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Posts
- Category: Introduction to Structural Dynamics and Aeroelasticity (continued)
- Traveling Wave Solution
- Using Orthogonality
- Orthogonality of Mode Shapes
- Standing Wave (Modal) Solution
- Uniform String Dynamics
- Structural Dynamics
- Systems with One Degree of Freedom
- The Notion of Stability
- Constitutive Law and Strain Energy for Coupled Bending and Torsion
- Composite Beams
- Bending
- Elementary Beam Theory
- Kinetic Energy
- Equations of Motion
- Kinetic Energy
- Euler’s Laws and Rigid Bodies
- Newton’s Laws
- Particles and Rigid Bodies
- Aeroelasticity
- Addendum for Second Edition
- Foreword
- Category: Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics
- Numerical Study of the Influence of Geometrical Uncertainties (Testcase SFB-401)
- Navier-Stokes Flow
- Euler Flow
- Numerical Results Considering Geometrical Uncertainties (Testcase RAE2822)
- Numerical Results
- Dimension Adaptive Sparse Grid
- Adaptive Sparse Grid
- Adaptive Sparse Grid for High-Dimensional Integration
- Reduction of the Dimension of the Probability Space Using a Goal-Oriented Karhunen-Loeve Basis
- Chance Constraint Formulations
- Semi-infinite Formulations
- Robust Shape Optimization Problem
- Karhunen-Loeve-Expansion
- Function-Valued Uncertainties
- Mathematical Description of the Uncertainties
- Aleatory Uncertainties in Aerodynamic Design
- Optimal Aerodynamic Design under Uncertainty
- Results and Discussion
- Gradient-Enhanced Point-Collocation Polynomial Chaos Method
- Gradient-Enhanced Kriging Method
- Quasi-Monte Carlo Quadrature
- Methods
- Test Case
- Efficient Quantification of Aerodynamic Uncertainties Using Gradient-Employing Surrogate Methods
- Numerics
- Bayesian Update of the Uncertain Airfoil Geometry
- Data Compression
- Update of the Low-Rank Response Surface via Computing the Residual
- Low-Rank Response Surface
- Discretisation Techniques
- Modelling of Uncertainties in the Airfoil Geometry
- Modelling of Uncertainties in Parameters
- Numerical Methods for Uncertainty Quantification and Bayesian Update in Aerodynamics
- Summary and Conclusion
- TAU Implementation
- Simulation Setup
- Error Determination
- Parameter Interaction
- ANOVA-Analysis
- Orthogonal Arrays
- The Taguchi-Method
- Statistical Analysis of Parameter Variations Using the Taguchi Method
- Summary
- Application to Complex Configuration
- Multi-disciplinary Wing Optimization-SFB-401-Wing
- Applications
- Interpolation Quality Comparison
- Error Correction
- Weighting by Interpolation Error
- Weighting by the Difference to the Local Average Deformation
- . Weighted Distances
- . Equidistant Reduction Method
- Base Point Reduction Methods
- Wall Distance Module
- Multivariate Interpolation Using Radial Basis Functions
- Radial Basis Functions in Mesh Deformation
- CFD Mesh Deformation Module
- Improved Mesh Deformation
- Coupled Simulations
- Comparison of the Projection Methods
- Interpolation Parameters of the MLS Method
- Interpolation Parameters of the GSB Method
- Interpolation Parameters of the MLS and GSB Methods
- Interpolation Parameters of the FIE Method for Beam Models
- Influence of Projection Parameters
- Shell Model Test Setup
- Beam Model Test Setup
- One-Dimensional Test Setup
- Error Sources in Spatial Coupling
- Insertion of Additional Support Points
- Moving-Least-Squares Interpolation (MLS)
- Global Spline-Based Interpolation (GSB)
- Additional Interpolation Schemes for FIE
- Finite Interpolation Element Method
- Spatial Coupling
- Flow Grid Deformation
- Structural Solver
- Flow Solver