Chapter 1 Introduction to Very Large Floating Structures 1
1.1 Basic Concepts of VLFS 1
1.2 History of the Research and Development of VLFS 4
1.3 Potential Usage of VLFS 7
1.4 Technical Problems Involved in the Development of VLFS 9
1.4.1 Fundamental Concepts 10
1.4.2 Realization of the System 10
1.4.3 Functional Requirement for the System 11
1.4.4 Design/Construction, Maintenance/ Inspection/ Repair,and Scrap 12
1.5 Importance of the Hydroelastic Response in the Design of VLFS 12
References 13
Chapter 2 A Historical Review of the Theory of Hydroelasticity 17
2.1 Basic Concepts 17
2.2 Brief Overview of the Historical Development 18
2.2.1 Analytical Approaches and Acoustic Problems 18
2.2.2 Hydroelastic Analysis of Floating Marine Structures 19
2.2.3 Linear Two-dimensional Hydroelastricity Theories 20
2.2.4 Linear Three-dimensional Hydroelasticity Theories 21
2.2.5 Nonlinear Hydroelasticity Theories 23
References 24
Chapter 3 Hydroelasticity Theory in Time Domain 29
3.1 Potential Theory for an Arbitrary Floating Body 30
3.1.1 The Potential Theory Formulated in an Equilibrium Coordinate System 32
3.1.2 The Steady Wave Making Problem 33
3.1.3 The Large Amplitude Motion Theory of a Floating Body 34
3.1.4 The Linearization with Respect to the Steady Wave Making Potential 35
3.1.5 Brief Introduction to the Boundary Element Method 37
3.2 Solution Methods to the Linear Hydroelasticity in Time Domain 41
3.2.1 Formulation of the Linear Hydroelasticity in Time Domain 41
3.2.2 Decomposition of the Problem 44
3.2.3 Expression of the Radiation Potential in Time Domain 45
3.2.4 Equation of Motion in Time Domain 47
3.2.5 Memorial Function Determined from the Hydrodynamic Results in Frequency Domain 49
3.2.6 Boundary Element Method in Time Domain 51
3.2.7 A Fast Algorithm for Calculating the Transient Free Surface Green Function 55
3.3 Nonlinear Hydroelasticity Theory in Time Domain 60
3.3.1 First Order Fluid Forces and Nonlinear Structural Dynamics 61
3.3.2 Second Order Fluid Forces and Linear Structural Dynamics 63
3.3.3 Fully Nonlinear Fluid Forces and Finite Structural Deformation 73
References 78
Chapter 4 Hydroelasticity Theory in Frequency Domain 83
4.1 Introduction 83
4.2 Potential Flow Analysis of a Floating Flexible Body 83
4.2.1 Dynamic Displacement 84
4.2.2 Velocity Potential and Boundary Conditions 86
4.2.3 Pressure Distribution on the Body Surface 89
4.2.4 Potential Flow Around a Floating Flexible Body 90
4.2.5 Green Functions and the Modified Rankine Source Method 95
4.3 Linear Structural Dynamics of Floating Bodies 98
4.3.1 Static and Dynamic Displacement 98
4.3.2 Element Stiffness Matrix and Mass Matrix 99
4.3.3 Damping 99
4.3.4 Nodal Forces and External Loads 100
4.3.5 Transformation of the Coordinates 100
4.3.6 Generalized Gravity Force 101
4.3.7 Hamilton's Principle 102
4.3.8 System of Equations of Motion 102
4.3.9 Natural Frequencies and Principal Modes of a Dry Structure 103
4.3.10 Orthogonality Conditions 106
4.3.11 Principal Coordinates 107
4.4 Hydroelastic Analysis 110
4.4.1 Generalized Fluid Force 110
4.4.2 Generalized Concentrated Force 112
4.4.3 Decomposition of the Responses 113
4.4.4 Added Mass and Damping Coefficients 113
4.4.5 Restoring Coefficients 114
4.4.6 Steady-state and Still Water Responses 116
4.4.7 Equation of Unsteady Response 117
4.5 Hydroelasiticity of Flexible Multi-body Structure 118
4.5.1 Equations of Motion for a Body in the Multi-body Structure 119
