This book was developed while teaching a graduate course at several universities in the United States. Europe and Israel. during the last two decades. The purpose of the book is to introduce the fundamentals and applications of optimum structural design. Much work has been done in this area recently and many studies have been published. The book is an attempt to collect together selected topics of this literature and to present them in a unified approach. It meets the need for an introductory text covering the basic concepts of modem structural optimization. A previous book by the author on this subject ("Optimum Structural Design". published by McGraw-Hill New York in 1981 and by Maruzen Tokyo in 1983). has been used extensively as a text in many universities throughout the world. The present book reflects the rapid progress and recent developments in this area. A major difficulty in studying structural optimization is that integration of concepts used in several areas. such as structural analysis. numerical optimization and engineering design. is necessary in order to solve a specific problem. To facilitate the study of these topics. the book discusses in detail alternative problem formulations. the fundamentals of different optimization methods and various considerations related to structural design. The advantages and the limitations of the presented approaches are illustrated by numerous examples.
1 Problem Statement.- 1.1 Introduction.- 1.1.1 Automated Structural Optimization.- 1.1.2 Structural Optimization Methods.- 1.1.3 Historical Perspective.- 1.1.4 Scope of Text.- 1.2 Analysis Models.- 1.2.1 Elastic Analysis.- 1.2.2 Plastic Analysis.- 1.3 General Formulation.- 1.3.1 Design Variables.- 1.3.2 Constraints.- 1.3.3 Objective Function.- 1.3.4 Mathematical Formulation.- 1.4 Typical Problem Formulations.- 1.4.1 Displacement Method Formulations.- 1.4.2 Force Method Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.1.1 Unconstrained Minimum.- 2.1.2 Constrained Minimum.- 2.2 Unconstrained Minimization.- 2.2.1 Minimization Along a Line.- 2.2.2 Minimization of Functions of Several Variables.- 2.3 Constrained Minimization: Linear Programming.- 2.3.1 Introduction.- 2.3.2 Problem Formulation.- 2.3.3 Method of Solution.- 2.3.4 Further Considerations.- 2.4 Constrained Minimization: Nonlinear Programming.- 2.4.1 Sequential Unconstrained Minimization.- 2.4.2 The Method of Feasible Directions.- 2.4.3 Other Methods.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.1.1 Design Sensitivity Analysis.- 3.1.2 Intermediate Variables.- 3.1.3 Sequential Approximations.- 3.2 Approximate Behavior Models.- 3.2.1 Basic Displacement Approximations.- 3.2.2 Combined Displacement Approximations.- 3.2.3 Homogeneous Functions.- 3.2.4 Displacement Approximations along a Line.- 3.2.5 Approximate Force Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.1.1 Plastic Design.- 4.1.2 Elastic Design.- 4.2 Feasible-Design Procedures.- 4.2.1 General Considerations.- 4.2.2 Optimization in Design Planes.- 4.3 Optimality Criteria Procedures.- 4.3.1 Stress Criteria.- 4.3.2 Displacement Criteria.- 4.3.3 Design Procedures.- 4.3.4 The Relationship Between OC and MP.- 4.4 Multilevel Optimal Design.- 4.4.1 General Formulation.- 4.4.2 Two-Level Design of Prestressed Concrete Systems.- 4.4.3 Multilevel Design of Indeterminate Systems.- 4.5 Optimal Design and Structural Control.- 4.5.1 Optimal Control of Structures.- 4.5.2 Improved Optimal Design by Structural Control.- 4.6 Geometrical Optimization.- 4.6.1 Simultaneous Optimization of Geometry and Cross Sections.- 4.6.2 Approximations and Multilevel Optimization.- 4.7 Topological Optimization.- 4.7.1 Problem Statement.- 4.7.2 Types of Optimal Topologies.- 4.7.3 Properties of Optimal Topologies.- 4.7.4 Approximations and Two-Stage Procedures.- 4.8 Interactive Layout Optimization.- 4.8.1 Optimization Programs.- 4.8.2 Graphical Interaction Programs.- 4.8.3 Design Procedure.- Exercises.- References.
This book introduces the fundamentals, methods and applications of structural optimization. It gives a survey of the literature on the subject published in recent years and presents selected topics in a unified approach. The text adresses both the student and the practising structural engineer. The book discusses in detail various problem formulations, the relative merit of different optimization methods and considerations related to practical applications. The emphasis throughout is on approximation concepts, which are essential in the solution of many practical design problems, and on multistage design procedures where various methods are combined to solve the overall design problem. The advantages as well as the limitations of the various problem formulations, solution methods and design procedures are discussed and illustrated by a variety of examples.
