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Mechanics of Composite Structures

Book Description

An increase in the use of composite materials in areas of engineering has led to a greater demand for engineers versed in the design of structures made from such materials. This book offers students and engineers tools for designing practical composite structures. Among the topics of interest to the designer are stress-strain relationships for a wide range of anisotropic materials; bending, buckling, and vibration of plates; bending, torsion, buckling, and vibration of solid as well as thin walled beams; shells; hygrothermal stresses and strains; finite element formulation; and failure criteria. More than 300 illustrations, 50 fully worked problems, and material properties data sets are included. Some knowledge of composites, differential equations, and matrix algebra is helpful but not necessary, as the book is self-contained. Graduate students, researchers, and practitioners will value it for both theory and application.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. List of Symbols
  8. 1. Introduction
  9. 2. Displacements, Strains, and Stresses
    1. 2.1 Strain–Displacement Relations
    2. 2.2 Equilibrium Equations
    3. 2.3 Stress-Strain Relationships
      1. 2.3.1 Generally Anisotropic Material
      2. 2.3.2 Monoclinic Material
      3. 2.3.3 Orthotropic Material
      4. 2.3.4 Transversely Isotropic Material
      5. 2.3.5 Isotropic Material
    4. 2.4 Plane–Strain Condition
      1. 2.4.1 Free End – Generally Anisotropic Material
      2. 2.4.2 Free End – Monoclinic Material
      3. 2.4.3 Free End – Orthotropic, Transversely Isotropic, or Isotropic Material
      4. 2.4.4 Built-In Ends – Generally Anisotropic Material
      5. 2.4.5 Built-In Ends – Monoclinic Material
      6. 2.4.6 Built-In Ends – Orthotropic, Transversely Isotropic, or Isotropic Material
    5. 2.5 Plane-Stress Condition
    6. 2.6 Hygrothermal Strains and Stresses
      1. 2.6.1 Plane-Strain Condition
      2. 2.6.2 Plane-Stress Condition
    7. 2.7 Boundary Conditions
    8. 2.8 Continuity Conditions
    9. 2.9 Stress and Strain Transformations
      1. 2.9.1 Stress Transformation
      2. 2.9.2 Strain Transformation
      3. 2.9.3 Transformation of the Stiffness and Compliance Matrices
    10. 2.10 Strain Energy
      1. 2.10.1 The Ritz Method
    11. 2.11 Summary
      1. 2.11.1 Note on the Compliance and Stiffness Matrices
  10. 3. Laminated Composites
    1. 3.1 Laminate Code
    2. 3.2 Stiffness Matrices of Thin Laminates
      1. 3.2.1 The Significance of the [A], [B], and [D] Stiffness Matrices
      2. 3.2.2 Stiffness Matrices for Selected Laminates
  11. 4. Thin Plates
    1. 4.1 Governing Equations
      1. 4.1.1 Boundary Conditions
      2. 4.1.2 Strain Energy
    2. 4.2 Deflection of Rectangular Plates
      1. 4.2.1 Pure Bending and In-Plane Loads
      2. 4.2.2 Long Plates
      3. 4.2.3 Simply Supported Plates – Symmetrical Layup
      4. 4.2.4 Plates with Built-In Edges – Orthotropic and Symmetrical Layup
    3. 4.3 Buckling of Rectangular Plates
      1. 4.3.1 Simply Supported Plates – Symmetrical Layup
      2. 4.3.2 Plates with Built-In and Simply Supported Edges – Orthotropic and Symmetrical Layup
      3. 4.3.3 Plates with One Free Edge – Orthotropic and Symmetrical Layup
