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Analysis of Aircraft Structures, Second Edition

Book Description

As with the first edition, this textbook provides a clear introduction to the fundamental theory of structural analysis as applied to vehicular structures such as aircraft, spacecraft, automobiles and ships. The emphasis is on the application of fundamental concepts of structural analysis that are employed in everyday engineering practice. All approximations are accompanied by a full explanation of their validity. In this new edition, more topics, figures, examples and exercises have been added. There is also a greater emphasis on the finite element method of analysis. Clarity remains the hallmark of this text and it employs three strategies to achieve clarity of presentation: essential introductory topics are covered, all approximations are fully explained and many important concepts are repeated.

Table of Contents

  1. Coverpage
  2. Analysis of Aircraft Structures
  3. Cambridge Aerospace Series
  4. Title page
  5. Copyright page
  6. Dedication
  7. Greek Alphabet
  8. Contents
  9. Introduction to the Second Edition
  10. Introduction to the First Edition
  11. List of Repeated Engineering Symbols
  12. Acknowledgments
  13. Part I The Fundamentals of Structural Analysis
    1. I.1 An Overview of Part I
    2. I.2 Summary of Taylor’s Series
    3. I.3 Summary of Newton’s Method for Finding Roots
    4. I.4 The Binomial Series
    5. I.5 The Chain Rule for Partial Differentiation
    6. 1 Stress in Structures
      1. 1.1 The Concept of Stress
      2. 1.2 The General Interior Equilibrium Equations
      3. 1.3 Equilibrium at the Outer or Inner Boundary
      4. 1.4 Plane Stress
      5. 1.5 Summary
      6. Chapter 1 Exercises
    7. 2 Stresses and Coordinate Axis Rotations
      1. 2.1 Introduction
      2. 2.2 Stress Values in Other Cartesian Coordinate Systems
      3. 2.3 The Determination of Maximum Stress Values
      4. 2.4 Mohr’s Circle
      5. 2.5 A Three-Dimensional View of Plane Stress
      6. 2.6 **Principal Stresses in the General Three-Dimensional Case**
      7. 2.7 Summary
      8. 2.8 Octahedral (von Mises) Shearing Stresses
      9. 2.9 **The Mathematical Description of Stresses**
      10. Chapter 2 Exercises
      11. Endnote (1) Solution for the Planes of Principal Stress
    8. 3 Displacements and Strains
      1. 3.1 Introduction
      2. 3.2 Displacements
      3. 3.3 Longitudinal Strains
      4. 3.4 Shearing Strains
      5. 3.5 Other Strain Definitions
      6. 3.6 The Strain–Displacement Equations
      7. 3.7 The Compatibility Equations
      8. 3.8 Plane Strain
      9. 3.9 Summary
      10. Chapter 3 Exercises
      11. Endnote (1) The Derivation of the Strain–Displacement Equations for Cylindrical Coordinates
      12. Endnote (2) A Third Derivation of the Compatibility Equations
    9. 4 Strains in Rotated Coordinate Systems
      1. 4.1 Introduction
      2. 4.2 Strains in Other Cartesian Coordinate Systems
      3. 4.3 Strain Gauges
      4. 4.4 The Mathematical Properties of Strains
      5. 4.5 Summary
      6. Chapter 4 Exercises
    10. 5 The Mechanical Behavior of Engineering Materials
      1. 5.1 Introduction
      2. 5.2 The Tensile Test
      3. 5.3 Compression and Shear Tests
      4. 5.4 Safety Factors
      5. 5.5 Factors Other than Stress That Affect Material Behavior
      6. 5.6 **Biaxial and Triaxial Loadings**
      7. 5.7 Simplifications of Material Behavior
      8. Chapter 5 Exercises
      9. Endnote (1) Residual Stress Example Problem