4.5.2 Velocity Potential of the Fluid Motion 121
4.5.3 Radiation Potential 122
4.5.4 Generalized Fluid Forces and Equations of Motion 123
4.6 Nonlinear Hydroelasticity in Frequency Domain 125
4.6.1 Problem Formulation 126
4.6.2 Evaluation of Potentials-monochromatic Waves 127
4.6.3 Evaluation of Potentials-bi-chromatic Waves 135
4.7 Analysis Method for the Mooring System of a Flexible Floating Body 139
4.7.1 Introduction 139
4.7.2 The Motion Equations of a Moored Flexible Floating Body 140
4.7.3 The Motion Equations of a Mooring Line 142
4.7.4 Goodman-Lance Method 147
4.7.5 Numerical Example 149
References 152
Chapter 5 Hydroelastic Response Analyses for Mat-Type VLFS 156
5.1 General Hydroelasticity Problem for Mat-Type VLFS 156
5.1.1 Introduction 156
5.1.2 Formulation of the Hydroelasticity Problem 157
5.1.3 Linearized Version 161
5.1.4 Time Harmonic Expressions 162
5.1.5 Transformation of 3D Problem into 2D Problem by Separation of Variable Technique 163
5.1.6 Eigenvalues and Eigenfunctions 166
5.2 Analytical Solutions for Plate Model 169
5.2.1 Ohkusu Methods 169
5.2.2 Tsubogo's BOEF Model 173
5.2.3 The Accurate BOEF Model 176
5.2.4 Discussion on Numerical Results 179
5.3 Eigenfunction Expansion Method 185
5.3.1 Kim-Ertekin Method 186
5.3.2 An Alternative Function Expansion Method 192
5.3.3 Shallow Water and Higher Approximations 195
5.4 Green Function Method for Plate Model 200
5.4.1 Integral Expression for Plate Deflection 200
5.4.2 Accurate Green Function for a Free Plate 203
5.4.3 Eatock Taylor-Ohkusu's Approximate Plate Green Function 207
5.4.4 A New Approximate Plate Green Function 211
5.5 Other Mixed Methods 212
5.5.1 Hybrid Method 212
5.5.2 Eigenfunction Expansion--BEM 213
5.5.3 Finite Difference--BEM 218
5.6 Time Domain Analysis 222
5.6.1 Traditional Method 222
5.6.2 Pressure Method 223
5.6.3 Acceleration Potential and Hybrid Method 224
5.7 Nonlinear Effects on Hydroelastic Responses of Plate 230
References 233
Chapter 6 Hydroelastic Response Analyses for MOB 237
6.1 Introduction to Mobile Offshore Base 237
6.1.1 MOB Frame Concepts 237
6.1.2 Connector Development 238
6.2 Connector Load Calculation Model 241
6.2.1 RMFC (Rigid Module Flexible Connector) Model 241
6.2.2 FMRC (Flexible Module Rigid Connector) Model 249
6.2.3 FMFC (Flexible Module Flexible Connector) Model 254
6.3 Model Test of a 3 Module MOB 255
6.3.1 MOB Model 256
6.3.2 Test of MOB Model 258
6.3.3 Comparison of Experimental and Numerical Results 259
6.4 Numerical Results and Analysis 262
6.4.1 Numerical Results of RMFC Model 262
6.4.2 Accuracy of RMFC Model 274
References 277
Chapter 7 Hydroelastic Responses of VLFS under Inhomogeneous Environments 283
7.1 Introduction 283
7.2 Inhomogeneous Oceanic Environments 284
7.2.1 Inhomogeneous Oceanic Environments Due to the Varying Ocean Bottom 284
7.2.2 Inhomogeneous Oceanic Environments Due to Atmosphere and Wind 286
7.3 Mass-momentum Conservation Model of Inhomogeneous Oceanic Environments 289
7.3.1 Formulation of the Basic Wave Theory 289
7.3.2 Varying Depth 290
7.3.3 Wave Current Interaction 312
7.3.4 Waves in a Harbor 316
7.3.5 Waves Through Breakwaters 317
7.4 Energy Balance Model of Inhomogeneous Oceanic Environments 318
7.4.1 The Third-generation Wave Model 318
7.4.2 Storm Surge Model 321
7.4.3 Description of the Inhomogeneity of Waves 322
7.4.4 The Inhomogeneous Environment Caused by Typhoon near China Sea 322
