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系統識別號 U0026-0708201710054000
論文名稱(中文) 拓樸最佳化方法於幾何非線性結構之最佳設計
論文名稱(英文) Optimal Design of Geometrically Nonlinear Structures using Topology Optimization
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 105
學期 2
出版年 106
研究生(中文) 胡德勇
研究生(英文) Ho Duc Dung
學號 N16047127
學位類別 碩士
語文別 英文
論文頁數 79頁
口試委員 指導教授-劉至行
口試委員-陳家豪
口試委員-陳國聲
中文關鍵字 none 
英文關鍵字 Topology optimization  geometrically nonlinear modelling  continuation method  Method of Moving Asymptotes  buckling analysis 
學科別分類
中文摘要 none
英文摘要 This study deals with stiffness design of geometrically nonlinear structures using topology optimization. Bi-directional Evolutionary Structures Optimization (BESO) is employed to implement the design process. The geometrically nonlinear behavior of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The topology optimization of linear and nonlinear modelling are implemented. The sensitivity of the objective function is found with the adjoint method and the optimization problem is solved using both the Method of Moving Asymptotes (MMA) and BESO’s update methods. Objective function of complementary work is evaluated. Special technique called continuation method is applied to solve the instability of nonlinear structure optimization. ANSYS APDL is also used to perform finite element analysis (FEA) of optimal topology to verify the effectiveness of geometrically nonlinear modelling. The results show that differences in stiffness of structures optimized using linear and nonlinear modelling are generally small but they can be large in some cases, especially for structures involving buckling behavior.
論文目次 ABSTRACT i
ACKNOWLEDGEMENTS ii
Contents iii
List of Figures v
List of Tables ix
Chapter 1: Introduction 1
1.1 Structural optimization 1
1.2 Topology optimization of continuum structures 2
1.3 Bi-directional Evolutionary Structural Optimization method 2
1.4 Topology optimization of geometrically nonlinear structures 4
1.5 Organization of the thesis 5
Chapter 2: Geometrically Nonlinear Structures Optimization Method 7
2.1 Bi-directional topology optimization method 7
2.1.1 Problem statement and sensitivity number 7
2.1.2 Filter scheme and stability process 8
2.1.3 Volume constraint and convergence criterion 12
2.1.4 Procedure of Bi-directional Evolutionary Structural Optimization method 12
2.2 Structural nonlinearity 14
2.2.1 Differences between structural linearity and nonlinearity 14
2.2.2 Types of structural nonlinearity 16
2.2.3 An example of geometrically nonlinear structure 16
2.2.4 Incremental-iterative approach 17
2.2.5 Finite element formulation 20
2.2.6 Objective functions and adjoint sensitivity analysis 21
2.3 Density-update methods 22
2.3.1 MMA Method 22
2.3.2 BESO’s update method 26
Chapter 3: Design Examples 28
3.1 Cantilever beam 28
3.1.1 Load magnitude of 60 kN 29
3.1.2 Load magnitude of 144 kN 35
3.2 Clamped beam 40
Chapter 4: Continuation Method 49
4.1 Penalty factor 49
4.2 Continuation method 49
4.3 Implementing continuation method 50
Chapter 5: Finite Element Analysis of Optimal Topology using ANSYS APDL 55
5.1 2D topology analysis using ANSYS APDL 55
5.2 Validation of ANSYS APDL command 57
5.3 Buckle behavior 62
Chapter 6: Conclusions and Suggestions 69
References 71
Appendix A: MMA Matlab Code 74
Appendix B: Geometrically Nonlinear FEA ANSYS APDL Code 77

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