Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function

Yunkang Sui, Xirong Peng

• Publisher: Butterworth-Heinemann
• Year: 2017
• Print ISBN: 9780128126554
• eBook ISBN: 9780128126561
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Modelling, Solving and Applications for Topology Optimization of Continuum Structures: ICM Method Based on Step Function provides an introduction to the history of structural optimization, along with a summary of the existing state-of-the-art research on topology optimization of continuum structures. It systematically introduces basic concepts and principles of ICM method, also including modeling and solutions to complex engineering problems with different constraints and boundary conditions. The book features many numerical examples that are solved by the ICM method, helping researchers and engineers solve their own problems on topology optimization.This valuable reference is ideal for researchers in structural optimization design, teachers and students in colleges and universities working, and majoring in, related engineering fields, and structural engineers.- Offers a comprehensive discussion that includes both the mathematical basis and establishment of optimization models- Centers on the application of ICM method in various situations with the introduction of easily coded software- Provides illustrations of a large number of examples to facilitate the applications of ICM method across a variety of disciplines

Chapter 1

Exordium

Abstract

This chapter discusses the concept of structural optimization, its general definition, developments and methodologies, and relevant mathematical theories involved within the current research.

The text offers information on current research and ways in which reliable and efficient methods of design improvement of structure have gradually become an important branch of mechanics. Included in the chapter is an explanation of the structural optimization model and its classification into models of continuous variables, discrete variables, and continuous and discrete mixed variables. The author defines the three levels of structural optimization: size, shape, and topology.

The history of structural optimization is traced from the 1890s through present day development. Progress in topology optimization of continuum structures is detailed; other methods and solution strategies are also mentioned, including the evolutionary structural optimization (ESO) method, and the bi-directional evolutionary structural optimization (BESO) method.

Keywords

Structural optimization; optimization algorithms; evolutionary structural optimization; optimal criteria method; Lagrange multiplier; continuum structures

Chapter Outline

1.1 Research History on Structural Optimization Design 3

1.1.1 Classification and Hierarchy for Structural Optimization Design 3

1.1.2 Development of Structural Optimization 5

1.2 Research Progress in Topology Optimization of Continuum Structures 13

1.2.1 Numerical Methods Solving Problems of Topology Optimization of Continuum Structures 13

1.2.2 Solution Algorithms for Topology Optimization of Continuum Structures 21

1.3 Concepts and Algorithms on Mathematical Programming 22

1.3.1 Three Essential Factors of Structural Optimization Design 22

1.3.2 Models for Mathematical Programming 24

1.3.3 Linear Programming 26

1.3.4 Quadratic Programming 28

1.3.5 Kuhn–Tucker Conditions and Duality Theory 29

1.3.6 K-S Function Method 32

1.3.7 Theory of Generalized Geometric Programming 33

1.3.8 Higher Order Expansion Under Function Transformations and Monomial Higher Order Condensation Formula 35

With the development of science, technology and social productivity, human activities expand continuously into the space and ocean, and the research scope of the structural optimization extensively expands. Structural optimization design is becoming more and more important due to limited resources, intense engineering technological competitions, and environmental protection problems. Higher operating requirements are demanded for components of various high-precision and advanced devices. Designing structures and components to satisfy various constraints, therefore, provides both new opportunities and new challenges to structural engineers and mechanics researchers. On the other hand, the real-world simulations coupled in several physical fields are inevitably involved in structural and multidisciplinary optimization, greatly expanding the scope of structural optimization design.

Structural optimization aims at producing a safe and economic structural design subject to various load cases and structural materials. To obtain optimal design, not only mechanical properties such as strength, stiffness, stability, dynamic, and fatigue should be taken into account but also requirements of the application and operation such as manufacturing processes, construction conditions, and limits in the specifications of construction, manufacturing, and design should be satisfied. All requirements, conditions, and limits are expressed as constraints, whereas the economic index or a mechanical property is taken as the objective function. Design parameters, including design details such as the structure type and sizes, are taken as design variables. Henceforth, the optimization expression of a structural design is formed, and the mathematical model of the optimization can be further established. Finally, th...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Acknowledgment
• Chapter 1. Exordium
• Chapter 2. Foundation of the ICM (independent, continuous and mapping) method
• Chapter 3. Stress-constrained topology optimization for continuum structures
• Chapter 4. Displacement-constrained topology optimization for continuum structures
• Chapter 5. Topology optimization for continuum structures with stress and displacement constraints
• Chapter 6. Topology optimization for continuum structures with frequency constraints
• Chapter 7. Topology optimization with displacement and frequency constraints for continuum structures
• Chapter 8. Topology optimization for continuum structures under forced harmonic oscillation
• Chapter 9. Topology optimization with buckling constraints for continuum structures
• Chapter 10. Other correlative methods
• References
• Afterword
• Index