Table of Contents

1. Cover
2. Title
3. Copyright
4. Foreword
5. Preface
6. Introduction
   1. I.1. Outlining the problem
7. 1 Stress
   1. 1.1. Notion of stress
   2. 1.2. Properties of the stress vector
   3. 1.3. Stress matrix
   4. 1.4. Equilibrium equation
   5. 1.5. Mohr’s circle
8. 2 Strain
   1. 2.1. Notion of strain
   2. 2.2. Strain matrix
   3. 2.3. Strain measurement: strain gage
9. 3 Behavior Law
   1. 3.1. A few definitions
   2. 3.2. Tension test
   3. 3.3. Shear test
   4. 3.4. General rule
   5. 3.5. Anisotropic materials: example of a composite
   6. 3.6. Thermoelasticity
10. 4 Resolution Methods
    1. 4.1. Assessment
    2. 4.2. Displacement method
    3. 4.3. Stress method
    4. 4.4. Finite element method
11. 5 Work-energy Theorem: Principle of Finite Element Method
    1. 5.1. Work-energy theorem
    2. 5.2. Finite element method
    3. 5.3. Application: triangle with plate finite element using Catia
12. 6 Sizing Criteria of an Aeronautical Structure
    1. 6.1. Introduction
    2. 6.2. Experimental determination of a sizing criterion
    3. 6.3. Normal stress or principal stress criterion: brittle material
    4. 6.4. Stress or maximum shear energy criterion: ductile material
    5. 6.5. Maximum shear criterion with friction: compression of brittle materials
    6. 6.6. Anisotropic criterion: example of the composite
13. 7 Plasticity
    1. 7.1. Introduction
    2. 7.2. Plastic instability: necking, true stress and true strain
    3. 7.3. Plastic behavior law: Ramberg-Osgood law
    4. 7.4. Example of an elastic-plastic calculation: plate with open hole in tension
14. 8 Physics of Aeronautical Structure Materials
    1. 8.1. Introduction
    2. 8.2. Aluminum 2024
    3. 8.3. Carbon/epoxy composite T300/914
    4. 8.4. Polymers
15. 9 Exercises
    1. 9.1. Rosette analysis
    2. 9.2. Pure shear
    3. 9.3. Compression of an elastic solid
    4. 9.4. Gravity dam
    5. 9.5. Shear modulus
    6. 9.6. Modulus of a composite
    7. 9.7. Torsional cylinder
    8. 9.8. Plastic compression
    9. 9.9. Bi-material beam tension
    10. 9.10. Beam thermal expansion
    11. 9.11. Cube under shear stress
    12. 9.12. Spherical reservoir under pressure
    13. 9.13. Plastic bending
    14. 9.14. Disc under radial tension
    15. 9.15. Bending beam: resolution by the Ritz method
    16. 9.16. Stress concentration in open hole
    17. 9.17. Bending beam
16. 10 Solutions to Exercises
    1. 10.1. Rosette analysis
    2. 10.2. Pure shear
    3. 10.3. Compression of an elastic solid
    4. 10.4. Gravity dam
    5. 10.5. Shear modulus
    6. 10.6. Modulus of a composite
    7. 10.7. Torsional cylinder
    8. 10.8. Plastic compression
    9. 10.9. Bi-material beam tension
    10. 10.10. Beam thermal expansion
    11. 10.11. Cube under shear stress
    12. 10.12. Spherical reservoir under pressure
    13. 10.13. Plastic bending
    14. 10.14. Disc under radial tension
    15. 10.15. Bending beam: resolution by the Ritz method
    16. 10.16. Stress concentration in open hole
    17. 10.17. Bending beam
17. Appendix: Analysis Formulas
    1. A.1. Analysis formulas in Cartesian coordinates
    2. A.2. Analysis formulas in cylindrical coordinates
    3. A.3. Analysis formulas in spherical coordinates
18. Bibliography
19. Index
20. End User License Agreement

List of Tables

1. 7 Plasticity
   1. Table 7.1. Mechanical characteristics of the main aeronautic metal alloys
2. 8 Physics of Aeronautical Structure Materials
   1. Table 8.1. Mechanical characteristics of the main materials in aeronautics
   2. Table 8.2. Mechanical characteristics of principal aluminum alloys in aeronautics
   3. Table 8.3. Composition of aluminum 2024
   4. Table 8.4. Comparison of three main resins in aeronautics

