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

(Associate Professor, College of Civil Engineering, Hunan City University, Yiyang, China), (Professor, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China)
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  • Ilmumisaeg: 29-Aug-2017
  • Kirjastus: Butterworth-Heinemann Inc
  • Keel: eng
  • ISBN-13: 9780128126561
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Modeling, Solving and Application for Topology Optimization of Continuum Structures: ICM Method Based on Step FunctionSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Aug-2017
  • Kirjastus: Butterworth-Heinemann Inc
  • Keel: eng
  • ISBN-13: 9780128126561
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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

Muu info

Provides a systematic and integrated account of topology optimization of structures using the ICM method, covering theories, methods, solutions and applications
Preface xv
Acknowledgment xxiii
Chapter 1 Exordium
1(36)
1.1 Research History on Structural Optimization Design
3(10)
1.1.1 Classification and Hierarchy for Structural Optimization Design
3(2)
1.1.2 Development of Structural Optimization
5(8)
1.2 Research Progress in Topology Optimization of Continuum Structures
13(9)
1.2.1 Numerical Methods Solving Problems of Topology Optimization of Continuum Structures
13(8)
1.2.2 Solution Algorithms for Topology Optimization of Continuum Structures
21(1)
1.3 Concepts and Algorithms on Mathematical Programming
22(15)
1.3.1 Three Essential Factors of Structural Optimization Design
22(2)
1.3.2 Models for Mathematical Programming
24(2)
1.3.3 Linear Programming
26(2)
1.3.4 Quadratic Programming
28(1)
1.3.5 Kuhn---Tucker Conditions and Duality Theory
29(3)
1.3.6 K-S Function Method
32(1)
1.3.7 Theory of Generalized Geometric Programming
33(2)
1.3.8 Higher Order Expansion Under Function Transformations and Monomial Higher Order Condensation Formula
35(2)
Chapter 2 Foundation of the ICM (independent, continuous and mapping) method
37(42)
2.1 Difficulties in Conventional Topology Optimization and Solution
39(2)
2.2 Step Function and Hurdle Function---Bridge of Constructing Relationship Between Discrete Topology Variables and Element Performances
41(2)
2.3 Fundamental Breakthrough---Polish Function Approaching to Step Function and Filter Function Approaching to Hurdle Function
43(4)
2.3.1 Polish Function
44(1)
2.3.2 Filter Function
45(1)
2.3.3 Filter Function Makes Solution of Topology Optimization Operable
46(1)
2.3.4 Relationship of Four Functions
46(1)
2.4 ICM Method and Its Application
47(19)
2.4.1 Whole Process of Identification Quantity of Element and Its Mapping Identification
47(2)
2.4.2 Several Typical Polish Functions and Filter Functions...
49(3)
2.4.3 Identification Speed of Different Functions and Determination of Their Parameters
52(8)
2.4.4 Transformation From the Parameter of the Power Function to the Parameter of the Logarithmic Function for the Filter Function
60(3)
2.4.5 Establishment of the Structural Topology Optimization Model Based on the ICM Method
63(1)
2.4.6 Inversion of Mapping
64(2)
2.5 Exploration of Performance of Polish Function and Filter Function
66(3)
2.5.1 Classification of Polish Functions and Filter Functions
66(1)
2.5.2 Type Judgment Theorem
67(1)
2.5.3 Theorem of Corresponding Relations of Polish Functions and Filter Functions
67(2)
2.6 Exploration of Filter Function With High Precision
69(7)
2.6.1 Application Criterion of Filter Function With High Precision
69(1)
2.6.2 Method on Constructing Fast Filter Function by Left Polish Function With High Precision
70(4)
2.6.3 Selection of Parameter for Exponent Type of Fast Filter Function
74(2)
2.7 Breakthrough on Basic Conceptions in ICM Method
76(3)
Chapter 3 Stress-constrained topology optimization for continuum structures
79(60)
3.1 ICM Method With Zero-Order Approximation Stresses and Solution of Model
82(7)
3.1.1 Topology Optimization Model With Zero-Order Approximation Stress Constraints for Continuum Structures
82(1)
3.1.2 Solution of Topology Optimization Model With Zero-Order Approximation Stress Constraints for Continuum Structures
82(2)
3.1.3 Other Strategies for Solution Algorithms
84(3)
3.1.4 Examples
87(2)
3.2 Global Stress Constraints to Replace Stress Constraints
89(15)
3.2.1 Globalization Strategy of Stress Constraints
89(4)
3.2.2 Correction Coefficients of Strain Energy Constraints
93(1)
3.2.3 Determination of Correction Coefficients by Using the Least Square Method
94(1)
3.2.4 Determination of Correction Coefficients by Using Numerical Simulation
95(1)
3.2.5 Effects of Allowable Stress on Topology Optimization of Continuum Structures
96(4)
3.2.6 Correction Coefficients of Strain Energy Constraints for Multiple Load Cases
100(1)
