Advanced Topics of Thin-Walled Structures

Contents
Preface
About the Author
1. Thin-Walled Structures
1.1. Introduction
1.2. Thin-Walled Structures-Definition and Examples
1.3. Fundamental Issues of Elasticity
1.3.1. Stresses, strains and rigid-body rotations
1.3.2. Equilibrium and compatibility equations in elasticity
1.3.3. Two-dimensional representations: Plane stress and plane strain
1.3.3.1. Plane stress problems
1.3.3.2. Plane strain problems
1.3.4. The Airy function φ (x, y)
1.3.5. Thermal field in elasticity
References
2. Laminated Composite Materials
2.1. Introduction
2.2. Unidirectional Composites
2.3. Properties of a Single Ply
2.4. Transformation of Stresses and Strains
2.5. Classical Lamination Theory
2.6. First-Order Shear Deformation Theory
2.7. Higher Order Theories
References
3. Buckling of Thin-Walled Structures
3.1. Introduction
3.2. Buckling of Columns
3.2.1. Euler buckling
3.2.2. Rankin–Gordon formula
3.2.3. Composite columns — CLT approach
3.2.3.1. Symmetric laminate (B11 = 0)
3.2.4. Non-symmetric laminate (B11 = 0)
3.4. Buckling of Columns: FSDT Approach
3.5. Buckling of Plates
3.5.1. Buckling of isotropic plates
3.5.2. Buckling of orthotropic plates
3.6. Buckling of Shells
3.6.1. Introduction to shells
3.6.2. Buckling of isotropic cylindrical shells
3.6.2.1. Axial compression
3.6.2.2. External pressure
3.6.2.3. Torsion
3.6.2.4. Combined loadings
3.6.2.5. Buckling of orthotropic cylindrical shells under axial compression
3.6.2.6. Buckling of orthotropic cylindrical shells under external pressure
3.6.2.7. Buckling of orthotropic cylindrical shells under torsion
3.6.2.8. Combined bending and axial compression of orthotropic cylindrical shells
References
Appendix A: Non-symmetric Laminated Composite Beam — CLT Approach
Appendix B: Energy Methods
References
4. Vibrations of Thin-Walled Structures
4.1. Introduction
4.2. CLPT Approach
4.3. FSDPT Approach
4.4. Vibrations of Columns — CLT Approach
4.4.1. Symmetric laminate (B11 = 0, I1 = 0)
4.4.2. Non-symmetric laminate (B11 = 0, I1 = 0)
4.5. Vibrations of Columns — FSDT Approach
4.5.1. Symmetric laminate (B11 = 0, I1 = 0)
4.5.2. Non-symmetric laminate (B11 = 0, I1 = 0)Following the derivation performed by Abramovich and Livshits
4.5.2. Non-symmetric laminate (B11 = 0, I1 = 0)
4.6. Vibrations of Plates — CLT Approach
4.6.1. Simply supported special orthotropic plates
4.6.2. Simply supported on two opposite edges of special orthotropic plates
4.7. Vibration of Cylindrical Shells
4.7.1. Isotropic shells
4.7.2. Soedel theory
4.8. Laminated Composite Shells — CLT Approach
References
Appendix A: General Solution for a Nonsymmetrical Beam Resting on any Boundary Conditions
Appendix B: Matrix Notation for the Equilibrium Equations Using CLT Approach
Appendix C: Governing Equations According to Various Shell Theories
Appendix D: Governing Equations for Orthotropic Circular Cylindrical Shells
5. The Vibration Correlation Technique
5.1. Introduction
5.2. Columns, Beams and Rods
5.3. Plates and Panels
5.4. Cylindrical Shells
5.5. The Influence of Initial Geometric Imperfections
5.6. Conclusions and Recommendations
References
Appendix A
Appendix B
Appendix C: Southwell’s Plot
References
Appendix D: Novel Excitation Methods
References
Appendix E: Summary of Axial Compression vs. Natural Frequencies Relationship for Thin-Walled Structures
References
6. Behavior of Circular and Annular Plates
6.1. Introduction
6.1.1. Stress distribution in a radially compressed circular plate
6.2. Buckling of a Circular Plate
6.3. The Initial Geometric Influence
6.4. Results
6.5. The Experimental Set-Up
6.6. Radially Compressed Annular Plates
6.7. Buckling of Orthotropic Circular Plates
6.8. Buckling of Orthotropic Annular Plates
6.9. Vibrations of Isotropic Annular Plates
References
Appendix A: Plate Boundary Conditions in Polar Coordinates-General Expressions
Appendix B: Buckling of an Annular Plate Under Uniform External Radial Compression
References
Appendix C: Buckling of an Annular Plate — A Detailed Example
References
7. Dynamic Buckling of Thin-Walled Structures
7.1. Introduction
7.2. Dynamic Buckling of Columns
7.2.1. Dynamic buckling of columns using CLT
7.2.2. Dynamic buckling of columns using FSDT
7.3. Dynamic Buckling of Plates
7.4. Dynamic Buckling of Thin-Walled Structures-Numerical and Experimental Results
References
Appendix A: Calculation of the Critical Buckling Load of a Uniaxial Loaded Plate from Test Results
8. Introduction to Piezoelectricity
8.1. Introduction
8.2. Piezoelectricity Books
8.3. Harvesting
8.4. Other Aspects of Piezoelectricity
References
9. Introduction to Shape Memory Alloys
9.1. Basic Characteristics of Shape Memory Alloys
9.2. The Shape Memory Effect
9.3. Pseudoelasticity
9.4. Applications
9.5. SMA Constitutive Equations
9.5.1. 1D constitutive equations for an SMA material
9.6. Heating an SMA Alloy Using Electrical Current
References
10. Introduction to Fiber Optic
10.1. Basic Characteristics of a Fiber Optic
10.2. Fiber Optic — Historical Aspects
10.3. Fiber Bragg Grating
10.4. Fiber Bragg Grating Used as Strain Sensor
10.5. Interrogators for Fiber Bragg Grating
References
11. Static and Dynamic Behavior of Nano-beams
11.1. Introduction
11.2. The Static Non-local Nano-beam Model and Buckling
11.3. The Dynamic Non-local Nano-beam Model — Vibrations and Natural Frequencies
11.4. The Dynamic Non-local Nano-beam Model — Dynamic Buckling
11.5. Conclusions
References
Appendix A: The Non-local Model
References
Index