1 Problem Statement.- 1.1 Introduction.- 1.2 Analysis Models.- 1.3 General Formulation.- 1.4 Typical Problem Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.2 Unconstrained Minimization.- 2.3 Constrained Minimization: Linear Programming.- 2.4 Constrained Minimization: Nonlinear Programming.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.2 Approximate Behavior Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.2 Feasible-Design Procedures.- 4.3 Optimality Criteria Procedures.- 4.4 Multilevel Optimal Design.- 4.5 Optimal Design and Structural Control.- 4.6 Geometrical Optimization.- 4.7 Topological Optimization.- 4.8 Interactive Layout Optimization.- Exercises.- References.
Inhaltsverzeichnis
1 Problem Statement.- 1.1 Introduction.- 1.1.1 Automated Structural Optimization.- 1.1.2 Structural Optimization Methods.- 1.1.3 Historical Perspective.- 1.1.4 Scope of Text.- 1.2 Analysis Models.- 1.2.1 Elastic Analysis.- 1.2.2 Plastic Analysis.- 1.3 General Formulation.- 1.3.1 Design Variables.- 1.3.2 Constraints.- 1.3.3 Objective Function.- 1.3.4 Mathematical Formulation.- 1.4 Typical Problem Formulations.- 1.4.1 Displacement Method Formulations.- 1.4.2 Force Method Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.1.1 Unconstrained Minimum.- 2.1.2 Constrained Minimum.- 2.2 Unconstrained Minimization.- 2.2.1 Minimization Along a Line.- 2.2.2 Minimization of Functions of Several Variables.- 2.3 Constrained Minimization: Linear Programming.- 2.3.1 Introduction.- 2.3.2 Problem Formulation.- 2.3.3 Method of Solution.- 2.3.4 Further Considerations.- 2.4 Constrained Minimization: Nonlinear Programming.- 2.4.1 Sequential Unconstrained Minimization.- 2.4.2 The Method of Feasible Directions.- 2.4.3 Other Methods.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.1.1 Design Sensitivity Analysis.- 3.1.2 Intermediate Variables.- 3.1.3 Sequential Approximations.- 3.2 Approximate Behavior Models.- 3.2.1 Basic Displacement Approximations.- 3.2.2 Combined Displacement Approximations.- 3.2.3 Homogeneous Functions.- 3.2.4 Displacement Approximations along a Line.- 3.2.5 Approximate Force Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.1.1 Plastic Design.- 4.1.2 Elastic Design.- 4.2 Feasible-Design Procedures.- 4.2.1 General Considerations.- 4.2.2 Optimization in Design Planes.- 4.3 Optimality Criteria Procedures.- 4.3.1 Stress Criteria.- 4.3.2 Displacement Criteria.- 4.3.3 Design Procedures.- 4.3.4 The Relationship Between OC and MP.- 4.4 Multilevel Optimal Design.- 4.4.1 General Formulation.- 4.4.2 Two-Level Design of Prestressed Concrete Systems.- 4.4.3 Multilevel Design of Indeterminate Systems.- 4.5 Optimal Design and Structural Control.- 4.5.1 Optimal Control of Structures.- 4.5.2 Improved Optimal Design by Structural Control.- 4.6 Geometrical Optimization.- 4.6.1 Simultaneous Optimization of Geometry and Cross Sections.- 4.6.2 Approximations and Multilevel Optimization.- 4.7 Topological Optimization.- 4.7.1 Problem Statement.- 4.7.2 Types of Optimal Topologies.- 4.7.3 Properties of Optimal Topologies.- 4.7.4 Approximations and Two-Stage Procedures.- 4.8 Interactive Layout Optimization.- 4.8.1 Optimization Programs.- 4.8.2 Graphical Interaction Programs.- 4.8.3 Design Procedure.- Exercises.- References.
Klappentext
This book was developed while teaching a graduate course at several universities in the United States. Europe and Israel. during the last two decades. The purpose of the book is to introduce the fundamentals and applications of optimum structural design. Much work has been done in this area recently and many studies have been published. The book is an attempt to collect together selected topics of this literature and to present them in a unified approach. It meets the need for an introductory text covering the basic concepts of modem structural optimization. A previous book by the author on this subject ("Optimum Structural Design". published by McGraw-Hill New York in 1981 and by Maruzen Tokyo in 1983). has been used extensively as a text in many universities throughout the world. The present book reflects the rapid progress and recent developments in this area. A major difficulty in studying structural optimization is that integration of concepts used in several areas. such as structural analysis. numerical optimization and engineering design. is necessary in order to solve a specific problem. To facilitate the study of these topics. the book discusses in detail alternative problem formulations. the fundamentals of different optimization methods and various considerations related to structural design. The advantages and the limitations of the presented approaches are illustrated by numerous examples.
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