本文選題：網(wǎng)格生成 + 單元尺寸場�。� 參考：《溫州大學(xué)》2017年碩士論文

【摘要】：網(wǎng)格生成是有限元分析的前置處理環(huán)節(jié),也是其主要性能瓶頸。為控制網(wǎng)格規(guī)模的同時保證后續(xù)分析的精度,網(wǎng)格生成算法需借助單元尺寸函數(shù),在問題域的不同位置布置不同尺寸的單元,以適應(yīng)幾何特征和物理量梯度在問題域的變化。給定的初始單元尺寸場通常不滿足光滑過渡的要求,距離靠得很近的點其單元尺寸值相差很大,其間不可避免會產(chǎn)生質(zhì)量很差的網(wǎng)格單元。因此,單元尺寸場光滑化是有限元網(wǎng)格生成研究的重要課題。已有方法主要利用直角背景網(wǎng)格定義尺寸場,存在背景網(wǎng)格規(guī)模過于龐大、相應(yīng)算法時空效率不佳等缺陷�；诜墙Y(jié)構(gòu)網(wǎng)格自動以及自適應(yīng)生成能力高這一特點,本文選用非結(jié)構(gòu)背景網(wǎng)格定義尺寸場,研究了相應(yīng)的尺寸場光滑化方法。主要工作包含兩個方面:(1)基于合理的基本假設(shè),將單元尺寸場在直線域、三角形域過渡受控的數(shù)學(xué)條件拓展到四面體域。繼而以最小化尺寸場的變化為目標(biāo),以尺寸場在三維體域過渡受控為約束,建立了適用于尺寸場光滑化問題的優(yōu)化模型。證明了模型的凸性和唯一最優(yōu)解的存在性。(2)基于內(nèi)點法開發(fā)了優(yōu)化模型的數(shù)值求解算法,并應(yīng)用算法于幾何自適應(yīng)尺寸場的光滑化。結(jié)合初始幾何自適應(yīng)尺寸場計算、Delaunay網(wǎng)格生成等算法,實現(xiàn)了一套幾何自適應(yīng)四面體網(wǎng)格全自動生成軟件流程。數(shù)值實驗表明,和已有也基于非結(jié)構(gòu)背景網(wǎng)格的經(jīng)典方法相比,新方法成功解決了 H-Correction方法無法保證單元尺寸場在背景單元內(nèi)光滑過渡(導(dǎo)致最終網(wǎng)格包含一定數(shù)量的低質(zhì)量過渡單元),以及GradH-Correction算法改動初始尺寸場過于劇烈(導(dǎo)致最終網(wǎng)格單元大范圍“過度細(xì)化”)等缺陷。
[Abstract]:Mesh generation is not only the preprocessing of finite element analysis, but also the main bottleneck of its performance. In order to control the size of the grid and ensure the accuracy of the subsequent analysis, the mesh generation algorithm needs to use the element size function to arrange different size elements in different positions of the problem domain, so as to adapt to the variation of the geometric characteristics and the gradient of physical quantities in the problem domain. The given initial element size field usually does not satisfy the requirement of smooth transition, and the size of the element is very different from the point close to it, so it is inevitable that the quality of the mesh element will be very poor. Therefore, the smoothing of element size field is an important topic in the research of finite element mesh generation. The existing methods mainly use right-angle background mesh to define the size field, which has some defects such as the large scale of background grid and the inefficient spatio-temporal efficiency of the corresponding algorithm. Based on the characteristics of automatic and adaptive generation of unstructured meshes, this paper uses unstructured background meshes to define dimension fields, and studies the corresponding smoothing methods of dimension fields. The main work includes two aspects: (1) based on the reasonable basic assumptions, the mathematical conditions of the transition control of the element size field in the straight line domain and the triangular domain are extended to the tetrahedron domain. With the objective of minimizing the change of the size field and the constraint of the transition of the size field in the three-dimensional volume domain, an optimization model for the smoothing of the size field is established. The convexity of the model and the existence of the unique optimal solution are proved. (2) based on the interior point method, the numerical solution algorithm of the optimization model is developed, and the algorithm is applied to the smoothing of the geometric adaptive size field. Based on the algorithm of Delaunay mesh generation based on the initial geometric adaptive dimension field, a set of automatic generation software flow of geometric adaptive tetrahedron mesh is implemented. Numerical experiments show that, compared with the classical methods based on unstructured background meshes, The new method successfully solves the problem that the H-Correction method can not guarantee the smooth transition of the element size field in the background element (resulting in the final grid containing a certain number of low-quality transition units), and the GradH-Correction algorithm changes the initial size field too violently. Resulting in the ultimate grid cells in a wide range of "excessive refinement") and other defects.
【學(xué)位授予單位】：溫州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 鄭耀;鄭建靖;陳建軍;解利軍;黃爭舸;楊永健;鄒建鋒;;高端數(shù)字樣機(jī)系統(tǒng)的前處理用戶環(huán)境[J];計算力學(xué)學(xué)報;2012年01期

2 陳建軍;黃爭舸;楊永健;鄭耀;鄭建靖;;復(fù)雜外形的非結(jié)構(gòu)四面體網(wǎng)格生成算法[J];空氣動力學(xué)學(xué)報;2010年04期

3 梁義;陳建軍;陳立崗;鄭耀;;幾何自適應(yīng)參數(shù)曲面網(wǎng)格生成[J];計算機(jī)輔助設(shè)計與圖形學(xué)學(xué)報;2010年02期

相關(guān)博士學(xué)位論文 前2條

1 陳立崗;面向工程與科學(xué)計算的表面網(wǎng)格處理方法的若干問題研究[D];浙江大學(xué);2008年

2 單菊林;自適應(yīng)有限元網(wǎng)格生成算法研究與應(yīng)用[D];大連理工大學(xué);2007年

，

本文編號：2098543