List of Illustrations

1. Introduction
   1. Figure I.1. Outlining the problem. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
2. 1 Stress
   1. Figure 1.1. Principle of internal cohesive forces. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 1.2. Decomposition of a stress vector. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 1.3. External force and associated normal vector. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 1.4. Tank under pressure
   5. Figure 1.5. Set of internal forces. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 1.6. Tensile test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 1.7. Bending test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 1.8. Reciprocal actions. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 1.9. Stress vectors on the faces of a square. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 1.10. Torsion of a welded tube. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 1.11. Stress vectors on the faces of a unit cube. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 1.12. Stress vectors on the faces of a square. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   13. Figure 1.13. Hydrostatic pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   14. Figure 1.14. Traction test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   15. Figure 1.15. Stress vectors in traction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   16. Figure 1.16. Equilibrium of a triangle of matter. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   17. Figure 1.17. Principal stresses and associated stress vectors. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   18. Figure 1.18. Stress vectors for pure shearing. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   19. Figure 1.19. Stress vectors on the faces of a square. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   20. Figure 1.20. Mohr’s circle. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   21. Figure 1.21. Mohr’s circle. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   22. Figure 1.22. Stress vectors on a facet with a normal vector n in traction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   23. Figure 1.23. Mohr’s circle in traction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
3. 2 Strain
   1. Figure 2.1. Displacement field of a solid
   2. Figure 2.2. Unit strain. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 2.3. Unit strain formula. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 2.4. Angular distortion. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 2.5. Angular distortion formula. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 2.6. Strain of a square
   7. Figure 2.7. Strain of a square
   8. Figure 2.8. Strain of a square and principal strains. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 2.9. Strain of a square and principal strains in pure shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 2.10. Volume expansion
   11. Figure 2.11. Unidirectional gage and rosette: three gages oriented at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
4. 3 Behavior Law
   1. Figure 3.1. Tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 3.2. Tensile test of a brittle material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 3.3. Tension test of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 3.4. Shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 3.5. Torsion test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 3.6. Brittle material shear test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 3.7. Shear test of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 3.8. Stress vectors on the faces of a square. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 3.9. Unidirectional composite carbon/epoxy. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 3.10. Young’s modulus of a UD composite versus the tension direction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 3.11. Thermal expansion with free stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 3.12. Thermal expansion with constrained strain. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
5. 5 Work-energy Theorem: Principle of Finite Element Method
   1. Figure 5.1. Definition of the initial and deformed states. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 5.2. External forces. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 5.3. Linearity of external forces. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 5.4. Tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 5.5. Setting the problem. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 5.6. Discretization of the structure in finite element method. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 5.7. Triangular finite element. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 5.8. Triangle subjected to a force. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 5.9. Displacement field of a triangle subjected to a force. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 5.10. Triangle subjected to a force and displacement field obtained by FE calculation. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 5.11. Stress field determined by FE calculation in a triangle subjected to a force. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 5.12. Problem of a triangle subjected to a force
6. 6 Sizing Criteria of an Aeronautical Structure
