1 Introduction /1 1.1 Background/ 1 1.2 Current Development /3 1.3 Software Platform /13 1.4 Key Topics in Buckling Topological Optimization Research /14 2 Topological Optimization for Continuous Structure with Bulking Constrain /17 2.1 Introduction/ 17 2.2 ICM Method /18 2.3 Determination of Filter Function /21 2.4 Model Establishment and Realization /28 2.5 Solution to Optimization /32 2.6 Optimization Strategy /34 2.7 Constrain Selection/ 36 2.8 Optimization Algorithms /48 2.9 Numerical Simulation and Case Study/ 49 2.10 Summary /108 3 Topological Optimization for Continuous Structure with Bulking and Displacement Constraint /109 3.1 Introduction /109 3.2 Model Establishment and Solution /110 3.3 Optimization Strategy /116 3.4 Constrain Selection /117 3.5 Optimization Algorithms /123 3.6 Numerical Simulation and Case Study /125 3.7 Summary /172 4 Topological Optimization for Continuous Structure with Buckling and Stress Constraints /174 4.1 Introduction/ 174 4.2 Deformation Energy /175 4.3 The Theoretical Background of Deformation Energy /176 4.4 Method of Globalization of Stress Constraints and Strain Revision Coefficient /176 4.5 Model Establishment and Solution /178 4.6 Optimization Strategy/ 184 4.7 Constraint Selection/ 185 4.8 Optimization Algorithms/ 190 4.9 Numerical Simulation and Case Study /191 4.10 Summary /238 5 Topological Optimization for Continuous Structure with Static Constraint/ 240 5.1 Introduction /240 5.2 Model Establishment and Solution /240 5.3 Upper Limit for Constraint/ 246 5.4 Optimization Algorithms /246 5.5 Numerical Simulation and Case Study/ 248 5.6 Summary/ 269 6 Software and User Instructions /274 6.1 Introduction /274 6.2 Compiling and Linking of a User Program/ 275 6.3 Setup for Analysis and Output /275 6.4 Topological Optimization Menu and Inputs/ 276 6.5 Output and Results Menu /282 6.6 Summary /292 7 Engineering Applications /293 7.1 Introduction /293 7.2 System Optimization in Industry via Mixed Programming/ 293 7.3 Topological Optimization in the Design of a Power Transformer Lifting Lug /297 7.4 Finite Element Method and Topological Optimization in a Small-sized Transformer Fuel Tank /306 7.5 Topological Optimization in the Design of Vacuum Tank/ 322 7.6 Summary /331 8 Prospect /333 References/ 336 Disclaimer for the software /340 Index /341