      10. Endnote (2) Crack Growth Example
    11. 6 Linearly Elastic Materials
      1. 6.1 Introduction
      2. 6.2 Orthotropic Materials
      3. 6.3 Isotropic and Other Linearly Elastic Materials
      4. 6.4 The Plane Stress Constitutive Equations
      5. 6.5 **Applications to Fiber Composites**
      6. 6.6 Summary
      7. Chapter 6 Exercises
      8. Endnote (1) Negative Poisson Ratios
  14. Part II **Introduction to the Theory of Elasticity**
    1. II.1 Introduction
    2. 7 The Theory of Elasticity
      1. 7.1 Introduction
      2. 7.2 A Theory of Elasticity Solution Using Stresses
      3. 7.3 A Theory of Elasticity Solution Using Displacements
      4. 7.4 Reprise
      5. 7.5 Summary
      6. Chapter 7 Exercises
      7. Endnote (1) General Problem Formulations
      8. Endnote (2) Another Solution to the Disk Displacement Equation
      9. Endnote (3) Example 7.1 Compatibility Equation
    3. 8 Plane Stress Theory of Elasticity Solutions
      1. 8.1 Introduction
      2. 8.2 Solution Examples
      3. 8.3 St. Venant’s Principle
      4. 8.4 **Review Problem**
      5. 8.5 Summary
      6. 8.6 **The Airy Stress Function**
      7. Chapter 8 Exercises
      8. Endnote (1) An Example of Calculating Displacements from a Stress Solution
    4. Parts I and II Review Questions
  15. Part III Engineering Theory for Straight, Long Beams
    1. III.1 Aircraft and Other Vehicular Structures
    2. III.2 The Method of Undetermined Coefficients
    3. III.3 Linear Independence
    4. III.4 The Mean Value Theorem
    5. 9 Bending and Extensional Stresses in Beams
      1. 9.1 Introduction
      2. 9.2 An Elaboration on the Scope of Strength of Materials
      3. 9.3 Stress Resultants
      4. 9.4 The Approximate Pattern for Beam Displacements
      5. 9.5 The Accuracy of the Beam Stress Equation
      6. 9.6 Calculation of the Area Properties of the Nonhomogeneous Cross-Section
      7. 9.7 Calculation of Equivalent Thermal Loads
      8. 9.8 Principal Axes for the Beam Cross-Section
      9. 9.9 Summary
      10. Chapter 9 Exercises
      11. Endnote (1) The Predominance of the Normal Axial Stress
      12. Endnote (2) Schwartz’s Inequality
    6. 10 Beam Bending and Extensional Deflections
      1. 10.1 Introduction
      2. 10.2 The Small Deflection Beam Equilibrium Equations
      3. 10.3 Nonlinear Beam Equilibrium Equations
      4. 10.4 Boundary Conditions and the Boundary Value Problem
      5. 10.5 Uncoupled Forms of the GDEs and the BCs
      6. 10.6 Solutions for Beam Deflection Problems
      7. 10.7 Summary
      8. Chapter 10 Exercises
      9. Endnote (1) Different BCs in Different Planes at the Same Beam End
      10. Endnote (2) The Nonlinear Form of the Axial Deflection Equation
      11. Endnote (3) The Presence of the Moment per Unit Length Terms in the Shear Force Boundary Condition Expressions
      12. Endnote (4) Exact Integrations for a Nonuniform Beam
    7. 11 Additional Beam Bending Topics
      1. 11.1 Introduction
      2. 11.2 The Concept of Elastic Boundary Conditions
      3. 11.3 Elastic Support Boundary Conditions
      4. 11.4 Concentrated and Partial Span Loads
      5. 11.5 Partial Span and Concentrated Load Example Problems
      6. 11.6 Introduction to Beam Buckling
      7. 11.7 **Additional Comments on Beam Buckling**
      8. 11.8 Summary
      9. Chapter 11 Exercises
      10. Endnote (1) The Bending Slope Sign Convention
      11. Endnote (2) Combined Beam Axial and Lateral Loadings
      12. Endnote (3) Heaviside Step Function Additional Comments
      13. Endnote (4) Combined Bending and Torsional Loadings
