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研究生： 鄭育家
Zheng, Yu-Jia
論文名稱： 基於三維高階實體元素之離岸管狀接頭應力集中分析與經驗公式建立
Stress Concentration Analysis and Empirical Formula Development for Offshore Tubular Joints Using 3D High-Order Solid Elements
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： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 396
中文關鍵詞： 離岸結構 、管狀接頭 、高階實體元素 、熱點應力法（HSS） 、應力集中因子（SCF） 、拉丁超立方抽樣（LHS） 、乘冪法則迴歸分析 、二階響應面法（RSM）
外文關鍵詞： Offshore structures, Tubular joints, Higher-order solid elements, Hot-spot stress (HSS), Stress concentration factor (SCF), Latin hypercube sampling (LHS), Power-law regression analysis, Second-order response surface methodology (RSM)
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    • 隨著離岸結構朝向深海化與大型化發展，其鋼管接頭交線處的疲勞評估成為核心課題。傳統 2D 薄殼模型無法精確捕捉三維應力梯度；若採用 3D 高階實體元素模型，管狀接頭的相交幾何邊界常面臨拓撲失效。
    為此，本研究開發基於 3D 高階實體元素與熱點應力法特徵線佈設的「參數化自適應管狀接頭網格生成與自動化應力集中分析」。由自行撰寫Fortran程式建構出高階實體元素網格；有限元素法求解與後處理階段則整合 Fortran 求解器與 Python 系統，實現 3D 應力張量提取、投影及表面應力外插。
    網格收斂性測試與 DNV 規範進行對照驗證，結果顯示本模型能準確解出陡峭的應力梯度，並證實 3D 實體模型在捕捉熱點應力全周方位角分佈上的物理真實性。
    最後，本研究運用約束型拉丁超立方抽樣進行多維參數採樣，透過有限元素法建立T/Y、X、對稱 K、對稱 KT 型接頭型態在軸力、面內與面外彎矩負載下的應力集中因子數據庫。迴歸分析表明，乘冪法則在全域綜合模型中展現高穩健性；使用二階響應面法捕捉非線性與參數交互作用，能獲得比乘冪法則更精準之經驗公式，在 KT 型接頭中凸顯了多支管參數交互作用的重要性。
    本研究建立之兩種新型 SCF 經驗公式，擴展了傳統規範適用範疇，為離岸風機管狀接頭的結構疲勞評估提供高精度之數值決策框架。本研究所使用之有限元素分析程式由朱聖浩研究團隊所開發，分析軟體與研究成果皆為公開資源。

    As offshore structures trend toward deeper waters and larger scales, fatigue assessment at the intersections of tubular joints has become a critical issue. Traditional two dimensional (2D) thin-shell models fail to accurately capture three-dimensional stress gradients, whereas three dimensional (3D) higher-order solid element models frequently encounter topological failures at the complex intersecting geometric boundaries of tubular joints.
    To address these challenges, this study develops a “Parametric Adaptive Mesh Generation and Automated Stress Concentration Analysis Framework for Tubular Joints” based on 3D higher-order solid elements and the feature-line layout of the hot-spot stress (HSS) method. A self-written Fortran program is utilized to construct the higher-order solid element mesh. For the finite element analysis (FEA) solving and post-processing stages, a Fortran solver is integrated with a Python system to achieve seamless execution of 3D stress tensor extraction, tensor projection, and surface stress extrapolation.
    Mesh convergence tests and cross-validation against DNV standards demonstrate that the proposed model accurately resolves steep stress gradients, confirming the physical authenticity of the 3D solid model in capturing the full-circumferential azimuthal distribution of HSSs.
    Finally, this study employs constrained Latin Hypercube Sampling (LHS) for multi-dimensional parametric sampling, establishing an extensive stress concentration factor (SCF) database via FEA for T/Y, X, balanced K, and balanced KT tubular joints under axial force, in-plane bending (IPB), and out-of-plane bending (OPB) loads. Regression analysis shows that the power-law model exhibits high robustness as a global comprehensive framework. Moreover, implementing the second-order response surface methodology (RSM) to capture nonlinearities and parametric interactions yields empirical formulas with superior accuracy compared to the power-law model, particularly highlighting the significance of multi-brace parametric interactions in KT-joints.
    The two types of novel empirical SCF formulas established in this study effectively extend the scope of traditional regulatory standards, providing a high-precision numerical decision-making framework for the structural fatigue assessment of offshore wind turbine tubular joints. The finite element analysis program used in this study was developed by Professor Shen-Haw Ju’s research team, and both the analysis software and the research findings are publicly available resources.

