Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function - 1st Edition - ISBN: 9780128126554, 9780128126561

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

1st Edition

Authors: Yunkang Sui Xirong Peng
eBook ISBN: 9780128126561
Paperback ISBN: 9780128126554
Imprint: Butterworth-Heinemann
Published Date: 31st August 2017
Page Count: 394
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Description

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.

Key Features

  • 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

Readership

Researchers in structural optimization design; teachers and students in colleges and universities working and majoring in related engineering fields; structural engineers in extensive engineering fields

Table of Contents

Preface
Chapter 1 Exordium
1.1 Research History on Structural Optimization Design
1.1.1 Classification and Hierarchy for Structural Optimization Design
1.1.2 Development of Structural Optimization
1.2 Research Progress in Topology Optimization of Continuum Structures
1.2.1 Numerical Methods Solving Problems of Topology Optimization of Continuum Structures
1.2.2 Solution Algorithms for Topology Optimization of Continuum Structures
1.3 Concepts and Algorithms on Mathematical Programming
1.3.1 Three Essential Factors of Structural Optimal Design
1.3.2 Models for Mathematical Programming
1.3.3 Linear Programming
1.3.4 Quadratic Programming
1.3.5 Kuhn-Tucker Conditions and Duality Theory
1.3.6 K-S Function Method
1.3.7 Theory of Generalized Geometric Programming
1.3.8 Higher-order Expansion under Function Transformations and Monomial Higher-order Condensation Formula
Chapter 2 Foundation of ICM (Independent Continuous and Mapping) Method
2.1 Difficulties in Conventional Topology Optimization and Solution
2.2 Step Function and Hurdle Function — Bridge of Constructing Relationship between Discrete Topology Variables and Element Performances
2.3 Fundamental Breakthrough—Polish Function Approaching to Step Function and Filter Function Approaching to Hurdle Function
2.3.1 Polish Function
2.3.2 Filter Function
2.3.3 Filter Function Make Solution of Topology Optimization is Operable
2.3.4 Relationship of Four Functions
2.4 ICM Method and Its Application
2.4.1 Whole Process of Identification Quantity of Element and Its Mapping Identification
2.4.2 Several Typical Polish Functions and Filter Functions
2.4.3 Identification Speed of Different Functions and Determination of Their Parameters
2.4.4 Establishment of Structural Topology Optimization Model Based on ICM Method
2.4.5 Inversion of Mapping
2.5 Exploration of Performance of Polish Function and Filter Functions
2.5.1 Classification of Polish Functions and Filter Functions
2.5.2 Type Judgment Theorem
2.5.3 Theorem of Corresponding Relations of Polish Functions and Filter Functions
2.6 Exploration of Filter Function with High Precision
2.6.1 Application Criterion of Filter Function with High Precision
2.6.2 Method on Constructing Fast Filter Function by Left Polish Function with High Precision
2.6.3 Selection of Parameter for Exponent Type of Fast Filter Function
2.7 Breakthrough on Basic Conceptions in ICM Method
 Chapter 3 Stress Constrained Topology Optimization for Continuum Structures
3.1 ICM Method with Zero-order Approximation Stresses and Solution of Model
3.1.1 Topology Optimization Model with Zero-order Approximation Stress Constraints for Continuum Structures
3.1.2 Solution of Topology Optimization Model with Zero-order Approximation Stress Constraints for Continuum Structures
3.1.3 Other Strategies for Solution Algorithms
3.1.4 Examples
3.2 Global Stress Constraints to Replace Stress Constraints
3.2.1 Globalization Strategy of Stress Constraints
3.2.2 Correction Coefficients of Strain Energy Constraints
3.2.3 Determination of Correction Coefficients by Using Least Square Method
3.2.4 Determination of Correction Coefficients by Using Numerical Simulation
3.2.5 Effects of Allowable Stress on Topology Optimization of Continuum Structures
3.2.6 Correction Coefficients of Strain Energy Constraints for Multiple Load Cases
3.2.7 Determination of Allowable Structural Strain Energy
3.3 Topology Optimization of Continuum Structures with Strain Energy Constraints
3.4 Topology Optimization of Continuum Structures with Constraints of Distortional Strain Energy Density
3.4.1 Global Strategy and Its Correction on Converting Stress Constraints into Constraints of Distortional Strain Energy Density of Structures
3.4.2 Topology Optimization Model with Constraints of Corrected Distortional Strain Energy Density of Structures for Continuum Structures Based on ICM Method
3.5 Ill-conditioned Loads and Its Solutions
3.5.1 Three kinds of Phenomenon Caused by Ill-conditioned Loads
3.5.2 Load Treatment by Taking Structural Strain Energy as Weights Coefficients
3.5.3 Ill-conditioned Loads Existing Only between Load Cases