      14. Endnote (5) Beams Continuous over Several Supports
    8. 12 Uniform Torsion of Beams
      1. 12.1 Introduction
      2. 12.2 The Stress Formulation for Uniform Torsion
      3. 12.3 Further Properties of the Prandtl Stress Function
      4. 12.4 The Membrane Analogy
      5. 12.5 Closed Form Beam Torsion Analytical Solutions
      6. 12.6 Open Form Uniform Beam Torsion Solutions
      7. 12.7 Summary
      8. Chapter 12 Exercises
      9. Endnote (1) A Comment on the Solution for a Circular Shaft with a Keyway
      10. Endnote (2) Orthogonality
      11. Endnote (3) A Separation of Variables Approach to Example 12.1
    9. 13 Beam Torsion Approximate Solutions
      1. 13.1 Introduction
      2. 13.2 Open Cross-Section Beam Torsion
      3. 13.3 Closed Section Beam Torsion
      4. 13.4 Accuracy of the Uniform Torsion Theory
      5. 13.5 Beams Subjected to a Variable Torque
      6. 13.6 Summary
      7. Chapter 13 Exercises
      8. Endnote (1) Torsion Constants for Rolled and Extruded Beams
      9. Endnote (2) Warping Constraint Due to Varying Torque
    10. Beam Bending and Torsion Review Questions
    11. 14 Beam Shearing Stresses Due to Shearing Forces
      1. 14.1 Introduction
      2. 14.2 Thin-Walled Open Cross-Sections
      3. 14.3 Thin-Walled Open Cross-Section Example Problems
      4. 14.4 The Open Section Shear Center
      5. 14.5 Shear Flows in Thin-Walled Closed Cross-Sections
      6. 14.6 Summary
      7. Chapter 14 Exercises
      8. Endnote (1) The Shear Center as the Center of Twist
  16. Part IV Work and Energy Principles
    1. IV.1 Preface
    2. IV.2 The Green–Gauss Theorem
    3. 15 Work and Potential Energy Principles
      1. 15.1 Introduction
      2. 15.2 Work and Potential Energy
      3. 15.3 Virtual Work and Virtual Potential Energy
      4. 15.4 The Variational Operator
      5. 15.5 The Principle of Virtual Work
      6. 15.6 Internal Virtual Work
      7. 15.7 Complementary Virtual Work
      8. 15.8 **Energy and Other Principles**
      9. 15.9 **Modifications for Temperature Changes**
      10. 15.10 Summary
      11. Chapter 15 Exercises
      12. Endnote (1) Further Explanation of the Variational Operator
      13. Endnote (2) Proof That the Principle of Virtual Work Is a Sufficient Condition for Equilibrium
      14. Endnote (3) Proof of the Pairing of BCs for the Beam Fourth Order Bending Equations and the Second Order Extension Equations
      15. Endnote (4) Derivation of the Uniform Torsion Beam Equations Using the Principle of Complementary Virtual Work
  17. Part V Energy-Based Numerical Solutions
    1. V.1 Preface
    2. 16 **Precursor Numerical Analyses**
      1. 16.1 Introduction
      2. 16.2 Numerical Methods of Note
      3. 16.3 Summary
      4. Chapter 16 Exercises
    3. 17 Introduction to the Finite Element Method
      1. 17.1 Introduction
      2. 17.2 Generalized Coordinates
      3. 17.3 The Beam Bending Finite Element
      4. 17.4 The Bar and Spring Element Stiffness Matrix Equations
      5. 17.5 Assembling the System Matrix Equation
      6. 17.6 Solving the System Matrix Equation
      7. 17.7 Example Beam Frame and Grid Problems
      8. 17.8 More Extensive Example Problems
      9. 17.9 Summary
      10. Chapter 17 Exercises
      11. Endnote (1) Distributed Coordinates
      12. Endnote (2) Accuracy of the Concentrated Load Approximation
      13. Endnote (3) The Reason for the Name “Generalized Coordinates”
    4. 18 Finite Element Truss Problems
      1. 18.1 Introduction
      2. 18.2 The Rotated Bar Element
      3. 18.3 Equivalent Thermal Loads