    摘要 i Abstract ii Acknowledgment iv Contents v List of Tables xv List of Figures xviii List of Listings xxiv List of Appendix A: Figures and Tables xxv A.1 List of Tables xxv A.2 List of Figures xxvi Chapter 1 Introduction 1 1.1 Background 1 1.2 Motivation and Purpose 2 1.3 Literature Review 4 1.3.1 Development and Limitations of Traditional Stress Concentration Factor Parametric Equations 4 1.3.2 Evolution of the Hot-Spot Stress Method 5 1.3.3 Finite Element Modeling and Mesh Challenges of Complex Tubular Joints 6 1.3.4 Design of Computer Experiments and Latin Hypercube Sampling Strategy for Data Post Processing 8 1.3.5 Structural Parametric Analysis and Non-linear Regression Models 10 1.4 Overview 11 Chapter 2 Hot-Spot Stress and Finite Element Analysis Theory 14 2.1 Fatigue Failure Mechanisms and Stress Concentration in Offshore Structures 14 2.1.1 Cyclic Loading and Welded Joint Vulnerability 14 2.1.2 Classification and Geometric Characteristics of Tubular Joints 15 2.1.2.1 Non-dimensional Geometric Parameters: 17 2.1.3 Geometric Stress Concentration and Hot-Spot Stress 19 2.2 Hot-Spot Stress Method 21 2.2.1 Classification of Stresses: Nominal, Hot-Spot, and Notch Stress 21 2.2.2 Surface Stress Extrapolation Method and Readout Location Regulations 22 2.2.3 Local Coordinate System and Stress Tensor Transformation 24 2.2.4 Component-Based Extrapolation and Equivalent Hot-Spot Stress Calculation 26 2.3 Comparison of Finite Element Modeling Strategies: Plate/Shell vs. 3D Solid Elements 28 2.3.1 Fundamental Concepts of the Finite Element Method 28 2.3.2 Constitutive Equations and Three-Dimensional Stress States 29 2.3.3 Geometric Representation of Weld Profiles and Notch Effects 30 2.3.4 Objectivity in DNV Extrapolation Compliance 31 2.4 Three-Dimensional High-Order Solid Element Theory 32 2.4.1 20-Node Hexahedral and 15-Node Wedge Higher-Order Elements 33 2.4.2 Coordinate Transformation, Strain-Displacement Relations, and the Jacobian Matrix 34 2.4.3 Material Constitutive Relations and Full Gaussian Quadrature Integration 35 2.4.4 Objectivity of Stress Extraction Utilizing Quadratic Shape Functions 36 2.5 Regulatory Standards and Sensitivity Analysis of S-N Curves 37 2.5.1 DNV-RP-C203 Fatigue Design Framework 37 2.5.2 Correlation Between S-N Curves and SCF Accuracy 38 Chapter 3 Mesh Generation and Mechanical Pre-processing for Tubular Joints 40 3.1 Parametric Framework of Guide Surface Mesh 40 3.1.1 Initial Mesh of Chord Surface 41 3.1.2 Decoupled Geometric Pipeline and Postponement of Brace Discretization 44 3.2 Development of 2D Surface Mesh with Improved Geometric Solver 45 3.2.1 Analytical Derivation and Geometric Screening of the Spatial Intersection Line 45 3.2.2 Mathematical Definition and Spatial Construction of Weld-Toe (W-), A-, and B-Curves 51 3.2.3 2D Surface Flattening and Delaunay Triangulation for Multi-brace Openings 57 3.2.4 Structural Mesh Reconstruction Between Feature Curves I and B on Chord 60 3.2.5 Transition from 2D Mesh to 3D Solid Model 62 3.3 Theoretical Basis of High-Order Solid Mesh Configuration and Compliance with International Standards 63 3.3.1 Layer Configuration in the Thickness Direction and Equivalency Analysis with Thin-Shell Theory 64 3.3.2 Precise Alignment of Feature Lines and Immunity to Mesh Aspect Ratio Constraints 65 3.4 Macro Surface Nodal Expansion and High-Resolution Feature Line Capture Strategy 66 3.4.1 Micro-subdivision for High-density Corner Nodes 67 3.4.2 Global Tag Management of Multi-regional Mesh 68 3.4.3 High-Resolution Feature Curve Snapping Based on Nearest Neighbor Search 71 3.5 Pure Radial Projection and Thickness Offset Algorithm for Chord Solid Meshing 73 3.5.1 Spatial Projection and Extraction of the Pure Radial Vector 74 3.5.2 Thickness Offset Generation of Multi-layer Nodes 75 3.6 Layout of Brace Geometric Feature Lines and Multi-layer Spatial Linear Interpolation Algorithm 76 3.6.1 Definition of Spatial Geometric Feature Lines 78 3.6.2 Piecewise