Mechanics of Aeronautical Solids, Materials and Structures

Christophe Bouvet is Professor of structural mechanics at the ISAE-SUPAÉRO in France. His research focuses on the sizing and damage of composite structures at the Institut Clément Adler (ICA) in Toulouse, France.

Review copy sent to The Aeronautical Journal 23/11/2017.

• Foreword ixPreface xiIntroduction xiiiChapter 1 Stress 11.1 Notion of stress 11.1.1 External forces 11.1.2 Internal cohesive forces 21.1.3 Normal stress, shear stress 21.2 Properties of the stress vector 31.2.1 Boundary conditions 31.2.2 Torsor of internal forces 51.2.3 Reciprocal actions 81.2.4 Cauchy reciprocal theorem 91.3 Stress matrix 111.3.1 Notation 111.3.2 Invariants of the stress tensor 131.3.3 Relation between the stress matrix and the stress vector 151.3.4 Principal stresses and principal directions 181.4 Equilibrium equation 211.5 Mohr’s circle 23Chapter 2 Strain 272.1 Notion of strain 272.1.1 Displacement vector 272.1.2 Unit strain 282.1.3 Angular distortion 302.2 Strain matrix 332.2.1 Definition of the strain matrix 332.2.2 Principal strains and principal directions 372.2.3 Volume expansion 392.2.4 Invariants of strain tensor 402.2.5 Compatibility condition 402.3 Strain measurement: strain gage 41Chapter 3 Behavior Law 433.1 A few definitions 433.2 Tension test 433.2.1 Brittle materials 443.2.2 Ductile materials 453.2.3 Particular cases 463.3 Shear test 463.3.1 Brittle materials 473.3.2 Ductile materials 483.4 General rule 483.4.1 Linear elasticity 483.5 Anisotropic materials: example of a composite 533.5.1 Elasticity 533.6 Thermoelasticity 54Chapter 4 Resolution Methods 594.1 Assessment 594.2 Displacement method 614.3 Stress method 614.4 Finite element method 62Chapter 5 Work-energy Theorem: Principle of Finite Element Method 635.1 Work-energy theorem 635.1.1 Hypotheses 635.1.2 Strain energy 645.1.3 Work of external forces 655.1.4 Strain energy 665.1.5 Energy minimization: Ritz method 685.2 Finite element method 695.2.1 General principle of finite element method 695.2.2 Example of the three-node triangular element 745.3 Application: triangle with plate finite element using Catia 80Chapter 6 Sizing Criteria of an Aeronautical Structure 836.1 Introduction 836.2 Experimental determination of a sizing criterion 856.3 Normal stress or principal stress criterion: brittle material 876.4 Stress or maximum shear energy criterion: ductile material 916.4.1 Tresca criterion 916.4.2 Von Mises criterion 936.4.3 Rupture of a ductile material 966.5 Maximum shear criterion with friction: compression of brittle materials 996.6 Anisotropic criterion: example of the composite 105Chapter 7 Plasticity 1097.1 Introduction 1097.2 Plastic instability: necking, true stress and true strain 1117.3 Plastic behavior law: Ramberg–Osgood law 1167.4 Example of an elastic–plastic calculation: plate with open hole in tension 118Chapter 8 Physics of Aeronautical Structure Materials 1278.1 Introduction 1278.2 Aluminum 2024 1308.3 Carbon/epoxy composite T300/914 1358.4 Polymers 140Chapter 9 Exercises 1519.1 Rosette analysis 1519.2 Pure shear 1549.3 Compression of an elastic solid 1549.4 Gravity dam 1559.5 Shear modulus 1569.6 Modulus of a composite 1579.7 Torsional cylinder 1589.8 Plastic compression 1609.9 Bi-material beam tension 1629.10 Beam thermal expansion 1649.11 Cube under shear stress 1659.12 Spherical reservoir under pressure 1669.13 Plastic bending 1699.14 Disc under radial tension 1719.15 Bending beam: resolution by the Ritz method 1739.16 Stress concentration in open hole 1749.17 Bending beam 178Chapter 10 Solutions to Exercises 18310.1 Rosette analysis 18310.2 Pure shear 19110.3 Compression of an elastic solid 19210.4 Gravity dam 19610.5 Shear modulus 20110.6 Modulus of a composite 20310.7 Torsional cylinder 20610.8 Plastic compression 21210.9 Bi-material beam tension 21510.10 Beam thermal expansion 22510.11 Cube under shear stress 23110.12 Spherical reservoir under pressure 23510.13 Plastic bending 24010.14 Disc under radial tension 24510.15 Bending beam: resolution by the Ritz method 25210.16 Stress concentration in open hole 25610.17 Bending beam 259Appendix 273Bibliography 279Index 281