3.5.4 Ill-conditioned Loads Existing Only in Some Load Cases Inner
3.5.5 Ill-conditioned Loads Existing between Load Cases and Also in Some Load Cases Inner
3.6 Discussion on Stress Singularity
3.7 Examples
3.8 Summary
Chapter 4 Displacement Constrained Topology Optimization for Continuum Structures
4.1 Explicit Approximation of Displacement Constraints
4.1.1 Direct Method of Displacement Sensitivity Analysis
4.1.2 Adjoint Method of Displacement Sensitivity Analysis
4.1.3 Explicit Approximation of Displacement Constraint by the First-order Taylor Expansion
4.1.4 Explicit Approximation of Displacement Constraint by Mohr Theorem
4.1.5 Consistency of the Two Ways of Explicit Displacement Approximation
4.2 Establishment and Solution of Optimization Model with Displacement Constraints for Multiple Load Cases
4.3 ICM Method with Requirement of Discrete Topology Variables
4.4 Solutions for Checkerboard Patterns and Mesh-dependent Problems
4.4.1 Checkerboard Patterns and Mesh-dependent Problems
4.4.2 Solving Checkerboard Patterns and Mesh-dependent Problems by Filtering Method
4.5 Examples
4.6 Summary
Chapter 5 Topology Optimization for Continuum Structures with Stress and Displacement Constraints
5.1 Dimensionless for Stress Constraints and Displacement Constraints
5.2 Establishment and Solution of Optimization Model with Stress Constraints and Displacement Constraints under Multiple Load Cases
5.3 Examples
5.4 Summary
Chapter 6 Topology Optimization for Continuum Structures with Frequency Constraints
6.1 Explicit Approximation of Frequency Constraints
6.2 Establishment and Solution of Optimization Model with Frequency Constraints
6.3 Solutions for Checkerboard Patterns and Mesh Dependence Problems
6.4 Solutions for Localized Modes and Mode Switching Problems
6.4.1 Localized Mode Problems
6.4.2 Solution of Localized Mode Problems
6.4.3 Mode Switching Problems
6.4.4 Solution of Mode Switching Problems
6.5 Examples
6.6 Summary
Chapter 7 Topology Optimization with Displacement and Frequency Constraints for Continuum Structures
7.1 Dimensionless Displacement and Frequency Constraints
7.2 Establishment and Solution of Optimization Model with Displacement and Frequency Constraints
7.3 Solutions for Numerical Unstable Problems
7.3.1 Solutions of Checkerboard Patterns and Mesh-dependent Problems
7.3.2 Solutions of Localized Mode and Mode Switching Problems
7.4 Examples
7.5 Summary
Chapter 8 Topology Optimization for Continuum Structures under Forced Harmonic Oscillation
8.1 Sensitivity Analysis of Displacement Amplitude for Forced Harmonic Oscillation
8.1.1 Methods of Sensitivity Analysis of Displacement Amplitude under Forced Harmonic Oscillation
8.1.2 Sensitivity Analysis of Displacement Amplitude for Undamped Structure under Forced Harmonic Oscillation
8.1.3 Sensitivity Analysis of Displacement Amplitude for Damping Structure under Forced Harmonic Oscillation
8.1.4 Derivatives of Matrix
8.1.5 Examples
8.2 Explicit Approximation of Displacement Amplitude Constraints
8.3 Establishment and Solution of Optimization Model with Displacement Amplitude Constraints for Forced Harmonic Oscillation
8.4 Examples
8.5 Summary
Chapter 9 Topology Optimization with Buckling Constraints for Continuum Structures
9.1 Basic Concepts for Buckling Analysis
9.2 Explicit Approximation of Buckling Constraints
9.3 Establishment and Solution of Topology Optimization Model of Continuum Structures with Buckling Constraints
9.4 Criterion of Selecting Upper Limit of Critical Buckling Force
9.4.1 Relationship between Upper Limit of Critical Buckling Force of First-order Mode and Structural Weight of Optimal Topology
9.4.2 Relationship between Upper Limit of Second-order Critical Buckling Force and Optimal Structural Weight
9.4.3 Relationship between Upper Limit of the Third-order Critical Buckling Force and Optimal Structural Weight
9.5 Examples
9.6 Summary
Chapter 10 Other Correlative Methods
10.1 Solid-void Combined Element Method and Its Applications in Topology Optimization of Continuum Structures
10.1.1 Solid-void Combined Elements for Plane Membrane
10.1.2 Allowable Stress for Solid-void Combined Element
10.1.3 Displacement Contributions of Solid-void Combined Element for Plane Membrane
10.1.4 Topology Optimization with Stress and Displacement Constraints by Solid-void Combined Element Method for Plane Membranes
10.1.5 Examples
10.2 Topology Optimization of Continuum Structures with Integration Constraints
10.2.1 Modeling and Solution by Integrated Stress Constraints
10.2.2 Modeling and Solution by Integrated Displacement Constraints
10.2.3 Modeling and Solution by Integrated Stress and Displacement Constraints
10.3 Structural Topology Optimization with Parabolic Aggregation Function
10.3.1 Parabolic Aggregation Function
10.3.2 Integrated Constraints by Parabolic Aggregation Function
10.4 Structural Topology Optimization with High-Quality Approximation of Step Function
10.5 Summary
References
Afterword