3.2.7 Determination of Allowable Structural Strain Energy...
100(4)
3.3 Topology Optimization of Continuum Structures With Strain Energy Constraints
104(4)
3.4 Topology Optimization of Continuum Structures With Constraints of Distortional Strain Energy Density
108(4)
3.4.1 Global Strategy and Its Correction on Converting Stress Constraints Into Constraints of Distortional Strain Energy Density of Structures
108(3)
3.4.2 Topology Optimization Model With Constraints of Corrected Distortional Strain Energy Density of Structures for Continuum Structures Based on the ICM Method
111(1)
3.5 Ill-Conditioned Loads and Their Solutions
112(7)
3.5.1 Three Kinds of Phenomenon Caused by Ill-Conditioned Loads
113(1)
3.5.2 Load Treatment by Taking Structural Strain Energy as Weights Coefficients
114(2)
3.5.3 Ill-Conditioned Loads Existing Only Between Load Cases
116(1)
3.5.4 Ill-Conditioned Loads Existing Only in Some Load Cases Inner
116(2)
3.5.5 Ill-Conditioned Loads Existing Between Load Cases and Also in Some Load Cases Inner
118(1)
3.6 Discussion on Stress Singularity
119(1)
3.7 Examples
119(17)
3.7.1 Example 1
119(2)
3.7.2 Example 2
121(5)
3.7.3 Example 3
126(2)
3.7.4 Example 4
128(2)
3.7.5 Example 5
130(3)
3.7.6 Example 6: An Engineering Application---Topology Optimization of Zhaozhou Bridge
133(3)
3.8 Summary
136(3)
Chapter 4 Displacement-constrained topology optimization for continuum structures
139(32)
4.1 Explicit Approximation of Displacement Constraints
141(6)
4.1.1 Direct Method of Displacement Sensitivity Analysis...
141(1)
4.1.2 Adjoint Method of Displacement Sensitivity Analysis
142(3)
4.1.3 Explicit Approximation of Displacement Constraint by the First-Order Taylor Expansion
145(1)
4.1.4 Explicit Approximation of Displacement Constraint by Mohr Theorem
145(1)
4.1.5 Consistency of the Two Ways of Explicit Displacement Approximation
146(1)
4.2 Establishment and Solution of Optimization Model With Displacement Constraints for Multiple Load Cases
147(3)
4.3 ICM Method With Requirement of Discrete Topology Variables
150(1)
4.4 Solutions for Checkerboard Patterns and Mesh-Dependent Problems
151(5)
4.4.1 Checkerboard Patterns and Mesh-Dependent Problems
151(3)
4.4.2 Solving Checkerboard Patterns and Mesh-Dependent Problems by the Filtering Method
154(2)
4.5 Examples
156(13)
4.5.1 Example 1
156(3)
4.5.2 Example 2
159(1)
4.5.3 Example 3
159(4)
4.5.4 Example 4
163(2)
4.5.5 Example 5
165(4)
4.6 Summary
169(2)
Chapter 5 Topology optimization for continuum structures with stress and displacement constraints
171(28)
5.1 Dimensionless Stress Constraints and Displacement Constraints
172(2)
5.2 Establishment and Solution of Optimization Model With Stress Constraints and Displacement Constraints Under Multiple Load Cases
174(5)
5.3 Examples
179(17)
5.3.1 Example 1
179(4)
5.3.2 Example 2
183(4)
5.3.3 Example 3
187(4)
5.3.4 Example 4
191(5)
5.4 Summary
196(3)
Chapter 6 Topology optimization for continuum structures with frequency constraints
199(24)
6.1 Explicit Approximation of Frequency Constraints
200(3)
6.2 Establishment and Solution of Optimization Model With Frequency Constraints
203(1)
6.3 Solutions for Checkerboard Patterns and Mesh Dependence Problems
204(1)
6.4 Solutions for Localized Modes and Mode Switching Problems
204(6)
6.4.1 Localized Mode Problems
204(2)
6.4.2 Solution of Localized Mode Problems
206(1)
6.4.3 Mode Switching Problems
207(2)
6.4.4 Solution of Mode Switching Problems
209(1)
6.5 Examples
210(11)
6.5.1 Example 1
210(3)
6.5.2 Example 2
213(2)
6.5.3 Example 3
215(1)
6.5.4 Example 4
216(5)
6.6 Summary
221(2)
Chapter 7 Topology optimization with displacement and frequency constraints for continuum structures
223(14)
