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Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function
- 1st Edition - August 29, 2017
- Authors: Yunkang Sui, Xirong Peng
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 2 6 5 5 - 4
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 2 6 5 6 - 1
Modelling, Solving and Applications for Topology Optimization of Continuum Structures: ICM Method Based on Step Function provides an introduction to the history of structura… Read more
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Request a sales quoteModelling, 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
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
PrefaceChapter 1 Exordium1.1 Research History on Structural Optimization Design1.1.1 Classification and Hierarchy for Structural Optimization Design1.1.2 Development of Structural Optimization1.2 Research Progress in Topology Optimization of Continuum Structures1.2.1 Numerical Methods Solving Problems of Topology Optimization of Continuum Structures1.2.2 Solution Algorithms for Topology Optimization of Continuum Structures1.3 Concepts and Algorithms on Mathematical Programming1.3.1 Three Essential Factors of Structural Optimal Design1.3.2 Models for Mathematical Programming1.3.3 Linear Programming1.3.4 Quadratic Programming1.3.5 Kuhn-Tucker Conditions and Duality Theory1.3.6 K-S Function Method1.3.7 Theory of Generalized Geometric Programming1.3.8 Higher-order Expansion under Function Transformations and Monomial Higher-order Condensation FormulaChapter 2 Foundation of ICM (Independent Continuous and Mapping) Method2.1 Difficulties in Conventional Topology Optimization and Solution2.2 Step Function and Hurdle Function — Bridge of Constructing Relationship between Discrete Topology Variables and Element Performances2.3 Fundamental Breakthrough—Polish Function Approaching to Step Function and Filter Function Approaching to Hurdle Function2.3.1 Polish Function2.3.2 Filter Function2.3.3 Filter Function Make Solution of Topology Optimization is Operable2.3.4 Relationship of Four Functions2.4 ICM Method and Its Application2.4.1 Whole Process of Identification Quantity of Element and Its Mapping Identification2.4.2 Several Typical Polish Functions and Filter Functions2.4.3 Identification Speed of Different Functions and Determination of Their Parameters2.4.4 Establishment of Structural Topology Optimization Model Based on ICM Method2.4.5 Inversion of Mapping2.5 Exploration of Performance of Polish Function and Filter Functions2.5.1 Classification of Polish Functions and Filter Functions2.5.2 Type Judgment Theorem2.5.3 Theorem of Corresponding Relations of Polish Functions and Filter Functions2.6 Exploration of Filter Function with High Precision2.6.1 Application Criterion of Filter Function with High Precision2.6.2 Method on Constructing Fast Filter Function by Left Polish Function with High Precision2.6.3 Selection of Parameter for Exponent Type of Fast Filter Function2.7 Breakthrough on Basic Conceptions in ICM Method Chapter 3 Stress Constrained Topology Optimization for Continuum Structures3.1 ICM Method with Zero-order Approximation Stresses and Solution of Model3.1.1 Topology Optimization Model with Zero-order Approximation Stress Constraints for Continuum Structures3.1.2 Solution of Topology Optimization Model with Zero-order Approximation Stress Constraints for Continuum Structures3.1.3 Other Strategies for Solution Algorithms3.1.4 Examples3.2 Global Stress Constraints to Replace Stress Constraints3.2.1 Globalization Strategy of Stress Constraints3.2.2 Correction Coefficients of Strain Energy Constraints3.2.3 Determination of Correction Coefficients by Using Least Square Method3.2.4 Determination of Correction Coefficients by Using Numerical Simulation3.2.5 Effects of Allowable Stress on Topology Optimization of Continuum Structures3.2.6 Correction Coefficients of Strain Energy Constraints for Multiple Load Cases3.2.7 Determination of Allowable Structural Strain Energy3.3 Topology Optimization of Continuum Structures with Strain Energy Constraints3.4 Topology Optimization of Continuum Structures with Constraints of Distortional Strain Energy Density3.4.1 Global Strategy and Its Correction on Converting Stress Constraints into Constraints of Distortional Strain Energy Density of Structures3.4.2 Topology Optimization Model with Constraints of Corrected Distortional Strain Energy Density of Structures for Continuum Structures Based on ICM Method3.5 Ill-conditioned Loads and Its Solutions3.5.1 Three kinds of Phenomenon Caused by Ill-conditioned Loads3.5.2 Load Treatment by Taking Structural Strain Energy as Weights Coefficients3.5.3 Ill-conditioned Loads Existing Only between Load Cases3.5.4 Ill-conditioned Loads Existing Only in Some Load Cases Inner3.5.5 Ill-conditioned Loads Existing between Load Cases and Also in Some Load Cases Inner3.6 Discussion on Stress Singularity3.7 Examples3.8 SummaryChapter 4 Displacement Constrained Topology