Spatial Linear Interpolation Logic 79 3.6.3 Multi-layer Geometric Collinear Constraint in the Thickness Direction 81 3.7 Macro-reorganization of 3D Solid Nodes and Transition to High-Order Elements 83 3.7.1 Macro-element Type Identification and Thickness Tensor Product Expansion 84 3.7.2 Mesh Degeneration and Index Mapping of 20-Node High-Order Hexahedral Solid Elements 85 3.7.3 Node Collapsing and Degeneration Technique for 15-Node Quadratic Wedge Elements 88 3.8 Solid Modeling of Weld Profile Geometry 89 3.8.1 Weld Geometry Definition and Element Type Selection 90 3.8.2 Interpolation and Global Registration of Weld Surface Mid-nodes 91 3.8.3 Spatial Mesh Mapping and Absolute Coordinate Search Method 92 3.8.4 Degenerated Element Assembly and Positive Volume Orientation 94 3.9 Global Node Merging and Conformal Suture Algorithm for Cross-Component Meshes 96 3.9.1 Global Coincidence Check Based on Proximity 97 3.9.2 Mesh Mapping Matrix and Performance Optimization 98 3.10 Multi-Level Mesh Refinement 101 3.10.1 Hierarchical Splitting of Mesh 102 3.10.2 Secondary Mesh Suture and Phantom Node Elimination 104 3.10.3 Multi-Regional Surface Projection and Saddle Curve Snapping 105 3.11 Local Mesh Refinement Scheme via Radial Insertion (Nrada and Nradb) 107 3.11.1 Geometric Subdivisions and Definitions 107 3.11.2 Mathematical Formulation: Interpolation and Radial Projection 108 3.11.3 Algorithmic Implementation 109 3.12 Generation of Variable Cross-Section (Canned) Tapering Profiles 110 3.12.1 Longitudinal Interval Segmentation and Target Thickness Evaluation 112 3.12.2 Tapering Scaling Formulations 113 3.13 Application of Boundary Conditions and External Loads 118 3.13.1 Fixed Boundary Conditions and Solid Element Constraint Logic at Chord Ends 119 3.13.2 Load Application at Brace Top: Analytical Traction Conversion and Consistent Nodal Loads 121 3.13.2.1 Establishment of Local Coordinate System and Analytical Traction Field 121 3.13.2.2 Derivation and Multi-Zone Formulation of Geometric Shear Shape Factors 123 3.13.2.3 Consistent Nodal Loads via the Principle of Virtual Work 128 3.13.3 Underlying Implementation of Isoparametric Mapping and Gaussian Quadrature 129 3.13.4 High-Order Mesh Extraction and Numerical Verification 131 3.14 Chapter Summary 133 Chapter 4 Finite Element System Solver Architecture and Post-processing 136 4.1 Overview of the Integrated FEA System and Computational Workflow 136 4.1.1 High-Order Mesh Generation Module: Mesh3D.exe 136 4.1.1.1 Input file for mesh3D.exe 136 4.1.1.2 Output files from mesh3D.exe 141 4.1.2 Matrix Assembly and Mesh Optimization: AB.exe 144 4.1.3 Visual Mesh Verification: AD.exe 145 4.1.4 Finite Element Solver: AN.exe 145 4.2 Automated Post-Processing and DNV Validation System Architecture 146 4.3 Modular Post-Processing Programs and Core Algorithms 147 4.3.1 Geometric Phase Calibration and Nondimensional Parameter Generation 147 4.3.1.1 True Phase Calibration (00_calibrate_geom.py): 147 4.3.1.2 Nondimensional Parameter Interpretation (00_generate_dnv_params.py): 149 4.3.2 Global Mesh Reconstruction and Stress Tensor Analysis (01_parse_fea.py) 149 4.3.3 Tensor Projection and Surface Hot-Spot Stress Extrapolation (02_extrapolate.py) 150 4.3.4 Theoretical Validation Engine and Data Visualization Rendering 151 4.3.4.1 Code-based Validation Engine (03_scf_engine.py): 151 4.3.4.2 Stress Distribution Rendering (04_plot_hss_distribution.py): 151 4.3.4.3 Error Parity Analysis (05_plot_single_validation.py): 153 4.4 LHS Data Post-Processing, Regression Analysis and Statistical Validation 157 4.4.1 Dynamic Power-Law Empirical Formula Fitting (10_LHS_Power.py) 157 4.4.2 Polynomial Response Surface Methodology (10_LHS_RSM.py) 158 4.4.3 Global Parity Analysis and Error Distribution Metrics (11_LHS_Parity.py, 12_LHS_error_distribution.py) 159 Chapter 5 Development and Validation of an Adaptive Tubular Joint Mesh Generator 161 5.1 Mesh Failure Mechanism in Automated Mesh Generation 161 5.1.1 