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研究生： 劉昱賢
LIU, Yu-Hsien
論文名稱： 套管式接頭中應力集中之有限元素建模
Finite Element Modeling of Stress Concentration in Jacket-Type joints
指導教授： 朱聖浩
Ju, Shen-Haw
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2025
畢業學年度： 113
語文別： 英文
論文頁數： 183
中文關鍵詞： 套管式接頭 、應力集中 、有限元素分析 、三角形與四邊形網格 、熱點應力
外文關鍵詞： Jacket-Type joints, stress concentration, finite element analysis, triangular and quadrilateral mesh, hot-spot stress
相關次數： 點閱：60  下載：0 
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    • 隨著海洋工程的快速發展，離岸風力發電機與海上平台等結構物已逐漸成為能源開發與基礎建設的核心要素。其中，管狀結構因其高強度與良好的耐腐蝕性能，在此類海洋構造中被廣泛採用。然而，長期暴露於海洋環境並承受重複載重作用，使得這些結構面臨嚴重的疲勞問題，尤其接頭區域常為應力集中與裂縫起始的關鍵位置。因此，準確掌握管狀接頭中熱點應力的分布情形，對於提升結構安全性與延長服役壽命至關重要。
    本研究旨在開發一套可廣泛應用於不同型式管狀接頭之有限元素分析軟體，並以自行撰寫之Fortran程式實現完整分析流程。程式內容涵蓋幾何建構、節點與元素生成、網格離散、邊界條件設定與載重施加，最終可輸出包含熱點應力與結構中各元素應力分布之分析結果，進而有效判別潛在疲勞破壞區域。為驗證模擬準確性，選用懸臂梁作為理論測試模型，並以基本變位理論與剪力變形理論進行比對。模擬結果顯示，在變位與正向應力估算方面均具高度一致性，證實所開發程式具備良好準確性與穩定性。於接頭模擬方面，本研究設計多組不同幾何與載重組合，涵蓋 T 型、K 型、X 型之常見接頭形式，分別施加軸力、剪力、彎矩與扭力等六種基本載重。模擬結果顯示，不同載重將導致熱點應力呈現不同的空間分布與放大倍率。此外，由於接頭區域存在幾何不連續性，主樑的應力傳遞過程中常出現震盪與不穩定現象，對接頭之疲勞評估提供了重要的設計依據與警示。
    整體而言，本研究成功整合理論分析與有限元素模擬技術，建構出一套具備參數化輸入、精準分析與靈活輸出能力之數值工具，未來可進一步應用於完整風機支撐結構與大型離岸平台之疲勞設計與壽命評估，具高度實務應用價值。
    本研究所使用的電腦輔助分析程式由朱聖浩教授研究團隊所開發，分析程式與研究成果皆為公開資源。

    With the rapid advancement of ocean engineering, offshore wind turbines and marine platforms have increasingly become critical components in energy development and infrastructure construction. Tubular structures, known for their high strength and excellent corrosion resistance, are widely adopted in such applications. However, prolonged exposure to harsh marine environments and cyclic loading conditions poses significant fatigue challenges, particularly at welded joints, which are often the critical locations for stress concentration and crack initiation. Accurately identifying the distribution of hot-spot stresses at these joints is therefore essential for ensuring structural safety and extending service life. This study aims to develop a finite element analysis (FEA) software package applicable to various types of tubular joints. A fully customized analysis workflow was implemented through a self-developed Fortran program, which includes geometry construction, node and element generation, mesh discretization, boundary condition assignment, and load application. The program outputs both the hot-spot stress distribution and the overall stress field across all structural elements, effectively identifying potential fatigue-critical regions. To verify the accuracy of the simulation, a cantilever beam was selected as a theoretical benchmark model. Comparison between numerical results and classical beam deformation and shear theory demonstrated strong agreement in terms of displacement and axial stress, confirming the high accuracy and stability of the developed code. For joint simulation, multiple geometries and loading scenarios were designed, covering common joint types such as T-, K-, and X-joints. Six basic loading conditions were applied, including axial force, shear force, bending moment, and torsion. The results show that different loads lead to varying spatial distributions and amplification levels of hot-spot stress, with shear and bending loads producing more pronounced effects. Additionally, due to geometric discontinuities in the joint regions, the main chord exhibited stress oscillations and instability during load transmission, providing critical insight for fatigue assessment and design considerations.
    In summary, this research successfully integrates theoretical mechanics with finite element simulation, developing a versatile tool featuring parameterized input, accurate computation, and flexible output. The system can be further extended for fatigue design and life prediction of complete offshore wind turbine support structures and large-scale marine platforms, offering substantial practical value.
    The analysis program used in this research was developed by Professor Shen-Haw Ju’s research team. Both the program and the research findings are released as open-source resources.