Optimization for Continuum Structures4.1 Explicit Approximation of Displacement Constraints4.1.1 Direct Method of Displacement Sensitivity Analysis4.1.2 Adjoint Method of Displacement Sensitivity Analysis4.1.3 Explicit Approximation of Displacement Constraint by the First-order Taylor Expansion4.1.4 Explicit Approximation of Displacement Constraint by Mohr Theorem4.1.5 Consistency of the Two Ways of Explicit Displacement Approximation4.2 Establishment and Solution of Optimization Model with Displacement Constraints for Multiple Load Cases4.3 ICM Method with Requirement of Discrete Topology Variables4.4 Solutions for Checkerboard Patterns and Mesh-dependent Problems4.4.1 Checkerboard Patterns and Mesh-dependent Problems4.4.2 Solving Checkerboard Patterns and Mesh-dependent Problems by Filtering Method4.5 Examples4.6 SummaryChapter 5 Topology Optimization for Continuum Structures with Stress and Displacement Constraints5.1 Dimensionless for Stress Constraints and Displacement Constraints5.2 Establishment and Solution of Optimization Model with Stress Constraints and Displacement Constraints under Multiple Load Cases5.3 Examples5.4 SummaryChapter 6 Topology Optimization for Continuum Structures with Frequency Constraints6.1 Explicit Approximation of Frequency Constraints6.2 Establishment and Solution of Optimization Model with Frequency Constraints6.3 Solutions for Checkerboard Patterns and Mesh Dependence Problems6.4 Solutions for Localized Modes and Mode Switching Problems6.4.1 Localized Mode Problems6.4.2 Solution of Localized Mode Problems6.4.3 Mode Switching Problems6.4.4 Solution of Mode Switching Problems6.5 Examples6.6 SummaryChapter 7 Topology Optimization with Displacement and Frequency Constraints for Continuum Structures7.1 Dimensionless Displacement and Frequency Constraints7.2 Establishment and Solution of Optimization Model with Displacement and Frequency Constraints7.3 Solutions for Numerical Unstable Problems7.3.1 Solutions of Checkerboard Patterns and Mesh-dependent Problems7.3.2 Solutions of Localized Mode and Mode Switching Problems7.4 Examples7.5 SummaryChapter 8 Topology Optimization for Continuum Structures under Forced Harmonic Oscillation8.1 Sensitivity Analysis of Displacement Amplitude for Forced Harmonic Oscillation8.1.1 Methods of Sensitivity Analysis of Displacement Amplitude under Forced Harmonic Oscillation8.1.2 Sensitivity Analysis of Displacement Amplitude for Undamped Structure under Forced Harmonic Oscillation8.1.3 Sensitivity Analysis of Displacement Amplitude for Damping Structure under Forced Harmonic Oscillation8.1.4 Derivatives of Matrix8.1.5 Examples8.2 Explicit Approximation of Displacement Amplitude Constraints8.3 Establishment and Solution of Optimization Model with Displacement Amplitude Constraints for Forced Harmonic Oscillation8.4 Examples8.5 SummaryChapter 9 Topology Optimization with Buckling Constraints for Continuum Structures9.1 Basic Concepts for Buckling Analysis9.2 Explicit Approximation of Buckling Constraints9.3 Establishment and Solution of Topology Optimization Model of Continuum Structures with Buckling Constraints9.4 Criterion of Selecting Upper Limit of Critical Buckling Force9.4.1 Relationship between Upper Limit of Critical Buckling Force of First-order Mode and Structural Weight of Optimal Topology9.4.2 Relationship between Upper Limit of Second-order Critical Buckling Force and Optimal Structural Weight9.4.3 Relationship between Upper Limit of the Third-order Critical Buckling Force and Optimal Structural Weight9.5 Examples9.6 SummaryChapter 10 Other Correlative Methods10.1 Solid-void Combined Element Method and Its Applications in Topology Optimization of Continuum Structures10.1.1 Solid-void Combined Elements for Plane Membrane10.1.2 Allowable Stress for Solid-void Combined Element10.1.3 Displacement Contributions of Solid-void Combined Element for Plane Membrane10.1.4 Topology Optimization with Stress and Displacement Constraints by Solid-void Combined Element Method for Plane Membranes10.1.5 Examples10.2 Topology Optimization of Continuum Structures with Integration Constraints10.2.1 Modeling and Solution by Integrated Stress Constraints10.2.2 Modeling and Solution by Integrated Displacement Constraints10.2.3 Modeling and Solution by Integrated Stress and Displacement Constraints10.3 Structural Topology Optimization with Parabolic Aggregation Function10.3.1 Parabolic Aggregation Function10.3.2 Integrated Constraints by Parabolic Aggregation Function10.4 Structural Topology Optimization with High-Quality Approximation of Step Function10.5 SummaryReferencesAfterword
- No. of pages: 394
- Language: English
- Edition: 1
- Published: August 29, 2017
- Imprint: Butterworth-Heinemann
- Paperback ISBN: 9780128126554
- eBook ISBN: 9780128126561
YS
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, ChinaXP
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, ChinaRead Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step Function on ScienceDirect