   1. Figure 6.1. Proportional loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 6.2. Bi-axial testing machine (source: http://www.directindustry.fr/prod/zwick). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 6.3. Normal and shear stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 6.4. Rupture of a brittle material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 6.5. Rupture criterion of a brittle material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 6.6. Edge dislocation displacement and screw dislocation under the action of a shear stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 6.7. Tension test of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 6.8. End of elasticity criteria of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 6.9. Hydrostatic pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 6.10. End of elasticity criteria of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 6.11. Maximum shear in a tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 6.12. Rupture of a ductile material with little plasticity (Source: https://fr.wikiversity.org/wiki/Introduction_à_la_science_des_matériaux). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   13. Figure 6.13. Rupture of a ductile material with much plasticity (Source: https://fr.wikiversity.org/wiki/Introduction_à_la_science_des_matériaux. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   14. Figure 6.14. Rupture of a composite under transverse tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   15. Figure 6.15. Rupture of a composite in transverse compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   16. Figure 6.16. Compression stress vector. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   17. Figure 6.17. Shear rupture without and with compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   18. Figure 6.18. Mohr–Coulomb, Von Mises and Tresca criteria. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   19. Figure 6.19. Tsai–Hill and maximum stress criteria. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
7. 7 Plasticity
   1. Figure 7.1. Plasticity of a ductile material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 7.2. Plasticity of a ductile material after prior strain hardening. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 7.3. Tension test in engineering and true stress/strain. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 7.4. Tension test of a 2024 aluminum alloy. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 7.5. Plasticity curve of stress versus plastic strain. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 7.6. Tension curves of the main aeronautical metal alloys. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 7.7. Open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 7.8. Open hole tension test
   9. Figure 7.9. FE modeling of an open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 7.10. Von Mises stress of an elastic tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 7.11. Elastic and elastic–plastic tension curves. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 7.12. Von Mises stress of an elastic–plastic open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   13. Figure 7.13. Von Mises plastic strain of an elastic–plastic open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   14. Figure 7.14. Global curve of an open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   15. Figure 7.15. Schematic mechanical behavior of an elastic–plastic structure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   16. Figure 7.16. Von Mises plastic stress and strain of an open hole tension test for σ₀ = 278 MPa. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
8. 8 Physics of Aeronautical Structure Materials
   1. Figure 8.1. Materials in a Boeing 787 (according to http://www.boeing.fr). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   2. Figure 8.2. Heat treatment of 2024. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   3. Figure 8.3. Al/Cu equilibrium diagram. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   4. Figure 8.4. Heat treatment of 2024. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   5. Figure 8.5. Heat treatment of 2024. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   6. Figure 8.6. Mass percentage of composite in the structure of Airbus aircraft (according to http://www.airbus.com/). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   7. Figure 8.7. Carbon/epoxy UD lay-up. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   8. Figure 8.8. Unidirectional and quasi-isotropic lay-up. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   9. Figure 8.9. Tension test in longitudinal direction in a composite: fiber, resin and composite behavior. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 8.10. Tension test in longitudinal direction: damaged area. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   11. Figure 8.11. Young’s Modulus according to density [ASH 80]. CFRP: Carbon Fiber Reinforced Plastic/GFRP: Glass Fiber Reinforced Plastic. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   12. Figure 8.12. Strength according to density [ASH 80]. CFRP: Carbon Fiber Reinforced Plastic/GFRP: Glass Fiber Reinforced Plastic. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   13. Figure 8.13. Structure of polyethylene. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   14. Figure 8.14. Polymer structure in monomer chains
   15. Figure 8.15. Polymer rigidity according to temperature. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   16. Figure 8.16. Behavior of polymers with temperature. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   17. Figure 8.17. Secondary bonds between monomer chains: cross-links. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   18. Figure 8.18. Polymer rigidity according to temperature and degree of cross-linking. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   19. Figure 8.19. Autoclave for thermoset curing. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   20. Figure 8.20. Photo of a prepreg roll (photo Hexcel). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   21. Figure 8.21. Sheet Moulding Compound (SMC) for thermoplastic heating and shaping. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   22. Figure 8.22. Tension test of a polymer. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   23. Figure 8.23. Crystalline phases and amorphous zones in a thermoplastic polymer. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   24. Figure 8.24. Rigidity of a thermoplastic polymer according to the temperature and degree of crystallinity. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
9. 9 Exercises
   1. Figure 9.1. 45° strain gage rosette
   2. Figure 9.2. 120° strain gage rosette
   3. Figure 9.3. Square sheared!
   4. Figure 9.4. Cylinder confined in compression
   5. Figure 9.5. Gravity dam
   6. Figure 9.6. Shear stress analysis
   7. Figure 9.7. Composite with long fibers
   8. Figure 9.8. Torsional cylinder
   9. Figure 9.9. Plastic compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   10. Figure 9.10. Compressive barrel effect
