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.
1. Cover image - p. Cover 2. Title page - p. iii 3. Table of Contents - p. iii 4. Copyright - p. iv 5. Dedication - p. v 6. Preface - p. xv 7. Acknowledgment - p. xxiii 8. Chapter 1. Exordium - p. 1 9. Chapter 2. Foundation of the ICM (independent, continuous and mapping) method - p. 37 10. Abstract - p. 37 11. 2.1 Difficulties in Conventional Topology Optimization and Solution - p. 39 12. 2.2 Step Function and Hurdle Function—Bridge of Constructing Relationship Between Discrete Topology Variables and Element Performances - p. 41 13. 2.3 Fundamental Breakthrough—Polish Function Approaching to Step Function and Filter Function Approaching to Hurdle Function - p. 43 14. 2.4 ICM Method and its Application - p. 47 15. 2.5 Exploration of Performance of Polish Function and Filter Function - p. 66 16. 2.6 Exploration of Filter Function With High Precision - p. 69 17. 2.7 Breakthrough on Basic Conceptions in ICM Method - p. 76 18. Chapter 3. Stress-constrained topology optimization for continuum structures - p. 79 19. Abstract - p. 79 20. 3.1 ICM Method With Zero-Order Approximation Stresses and Solution of Model - p. 82 21. 3.2 Global Stress Constraints to Replace Stress Constraints - p. 89 22. 3.3 Topology Optimization of Continuum Structures With Strain Energy Constraints - p. 104 23. 3.4 Topology Optimization of Continuum Structures With Constraints of Distortional Strain Energy Density - p. 108 24. 3.5 Ill-Conditioned Loads and Their Solutions - p. 112 25. 3.6 Discussion on Stress Singularity - p. 119 26. 3.7 Examples - p. 119 27. 3.8 Summary - p. 136 28. Chapter 4. Displacement-constrained topology optimization for continuum structures - p. 139 29. Chapter 5. Topology optimization for continuum structures with stress and displacement constraints - p. 171 30. Chapter 6. Topology optimization for continuum structures with frequency constraints - p. 199 31. Chapter 7. Topology optimization with displacement and frequency constraints for continuum structures - p. 223 32. Chapter 8. Topology optimization for continuum structures under forced harmonic oscillation - p. 237 33. Chapter 9. Topology optimization with buckling constraints for continuum structures - p. 263 34. Chapter 10. Other correlative methods - p. 295 35. Abstract - p. 295 36. 10.1 Solid–Void Combined Element Method and Its Applications in Topology Optimization of Continuum Structures - p. 296 37. 10.2 Topology Optimization of Continuum Structures With Integration Constraints - p. 304 38. 10.3 Structural Topology Optimization With Parabolic Aggregation Function - p. 319 39. 10.4 Structural Topology Optimization With High-Quality Approximation of Step Function - p. 327 40. 10.5 Summary - p. 333 41. References - p. 335 42. Afterword - p. 355 43. Index - p. 363
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.
1. Cover image - p. Cover 2. Title page - p. iii 3. Table of Contents - p. iii 4. Copyright - p. iv 5. Dedication - p. v 6. Preface - p. xv 7. Acknowledgment - p. xxiii 8. Chapter 1. Exordium - p. 1 9. Chapter 2. Foundation of the ICM (independent, continuous and mapping) method - p. 37 10. Abstract - p. 37 11. 2.1 Difficulties in Conventional Topology Optimization and Solution - p. 39 12. 2.2 Step Function and Hurdle Function—Bridge of Constructing Relationship Between Discrete Topology Variables and Element Performances - p. 41 13. 2.3 Fundamental Breakthrough—Polish Function Approaching to Step Function and Filter Function Approaching to Hurdle Function - p. 43 14. 2.4 ICM Method and its Application - p. 47 15. 2.5 Exploration of Performance of Polish Function and Filter Function - p. 66 16. 2.6 Exploration of Filter Function With High Precision - p. 69 17. 2.7 Breakthrough on Basic Conceptions in ICM Method - p. 76 18. Chapter 3. Stress-constrained topology optimization for continuum structures - p. 79 19. Abstract - p. 79 20. 3.1 ICM Method With Zero-Order Approximation Stresses and Solution of Model - p. 82 21. 3.2 Global Stress Constraints to Replace Stress Constraints - p. 89 22. 3.3 Topology Optimization of Continuum Structures With Strain Energy Constraints - p. 104 23. 3.4 Topology Optimization of Continuum Structures With Constraints of Distortional Strain Energy Density - p. 108 24. 3.5 Ill-Conditioned Loads and Their Solutions - p. 112 25. 3.6 Discussion on Stress Singularity - p. 119 26. 3.7 Examples - p. 119 27. 3.8 Summary - p. 136 28. Chapter 4. Displacement-constrained topology optimization for continuum structures - p. 139 29. Chapter 5. Topology optimization for continuum structures with stress and displacement constraints - p. 171 30. Chapter 6. Topology optimization for continuum structures with frequency constraints - p. 199 31. Chapter 7. Topology optimization with displacement and frequency constraints for continuum structures - p. 223 32. Chapter 8. Topology optimization for continuum structures under forced harmonic oscillation - p. 237 33. Chapter 9. Topology optimization with buckling constraints for continuum structures - p. 263 34. Chapter 10. Other correlative methods - p. 295 35. Abstract - p. 295 36. 10.1 Solid–Void Combined Element Method and Its Applications in Topology Optimization of Continuum Structures - p. 296 37. 10.2 Topology Optimization of Continuum Structures With Integration Constraints - p. 304 38. 10.3 Structural Topology Optimization With Parabolic Aggregation Function - p. 319 39. 10.4 Structural Topology Optimization With High-Quality Approximation of Step Function - p. 327 40. 10.5 Summary - p. 333 41. References - p. 335 42. Afterword - p. 355 43. Index - p. 363
