Fluid-Structure Interactions and Uncertainties

El Hami Abdelkhalak, Professor at INSA Rouen - Normandy University. Radi Bouchaib, Professor of Higher Education Hassan First University, Settat.

• Preface ixChapter 1. Fluid–Structure Interaction 11.1. Introduction 11.2. Fluid–structure interaction problem 21.2.1. Fluid–structure coupling methods 51.2.2. Temporal coupling 81.2.3. Spatial coupling 111.3. Vibroacoustics 141.3.1. Vibrations of three-dimensional solids 151.3.2. Acoustics of fluids 171.3.3. Numerical methods for calculating a structure coupled with a stagnant fluid 181.4. Aerodynamics 211.4.1. Aeroelastic problems 231.4.2. Aerodynamic loads 261.4.3. Problem equations 29Chapter 2. Fluid–Structure Interaction with Ansys/Fluent 352.1. Presentation of Ansys 352.2. Coupling with Ansys 372.2.1. Types of coupling analysis 382.3. Example of fluid–structure interaction using the “physics” environment 402.3.1. Fluid in motion 402.3.2. Stagnant fluid 482.4. Example of interaction using Fluent 54Chapter 3. Vibroacoustics 593.1. Introduction 593.2. Equations of the acoustic and structure problems 603.2.1. Equation of the acoustic problem 603.2.2. Boundary conditions of the acoustic problem 613.2.3. Equation of the structure problem 623.2.4. Boundary conditions of the structure problem 623.3. Vibroacoustic problem 633.3.1. Problem statement 643.3.2. Boundary conditions at the interface 653.3.3. Finite element approximation 663.4. Study of an elastic plate coupled with a fluid cavity 863.4.1. Equations of the coupled fluid–structure problem 873.4.2. Variational formulation of the fluid 883.4.3. Variational formulation of the plate 923.4.4. Numerical results 943.5. Study of the propeller of a boat 973.5.1. Numerical results 99Chapter 4. Aerodynamics 1034.1. Introduction 1034.2. Computational method 1044.2.1. Conformal mesh 1044.2.2. Immersed boundary methods 1054.2.3. Volume-based fictitious domain methods 1064.3. Aerodynamic problem’s resolution 1074.3.1. Mobile domain 1074.3.2. Weak formulation 1084.3.3. Evaluating the energy of the system 1114.3.4. Numerically solving the system 1164.3.5. Discretization by finite elements 1204.4. Finite element method for the solid 1234.4.1. Discretization 1244.4.2. Assembling the system 1264.4.3. Solving the system of algebraic equations 1264.4.4. Integration by Gaussian quadrature 1264.4.5. Advancing the time step using the Hilbert–Hugues–Taylor algorithm 1274.4.6. Linearization using the Newton–Raphson algorithm 1294.5. Finite volumes for the fluid 1304.5.1. Generic transport equation 1304.5.2. Conservation property of the method 1314.5.3. The different steps in the method 1314.5.4. Integrating the model equation 1324.5.5. Control volumes 1334.5.6. Physical interpolation 1354.5.7. Evaluating the flux through the faces 1354.5.8. Centered scheme 1364.5.9. Upwind scheme 1384.5.10. Hybrid scheme 1394.5.11. Discretization 1394.6. Coupling procedures 1414.6.1. Coupling strategies 1414.6.2. Implicit partitioned coupling 1424.7. Numerical results 1454.7.1. Static analysis 1454.8. Study of a 3D airplane wing 1504.8.1. Modal analysis 1534.9. Transient analysis 154Chapter 5. Modal Reduction for FSI 1635.1. Introduction 1635.2. Dynamic substructuring methods 1645.2.1. Linear problems 1655.2.2. Nonlinear problems 1675.3. Nonlinear substructuring method 1695.3.1. Vibrational equations of a substructure 1705.3.2. Fixed-interface problem 1715.3.3. Static bearing problem 1725.3.4. Representing the system with the linear Craig–Bampton basis 1735.3.5. Model reduction using the approach of Shaw and Pierre 1745.3.6. Assembling the substructures 1765.4. Proper orthogonal decomposition for flows 1785.4.1. Properties of POD modes 1795.4.2. Snapshot POD 1795.4.3. Finding low-order expressions for dynamic systems 1805.5. Dynamic substructure/acoustic subdomain coupling 1855.5.1. Basic equations 1875.5.2. Variational formulations 1905.5.3. Discretization by finite elements 1915.5.4. Calculating the local modes 1945.5.5. Modal synthesis 1965.6. Numerical simulation 1995.6.1. Elastic ring 1995.6.2. Boat propeller 206Chapter 6. Reliability-based Optimization for FSI 2116.1. Introduction 2116.2. Reliability in mechanics 2126.2.1. Random variables 2126.2.2. Reliability function 2146.3. Failure in mechanics 2156.3.1. Failure scenarios 2166.3.2. Expression of the failure probability 2176.4. Reliability index 2176.4.1. Rjanitzyne–Cornell index 2176.4.2. Hasofer–Lind index 2186.5. Mechanoreliability coupling 2186.5.1. Reliability-based calculation methods 2196.5.2. Monte Carlo method 2206.5.3. FORM/SORM approximation methods 2216.6. Reliability-based optimization in mechanics 2246.6.1. Deterministic optimization 2256.6.2. Different approaches to RBDO 2266.6.3. Classical approach 2286.6.4. Hybrid approach 2296.6.5. Frequency-based hybrid approach 2316.7. SP method 2346.7.1. Formulation of the problem 2346.8. Numerical results 2376.8.1. Reliability calculation for an airplane wing 2376.8.2. Application of RBDO to the airplane wing 239Bibliography 253Index 263