Foreword by Manfred Curbach v
Foreword by Werner Sobek ix
Preface xiii
List of Examples xix
Acronyms xxi
About the Authors xxiii
Acknowledgments xxv
1 Introduction 1
1.1 Preliminaries 1
1.2 Outer and Inner Shaping 2
1.3 Environmental Demands 6
1.4 Optimization Aided Design (OAD) 11
1.5 Structure of the Book 14
References 15
2 Fundamentals of Reinforced Concrete (RC) Design 19
2.1 Basic Principles 19
2.2 Verification Concept 21
2.3 Safety Concept 22
2.4 Materials 23
2.4.1 Plain Concrete 23
2.4.2 Fiber-Reinforced Concrete (FRC) 24
2.4.3 Ultra-High Performance Concrete (UHPC) 26
2.4.4 Reinforcement 27
2.5 Load-Bearing Behavior 28
2.5.1 Bending Design 28
2.5.1.1 Fundamentals 28
2.5.1.2 Equilibrium for Composite Sections 29
2.5.2 Strut-and-Tie Models (STMs) 32
References 35
3 Fundamentals of Structural Optimization 37
3.1 Structural Optimization Approaches 37
3.1.1 General Procedure 37
3.1.2 Classification of Methods 38
3.2 Problem Statement 40
3.3 Lagrange Function 43
3.4 Sensitivity Analysis 44
3.4.1 Numerical Approach 44
3.4.2 Analytical Approach 45
3.5 Solution Methods 46
3.5.1 Mathematical Programming 46
3.5.2 Optimality Conditions (OC) 47
References 47
4 Identification of Structures 51
4.1 One-material Structures 52
4.1.1 Problem Statement 52
4.1.2 Sensitivity Analysis 54
4.1.3 Filtering 54
4.1.4 Solving 56
4.1.5 Optimization Process 57
4.1.6 Multiple Load Cases 58
4.2 One-material Stress-biased Structures 59
4.2.1 Problem Statement 59
4.2.2 Sensitivity Analysis and Stress Bias 60
4.2.3 Solving 62
4.2.4 Optimization Process 63
4.3 Bi-material Structures 64
4.3.1 Problem Statement 64
4.3.2 Sensitivity Analysis and Stress Differentiation 65
4.3.3 Bi-material Filtering 68
4.3.4 Solving 69
4.3.5 Optimization Process 70
4.4 Examples 71
4.4.1 One-material Structures 71
4.4.2 One-material Stress-biased Structures 81
4.4.3 Bi-material Structures 83
4.5 Applications 89
4.5.1 Solar Thermal Collectors 89
4.5.1.1 Parabolic Trough Collectors 90
4.5.1.2 Heliostats 95
4.5.2 Ultra-light Beams 100
References 102
5 Internal Force Flow 109
5.1 Preliminaries 110
5.2 Continuum Topology Optimization (CTO) Approach 111
5.3 Truss Topology Optimization (TTO) Approach 112
5.3.1 Problem Statement 112
5.3.2 Sensitivity Analysis and Solving 117
5.3.3 Optimization Process 119
5.3.4 Recommendations for Practical Application 120
5.3.4.1 Setting Up the Optimization Problem 120
5.3.4.2 Procedure 123
5.4 Continuum-Truss Topology Optimization (CTTO) Approach 124
5.4.1 Problem Statement 125
5.4.2 Sensitivity Analysis and Solving 128
5.4.3 Post-Processing 130
5.4.4 Optimization Process 132
5.5 Examples 133
5.5.1 CTO Approach 133
5.5.2 TTO Approach 138
5.6 Applications 151
5.6.1 Joints in Tunnel Linings 151
5.6.2 Partial Area Loading in Tunnel Linings 153
References 153
6 Design of Cross-sections 157
6.1 Problem Statement 159
6.2 Equilibrium Iteration 161
6.3 Sectional Optimization 163
6.3.1 Reinforcement Amounts 165
6.3.2 Cross-sectional Layout 165
6.3.3 Material Weighting 165
6.4 Solving 166
6.4.1 Stress Integrals 166
6.4.2 Optimization Problem 167
6.5 Parameterization 167
6.5.1 Plane Case 167
6.5.2 Spatial Case 168
6.5.3 Parameterization with Intentional Steering 169
6.6 Examples 170
6.6.1 Equilibrium Iteration 170
6.6.2 Sectional Optimization 175
References 183
