Biobjective shape optimization algorithms enhanced by derivative information / vorgelegt von Onur Tanil Doganay, M.Sc. Wuppertal, Oktober 2021
Inhalt
- Introduction
- Ceramics: Linear Elasticity Equation and Finite Element Discretization
- Mechanical Properties of Ceramic Materials
- Elliptic Boundary Value Problems
- PDEs with Dirichlet and Neumann Boundary Conditions
- Weak Solutions of Elliptic PDEs
- Linear Elasticity Theory
- Finite Element Discretization
- Biobjective Shape Optimization (of Ceramic Structures)
- Admissible Shapes and State Equation
- Probability of Failure
- Material Consumption
- Biobjective Optimization
- Weighted Sum Scalarization
- Existence of Pareto-optimal Shapes
- Discretization of the Objective Functionals and the Numerical Test Cases
- Discretization of the Objective Functionals
- Adjoint Equation
- Geometry Definition and Finite Element Mesh
- Test Cases
- Gradient Based Biobjective Shape Optimization to Improve Reliability and Cost of Ceramic Components
- Pareto Tracing by Numerical Integration
- A Brief Overview of First-Order Ordinary Differential Equations
- Pareto Tracing Using ODEs
- Implicit and Explicit ODEs for Local Pareto Optimality
- Approximately Pareto Critical Initial Conditions and Numerical Stability
- Pareto Front Tracing by Numerical Integration
- A Related Method: Pareto Tracer
- Numerical Results
- EGO and Gradient Enhanced Kriging
- Random Variables and Random Fields
- Finite-Dimensional Distributions
- Expected Value and Covariance
- Positive Definiteness
- Gaussian Random Fields
- Analytical Properties of Random Fields
- Gradient Enhanced Kriging
- Latin Hypercube Sampling
- Stochastic Model
- DIvision of RECTangles (DIRECT) Algorithm
- The Kriging Model
- Bayesian Approach
- Gradient Enhanced Kriging
- Efficient Global Optimization (EGO)
- Coupling With Dakota
- Numerical Results
- Conclusion and Outlook