博碩士論文 111323098 詳細資訊




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姓名 蔡敬崙(Ching-Lun Tsai)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 四邊形網格自動建構之網格品質改善研究
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摘要(中) 在電腦輔助工程(Computer aided engineering)分析中,需要將CAD模型轉換成實體網格(Solid mesh),提供求解器(Solver)進行計算,與傳統四面體網格相比,六面體網格被認為是品質最佳的網格類型,但人工構建過程耗時耗力且難以保證一致性。在建構六面體網格前需生成四邊形表面網格,因此本實驗室進行四邊形網格自動建構技術之開發,但該技術中仍有些許問題及可改進的空間。網格相交是自動建構四邊形網格的一大挑戰,該狀況會導致網格建構失敗,本研究針對各種可能的相交情形,設計了檢測和處理方法,確保網格正確無誤地建構。另外,本研究開發了一套品質計算方法,包含最小角度、展弦比、長寬比及平行偏差指標,用於評估整體網格之品質,也讓使用者能偵測品質不佳的網格並進行改善。本研究運用上述方法對建構技術的參數進行測試,比較各參數建構後之網格品質,以求得最佳參數。另外本研究也對建構完成的網格進行品質改善,透過多種方法進行改良,測試的六個案例中,最小內角及最差1%角度平均值均有顯著的提升。各案例中最小內角的數值最少有30.73°的提升,而各案例中最差1%角度平均值則提升89.7%至140.8%不等,證明本研究可有效提升整體網格之品質。
摘要(英) In computer aided engineering analysis, it is necessary to convert CAD models into solid meshes to provide solvers for computation. Compared to traditional tetrahedral meshes, hexahedral meshes are considered the best type. However, the manual construction process is long and laborious, and it is difficult to ensure consistency. Before constructing hexahedral meshes, it is necessary to generate quadrilateral surface meshes. Therefore, our laboratory is developing an automatic construction technique for quadrilateral meshes, but there are still some problems and room for improvement in this technique. Mesh intersection is a major challenge in automatically constructing quadrilateral meshes, which can lead to mesh generation failure or even program crashes. This study designed detection and processing methods for various possible intersection situations to ensure that meshes are generated correctly. Additionally, this study developed a set of quality calculation methods, including minimum angle, aspect ratio, edge ratio, and Parallel Deviation. This method evaluate the overall mesh quality and allow users to detect and improve poor-quality meshes. This study tested the construction technique′s parameters using the above methods, comparing the mesh quality after construction with different parameters to obtain the optimal parameters. Furthermore, this study also improved the quality of the constructed meshes through various methods. Among the six test cases, the minimum angle and the average of the worst 1% angle showed significant improvements. The minimum angle increased by at least 30.73 degrees, and the average of the worst 1% angle improved by 89.7% to 140.8%, depending on the cases, proving that this study can effectively enhance the overall mesh quality.
關鍵字(中) ★ 四邊形網格
★ 自動化網格建構
★ 網格相交處理
★ 網格品質量測
★ 網格品質改善
關鍵字(英) ★ Quadrilateral mesh
★ Automatic mesh construction
★ Mesh intersection handling
★ Mesh quality measurement
★ Mesh quality improvement
論文目次 摘要. . . . . . . . . .i
Abstract. . . . . . . . . .ii
致謝. . . . . . . . . .iii
目錄. . . . . . . . . .iv
圖目錄. . . . . . . . . .vii
表目錄. . . . . . . . . .xi
第一章 緒論. . . . . . . . . .1
1.1 前言. . . . . . . . . .1
1.2 文獻回顧. . . . . . . . . .1
1.2.1 網格建構. . . . . . . . . .1
1.2.2 網格品質量測與改善. . . . . . . . . .3
1.3 研究目的. . . . . . . . . .4
1.4 研究方法. . . . . . . . . .5
1.5 論文架構. . . . . . . . . .6
第二章 四邊形網格自動建構之網格相交偵測與處理. . . . . . . . . .7
2.1 前言. . . . . . . . . .7
2.2 四邊形網格建構方法整體流程概述. . . . . . . . . .7
2.2.1 網格建構流程. . . . . . . . . .9
2.2.2 建構過程問題介紹. . . . . . . . . .17
2.3 「初始尖角與微小圓弧處理」(S2). . . . . . . . . .20
2.4 「迴圈間網格相交預測與迴圈合併」(S9). . . . . . . . . .24
2.4.1 迴圈間網格相交狀況預測. . . . . . . . . .27
2.4.2 迴圈合併方法. . . . . . . . . .30
2.5 「迴圈內網格自交預測與迴圈分割」(S10). . . . . . . . . .34
2.5.1 迴圈內網格自交狀況預測. . . . . . . . . .34
2.5.2 迴圈分割方法. . . . . . . . . .38
第三章 網格品質指標與網格相交偵測之參數影響. . . . . . . . . .47
3.1 前言. . . . . . . . . .47
3.2 四邊形網格品質檢測程式介紹. . . . . . . . . .48
3.2.1 四邊形網格各項品質數值指標介紹. . . . . . . . . .48
3.2.2 指標數值檢測方法說明. . . . . . . . . .49
3.3 「迴圈間網格相交預測與迴圈合併」參數調整與網格品質之關聯性. . . . . . . . . .71
3.4 「迴圈內網格自交預測與迴圈分割」參數調整與網格品質之關聯性. . . . . . . . . .78
第四章 四邊形網格品質改善方法. . . . . . . . . .83
4.1 前言. . . . . . . . . .83
4.2 品質改善整體方法說明. . . . . . . . . .83
4.3 網格結構改善. . . . . . . . . .89
4.3.1 「相鄰兩節點含有三相鄰網格」. . . . . . . . . .89
4.3.2 「兩節點位於六個節點內部」. . . . . . . . . .91
4.3.3 「四節點位於八個節點內部」. . . . . . . . . .93
4.3.4 「一節點相鄰兩網格」. . . . . . . . . .96
4.3.5 網格結構改善後品質比較. . . . . . . . . .96
4.4 網格平滑化. . . . . . . . . .99
4.4.1 「所有網格平滑化」. . . . . . . . . .100
4.4.2 網格平滑化後品質比較. . . . . . . . . .102
4.5 網格最小內角改善. . . . . . . . . .104
4.5.1 「調整最小內角網格」. . . . . . . . . .104
4.5.2 網格最小內角改善後品質比較. . . . . . . . . .108
4.6 品質改善結果分析. . . . . . . . . .108
第五章 結論與未來展望. . . . . . . . . .111
5.1 結論. . . . . . . . . .111
5.2 未來展望. . . . . . . . . .112
參考文獻. . . . . . . . . .114
參考文獻 參考文獻
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指導教授 賴景義(Jiing-Yih Lai) 審核日期 2024-7-9
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