      4. 4.3.4 Plates with Rotationally Restrained Edges – Orthotropic and Symmetrical Layup
      5. 4.3.5 Long Plates
    4. 4.4 Free Vibration of Rectangular Plates
      1. 4.4.1 Long Plates
      2. 4.4.2 Simply Supported Plates – Symmetrical Layup
      3. 4.4.3 Plates with Built-In and Simply Supported Edges – Orthotropic and Symmetrical Layup
    5. 4.5 Hygrothermal Effects
      1. 4.5.1 Change in Thickness Due to Hygrothermal Effects
    6. 4.6 Plates with a Circular or an Elliptical Hole
    7. 4.7 Interlaminar Stresses
  12. 5. Sandwich Plates
    1. 5.1 Governing Equations
      1. 5.1.1 Boundary Conditions
      2. 5.1.2 Strain Energy
      3. 5.1.3 Stiffness Matrices of Sandwich Plates
    2. 5.2 Deflection of Rectangular Sandwich Plates
      1. 5.2.1 Long Plates
      2. 5.2.2 Simply Supported Sandwich Plates – Orthotropic and Symmetrical Layup
    3. 5.3 Buckling of Rectangular Sandwich Plates
      1. 5.3.1 Long Plates
      2. 5.3.2 Simply Supported Plates – Orthotropic and Symmetrical Layup
      3. 5.3.3 Face Wrinkling
    4. 5.4 Free Vibration of Rectangular Sandwich Plates
      1. 5.4.1 Long Plates
      2. 5.4.2 Simply Supported Plates – Orthotropic and Symmetrical Layup
  13. 6. Beams
    1. 6.1 Governing Equations
      1. 6.1.1 Boundary Conditions
      2. 6.1.2 Stiffness Matrix
      3. 6.1.3 Compliance Matrix
      4. 6.1.4 Replacement Stiffnesses
    2. 6.2 Rectangular, Solid Beams Subjected to Axial Load and Bending
      1. 6.2.1 Displacements – Symmetrical Layup
      2. 6.2.2 Displacements – Unsymmetrical Layup
      3. 6.2.3 Stresses and Strains
    3. 6.3 Thin-Walled, Open-Section Orthotropic or Symmetrical Cross-Section Beams Subjected to Axial Load and Bending
      1. 6.3.1 Displacements of T-Beams
      2. 6.3.2 Displacements of L-Beams
      3. 6.3.3 Displacements of Arbitrary Cross-Section Beams
      4. 6.3.4 Stresses and Strains
    4. 6.4 Thin-Walled, Closed-Section Orthotropic Beams Subjected to Axial Load and Bending
    5. 6.5 Torsion of Thin-Walled Beams
      1. 6.5.1 Thin Rectangular Cross Section
      2. 6.5.2 Open-Section Orthotropic Beams
      3. 6.5.3 Closed-Section Orthotropic Beams – Single Cell
      4. 6.5.4 Closed-Section Orthotropic Beams – Multicell
      5. 6.5.5 Restrained Warping – Open-Section Orthotropic Beams
      6. 6.5.6 Restrained Warping – Closed-Section Orthotropic Beams
    6. 6.6 Thin-Walled Beams with Arbitrary Layup Subjected to Axial Load, Bending, and Torsion
      1. 6.6.1 Displacements of Open- and Closed-Section Beams
      2. 6.6.2 Stresses and Strains in Open- and Closed-Section Beams
      3. 6.6.3 Centroid
      4. 6.6.4 Restrained Warping
    7. 6.7 Transversely Loaded Thin-Walled Beams
      1. 6.7.1 Beams with Orthotropic Layup or with Symmetrical Cross Section
      2. 6.7.2 Beams with Arbitrary Layup
      3. 6.7.3 Shear Center
    8. 6.8 Stiffened Thin-Walled Beams
    9. 6.9 Buckling of Beams
      1. 6.9.1 Beams Subjected to Axial Load (Flexural–Torsional Buckling)
      2. 6.9.2 Lateral–Torsional Buckling of Orthotropic Beams with Symmetrical Cross Section
      3. 6.9.3 Local Buckling
    10. 6.10 Free Vibration of Beams (Flexural–Torsional Vibration)
      1. 6.10.1 Doubly Symmetrical Cross Sections
      2. 6.10.2 Beams with Symmetrical Cross Sections
      3. 6.10.3 Beams with Unsymmetrical Cross Sections
    11. 6.11 Summary
