臺灣博碩士論文加值系統

本文針對演化率相依問題與加工限制，修正篩選機制與元素增減準則，提出修正式結構最佳化雙向演進法。修正式篩選機制隨著演化過程逐漸縮小篩選半徑，而非選用固定長度的篩選半徑。此修正有助於抑制演化率相依問題，進而提升結構最佳化雙向演進法之穩定性。另一方面，由所需的加工方式而決定的拉拔方向限制，可藉由修正元素增減準則來實現。修正式元素增減準則從拉拔方向的表面往設計區域的內部逐漸移除元素。有拉拔方向限制的最佳設計可避免出現中空或封閉孔洞等難以加工的幾何形狀，因此提升結構最佳化雙向演進法的實用性。本文整合修正式結構最佳化雙向演進法與有限元素分析軟體，發展出一套結構拓樸最佳化軟體。其結果驗證本文所提出的修正方法在結構拓璞最佳化中之可行性及實用性。

This thesis proposes a modified bi-directional evolutionary structural optimization (BESO) method which combines a modified filter scheme and a modified element removal/addition criterion for evolution ratio dependence problem and manufacturing constraints. Instead of selecting a fixed length of filter radius, the modified filter scheme decreases the length of filter radius through the evolution process. Such modification contributes to the suppression of evolution ratio dependence problem, and therefore enhances the stability of BESO method. On the other hand, draw direction constraints, defined by required manufacturing process, are achieved by modifying the element removal/addition criterion. Modified element removal/addition criterion gradually removes elements from top surface of the draw direction to the inner design domain. The optimal designs with draw direction constraints are free from hollow or closed cavity geometries which are infeasible for manufacturing, and therefore the practicability of BESO method is enhanced. A structural topology optimization program which combines the proposed modified BESO method and ANSYS is developed. The results prove the validity and practicability of the proposed modifications in structural topology optimization.

誌謝 I
中文摘要 III
ABSTRACT IV
CONTENTS V
LIST OF FIGURES IX
LIST OF TABLES XIV
LIST OF SYMBOLS XVI
Chapter 1 Introduction 1
1.1 Introduction of Structural Topology Optimization 1
1.2 Paper Review 3
1.3 Motivation 7
1.4 Thesis Outline 8
Chapter 2 Theoretical Review 10
2.1 Evolutionary Structural Optimization (ESO) Method 10
2.1.1 ESO method based on stress level 10
2.1.2 ESO method for stiffness optimization problem 11
2.1.3 Discussion of ESO method 14
2.2 Bi-Directional Evolutionary Structural Optimization (BESO) Method 17
2.2.1 Concept of BESO method 17
2.2.2 Discussion of BESO method 18
2.3 Checkerboard and Mesh Dependence Problem 19
2.3.1 Checkerboard pattern 20
2.3.2 Mesh dependence problem 22
2.4 Mesh-Independency Filter Integrated into BESO Method 24
2.4.1 Sensitivity calculation 25
2.4.2 Element removal/addition and convergence criterion 27
2.5 Numerical Examples of Mesh-Independency Filter Integrated into BESO Method 29
2.5.1 Example: mesh independent solutions 29
2.5.2 Example: member size control 31
Chapter 3 Modified Bi-Directional Evolutionary Structural Optimization Method 33
3.1 Modified Filter Scheme for Evolution Ratio Dependence Problem 33
3.1.1 Example: BESO method with different evolution ratios 34
3.1.2 Modified filter scheme 39
3.2 Modified Element Removal/Addition Criterion for Draw Direction Constraints 40
3.2.1 Introduction of draw direction constraints in topology optimization 40
3.2.2 Modified element removal/addition criterion 41
3.3 Numerical Implementation of BESO Program 46
Chapter 4 Numerical Examples of Modified Filter Scheme 51
4.1 Short Cantilever Beam 51
4.2 Long Cantilever Beam 55
4.3 MBB beam 59
Chapter 5 Numerical Examples of Modified Element Removal/Addition Criterion 65
5.1 3D Arch Structure under Self-Weight Loading 65
5.2 3D Beam under Torsion Load 68
5.3 3D Beam under Bending Load 71
5.4 3D Plate under Bending Load 73
Chapter 6 Practical Example Demonstration 77
6.1 Static Structural Analysis of the Front Cover 77
6.1.1 Introduction of the front cover of the motor 77
6.1.2 Convergence test 80
6.1.3 Load and support setting 81
6.1.4 Analysis result 84
6.2 BESO Design Process 86
Chapter 7 Conclusions and Suggestions 95
7.1 Conclusions 95
7.2 Suggestions 96
REFERENCE 98
Appendix A: Element Sensitivity Formulation Derivation 104
A-1 Stiffness Maximization under Fix Load 104
A-2 Stiffness Maximization under Self-Weight Load 106
Appendix B: User Manual of BESO Program 108
B-1 Operation Steps of BESO Program 108
B-2 Input Data of BESO Program 109
B-3 Output Data of BESO Program 113
B-4 Tips of using BESO Program 114

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