      4. 18.4 Other Initial Strains
      5. 18.5 Enforced Deflections
      6. 18.6 Summary
      7. Chapter 18 Exercises
      8. Endnote (1) Substructuring in Static Analyses
    5. 19 Basic Aspects of Multidimensional Finite Elements
      1. 19.1 Introduction
      2. 19.2 A Rectangular Plane Stress Finite Element
      3. 19.3 A Triangular Plane Stress Element in Brief
      4. 19.4 Three-Dimensional Finite Elements
      5. 19.5 Refined Finite Elements of Simple Shapes
      6. 19.6 **The Finite Element Method with Time-Varying Loads**
      7. 19.7 Summary
      8. Chapter 19 Exercises
      9. Endnote (1) An Explanation for Rigid Body Motion-Induced False Strains
      10. Endnote (2) Reducing the Number of DOF in a Dynamic Analysis
    6. 20 The Unit Load Method for Determinate Structures
      1. 20.1 Introduction
      2. 20.2 External Complementary Virtual Work in the Unit Load Method
      3. 20.3 Internal CVW for Beam Bending and Extension
      4. 20.4 Internal Complementary Virtual Work for Beam Torsion
      5. 20.5 **Internal CVW for Beam Shearing**
      6. 20.6 Additional Illustrative Examples
      7. 20.7 **Examples of Using the ULM for Design Purposes**
      8. 20.8 **General Deflection Solutions**
      9. 20.9 **Large Radius Curved Beams**
      10. 20.10 Summary
      11. 20.11 Maxwell’s Reciprocity Theorem
      12. Chapter 20 Exercises
      13. Endnote (1) ULM Limitations
      14. Endnote (2) Internal Complementary Virtual Work
    7. 21 The Unit Load Method for Indeterminate Structures
      1. 21.1 Introduction
      2. 21.2 Identifying Redundant Forces and Moments
      3. 21.3 The Coiled Spring Structural Elements
      4. 21.4 The Strategy of Releases and Reattachments
      5. 21.5 Example Problems
      6. 21.6 **Further Example Problems**
      7. 21.7 Summary
      8. Chapter 21 Exercises
    8. Parts IV and V Review Questions
  18. Part VI Thin Plate Theory and Structural Stability
    1. VI.1 Introduction
    2. 22 Thin Plate Theory
      1. 22.1 Introduction
      2. 22.2 The Plate Midplane
      3. 22.3 The Plate Stress Resultants
      4. 22.4 The Approximate Pattern for Plate Displacements
      5. 22.5 The Small Deflection Thin Plate Bending Equation
      6. 22.6 Thin Plate Boundary Conditions
      7. 22.7 **Classical Small Deflection Plate Bending Solutions**
      8. 22.8 **Plate Buckling and Its Uses**
      9. 22.9 A Simple Plate Bending Finite Element
      10. 22.10 Summary
      11. Chapter 22 Exercises
      12. Endnote (1) The Second Finite Deflection Plate Equation
    3. 23 Elastic and Aeroelastic Instabilities
      1. 23.1 Introduction
      2. 23.2 An Energy Formulation of the Beam Buckling Problem
      3. 23.3 A Beam Buckling Finite Element
      4. 23.4 Further Aspects of the Energy Formulation
      5. 23.5 Types of Fluid–Structure Interaction Instabilities
      6. 23.6 Airfoil Divergence
      7. 23.7 Airfoil Flutter
      8. 23.8 Matrix Iteration for Symmetric Matrices
      9. Chapter 23 Exercises
      10. Endnote (1) Resonance
      11. Endnote (2) Diagonalization and Functions of Matrices
  19. Appendix A Additional Topics
    1. A.1 Integration of the Strains to Obtain Displacements
    2. A.2 Proof of the Symmetry of the Compliance Matrix
    3. A.3 Uniform Torsion Stress Resultants for Multiply Connected Cross-Sections
    4. A.4 The Uniform Torsion GDE for Multiply Connected Cross-Sections
    5. A.5 Calculation of the Twist per Unit Length of a Single Cell of an N-Cell Cross-Section
  20. Appendix B Selected Answers to Exercises
  21. References
  22. Index