Higher-Order Theories of Functionally Graded Circular Cylindrical Beams and Columns provides a detailed exploration of the mechanical behaviors of functionally graded circular cylindrical beams and columns, including bending, vibration, and stability, and considering factors such as shear deformation, cross-section warping, elastic foundation interaction, non-local effects in nanoscale and piezoelectric and flexoelectric, and more. With a focus on higher-order theories and advanced analytical methods, the book enables researchers to gain a deeper understanding of the fundamental principles governing the behavior of circular cylindrical structures.
The detailed derivations and explanations of complex equations and concepts assist in the development of new research. This book will help engineers identify and address potential issues in the design and analysis of circular cylindrical structures. Detailed discussions on factors affecting mechanical performance, such as material selection, geometric parameters, and loading conditions enable engineers to make informed decisions and optimize their designs for improved performance and safety.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Bending of higher-order functionally graded circular cylindrical beams - p. 15 3. Chapter 3. Vibration of higher-order Functionally Graded circular cylindrical beams - p. 41 4. 3.1 Introduction - p. 41 5. 3.2 Assumption and governing equations - p. 41 6. 3.3 Foundation of free vibration - p. 49 7. 3.4 Vibration analysis of circular cylindrical beams - p. 53 8. 3.5 Vibration analysis of a cylinder beam with axial force - p. 62 9. Chapter 4. Stability of higher-order functionally graded circular cylindrical columns - p. 77 10. 4.1 Introduction - p. 77 11. 4.2 Assumption and governing equations - p. 77 12. 4.3 The formulation of stability - p. 77 13. 4.4 The buckling analysis - p. 77 14. 4.5 Effects of Engesser’s and Haringx’s hypotheses - p. 77 15. Chapter 5. Buckling and stability with various elastic foundations - p. 121 16. 5.1 Introduction - p. 121 17. 5.2 Winkler–Pasternak foundation - p. 126 18. 5.3 Kerr foundation - p. 130 19. 5.4 Viscoelastic foundation - p. 131 20. 5.5 The formulation of stability and results - p. 133 21. Chapter 6. Nonlocal effects in nanoscale - p. 171 22. 6.1 Introduction of nonlocal elastic theories - p. 171 23. 6.2 Assumption and governing equations - p. 172 24. 6.3 Bending wave of carbon nanotubes (CNTs) - p. 181 25. 6.4 Vibration analysis of tube beams - p. 195 26. Chapter 7. Some advanced topics and applications - p. 211 27. 7.1 Introduction - p. 211 28. 7.2 Thermoelastic coupling effects - p. 212 29. 7.3 Surface effects - p. 219 30. 7.4 Piezoelectric and flexoelectric effects - p. 230 31. 7.5 The coupled stress effects - p. 241 32. Index - p. 253
Higher-Order Theories of Functionally Graded Circular Cylindrical Beams and Columns provides a detailed exploration of the mechanical behaviors of functionally graded circular cylindrical beams and columns, including bending, vibration, and stability, and considering factors such as shear deformation, cross-section warping, elastic foundation interaction, non-local effects in nanoscale and piezoelectric and flexoelectric, and more. With a focus on higher-order theories and advanced analytical methods, the book enables researchers to gain a deeper understanding of the fundamental principles governing the behavior of circular cylindrical structures.
The detailed derivations and explanations of complex equations and concepts assist in the development of new research. This book will help engineers identify and address potential issues in the design and analysis of circular cylindrical structures. Detailed discussions on factors affecting mechanical performance, such as material selection, geometric parameters, and loading conditions enable engineers to make informed decisions and optimize their designs for improved performance and safety.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Bending of higher-order functionally graded circular cylindrical beams - p. 15 3. Chapter 3. Vibration of higher-order Functionally Graded circular cylindrical beams - p. 41 4. 3.1 Introduction - p. 41 5. 3.2 Assumption and governing equations - p. 41 6. 3.3 Foundation of free vibration - p. 49 7. 3.4 Vibration analysis of circular cylindrical beams - p. 53 8. 3.5 Vibration analysis of a cylinder beam with axial force - p. 62 9. Chapter 4. Stability of higher-order functionally graded circular cylindrical columns - p. 77 10. 4.1 Introduction - p. 77 11. 4.2 Assumption and governing equations - p. 77 12. 4.3 The formulation of stability - p. 77 13. 4.4 The buckling analysis - p. 77 14. 4.5 Effects of Engesser’s and Haringx’s hypotheses - p. 77 15. Chapter 5. Buckling and stability with various elastic foundations - p. 121 16. 5.1 Introduction - p. 121 17. 5.2 Winkler–Pasternak foundation - p. 126 18. 5.3 Kerr foundation - p. 130 19. 5.4 Viscoelastic foundation - p. 131 20. 5.5 The formulation of stability and results - p. 133 21. Chapter 6. Nonlocal effects in nanoscale - p. 171 22. 6.1 Introduction of nonlocal elastic theories - p. 171 23. 6.2 Assumption and governing equations - p. 172 24. 6.3 Bending wave of carbon nanotubes (CNTs) - p. 181 25. 6.4 Vibration analysis of tube beams - p. 195 26. Chapter 7. Some advanced topics and applications - p. 211 27. 7.1 Introduction - p. 211 28. 7.2 Thermoelastic coupling effects - p. 212 29. 7.3 Surface effects - p. 219 30. 7.4 Piezoelectric and flexoelectric effects - p. 230 31. 7.5 The coupled stress effects - p. 241 32. Index - p. 253
