Topology Optimization of Compliant Mechanisms (eBook)

Xianmin ZHANG: Received PhD degree of mechanical engineering from Beihang University in 1993, and now working at South China University of Technology as a Chair Professor. His is the Dean of the School of Mechanical and Automotive Engineering in South China University of Technology and the Director of the Guangdong Province Key laboratory of Precision Equipment and Manufacturing Technology. His research interests include Compliant mechanism, Robotics, Precision instrument, Dynamics and vibration control of mechanisms. He has finished over 60 projects and authored or co-authored over 300 technical papers and over 100 patents. He obtained the first-class technique prize of Guangdong Province in 2009 and 2014; and obtained the national patent award of China in 2012 and 2015, respectively. He has served as the chair of China Committee of IFToMM (International Federation for the Promotion of Mechanism and Machine Science) since June 2016.  Benliang ZHU: Received PhD degree of mechanical engineering from South China University of Technology in 2014, and now working in South China University of Technology as a lecturer. His research interests involve MEMS technique, Precision positioning, Manipulation in the Micro- and Nano-scale.

Preface 5
Contents 8
1 Introduction to Compliant Mechanisms and Design Methods 11
1.1 Concept of a Compliant Mechanism 11
1.2 Applications of Compliant Mechanisms 13
1.3 Approaches to Designing Compliant Mechanisms 15
1.3.1 Kinematics-Based Approach 15
1.3.2 Topology Optimization Approach 17
References 29
2 Topology Optimization of Flexure Hinges 35
2.1 Introduction 35
2.2 Optimization Problem Setting 37
2.2.1 Optimization Model 38
2.2.2 Translational Flexure Hinges 39
2.2.3 Revolute Flexure Hinges 40
2.2.4 Sensitivity Analysis 42
2.2.5 Examples 43
2.3 Stress-Constrained Flexure Hinges 47
2.3.1 Stress Criterion 49
2.3.2 Sensitivity Analysis 51
2.3.3 Examples 54
2.4 Redesign of Notch Flexure Hinges 59
2.4.1 Design Domain Setting 60
2.4.2 Optimization Models 61
2.4.3 Topology Results 63
2.5 Post-design Modeling 66
2.5.1 Quasi-V-Shaped Flexure Hinge (QVFH) 66
2.5.2 Multi-notched Flexure Hinge 78
2.6 Conclusions 88
References 89
3 Topology Optimization of Distributed Compliant Mechanisms 91
3.1 Introduction 91
3.2 Point Flexures 93
3.3 A Method of Reducing Two Output Performances 95
3.3.1 A GA-Based Formulation 97
3.3.2 A Self-adjust Scheme for Setting Weighting Factors 102
3.4 A Compliance-Based Method 108
3.4.1 Compliance Formulations 108
3.4.2 A GA-Based Formulation 110
3.4.3 A Mutual Mean Compliance-Based Optimization Model 112
3.5 Compliant Mechanisms with Multiple Outputs 122
3.5.1 Optimization Formulation 123
3.5.2 Validation 124
3.6 Conclusions 128
References 128
4 Topology Optimization of Compliant Parallel Mechanisms 130
4.1 Introduction 130
4.2 Design of CPMs Using the Traditional Topology Optimization Method 132
4.2.1 Multi-criterion Topology Optimization 132
4.2.2 Design Example 134
4.3 Jacobian-Based Topology Optimization 135
4.3.1 Motivation 136
4.3.2 Basic Idea 136
4.3.3 Topology Analysis 137
4.3.4 Optimization Model 143
4.3.5 Case Studies 145
4.4 An Improved Stiffness Evaluation Method for Jacobian-Based Topology Optimization 151
4.4.1 Properties of the Jacobian Matrix 151
4.4.2 Differences Between the C-stiffness and the Stiffness 152
4.4.3 Formulations Using the New Stiffness Evaluation Process 153
4.4.4 Sensitivity Analysis 156
4.4.5 Design of a 2-DOF CPM 157
4.4.6 Design of a 3-DOF CPM 162
4.4.7 Solving Benchmark Problems 163
4.5 Conclusions 166
References 167
5 Extensions 170
5.1 Improving the Computational Efficiency of the Level Set Method 170
5.1.1 A Velocity Predictor-Corrector Construction Scheme 171
5.1.2 Optimization Algorithm 172
5.1.3 Examples 174
5.2 Topology Optimization of Compliant Mechanisms Considering Geometric Nonlinearity 178
5.2.1 Geometrically Nonlinear Finite Element Analysis 178
5.2.2 Optimization Algorithm 179
5.2.3 Numerical Examples 183
5.3 Reliability-Based Topology Optimization of Compliant Mechanisms 184
5.3.1 Reliability Analysis 184
5.3.2 Reliability-Based Topology Optimization 185
5.3.3 Examples 186
5.4 Topology Optimization of Multi-material Compliant Mechanisms 188
5.4.1 Relationship Between Material and Objective 188
5.4.2 Problem Formulation 189
5.4.3 Numerical Implementation 190
5.4.4 Examples 191
References 192
6 Erratum to: Topology Optimization of Compliant Mechanisms 194
Erratum to:& #6
Appendix 195
A.1 Proof in Chap. 5 195
A.2 A 169 Line Matlab Code 197
A.2.1 Matlab Implementation 197
A.2.2 Matlab Code 198