    摘要 I Abstract II Acknowledgment IV Contents V List of Tables IX List of Figures X Chapter 1 Introduction 1 1.1 Background and Purpose 1 1.2 Literature Review 2 1.2.1 Fatigue analysis using hot spot stress in Tubular Joints 2 1.2.2 Delaunay Triangulation Mesh for Finite Element Analysis 4 1.2.3 Finite Element Analysis in jacket substructure of OWTs 7 1.3 Overview 9 Chapter 2 Motivation for FE Modeling and Structural Analysis Requirements 10 2.1 Fatigue Failure Mechanisms and Analysis Methods for Tubular Joints 10 2.1.1 Comparison of Common Fatigue Analysis Approaches 10 2.1.2 The Hot-Spot Stress Method 13 2.2 Application of Finite Element Modeling in Fatigue Analysis 14 2.2.1 Geometric and Mesh Considerations for HSS Estimation 15 2.2.2 Advantages of Developing Customized Finite Element Models 15 2.3 Loading Conditions and Boundary Constraints for Local Joint Models 16 2.3.1 Definition of Boundary Constraints for Local Joint Models 17 2.3.2 Loading Conditions and Application Methods 19 Chapter 3 Discrete Points in FE Modeling 28 3.1 Points on Tubular Surfaces for Numerical Modeling 28 3.1.1 Definition of the 3D Circular Tube Equation 28 3.1.2 A Method for Determining u1 and u2 29 3.1.3 Discrete Points of the Tube Equation in 3D 31 3.2 Discrete Points at the Intersection of Two Tubes in 3D 32 3.2.1 Delete the points of the brace inside the main beam 32 3.2.2 Determination of the Discrete Points at the Intersection 35 3.2.3 Newton-Raphson Method for Intersection Points 36 3.2.4 Solve the Newton-Raphson Method starting point 37 3.3 Find points from intersection points with a or b length 39 3.3.1 A or b length on the brace 41 3.3.2 A or b length on the main beam 42 3.4 Discrete Points on the Main Beam and Braces 51 3.5 Application of the Main Program 53 Chapter 4 Triangular and Quadrilateral Meshes 55 4.1 Tube Equation in Delaunay Triangulation 55 4.2 Delaunay Triangulation Mesh Using These Discrete Points 55 4.2.1 Projecting three-dimensional points onto a two-dimensional 55 4.2.2 Generation of a Delaunay Triangular Mesh 58 4.2.3 3D Positions from the Generated 2D Triangular Mesh 64 4.2.4 Optimization of the triangulation 64 4.2.5 Flowchart of the Mesh Generation Process 65 4.3 Quadrilateral elements 66 4.3.1 Merging the majority of triangular elements 67 4.3.2 Extraction of Common Edges for Mesh Reconstruction 67 4.3.3 Record the numbers of the four points of the quadrilateral 68 4.3.4 Calculate all angles of a quadrilateral 70 4.3.5 High-Quality Quadrilaterals and Remaining Triangles 71 4.3.6 Generated Quadrilateral Mesh and Remaining Triangular Mesh 73 4.3.7 Preservation and Elimination of Midpoints on Shared Edges 74 4.3.8 Nodal Numbering of Elements 75 4.3.9 Identification of Element Types Based on Node Indexing 76 4.4 Refinement Methodology for Finite Element Models 78 4.5 Application of the Main Program in Mesh Generation 79 Chapter 5 Programs for FEA and Cantilever Beam of examples 81 5.1 Introducing the program for FEA 81 5.1.1 Input Parameters and Format Specification 81 5.1.2 The program of meshd12.exe 83 5.1.3 The program of AB.exe 83 5.1.4 The program of AD.exe 83 5.1.5 The program of AN.exe 83 5.1.6 The program of fstress.exe 84 5.1.7 Program usage flow chart 87 5.2 Program Verification Using a Cantilever Beam Example 88 5.2.1 Displacement and Normal Stress on a Cantilever Beam 89 5.2.2 Cantilever Beam Example for Displacement Validation 92 5.2.3 Further Results of Cantilever Beam Analyses 94 Chapter 6 Analysis Results and Program Integration 100 6.1 Design of Various Joint Configurations 100 6.2 Verification of Displacement Accuracy 102 6.3 Hot-Spot Stress Analysis Results 105 6.3.2 Hot-Spot Stress Analysis of Case 1 (T-Joint Configuration) 106 6.3.3 Hot-Spot Stress Analysis of Case 2 (K-Joint Configuration) 111 6.3.4 Hot-Spot Stress Analysis of Case 3 (X-Joint Configuration) 118 Chapter 7 Conclusions and Future Work 125 7.1 Conclusions 125 7.2 Future Work 126 References 128 Appendix A 131

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