7.1 Dimensionless Displacement and Frequency Constraints
224(2)
7.2 Establishment and Solution of Optimization Model With Displacement and Frequency Constraints
226(1)
7.3 Solutions for Numerical Unstable Problems
227(1)
7.3.1 Solutions of Checkerboard Patterns and Mesh-Dependent Problems
227(1)
7.3.2 Solutions of Localized Mode and Mode Switching Problems
227(1)
7.4 Examples
228(1)
74.1 Example 1
228(8)
7.4.2 Example 2
229(4)
7.4.3 Example 3
233(3)
7.5 Summary
236(1)
Chapter 8 Topology optimization for continuum structures under forced harmonic oscillation
237(26)
8.1 Sensitivity Analysis of Displacement Amplitude for Forced Harmonic Oscillation
238(13)
8.1.1 Methods of Sensitivity Analysis of Displacement Amplitude Under Forced Harmonic Oscillation
238(1)
8.1.2 Sensitivity Analysis of Displacement Amplitude for Undamped Structure Under Forced Harmonic Oscillation
239(3)
8.1.3 Sensitivity Analysis of Displacement Amplitude for Damping Structure Under Forced Harmonic Oscillation
242(3)
8.1.4 Derivatives of Matrix
245(1)
8.1.5 Examples
246(5)
8.2 Explicit Approximation of Displacement Amplitude Constraints
251(3)
8.3 Establishment and Solution of Optimization Model With Displacement Amplitude Constraints for Forced Harmonic Oscillation
254(1)
8.4 Examples
255(7)
8.4.1 Example 1
255(1)
8.4.2 Example 2
255(7)
8.5 Summary
262(1)
Chapter 9 Topology optimization with buckling constraints for continuum structures
263(32)
9.1 Basic Concepts for Buckling Analysis
265(2)
9.2 Explicit Approximation of Buckling Constraints
267(3)
9.3 Establishment and Solution of Topology Optimization Model of Continuum Structures With Buckling Constraints
270(1)
9.4 Criterion of Selecting Upper Limit of Critical Buckling Force
270(11)
9.4.1 Relationship Between Upper Limit of Critical Buckling Force of First-Order Mode and Structural Weight of Optimal Topology
271(4)
9.4.2 Relationship Between Upper Limit of Second-order Critical Buckling Force and Optimal Structural Weight
275(2)
9.4.3 Relationship Between Upper Limit of the Third-order Critical Buckling Force and Optimal Structural Weight
277(4)
9.5 Examples
281(13)
9.5.1 Example 1
281(5)
9.5.2 Example 2
286(2)
9.5.3 Example 3
288(2)
9.5.4 Example 4
290(4)
9.6 Summary
294(1)
Chapter 10 Other correlative methods
295(40)
10.1 Solid-Void Combined Element Method and Its Applications in Topology Optimization of Continuum Structures
296(8)
10.1.1 Solid---Void Combined Elements for Plane Membrane
297(1)
10.1.2 Allowable Stress for Solid---Void Combined Element
298(1)
10.1.3 Displacement Contributions of Solid---Void Combined Element for Plane Membrane
299(1)
10.1.4 Topology Optimization With Stress and Displacement Constraints by Solid---Void Combined Element Method for Plane Membranes
300(1)
10.1.5 Examples
301(3)
10.2 Topology Optimization of Continuum Structures With Integration Constraints
304(15)
10.2.1 Modeling and Solution by Integrated Stress Constraints
304(7)
10.2.2 Modeling and Solution by Integrated Displacement Constraints
311(5)
10.2.3 Modeling and Solution by Integrated Stress and Displacement Constraints
316(3)
10.3 Structural Topology Optimization With Parabolic Aggregation Function
319(8)
10.3.1 Parabolic Aggregation Function
319(3)
10.3.2 Integrated Constraints by Parabolic Aggregation Function
322(5)
10.4 Structural Topology Optimization With High-Quality Approximation of Step Function
327(6)
10.5 Summary
333(2)
References 335(20)
Afterword 355(8)
Index 363
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 Structurese 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. 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.
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