  14. 7. Beams with Shear Deformation
    1. 7.1 Governing Equations
      1. 7.1.1 Strain–Displacement Relationships
      2. 7.1.2 Force–Strain Relationships
      3. 7.1.3 Equilibrium Equations
      4. 7.1.4 Summary of Equations
      5. 7.1.5 Boundary Conditions
    2. 7.2 Stiffnesses and Compliances of Beams
      1. 7.2.1 Shear Stiffnesses and Compliances of Thin-Walled Open-Section Beams
      2. 7.2.2 Shear Stiffnesses and Compliances of Thin-Walled Closed-Section Beams
      3. 7.2.3 Stiffnesses of Sandwich Beams
    3. 7.3 Transversely Loaded Beams
    4. 7.4 Buckling of Beams
      1. 7.4.1 Axially Loaded Beams with Doubly Symmetrical Cross Sections (Flexural and Torsional Buckling)
      2. 7.4.2 Axially Loaded Beams with Symmetrical or Unsymmetrical Cross Sections (Flexural–Torsional Buckling)
      3. 7.4.3 Lateral–Torsional Buckling of Beams with Symmetrical Cross Section
      4. 7.4.4 Summary
    5. 7.5 Free Vibration of Beams
      1. 7.5.1 Beams with Doubly Symmetrical Cross Sections
      2. 7.5.2 Beams with Symmetrical or Unsymmetrical Cross Sections
      3. 7.5.3 Summary
    6. 7.6 Effect of Shear Deformation
  15. 8. Shells
    1. 8.1 Shells of Revolution with Axisymmetrical Loading
    2. 8.2 Cylindrical Shells
      1. 8.2.1 Membrane Theory
      2. 8.2.2 Built-In Ends
      3. 8.2.3 Temperature – Built-In Ends
    3. 8.3 Springback
      1. 8.3.1 Springback of Cylindrical Shells
      2. 8.3.2 Doubly Curved Shells
    4. 8.4 Buckling of Shells
      1. 8.4.1 Buckling of Cylinders
  16. 9. Finite Element Analysis
    1. 9.1 Three-Dimensional Element
    2. 9.2 Plate Element
    3. 9.3 Beam Element
    4. 9.4 Sublaminate
      1. 9.4.1 Step 1. Elements of [J ] due to In-Plane Stresses
      2. 9.4.2 Step 2. Elements of [J ] due to Out-of-Plane Normal Stresses
      3. 9.4.3 Step 3. Elements of [J ] due to Out-of-Plane Shear Stresses
      4. 9.4.4 Step 4. The Stiffness Matrix
  17. 10. Failure Criteria
    1. 10.1 Quadratic Failure Criterion
      1. 10.1.1 Orthotropic Material
      2. 10.1.2 Transversely Isotropic Material
      3. 10.1.3 Isotropic Material
      4. 10.1.4 Plane-Strain and Plane-Stress Conditions
      5. 10.1.5 Proportional Loading – Stress Ratio
    2. 10.2 “Maximum Stress” Failure Criterion
    3. 10.3 “Maximum Strain” Failure Criterion
    4. 10.4 Plate with a Hole or a Notch
      1. 10.4.1 Plate with a Circular Hole
      2. 10.4.2 Plate with a Notch
      3. 10.4.3 Characteristic Length
  18. 11. Micromechanics
    1. 11.1 Rule of Mixtures
      1. 11.1.1 Longitudinal Young Modulus E[sub(1)]
      2. 11.1.2 Transverse Young Modulus E[sub(2)]
      3. 11.1.3 Longitudinal Shear Modulus G[sub(12)]
      4. 11.1.4 Transverse Shear Modulus G[sub(23)]
      5. 11.1.5 Longitudinal Poisson Ratio ν[sub(12)]
      6. 11.1.6 Transverse Poisson Ratio ν[sub(23)]
      7. 11.1.7 Thermal Expansion Coefficients
      8. 11.1.8 Moisture Expansion Coefficients
      9. 11.1.9 Thermal Conductivity
      10. 11.1.10 Moisture Diffusivity
      11. 11.1.11 Specific Heat
    2. 11.2 Modified Rule of Mixtures
    3. 11.3 Note on the Micromechanics Models
  19. Appendix A: Cross-Sectional Properties of Thin-Walled Composite Beams
  20. Appendix B: Buckling Loads and Natural Frequencies of Orthotropic Beams with Shear Deformation
  21. Appendix C: Typical Material Properties
  22. Index