本文選題：網(wǎng)格生成 + 修復(fù)��； 參考：《浙江大學(xué)》2015年博士論文

【摘要】：前處理是復(fù)雜問(wèn)題數(shù)值模擬的主要性能瓶頸,涉及大量人工干預(yù),其效率嚴(yán)重依賴(lài)于用戶(hù)經(jīng)驗(yàn)�？煽扛咝У淖詣�(dòng)前處理算法是提高數(shù)值模擬效率和精度的關(guān)鍵。前處理研究主要包含2項(xiàng)內(nèi)容：網(wǎng)格生成和面向網(wǎng)格生成的CAD模型處理。進(jìn)一步細(xì)分,CAD模型處理包括模型修復(fù)和特征簡(jiǎn)化。模型修復(fù)算法負(fù)責(zé)將存在“錯(cuò)誤”的“臟”幾何轉(zhuǎn)換為滿(mǎn)足網(wǎng)格生成要求的“干凈”幾何；特征簡(jiǎn)化在模型修復(fù)之后進(jìn)行,負(fù)責(zé)消除不必要的設(shè)計(jì)細(xì)節(jié),以得到性?xún)r(jià)比更高的網(wǎng)格模型。自動(dòng)網(wǎng)格生成的研究已取得很大進(jìn)步。相比而言,自動(dòng)CAD模型處理的研究雖也受到持續(xù)的關(guān)注,但其研究現(xiàn)狀和實(shí)際需求仍有很大差距。數(shù)值模擬中,模型表面是幾何錯(cuò)誤和幾何特征最為集中的區(qū)域,模型處理后緊接著生成曲面網(wǎng)格,且通常情形下,后續(xù)的體網(wǎng)格生成以曲面網(wǎng)格生成結(jié)果為輸入,不再訪(fǎng)問(wèn)幾何模型數(shù)據(jù)�；谶@一考慮,本文的主要研究?jī)?nèi)容設(shè)定為面向曲面的CAD模型處理方法。曲面模型處理算法研究有2條平行的研究路線(xiàn),一類(lèi)基于連續(xù)曲面；另一類(lèi)基于離散曲面。商業(yè)CAD系統(tǒng)構(gòu)建的模型通�；谶B續(xù)曲面,它數(shù)學(xué)表達(dá)嚴(yán)格,幾何精度高,但定義在其上的幾何計(jì)算通常是非線(xiàn)性的,數(shù)值穩(wěn)定性差；離散曲面的基本元素為三角面片,相關(guān)幾何計(jì)算是線(xiàn)性的,快速有效,但幾何精度低。此外,離散曲面表征只涉及面片相鄰等低層拓?fù)?應(yīng)用于需高層拓?fù)渲С值牟僮鲿r(shí),需構(gòu)造連續(xù)曲面模型中常用的B-rep。本論文提出一類(lèi)混合曲面造型方法,并系統(tǒng)性地研究了幾類(lèi)基于混合曲面造型的模型修復(fù)、特征簡(jiǎn)化和網(wǎng)格生成算法。相比單純的基于連續(xù)曲面或離散曲面的方法,本論文所研究方法可兼顧兩類(lèi)方法長(zhǎng)處,在底層系統(tǒng)設(shè)計(jì)、具體算法實(shí)現(xiàn)、網(wǎng)格生成質(zhì)量等方面展現(xiàn)出獨(dú)特的優(yōu)勢(shì)。將混合CAD造型方法應(yīng)用于數(shù)值模擬前處理過(guò)程的思想對(duì)其它相關(guān)領(lǐng)域的研究有啟發(fā)作用。具體地,本文在以下3點(diǎn)上做出了創(chuàng)新：(1)為兼顧基于連續(xù)曲面和離散曲面的模型修復(fù)和特征簡(jiǎn)化方法的優(yōu)點(diǎn),提出并實(shí)現(xiàn)了混合曲面造型；繼而為支持僅改變模型拓?fù)�、不改變模型幾何定義的虛操作算法,引入虛拓?fù)?擴(kuò)展B-rep的適用能力；最后基于上述增強(qiáng)的CAD模型表征方法,從軟件工程的角度設(shè)計(jì)了一套分層的CAD/CAE系統(tǒng)集成方案,以屏蔽底層CAD數(shù)據(jù)來(lái)源和算法實(shí)現(xiàn)的多樣性對(duì)上層CAE算法的影響。(2)基于混合曲面造型方法實(shí)現(xiàn)了連續(xù)曲面的自動(dòng)拓?fù)渖伤惴?以處理曲面邊界存在曲線(xiàn)交纏和細(xì)縫等缺陷的“臟”幾何。幾何計(jì)算在離散曲面上完成；拓?fù)溆?jì)算先在離散曲面上完成,繼而利用離散曲面和連續(xù)曲面之間的基本映射關(guān)系拓展到曲面B-rep。新算法不需要修改連續(xù)曲面的幾何表征,修復(fù)后的模型滿(mǎn)足后續(xù)特征簡(jiǎn)化和曲面網(wǎng)格生成算法的要求。(3)從高質(zhì)量曲面網(wǎng)格生成的需求出發(fā),基于混合曲面表征,提出了一類(lèi)針對(duì)復(fù)雜組合參數(shù)曲面模型的自動(dòng)特征簡(jiǎn)化算法,4類(lèi)曲面特征的自動(dòng)識(shí)別和簡(jiǎn)化。特征簡(jiǎn)化涉及到的所有操作均為虛操作,不涉及復(fù)雜的幾何計(jì)算,可逆,且不改變模型的幾何定義。針對(duì)“虛面”缺乏統(tǒng)一的連續(xù)曲面參數(shù)表達(dá),無(wú)法直接復(fù)用已有網(wǎng)格生成算法的難題,提出了一類(lèi)基于混合曲面造型的虛面網(wǎng)格生成算法。新算法先獲得虛面離散模型的參數(shù)化表達(dá)；繼而擴(kuò)展連續(xù)曲面網(wǎng)格生成算法到任意參數(shù)曲面,實(shí)現(xiàn)離散曲面的網(wǎng)格化；最后基于離散模型和連續(xù)模型的映射關(guān)系,將定義在虛面離散模型上的曲面網(wǎng)格反映射回連續(xù)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.

【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：TP391.72

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本文編號(hào)：1825226