   11. Figure 9.11. Bi-compression
   12. Figure 9.12. Bi-compression with rods ([BOU 01]). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   13. Figure 9.13. Tension of a bi-material beam
   14. Figure 9.14. Thermal expansion of a constrained and free beam
   15. Figure 9.15. Thermal expansion of a constrained and free bi-material beam
   16. Figure 9.16. Cube under shear stress
   17. Figure 9.17. Ariane 5 storable propellant stage (according to http://www.capcomespace.net). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   18. Figure 9.18. Reservoir under pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   19. Figure 9.19. Plastic bending
   20. Figure 9.20. Perfect plasticity. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   21. Figure 9.21. Disc under radial tension
   22. Figure 9.22. Simply supported beam in bending
   23. Figure 9.23. Open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   24. Figure 9.24. Results of the FE calculation for open hole tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   25. Figure 9.25. Results of the FE calculation for open hole tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   26. Figure 9.26. Bending beam
   27. Figure 9.27. Bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
   28. Figure 9.28. Results of the FE calculation for a bending beam
10. 10 Solutions to Exercises
    1. Figure 10.1. 45° strain gage rosette
    2. Figure 10.2. Stress vector and principal stresses. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    3. Figure 10.3. Tension failure of a brittle material. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    4. Figure 10.4. Maximum shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    5. Figure 10.5. 120° strain gage rosette
    6. Figure 10.6. Sheared square
    7. Figure 10.7. Stress vectors and maximum shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    8. Figure 10.8. Compression of a confined cylinder
    9. Figure 10.9. Gravity dam
    10. Figure 10.10. Shear stress analysis
    11. Figure 10.11. Stress vectors and maximum shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zipEssentially, in the coordinate system (u,v,z) we have:
    12. Figure 10.12. Composite with long fibers
    13. Figure 10.13. Parallel and serial homogenization models
    14. Figure 10.14. Young’s modulus according to parallel and serial homogenization models. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    15. Figure 10.15. Torsional cylinder
    16. Figure 10.16. Principal coordinate system. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    17. Figure 10.17. Torsion stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    18. Figure 10.18. Plastic compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    19. Figure 10.19. True and engineering stress/strain tension curves. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    20. Figure 10.20. Compressive barrel effect
    21. Figure 10.21. Bi-compression
    22. Figure 10.22. Tension of a bi-material beam
    23. Figure 10.23. Stress and strain through bi-material tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    24. Figure 10.24. Stress at the end of a bi-material beam under tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    25. Figure 10.25. Bi-material beam tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    26. Figure 10.26. Strain during bi-material tension/bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    27. Figure 10.27. Stress and strain during bi-material tension/bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    28. Figure 10.28. Thermal expansion of a constrained beam
    29. Figure 10.29. Thermal expansion of a free beam
    30. Figure 10.30. Thermal expansion of a constrained bi-material beam
    31. Figure 10.31. Thermal expansion of a free bi-material beam
    32. Figure 10.32. Strain due to thermal expansion of a free bi-material beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    33. Figure 10.33. Stress and strain field due to thermal expansion of a free bi-material beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    34. Figure 10.34. Cube under shear stress
    35. Figure 10.35. Stress vectors on a cube under shear stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    36. Figure 10.36. Reservoir under pressure
    37. Figure 10.37. Stress in a reservoir under pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    38. Figure 10.38. Plastic bending where is the bending moment, here:
    39. Figure 10.39. Stress in a beam under elastic bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    40. Figure 10.40. Stress and strain in an elastic–plastic bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    41. Figure 10.41. Plastic zone in an elastic–plastic bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    42. Figure 10.42. Plastic behavior of an elastic–plastic bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    43. Figure 10.43. Stress in an elastic–plastic bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    44. Figure 10.44. Disc under radial tension
    45. Figure 10.45. Simply supported beam in bending
    46. Figure 10.46. Kinematic of a bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    47. Figure 10.47. Stress in a simply supported bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    48. Figure 10.48. Open hole tension test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    49. Figure 10.49. Stress field around a hole. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    50. Figure 10.50. Bending beam
    51. Figure 10.51. Stress in a bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    52. Figure 10.52. Stress in a bending beam. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
11. Appendix: Analysis Formulas
    1. Figure A.1. Coordinates of a point in Cartesian coordinates. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    2. Figure A.2. Coordinates of a point in cylindrical coordinates. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip
    3. Figure A.3. Coordinates of a point in spherical coordinates. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical.zip

Guide

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2. Table of Contents
3. Begin Reading