data. Based on this consideration, the main research content of this paper is a surface oriented CAD model processing method. There are 2 parallel research routes in the study of surface model processing algorithm, one based on continuous surface and another class basis. In the discrete surface. The model constructed by commercial CAD system is usually based on continuous surface. It is strict in mathematical expression and high in geometric precision. But the geometric calculation on it is usually nonlinear, and the numerical stability is poor; the basic elements of the discrete surface are triangular facets, the related geometric calculation is linear, fast and effective, but also the geometric precision is low. Besides, the geometric precision is low. The representation of discrete surfaces only involves low level topologies such as contiguous surfaces. When applied to operations requiring high-level topologic support, a kind of hybrid surface modeling method is proposed in this paper, which is commonly used in B-rep., which is commonly used in the continuous curved surface model. Several types of model restoration based on mixed surface modeling, feature simplification and mesh generation algorithms are systematically studied. A simple method based on continuous surface or discrete surface can give consideration to the advantages of the two kinds of methods, and show unique advantages in the design of the underlying system, the implementation of the concrete algorithm and the quality of the grid generation. The idea of applying the hybrid CAD modeling method to the numerical simulation process has been studied in other related fields. In detail, this paper makes innovations in the following 3 points: (1) to give consideration to the advantages of model restoration and feature simplification based on continuous surface and discrete surface, this paper proposes and implements the modeling of mixed surfaces, and then supports virtual operation algorithm that only changes model topology and does not change model geometry definition, and introduces virtual topology to extend B. -rep's application ability; finally, based on the above enhanced CAD model characterization method, a set of hierarchical CAD/CAE system integration scheme is designed from the perspective of software engineering to shield the influence of the diversity of the underlying CAD data source and algorithm implementation on the upper CAE algorithm. (2) the automatic topology of the continuous surface is realized based on the hybrid surface modeling method. The generation algorithm is used to deal with the "dirty" geometry of defects such as curve intertwining and slit on the surface boundary. Geometric calculation is completed on the discrete surface. The topological calculation is completed on the discrete surface first. Then, the basic mapping relation between the discrete surface and the continuous surface is extended to the new algorithm of the surface B-rep. without modifying the continuous surface. What is the representation, the repaired model satisfies the requirements of subsequent feature simplification and surface mesh generation algorithm. (3) based on the requirement of high quality surface mesh generation, based on the mixture surface characterization, an automatic feature simplification algorithm for complex composite parametric surface models is proposed, and the feature simplification and simplification of the 4 types of surface features are simplified. All operations are virtual, and do not involve complex geometric calculations, reversible, and no change in the geometric definition of the model. A new algorithm for virtual surface grid generation based on mixed surface modeling is proposed for the problem that the "virtual surface" is lack of unified continuous surface parameter expression and can not directly reuse existing grid generation algorithms. The parameterized expression of the virtual surface discrete model is obtained, and then the continuous surface mesh generation algorithm is extended to the arbitrary parametric surface, and the discrete surface is meshed. Finally, based on the mapping relationship between the discrete model and the continuous model, the surface mesh defined on the virtual surface discrete model reflects the ejection of the continuous curved surface.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP391.72

【参考文献】