7.5 Effects of Boundaries on the Hydroelastic Responses 324
7.5.1 Floating Body in an Irregular Bay 324
7.5.2 Floating Thin Plate in a Rectangular Bay 326
7.5.3 Structure Responses of a Plate Strip on Waves over 2D Varying Depth 328
7.5.4 Hydroelastic Responses of a Mat-like VLFS to Waves over 3D Varying Depth 334
References 342
Chapter 8 Experimental Techniques for VLFS 351
8.1 Introduction 351
8.2 Progress of the Experimental Research on VLFS 352
8.2.1 Model Experiment on Hydroelasticity of VLFS 352
8.2.2 Model Experiment on Hydroelasticity of VLFS in Non-uniform Ocean Environment 354
8.2.3 Mooring System Experiment of VLFS 355
8.2.4 Experiment of Multi-module VLFS 356
8.3 Experimental Method of VLFS 358
8.3.1 Law of Similitude 358
8.3.2 Design and Construction of VLFS Model 362
8.3.3 Main Facilities Needed in VLFS Model Tests 364
8.3.4 Analysis of Experimental Data and Errors 365
8.4 Examples of VLFS Model Tests 371
8.4.1 Hydroelastic Model Test on Box-typed VLFS 371
8.4.2 Model Test on Hydroelastic Responses of VLFS in Non-uniform Ocean Environment 373
8.4.3 Multi-module Test of Semi-submersible VLFS 375
References 379
Appendix A Introduction to Some Mathematical Background 381
A.1 Gauss Formula 381
A.2 Three Dimensional Green's Formula 382
A.3 Stokes Formula and Its Variants 383
A.4 Transport Equation 384
A.5 Conservation Laws 384
A.6 Constitutive Equation 386
A.7 State Equation 386
A.8 B-Splines and NURBS (Non-uniform Rational B-splines) 387
A.8.1 B-spline Basis Function 387
A.8.2 NURBS Basis Functions 387
References 389
Appendix B Introduction to Dynamics of Surface Gravity Waves 391
B.1 Basic Formulation for an Incompressible Fluid of Constant Density 391
B.1.1 Governing Equations 391
B.1.2 Boundary Conditions for an Inviscid and Irrotational Flow 392
B.2 Derivation and Classification of Approximate Equations 394
B.2.1 Dimensional Analysis 394
B.2.2 Airy's Theory for Very Long Waves: μ→0,？=O(１) 397
B.2.3 Boussinesq Theory: O(？) =O(μ2)<1 398
B.2.4 Variable Depth 398
B.3 Linearized Approximation for Small Amplitude Waves 399
B.3.1 Linear Theory of Water Waves 399
B.3.2 The Mild Slope Equation for Slowly Varying Depth 402
B.3.3 Harbor Oscillations Excited by Incident Long Waves 403
B.4 A Numerical Method Based on Finite Elements for General Water Wave Problem 406
B.4.1 The Variational Principle 407
B.4.2 Finite Element Approximation 408
References 413
Appendix C Introduction to Structural Mechanics 415
C.1 Structural Dynamics 415
C.1.1 Strain and Stress for Large Displacement 415
C.1.2 Principle of Virtual Work and Its Incremental Form 421
C.1.3 Finite Element Models Derived from the Incremental Variational Principle 428
C.1.4 Constitutive Relations for Large Deformation 439
C.2 Plate Model 446
C.2.1 Strains in a Plate 447
C.2.2 The Stress of a Homogeneous and Isotropic Plate 449
C.2.3 Hamilton's Principle 449
C.2.4 The von Karman's Plate Equations for Large Deflection 453
C.2.5 Linear Equations of Thin Plate for Small Deflection 455
C.2.6 The Linear Equations of Mildly Thick Plate for Small Deflection 456
C.3 Shell Model 460
C.3.1 General Orthogonal Curvilinear Coordinate System 460
C.3.2 The Orthogonal Curvilinear Coordinate System for Shell Analysis 461
C.3.3 Displacements and Deformations in the Thin Shell 464
C.3.4 A Nonlinear Thin Shell Theory 467
References 473
Appendix D Unit Normal Vector of Deformable Structures 475
References 476