本文選題：四叉樹　切入點：四邊形網(wǎng)格　出處：《東北大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：網(wǎng)格生成是有限元分析中不可缺少的前處理階段,被處理對象只有在被網(wǎng)格化之后才能運用有限元方法進行求解。通常典型的適體網(wǎng)格生成方法不適于對復(fù)雜邊界進行自適應(yīng)網(wǎng)格生成,作為一種典型的非適體網(wǎng)格生成方法,笛卡爾網(wǎng)格越來越受人們的青睞。 目前,笛卡爾切割網(wǎng)格法中的邊界切割的形式僅僅局限于單邊切割,對于邊界切割單元的處理也多局限于合并處理。某些情況下不方便甚至不可能將其劃分至單邊切割的形式。此外,還存在如對于切割單元的合并處理會導(dǎo)致有限元分析中不要的懸點的產(chǎn)生等情況。 本文以上述問題為切入點,對笛卡爾切割網(wǎng)格進行了深入研究。本文首先將平衡四叉樹網(wǎng)格生成的終止條件之一修改為雙邊切割。為了便于分析和判斷,對兩線段的位置關(guān)系和網(wǎng)格類型做了詳細(xì)的分類,并給出嚴(yán)格的說明和定義；在此基礎(chǔ)上,給出了兩線段位置關(guān)系的判別算法和網(wǎng)格節(jié)點內(nèi)外類型判別方法。在判定網(wǎng)格是否被域邊切割時,創(chuàng)新性地提出了網(wǎng)格對角線標(biāo)準(zhǔn)相交判別法。 其次,本文深入研究了懸點的特點和規(guī)律,提出了懸點環(huán)和懸點鏈的概念,并用來處理初始生成的網(wǎng)格中的懸點。在這個過程中,本文給出了懸點環(huán)和懸點鏈的懸點處理模板。為進一步消除邊界頂點式懸點和小面積網(wǎng)格,本文對懸點處理后的網(wǎng)格進行了移點處理。 第三,在邊界切割處理環(huán)節(jié),本文研究了多種邊界切割情況,并從中總結(jié)出了邊界切割規(guī)律。本文提出了單邊切割和域點切割兩種基本網(wǎng)格切割類型,其他網(wǎng)格切割類型都可看成這兩種基本切割類型的組合。通過這兩種基本切割類型,本文有效地求解了三邊以下的網(wǎng)格切割,得到了8種切割單元類型。針對每種切割單元類型,本文都給出了相應(yīng)的四邊形化模板,應(yīng)用這些模板將切割單元進行四邊形化不會產(chǎn)生新的懸點,并通過多個實例驗證了其中較為常用的模板的正確性。 最后,本文采用了拉普拉斯方法對網(wǎng)格進行優(yōu)化,并將優(yōu)化后的網(wǎng)格應(yīng)用于卡門渦街和后臺階流動兩個典型的實例,驗證了本文網(wǎng)格劃分方法可行性和有效性。
[Abstract]:Mesh generation is an indispensable pre-processing stage in finite element analysis. Usually the typical adaptive mesh generation method is not suitable for adaptive mesh generation of complex boundaries, which can be used as a typical non-adaptive mesh generation method. Descartes grid is more and more popular. At present, the form of boundary cutting in Cartesian mesh method is limited to unilateral cutting. In some cases, it is not convenient or even possible to divide the boundary cutting unit into the form of unilateral cutting. In addition, There are also cases such as the combination of cutting elements will lead to the generation of unwanted suspensions in finite element analysis and so on. In this paper, the Cartesian mesh cutting is deeply studied from the above point of view. In this paper, one of the termination conditions for balanced quadtree mesh generation is first modified as bilateral cutting. The location relation and mesh type of the two segments are classified in detail, and the strict explanation and definition are given. In this paper, an algorithm for judging the position relationship between two segments and a method for judging the type of grid nodes inside and outside are presented, and a standard grid diagonal intersection method is proposed to determine whether the grid is cut by the edge of the grid. Secondly, in this paper, the characteristics and laws of suspension point are deeply studied, and the concepts of suspension ring and catenary are put forward, which are used to deal with the suspending point in the initial generated mesh. In this paper, the template of catenary processing for suspensions and catenary is given. In order to eliminate the boundary vertex suspensions and small area meshes, this paper deals with the meshes after the suspensions are processed. Thirdly, in the process of boundary cutting, this paper studies many kinds of boundary cutting, and summarizes the law of boundary cutting. In this paper, two kinds of basic mesh cutting types, single edge cutting and domain point cutting, are proposed. Other mesh cutting types can be regarded as a combination of these two basic cutting types. Eight cutting unit types are obtained. For each cutting unit type, the corresponding quadrilateral template is given in this paper. Several examples are given to verify the correctness of the more commonly used templates. Finally, the Laplace method is used to optimize the grid, and the optimized mesh is applied to two typical examples of Carmen vortex street and back step flow, which proves the feasibility and effectiveness of the mesh generation method in this paper.
【學(xué)位授予單位】：東北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH123

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