前辅文
1. Introduction
1.1 Fluid-solid interaction dynamics and its characteristics
1.2 Fluid-solid interaction problems in engineering
1.3 Solution approaches to fluid-solid interaction problems
1.3.1 Approximate solution with no fluid-solid interaction
1.3.2 Quasicoupling approximation method
1.3.3 Solution of integrated coupling fields
1.4 Approaches to deriving numerical equations
1.4.1 Problem and its governing equations
1.4.2 Analytical solution
1.4.3 Variational formulations and Rayleigh-Ritz method
1.4.4 Finite element method
1.4.5 Weighted residual methods
1.4.6 Finite difference method
1.5 Short historical review on fluid-solid interaction
1.5.1 Terms of fluid-solid interaction and its subdisciplines in literatures
1.5.2 Historical remarkable events and progress on fluid-solid interaction
1.5.3 World-recognized conferences
1.5.4 Influential review papers
1.5.5 Important books on fluid-solid interaction
1.6 Main aim and characteristics of this book
1.7 Suggestions how to choose some contents as lecture notes
2. Cartesian tensor and matrix calculus
2.1 Cartesian tensor
2.1.1 Vector
2.1.2 Summation convention
2.1.3 Kronecker delta
2.1.4 Permutation symbol
2.1.5 e-δ Identity
2.1.6 Differentiation of a function f(x1,x2,x3)
2.1.7 Transformation of coordinates
2.1.8 Tensor
2.1.9 Quotient rule
2.1.10 Index forms of some important variables
2.1.11 Two primary identities
2.2 Matrix calculus
2.2.1 Types of matrix derivatives
2.2.2 Derivatives with vectors
2.2.3 Derivatives with matrices
2.2.4 Identities
2.3 Exercise problems
2.3.1 Problem 1: prove the following formulations
2.3.2 Problem 2: prove the identity of three arbitrary vectors
2.3.3 Problem 3: express the constitutive equation in a tensor form
2.3.4 Problem 4: write the tensor equation in a coordinate (xyz) form
2.3.5 Problem 5: prove the following identities using index notations
2.3.6 Problem 6: prove eijkaiajbk=0 for nonzero vectors a and b
3. Fundamentals of continuum mechanics
3.1 Descriptions of the motion of a continuum
3.1.1 Material frame of reference
3.1.2 Spatialf rame of reference
3.1.3 Arbitrary Lagrange Euler frame of reference
3.1.4 Updated Lagrangian system
3.1.5 Updated arbitrary Lagrange Euler system
3.2 Analysis of deformation
3.2.1 Displacement and strain
3.2.2 Velocity field and rate of deformation of fluids
3.3 Stress tensor
3.3.1 Cauchy's stress
3.3.2 Piola-Kirchhoff stress
3.4 Constitutive equation
3.4.1 Solids
3.4.2 Fluids
3.5 Laws of conservation
3.5.1 Green theorem
3.5.2 Material derivatives of volume integral with mass density
3.5.3 Material derivatives of arbitrary integrands in a spatial system
3.5.4 Material derivatives of arbitrary integrands in the arbitrary Lagrange Euler system
3.5.5 General forms of the conservation laws
3.5.6 Jump condition and equation
3.5.7 Conservation of mass and the equation of continuity
3.5.8 Conservation of momentum and equations of motion
3.5.9 Conservation of energy and equation of energy
3.6 Navier-Stokes equations and boundary conditions
3.6.1 Displacement solution of solid mechanics
3.6.2 Velocity-pressure solution equations of fluid mechanics
3.6.3 Bernoulli equation and potential flows
3.6.4 Linear waves in fluids
4. Variational principles of linear fluid-solid interaction systems
4.1 Short review on historic background
4.2 Fluid-solid interaction problems and interaction conditions
4.2.1 Geometric and dynamic conditions on material interfaces
4.2.2 Interactions on nonfloating fluid-solid interaction interface
4.2.3 Interaction on floating fluid-solid interaction interface
4.2.4 Interactions on air-liquid interface
4.2.5 Conditions of surface-tension interactions
4.2.6 Boundary conditions on infinity and moving structures
4.3 A complementary energy model: pressure-acceleration form
4.3.1 Governing equations
4.3.2 Variational formulation
4.4 A potential-energy model: displacement-velocity potential form
4.4.1 Governing equations
4.4.2 Variational formulation
4.5 Mixed energy models: displacement-pressure and acceleration-velocity potential forms
4.5.1 Displacement-pressure form
4.5.2 Acceleration-velocity potential form
4.6 Three field variational formulations
4.6.1 Displacement-pressure-velocity potential form
4.6.2 Displacement-acceleration-pressure form
4.7 Formulations with displacement potential or pressure impulse as a variable
