An Algorithmic Approach to Generate Hexahedral Mesh on Thin-shell Models by Recognizing Face Type and Decomposing Volume

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游狄歐(Pradiktio Putrayudanto) 查詢紙本館藏

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機械工程學系

論文名稱

(An Algorithmic Approach to Generate Hexahedral Mesh on Thin-shell Models by Recognizing Face Type and Decomposing Volume)

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摘要(中)

薄殼零件通常因為其複雜的幾何結構而採用模具製造或鑄造技術。這些零件的厚度與寬度（或長度）比通常較小，並且具有突起特徵以增強其機械性能。然而，由於薄殼結構的複雜性，使用傳統有限元素法進行模擬會面臨挑戰。儘管四面體網格元素能夠處理複雜的幾何形狀，但與六面體網格元素相比，其計算成本較高。即便如此，目前的六面體網格生成演算法仍然限於較簡單的基本形狀，且手動體積分解方法—雖然在某些情況下有效—卻可能引入錯誤。本研究旨在解決自動化薄殼結構六面體網格生成的挑戰，提出一種能夠有效處理複雜幾何結構的演算法。此過程首先是對模型進行分類，並識別薄殼零件每個面類型。薄殼模型根據幾何形狀和拓撲結構可分為規則型和不規則型。完成分類後，演算法會生成簡化幾何形狀並有助於體積分解的（cap face）。本研究還引入了突起特徵圖（Protrusion Feature Graph, PFG），以協助有效地生成這些蓋面。接著，通過利用蓋面進行模型的分割與合併，生成子體積。本研究提出了兩種六面體網格生成方案：一種是使用 CUBIT，另一種是使用 Moldex3D。CUBIT 允許完全自動化生成六面體網格，無需進行額外的幾何編輯；而 Moldex3D 提供了類似的過程，但目前僅限於單一來源和單一目標方案。為了測試演算法的效能，本研究提出了35個面類型識別的測試案例以及8個體積分解與網格生成的測試案例，涵蓋各種幾何形狀和拓撲結構。

摘要(英)

Thin-shell parts are often produced using molding or casting techniques due to their complex geometry. These parts typically feature a small thickness-to-width (or length) ratio and include protrusions that enhance their mechanical properties. However, simulating such thin-shell structures using traditional finite element methods is challenging due to their complexity. While tetrahedral mesh elements can accommodate complex geometries, they come with a high computational cost compared to hexahedral meshes. Despite this, current hex mesh generation algorithms are limited to simpler, primitive shapes, and manual volume decomposition—while effective in some cases—can introduce errors. This research addresses the challenge of automating hexahedral mesh generation for thin-shell structures by proposing an algorithmic approach that effectively handles complex geometries. The process begins with classifying the model and identifying face types for each face of the thin-shell part. Thin-shell models are classified into regular and irregular categories based on their geometry and topology. Once classification is complete, the algorithm generates "cap faces" that simplify the geometry and aid in volume decomposition. A protrusion feature graph (PFG) is also introduced to help create these cap faces efficiently. The model is then split and merged using the cap faces to generate subvolumes. Two schemes for hex mesh generation are proposed: one using CUBIT and the other using Moldex3D. CUBIT allows for fully automated hex mesh generation without requiring additional geometry edits, while Moldex3D offers a similar process, though it is currently limited to single-source, single-target schemes. To test the algorithm′s performance, 35 test cases for face type recognition and 8 test cases for volume decomposition and mesh generation, covering a range of geometries and topologies, are presented.

關鍵字(中)

★ 薄殼部件
★ 劃分
★ cap face
★ 六面體網格

關鍵字(英)

★ thin-shell part
★ decomposition
★ cap face
★ hex mesh

論文目次

TABLE OF CONTENTS
提要 i
ABSTRACT ii
LIST OF FIGURES vi
LIST OF TABLES xi
EXPLANATION OF SYMBOLS xii
CHAPTER I INTRODUCTION 1
1.1 Background 1
1.2 Literature Review 2
1.2.1 Recognizing face types 2
1.2.2 Decomposing volume 4
1.2.3 Constructing solid hex mesh 6
1.3 Proposed Study 6
1.4 Research method 7
1.4.1 Preliminary computation 10
1.4.2 Face type recognition 10
1.4.3 Subvolume generation 12
1.4.4 Mesh Generation 12
1.5 Dissertation Structure 14
CHAPTER II FACE TYPES RECOGNITION 16
2.1 Inner and outer regions separation 19
2.1.1 Initial categorization 19
2.1.2 Group category evaluation 21
2.1.3 Transition edge construction 22
2.1.4 Further evaluation of segregating inner/outer region 25
2.2 Applying transition face types 27
2.3 Classifying thin-shell model 35
2.4 Assigning inner face type for regular model 37
2.4.1 Wall face type recognition 39
2.4.2 Bottom face type recognition 40
2.4.3 Step-wall face type recognition 42
2.4.4 Protrusion face type recognition 43
2.5 Assigning Surface Attributes for irregular model 46
2.5.1 Classifying the type of irregular model 46
2.5.2 First type of irregular model face attributes 47
2.5.3 Second type of irregular model face attributes 47
2.5.4 Third type of irregular model face attributes 47
CHAPTER III VOLUME DECOMPOSITION 50
3.1 Cap face generation 50
3.1.1 Overview of cap face 50
3.1.2 Group face data for cap face 54
3.1.3 Vertex component of cap face 55
3.1.4 Edge component of cap face 61
3.1.5 Face component of cap face 64
3.1.6 Overview of protrusion feature graph 65
3.1.7 Composing protrusion feature graph 68
3.2 Sub-volume generation 79
3.2.1 Stage one decomposition 81
3.2.2 Stage two decomposition 82
CHAPTER IV MESH GENERATION 88
4.1 Mesh generation using CUBIT 88
4.2 Proposed method for mesh generation 89
4.2.1 The framework of the proposed method 89
4.2.2 The sweepability check 94
4.2.3 Determining node location using map algorithm 95
4.2.4 Determining node location using submap algorithm 95
4.2.5 Hex mesh generation using Moldex3D 98
CHAPTER V RESULTS & DISCUSSION 99
5.1 The results of face type recognition 99
5.2 Results of subvolumes decomposition 104
5.3 Results of mesh generation 106
CHAPTER VI CONCLUSION 133
6.1 Conclusion 133
6.2 Future work 135
REFERENCE 136

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指導教授

賴景義(Jiing-Yih Lai)

審核日期

2024-12-31

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