Details

No. of pages:
394
Language:
English
Copyright:
© Butterworth-Heinemann 2018
Published:
Imprint:
Butterworth-Heinemann
eBook ISBN:
9780128126561
Paperback ISBN:
9780128126554

About the Author

Yunkang Sui

Professor, College of mechanical engineering and applied electronics technology in the Beijing University of Technology, Beijing, China.

His research fields are structural-multidisciplinary optimization, computational mechanics and applied mathematical programming. One of his main contributions is the proposition of ICM (Independent Continuous and Mapping) Method for Topology Optimization of Continuum Structures

e is member of ISSMO (International Society for Structural and Multidisciplinary Optimization), the vice chairman of Beijing society of mechanics and the deputy editor in chief of Journal Engineering Mechanics. He has presided over many projects supported by Natural Science Foundation of China and industrial fields. He has published more than 400 papers, 6 academic monographs and obtained more than 40 software copyrights. He won 4 science awards including the second-class national award in natural sciences of China and the third-class national science and technology progress award.

Affiliations and Expertise

Professor, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China

Xirong Peng

After receiving a doctorate degree from Beijing University of Technology under the guidance of Professor Yunkang Sui in December, 2004, he worked for Altair company as a senior developer of the structural optimization software OptiStruct, in the United States. As a postdoctoral researcher, he worked for Tsinghua University, China. As an associate professor, he worked for Shenzhen Graduate School, Harbin Institute of Technology, China. His interests/research fields are structural optimization and structural health monitoring.

Affiliations and Expertise

Associate Professor, College of Civil Engineering, Hunan City University, Yiyang, China