4.7.1 Displacement-potential form
4.7.2 Pressure impulse form
4.8 Variational formulations for dissipative systems
4.8.1 Damping types
4.8.2 Virtual variational formulations
4.8.3 Complex variational formulation
4.9 Variational formulations for pipes conveying fluid
4.9.1 Description and assumptions of the problem
4.9.2 Variational formulation
4.9.3 Variational stationary conditions for governing equations
4.9.4 Natural vibrations and first approximate frequency
5. Solutions of some linear fluid-solid interaction problems
5.1 One-dimensional problems
5.1.1 Dynamic response of one-dimensional fluid-solid interaction system to a pressure wave
5.1.2 A mass-spring system coupled to a one-dimensional infinite fluid domain
5.1.3 Dynamic response of a Sommerfeld system
5.1.4 Natural vibration of an fluid-solid interaction system with free surface wave
5.1.5 Natural vibration of a vertical system with a floating fluid-solid interaction interface
5.2 Two dimensional problems
5.2.1 Sloshing modes of a two dimensional rectangular water container
5.2.2 Radiations of mixed compressive and gravity waves
5.2.3 Dam-water pond excited by earthquake
5.2.4 Beam-water interaction
5.3 Three-dimensional problems
5.3.1 Vibrations of a floating rigid mass on the water
5.3.2 A water-sphericalshell-damping layer interaction system
6. Preliminaries of waves
6.1 d'Alembert's solution, dispersive, dissipation
6.1.1 d'Alembert's solution
6.1.2 Dispersive wave
6.1.3 Dissipation wave
6.2 Nonlinear waves
6.2.1 A nonlinear wave and its characteristic solution
6.2.2 Burgers' equation
6.2.3 Korteweg-de Vries equation
6.2.4 Generalized nonlinear water wave equation
6.2.5 Analytical solutions of nonlinear wave equations
6.3 Linear water waves
6.3.1 Three-dimensional water waves
6.3.2 Plane water wave
6.3.3 Approximate theory for long waves
7. Finite element models for linear fluid-structure interaction problems
7.1 Introduction on finite element models for linear fluid-structure interaction
7.2 Displacement-velocity potential finite element model
7.2.1 Description of the problem
7.2.2 Governing equations
7.2.3 Variational formulation
7.2.4 Finite element equations
7.2.5 Natural vibration
7.2.6 Examples
7.3 Mixed finite element displacement-pressure model
7.3.1 General description of the problem
7.3.2 Variational formulation
7.3.3 Mixed finite element model
7.3.4 Symmetric matrix equations and approximations
7.3.5 Effect of solid/fluid natural frequencies on fluid-structure interaction process
7.4 Substructure-subdomain approaches
7.4.1 Variational formulations in substructure-subdomain form
7.4.2 Displacement consistency model for solid substructure
7.4.3 Hybrid displacement model of solid substructure
7.4.4 Pressure equilibrium model of fluid domain
7.4.5 Mixed model of substructure-subdomain
7.4.6 Special techniques for fluid-structure interaction systems
7.4.7 A simple example: one-dimensional fluid-structure interaction problem
7.4.8 Computer code design
7.4.9 Application examples
8. Mixed finite element-boundary element model for linear water-structure interactions
8.1 Formulation of the boundary element method
8.1.1 Fundamental solution of Laplace equation
8.1.2 Formulation of boundary integral equation
8.2 Mixed finite element-boundary element method for very large floating structure subjected to airplane landing impacts
8.2.1 Introduction
8.2.2 General description of the problem
8.2.3 Governing equations
8.2.4 Mixed finite element-boundary element method
8.3 Finite element-boundary element modeling for dynamic response of structures excited by incident water waves
8.3.1 General description of the problem and governing equations
8.3.2 Solution approach
8.3.3 Variational formulation
8.3.4 Mixed finite element-boundary element equations
8.4 Mirrorimage method for acoustic radiations of underwater structures
8.4.1 Green functions of Helmholtz equation
8.4.2 Green identity
8.4.3 Acoustic radiation in infinite fluid domain
8.4.4 Generalized acoustic radiation problems
9. Hydroelasticity theory of ship-water interactions
9.1 Fundamentals for ship-water interactions
9.1.1 Frames of reference
9.1.2 Governing equations
9.1.3 Equations for static equilibrium state
9.1.4 Equations for steady motion
9.2 Incident waves
