Rheology, Physical and Mechanical Behavior of Materials 3

Maurice Leroy is a lecturer and professor at the University of Nantes, France, as well as director of the Composite and Metallic Formations research laboratory at the IUT. He was instrumental in the creation of France's first Materials Science and Engineering department.

• Preface ixChapter 1 Elasticity, Rigidity 11.1 Elasticity and rigidity tensors 11.1.1 Hooke’s law 11.1.2 Matrix notation 21.1.3 Relationships between stresses and strains for isotropic bodies 21.1.4 Tensors [σ] and [ε] and deviators 41.2 Elastic energy 301.2.1 Elastic energy of a body subjected to stresses 301.2.2 Expansion energies Wϴ and distortion WD 311.3 Generalized stresses and strains 331.3.1 Generalized or equivalent Von Mises stress 331.3.2 Generalized or equivalent Von Mises strain 35Chapter 2 Scaling Criteria: Tresca, Von Mises, Hill 372.1 Isotropic criteria 372.1.1 Tresca criterion 372.1.2 Von Mises criterion 412.1.3 Load surfaces 472.2 Anisotropic criteria 822.2.1 Influence of anisotropy on the elastic limit 822.2.2 The Hill criterion for anisotropic materials 852.2.3 Hill’s criterion, scaling of composites 89Chapter 3 Elastic Mechanics of Parts and Structures: Rigidity, Strength, Scaling 1153.1 Statics of solids, basic concepts 1163.1.1 Load on a solid S 1163.1.2 Bonds: inventory of the primary bonds and cases of a spatial problem 1173.1.3 Equilibrium of a solid S 1193.1.4 Internal stresses 1193.1.5 Isostatic or hyperstatic pieces and structures 1253.2 Elasticity of parts and structures: method for calculating the three moments 1303.2.1 Calculation of rotations 1313.2.2 Generalization, equation of the three moments 1383.3 The force method 1403.3.1 Example of associated isostatic systems 1413.3.2 Castigliano’s theorem 1423.3.3 Manabrea’s theorem 1433.3.4 Maxwell’s influence coefficients 1463.4 Mohr integrals 1493.4.1 Application to the force method 1533.5 Movement method: application of Castigliano’s theorem to the calculation of elastic movements at a point of a part or a structure 1623.5.1 Calculation of the movements on a bending planar structure 1643.6 Matrix method, elastic stiffness [K] 1683.6.1 Lattice structures with flat articulated nodes 168Chapter 4 Tension, Torsion, Bending, Shearing: Static and Dynamic 2074.1 Introduction: static and dynamic tensions 2074.2 Torsion: basic concepts 2144.2.1 Stress for any section that does not have an angular point 2214.2.2 The case of a prism-shaped beam with rectangular section 2224.2.3 The case of a prism-shaped beam with a hollow section 2244.2.4 The case of a prism-shaped beam with a straight section in profile 2264.2.5 Internal energy of torsion strain 2274.2.6 Dynamic torsion 2284.3 Bending 2314.3.1 Planar bending 2314.3.2 Pure bending, T = 0 2324.3.3 Non-symmetrical bending 2364.3.4 Bending of curved beams 2394.3.5 Single bending, T ≠ 0 2424.4 Elastic deflection of beams 2424.4.1 The diagram method 2434.4.2 Double integration method and deflection curve 2554.4.3 Deformation energy method 267Chapter 5 Plastic Hinge 2815.1 Elastic limit deflection 2815.1.1 Any potential section with double symmetry 2825.1.2 A beam with symmetry only on its vertical axis 2875.1.3 Plastic ball joint 2905.2 Dynamic deflection 2995.2.1 Localized loading of beams and sheets 2995.2.2 Distributed loading of beams and sheets 3035.3 Bending of circular plates: elastic limit, bending of symmetrically loaded circular plates 3145.3.1 Circumferential and radial extensions, stresses and moments 314Chapter 6 Cutting Force, Shearing 3336.1 Distribution of shear stresses 3336.1.1 Full section: extent of boundary conditions 3336.1.2 Calculation of the distribution of stresses 3346.2 Balance of a beam element: balance of a solid (ABC A’B’C’) 3356.2.1 Resulting Breakdown of Forces 0 X 3356.2.2 Balance of Forces on 0 X 3366.3 Thin-walled section 3376.3.1 Torsion moment and shear center 3406.4 Shear in bending beams 3426.5 Shear flux 3436.6 Bredt’s formula 3446.6.1 Applications 3456.7 Deformation energy and strain: introduction of reduced sections and sag 355Appendix Page Numbers of the One Hundred Examples Examined with Their Solutions 363References 367Index 369