Advanced Topics of Thin-Walled Structures

Description

This unique compendium presents some new topics related to thin-walled structures, like beams, plates and shells used in aerospace structures. It highlights their dynamic behaviors and also the correlation between compressive loading and natural frequency to enable a correlation between the two, yielding a valuable non-destructive tool, to predict buckling for thin-walled structures.This useful reference text combines valuable data on metal materials and composite materials together with new adaptive and smart materials like piezoelectricity, shape memory alloys and optic fibers, which form the present state of the art in thin-walled structure domain. 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