9.2.1 Equation of incident water waves
9.2.2 Linear plane gravity waves
9.2.3 Frequency ofwave encounter
9.3 Linear hydroelasticity theory
9.3.1 Linearized governing equations
9.3.2 Equations in the modal space
9.3.3 Numerical solutions
9.3.4 Examples
10. Variational principles for nonlinear fluid-solid interactions
10.1 A short review on variational principles for nonlinear dynamical systems
10.2 Fundamental variational concepts for nonlinear systems
10.2.1 The motion of a continuum
10.2.2 Translation and transmission velocities of a curved surface
10.2.3 Time derivative of an integral over a moving volume in space
10.2.4 local variation and a material variation
10.2.5 Local variation of an integral over a moving volume in space
10.3 Governing equations
10.3.1 Solid domain
10.3.2 Fluid domain
10.3.3 Fluid-structure interface
10.3.4 Variational conditions at initial time t1 and final time t2
10.4 Variational principles
10.4.1 Fluid motion assumed rotational
10.4.2 Fluid flow assumed irrotational
10.4.3 Discussion
10.5 Two simple examples of applications
10.5.1 A one-dimensional water-mass-spring interaction problem
10.5.2 A forced one-dimensional gas-mass-spring dynamic interaction problem
10.6 Variational principles for nonlinear elastic ship-water interactions
10.6.1 Short introduction
10.6.2 Governing equations in the moving reference frame
10.6.3 Variational formulations in the moving reference frame
10.6.4 Rigid ship dynamics
10.6.5 Offshore and hydroelastic examples
11. Mixed finite element-computational fluid dynamics method for nonlinear fluid-solid interactions
11.1 Updated Lagrangian formulation in finite element methods
11.1.1 Principle of virtual work and dynamic equilibrium equations
11.1.2 Expression of stress virtual work
11.1.3 Total Lagrangian formulation in solid dynamics
11.1.4 Updated Lagrangian formulation in solid dynamics
11.1.5 Solution of nonlinear equations
11.1.6 A one-dimensional example
11.2 Updated arbitrary Lagrangian-Eulerian formulationsin computational fluid dynamics
11.2.1 History and development of arbitrary Lagrangian-Eulerian description
11.2.2 Basic discretization techniques of computational fluid dynamics
11.2.3 Consistency, stability, and convergence of numerical schemes
11.2.4 Updated arbitrary Lagrangian-Eulerian formulations in finite difference method and finite volume method
11.3 Mixed finite element-computational fluid dynamics solutions for nonlinear fluid-solid interaction problems
11.3.1 Direct or simultaneous integration
11.3.2 Partitioned iteration
11.3.3 A simple example
11.4 Numerical examples by the mixed finite element-finite difference method
11.4.1 Description of nonlinear rigid body-water fluid-solid interaction systems
11.4.2 Arbitrary Lagrangian-Eulerian description of the water motion
11.4.3 Numerical formulations
11.4.4 A fluid-mass-spring interaction system
11.4.5 A spring-supported fluid-rigid-dam interaction system
11.4.6 Two-dimensional rigid body floatingin a free-surface fluid
11.4.7 Prescribed motion of a rigid cylinder floating in the water
11.4.8 Flows around a bluff body
12. Mixed finite element-smoothed particle methods for nonlinear fluid-solid interactions
12.1 Introduction
12.1.1 Limitations of grid-based methods for violent flows
12.1.2 Key ideas of meshfree particle methods
12.1.3 History and developments with applications
12.2 Fundamentals of smoothed particle hydrodynamics
12.2.1 Smoothed particle hydrodynamics interpolations
12.2.2 Particle approximation
12.2.3 Construction ofsmoothing functions
12.2.4 Smoothed particle hydrodynamics formulation for Navier-Stokes equations
12.2.5 Numerical techniques for fluid flows
12.2.6 Improved methods based on smoothed particle hydrodynamics
12.3 Meshfree Galerkin methods
12.3.1 Moving least square representing kernel interpolant
12.3.2 Shepard interpolant
12.3.3 Orthogonal basis for local approximations
12.3.4 Applications of the moving least square reproducing kernels
12.4 Mixed finite element-smoothed particle method for fluid-solid interaction problems
12.4.1 Generalized solution procedure
12.4.2 Modeling offluid-solid interaction involving large rigid motions with small elastic deformation
12.4.3 Application examples
Appendix: Numerical methods solving finite element dynamic equations
Bibliography
Index