Mesh Generation Failure from Stress Extrapolation Lines 161 5.1.2 Mesh Failure from Triangle Merging 163 5.1.3 Mesh Mismatch at the Weld Interface 165 5.1.4 Limitations of Fixed Tolerance and the Need for Dynamic Constraints 167 5.2 Parametric Adaptive Mesh Pre-processing System 167 5.2.1 Parametric Decoupling and 3D Vector Mapping 168 5.2.1.1 Dynamic Gap Control 169 5.2.1.2 3D Vector Projection and Direction Cosine Transformation 169 5.2.1.3 Coordinate System Transformation for Inclined Chords 171 5.2.1.4 Eccentricity Identification and Boundary Handling 172 5.2.2 Dynamic Mesh Generation Algorithm Based on Element Distortion Compensation 173 5.2.3 Validity Bounds and Exception Handling of the Mesh Generator 175 5.2.3.1 Test Matrix Design 176 5.2.3.2 Test Results and Safe Envelope Bounds 176 5.3 Mesh Convergence Analysis 178 5.3.1 Preliminary Convergence Study via Circumferential Divisions (Nthc) 179 5.3.2 Methodological Linkage to Thickness-Driven Mesh Sizing 182 5.3.3 Cross-Verification and Hot-Spot Stress Convergence 183 5.3.4 Numerical Evaluation of Through-Thickness Discretization Density 188 5.3.5 Engineering Justification for the LHS Baseline Discretization 192 Chapter 6 Latin Hypercube Sampling and Parametric Regression of SCF 194 6.1 Introduction of Latin Hypercube Sampling 194 6.2 Boundary Hypotheses and Dimensionality Reduction Strategy 195 6.2.1 Saint-Venant's Principle and Dual-Baseline Dimensionality Reduction Hypothesis 195 6.2.1.1 Baseline for Standard Joint Configurations (α=8.0) 196 6.2.1.2 Extended Baseline for Complex Multi-Brace Configurations (α=12.0) 197 6.2.2 Advantages of Mathematical Dimensionality Reduction 197 6.3 Sampling Strategy and Constrained LHS Design 198 6.3.1 Baseline Parameter Bounds and Configurations 198 6.3.2 Dynamic Constraints and Protection Mechanisms 199 6.3.2.1 Limitations of Conventional Independent Sampling 200 6.3.2.2 Implemented Constrained LHS Mechanism for Diameter Ratio (β) 200 6.3.2.3 Gap Parameter (ζ) and Overlap Protection Mechanism 201 6.4 Global Evaluation of Existing DNV-RP-C203 Empirical Formulations 204 6.4.1 Applicability and Operational Limits of Regulatory Equations 204 6.4.2 Global Consistency and Error Distribution Analysis 205 6.4.2.1 Data Discussion on T/Y-Joint 205 6.4.2.2 Data Discussion on KT-Joint 208 6.5 Construction of Proposed Parametric Regression Models 212 6.6 Proposed SCF Formulations and Prediction Accuracy Evaluation 214 6.6.1 Statistical Metrics for Model Evaluation 215 6.6.2 Global Overview of Joint Meshes and Evaluation Strategy 215 6.6.3 T/Y-Joint Regression Results and Geometric Sensitivity Analysis 217 6.6.3.1 Power-Law Regression Analysis 217 6.6.3.2 RSM Regression Analysis 220 6.6.4 KT-Joints Regression Bottlenecks and Component-wise Partitioning Optimization for Multi-Brace Symmetric 224 6.7 Global Sensitivity and Parametric Correlation Discussion 234 6.7.1 Pearson Correlation Analysis 234 6.7.2 Parameter Sweep and Non-linear Effects 239 6.8 Chapter Summary 242 Chapter 7 Conclusion and Future Work 244 7.1 Conclusion 244 7.1.1 Summary of Research 244 7.1.2 Key Findings 245 7.1.3 Contributions 248 7.2 Future Work 250 References 254 Appendix A Figures and Tables 260 A.1 Tables 260 A.2 Figures 265 Appendix B Fortran mesh3D.f90 Code 270 Appendix C Python Post Processing Code 329 C.1 python 00_calibrate_geom.py 329 C.2 python 00_generate_dnv_params.py 330 C.3 python 01_parse_fea.py 332 C.4 python 02_extrapolate.py 335 C.5 python 03_scf_engine.py 337 C.6 python 04_plot_hss_distribution.py 339 C.7 python 05_plot_single_validation.py 343 C.8 python LHS_Sampling_TY.py 346 C.9 python LHS_ Sampling_X.py 347 C.10 python LHS_ Sampling_K.py 349 C.11 python LHS_ Sampling_KT.py 351 C.12 python 10_LHS_Power_KT.py 353 C.13 python 10_LHS_Power.py 355 C.14 python 10_LHS_RSM.py 358 C.15 python 10_LHS_RSM_KT.py 361 C.16 python 11_LHS_parity.py 364 C.17 python 12_LHS_error_distributions.py 366

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