Shape design sensitivity analysis of dynamic crack propagation using Peridynamics

다국어 초록 (Multilingual Abstract)

The shape design sensitivity analysis based on the mesh-free method for the bond-based peridynamics theory is developed for the solution to dynamic crack propagation problems. The methods may serve for the following two purposes. First, for the shortcomings of the Finite Difference Method that is involved. Specifically, the FDM is very sensitive to the amount of design perturbation. Second, it may serve for the foundation of the basis in proceeding shape design optimization. To solve large scale problems and to improve numerical efficiency, the binary decomposition method is employed for parallel computation. A shape design sensitivity analysis method is developed by using the direct differentiation method (DDM) and the adjoint variable method (AVM). Shape design sensitivity is developed using the Lagrangian approach since the geometry and finite grids perturb together during the shape variation. -continuous volume fraction that arises from numerical discretization is necessary for accurate analytical shape design sensitivity. The accuracy of the analytical design sensitivity is verified by comparing it with the Finite Difference Method.

목차 (Table of Contents)

• Chapter 1. Introduction 1
• 1.1. Motivation 1
• 1.2. Literature review 3
• Chapter 2. Peridynamic theory 6
• 2.1. Formulation 6
• 2.1.1. Peridynamic stress tensor 6
• 2.1.2. General bond based model 8
• 2.1.3. A linearized peridynamics model for microelastic material 10
• 2.1.4. Damage model 11
• 2.1.5. Short range force 15
• 2.2. Discretization for peridynamics 16
• Chapter 3. Design Sensitivity Analysis 19
• 3.1. Shape DSA formulation 19
• 3.2. Adjoint Variable Method 22
• Chapter 4. Efficient computation for peridynamic systems 25
• 4.1. Time-reversal symmetry 25
• 4.2. Path dependency 27
• 4.3. Parallel computation 28
• Chapter 5. Numerical Examples 31
• 5.1. Successive Branching 33
• 5.2. Validation for the fraction of volume 36
• 5.3. FDM in terms of perturbation amount 42
• 5.4. The verificataion of AVM 43
• Chapter 6. Conclusions 47
• Chapter 7. Bibliography 49