| Abstract | 第1-8页 |
| List of Figures | 第8-11页 |
| List of Tables | 第11-12页 |
| Chapter 1: Introduction | 第12-20页 |
| Chapter 2: Basic Formulations of the Reproducing Kernel Particle Method | 第20-39页 |
| 2．1 Kernel functions and support domain | 第20-23页 |
| 2．2 Kernel estimation | 第23页 |
| 2．3 Continuous reproducing kernel approximation | 第23-26页 |
| 2．4 Discrete reproducing kernel approximation: RKPM shape function and its derivatives | 第26-31页 |
| 2．5 Essential boundary conditions | 第31-33页 |
| 2．6 Weak form and discrete equations in RKPM | 第33-39页 |
| 2．6．1 Preliminaries and the statement of the problem | 第33-35页 |
| 2．6．2 Weak form of the momentum equation | 第35-36页 |
| 2．6．3 Discretization of the momentum equation in RKPM | 第36-39页 |
| Chapter 3: A General Benchmark Test for Nonlinear Dynamic Problems | 第39-47页 |
| 3．1 Standard Patch Test | 第40-41页 |
| 3．2 Patch test in explicit programs | 第41-42页 |
| 3．3 Benchmark test procedure | 第42-46页 |
| 3．4 Error estimation | 第46-47页 |
| Chapter 4: Lower Integration Rules | 第47-67页 |
| 4．1 Two-dimensional lower integration | 第48-49页 |
| 4．2 Three-dimensional lower integration | 第49-51页 |
| 4．3 Benchmark test of the integration schemes through numerical applications | 第51-67页 |
| 4．3．1 Two-dimensional example | 第52-57页 |
| 4．3．2 Three-dimensional example | 第57-67页 |
| Chapter 5: RKPM for Contact-Impact Problems | 第67-96页 |
| 5．1 Introduction | 第67-71页 |
| 5．2 Interface equations | 第71-76页 |
| 5．2．1 Preliminaries | 第71-74页 |
| 5．2．2 Impenetrability condition | 第74-75页 |
| 5．2．3 Traction condition | 第75-76页 |
| 5．2．4 Unitary contact condition | 第76页 |
| 5．2．5 Interpenetration measure | 第76页 |
| 5．3 Friction model: Coulomb friction | 第76-77页 |
| 5．4 Statement of the contact-impact problems | 第77-78页 |
| 5．5 Contact constraints methods | 第78-82页 |
| 5．5．1 Penalty method | 第79-81页 |
| 5．5．2 Lagrange multiplier method | 第81-82页 |
| 5．6 Discretization of contact problems in RKPM | 第82-84页 |
| 5．7 The particle to segment contact algorithm | 第84-94页 |
| 5．7．1 Three-dimensional particle to segment contact algorithm | 第84-91页 |
| 5．7．2 Two-dimensional particle to segment contact algorithm | 第91-94页 |
| 5．8 Evaluation of the contact forces by penalty method | 第94-96页 |
| Chapter 6: Numerical Applications of the Particle to Segment Contact Algorithm in RKPM | 第96-118页 |
| 6．1 Taylor bar impact | 第98-103页 |
| 6．1．1 Two-dimensional Taylorbar impact simulation | 第99-101页 |
| 6．1．2 Three dimensional Taylor bar impact simulation | 第101-103页 |
| 6．2 Backward extrusion | 第103-107页 |
| 6．2．1 Two-dimensional backward extrusion | 第103-106页 |
| 6．2．2 Three-dimensional backward extrusion | 第106-107页 |
| 6．3 Analysis of forging process | 第107-110页 |
| 6．3．1 Two-dimensional analysis of forging process | 第107-109页 |
| 6．3．2 Three-dimensional Analysis of forging process | 第109-110页 |
| 6．4 Sheet metal forming: draw bending | 第110-113页 |
| 6．4．1 Two-dimensional draw bending | 第112页 |
| 6．4．2 Three-dimensional draw bending | 第112-113页 |
| 6．5 Penetration simulation | 第113-116页 |
| 6．5．1 Two-dimensional penetration simulation | 第114-115页 |
| 6．5．2 Three-dimensional penetration simulation | 第115-116页 |
| 6．6 Comparison of CPU times | 第116-118页 |
| 6．6．1 Comparison of the CPU times in 3D | 第116页 |
| 6．6．2 Comparison of the CPU times in 2D | 第116-118页 |
| Chapter 7: Conclusions | 第118-119页 |
| References | 第119-126页 |
| Acknowledgements | 第126-127页 |
| Publications | 第127-128页 |
| Appendix: Summary in Chinese (摘要) | 第128-157页 |
