Rheology, Physical and Mechanical Behavior of Materials 3: Rigidity and Resistance of Materials, Sizings, Pieces and Structures(ISTE Invoiced)

This book studies metallic and composite materials and their mechanical properties in terms of stiffness and strength, illustrated through several case studies and exercises. Rheology, Physical and Mechanical Behavior of Materials 3 introduces the concepts of stiffness, strength, elastic energy, generalized stress and strain, as well as the main criteria for dimensioning isotropic and anisotropic materials. It covers the elastic mechanics of pieces and structures using various techniques such as the force method, Maxwell's influence coefficients, Castigliano and Menabrea's work, Mohr’s integrals and the displacement method, as well as the design and use of stiffness matrices. It also compares the behavior of static and dynamic impact actions and studies the elastic limits of plastic hinges, their influences and shear forces. This book is aimed at those studying technical or technological training courses, researchers involved in the mechanics of deformation, and industrial design and manufacturing departments.

Table of Contents:
Preface ix Chapter 1 Elasticity, Rigidity 1 1.1 Elasticity and rigidity tensors 1 1.1.1 Hooke’s law 1 1.1.2 Matrix notation 2 1.1.3 Relationships between stresses and strains for isotropic bodies 2 1.1.4 Tensors [σ] and [ε] and deviators 4 1.2 Elastic energy 30 1.2.1 Elastic energy of a body subjected to stresses 30 1.2.2 Expansion energies Wϴ and distortion WD 31 1.3 Generalized stresses and strains 33 1.3.1 Generalized or equivalent Von Mises stress 33 1.3.2 Generalized or equivalent Von Mises strain 35 Chapter 2 Scaling Criteria: Tresca, Von Mises, Hill 37 2.1 Isotropic criteria 37 2.1.1 Tresca criterion 37 2.1.2 Von Mises criterion 41 2.1.3 Load surfaces 47 2.2 Anisotropic criteria 82 2.2.1 Influence of anisotropy on the elastic limit 82 2.2.2 The Hill criterion for anisotropic materials 85 2.2.3 Hill’s criterion, scaling of composites 89 Chapter 3 Elastic Mechanics of Parts and Structures: Rigidity, Strength, Scaling 115 3.1 Statics of solids, basic concepts 116 3.1.1 Load on a solid S 116 3.1.2 Bonds: inventory of the primary bonds and cases of a spatial problem 117 3.1.3 Equilibrium of a solid S 119 3.1.4 Internal stresses 119 3.1.5 Isostatic or hyperstatic pieces and structures 125 3.2 Elasticity of parts and structures: method for calculating the three moments 130 3.2.1 Calculation of rotations 131 3.2.2 Generalization, equation of the three moments 138 3.3 The force method 140 3.3.1 Example of associated isostatic systems 141 3.3.2 Castigliano’s theorem 142 3.3.3 Manabrea’s theorem 143 3.3.4 Maxwell’s influence coefficients 146 3.4 Mohr integrals 149 3.4.1 Application to the force method 153 3.5 Movement method: application of Castigliano’s theorem to the calculation of elastic movements at a point of a part or a structure 162 3.5.1 Calculation of the movements on a bending planar structure 164 3.6 Matrix method, elastic stiffness [K] 168 3.6.1 Lattice structures with flat articulated nodes 168 Chapter 4 Tension, Torsion, Bending, Shearing: Static and Dynamic 207 4.1 Introduction: static and dynamic tensions 207 4.2 Torsion: basic concepts 214 4.2.1 Stress for any section that does not have an angular point 221 4.2.2 The case of a prism-shaped beam with rectangular section 222 4.2.3 The case of a prism-shaped beam with a hollow section 224 4.2.4 The case of a prism-shaped beam with a straight section in profile 226 4.2.5 Internal energy of torsion strain 227 4.2.6 Dynamic torsion 228 4.3 Bending 231 4.3.1 Planar bending 231 4.3.2 Pure bending, T = 0 232 4.3.3 Non-symmetrical bending 236 4.3.4 Bending of curved beams 239 4.3.5 Single bending, T ≠ 0 242 4.4 Elastic deflection of beams 242 4.4.1 The diagram method 243 4.4.2 Double integration method and deflection curve 255 4.4.3 Deformation energy method 267 Chapter 5 Plastic Hinge 281 5.1 Elastic limit deflection 281 5.1.1 Any potential section with double symmetry 282 5.1.2 A beam with symmetry only on its vertical axis 287 5.1.3 Plastic ball joint 290 5.2 Dynamic deflection 299 5.2.1 Localized loading of beams and sheets 299 5.2.2 Distributed loading of beams and sheets 303 5.3 Bending of circular plates: elastic limit, bending of symmetrically loaded circular plates 314 5.3.1 Circumferential and radial extensions, stresses and moments 314 Chapter 6 Cutting Force, Shearing 333 6.1 Distribution of shear stresses 333 6.1.1 Full section: extent of boundary conditions 333 6.1.2 Calculation of the distribution of stresses 334 6.2 Balance of a beam element: balance of a solid (ABC A’B’C’) 335 6.2.1 Resulting Breakdown of Forces 0 X 335 6.2.2 Balance of Forces on 0 X 336 6.3 Thin-walled section 337 6.3.1 Torsion moment and shear center 340 6.4 Shear in bending beams 342 6.5 Shear flux 343 6.6 Bredt’s formula 344 6.6.1 Applications 345 6.7 Deformation energy and strain: introduction of reduced sections and sag 355 Appendix Page Numbers of the One Hundred Examples Examined with Their Solutions 363 References 367 Index 369

About the Author :
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.