Theory of elasticity and plasticity : a textbook of solid body mechanics / / Valentin Molotnikov, Antonina Molotnikova

• Autore: Molotnikov Valentin
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (447 pages)
• Disciplina: 531.382
• Soggetto topico: Elasticity
• Persona (resp. second.): MolotnikovaAntonina
• Nota di contenuto: Intro -- Dedication -- Preface to the English-Language Edition -- Preface -- Abstract -- Contents -- Notation Conventions -- Loads and Stresses -- Deformations and Movements -- Physical and Mechanical Characteristics of Materials -- Part I Basis of Elasticity Theory -- 1 Summary of Elasticity Theory: Basic Concepts -- 1.1 From the History of Elasticity Theory -- 1.2 Elasticity of Solid Bodies -- 1.3 Homogeneous Strain -- 1.4 Internal Forces: Method of Sections -- 1.5 Homogeneous Body -- 1.6 Stress Vector -- 1.7 Elongation of Steel Specimens -- 1.8 Permanent Deformations -- 1.9 Elastic Limit -- 1.10 Elastic Shear Deformation -- 1.11 Law of Twoness of Tangential Stresses -- 1.12 Homogeneous Stressed State -- 1.13 Generalized Hooke's Law -- 1.14 Another Form of Hooke's Law -- 1.15 Plane Stress-Strain State -- 1.16 Homogeneous Model of a Solid Body -- 1.17 Axisymmetric Plane Strain -- 1.18 Lame Task -- 1.19 Phenomenon of Stress Concentration -- 1.20 Saint-Venant Principle -- References -- 2 The First Basic Problem of Elasticity Theory -- 2.1 Equilibrium Equations -- 2.2 Expression of Strains Through Movements -- 2.3 Definition of Movements -- 2.4 Saint-Venant Identities -- 2.5 Compatibility Conditions -- 2.6 Boundary Conditions -- 2.7 The First Basic Problem of Elasticity Theory -- References -- 3 The Second Primary Problem of Elasticity Theory -- 3.1 Definition of Stresses Through Deformations -- 3.2 Equations of Elastic Body Strain -- 3.3 Application of Harmonic Functions -- 3.4 Trefftz Integral -- 3.5 Grodsky-Neyber-Papkovich Integral -- References -- 4 Three-Dimensional Harmonic Function -- 4.1 Simplest Examples of Harmonic Functions -- 4.2 Green Function -- 4.3 Green's Spatial Functions -- 4.4 Boundary Problems for Half-Space -- 4.5 Other Properties of Harmonic Functions -- References -- 5 Elastic Half-Space. ; 5.1 Volumetric Expansion on Surface -- 5.2 Stress on Surface -- 5.3 Strain of Elastic Half-Space -- 5.3.1 Integral Operator of Formulas (5.18)-(5.20) -- 5.4 Examples -- References -- 6 Herz's Task -- 6.1 Deformation of Adjoining Bodies -- 6.2 Primary Assumptions -- 6.3 Axisymmetric Hertz Problem -- 6.4 Compression of Orthogonal Cylinders -- 6.4.1 Simplest Case -- 6.4.2 Primary Case -- 6.5 Compression of Barrel-Shaped Bodies -- 6.5.1 Rotation Bodies with Parallel Axes -- 6.5.2 Case of Intersecting Axes -- 6.6 Elongated Contact Area -- 6.7 Compression of Parallel Cylinders -- References -- 7 Stressed State in a Body Point -- 7.1 Principal Stresses -- 7.2 Maximum Stresses -- 7.3 Intensity of Stresses -- 7.4 Some Properties of Tangential Stresses -- References -- 8 Linear Elastic Systems -- 8.1 General Comments -- 8.2 Linear System -- 8.3 Potential Energy of a Helical Spring -- 8.4 Principle of Mutuality of Works -- 8.5 Castigliano's Theorem -- 8.6 Specific Potential Energy of Elastic Deformation -- References -- 9 Plane Problem of Elasticity Theory -- 9.1 Functions of Stresses -- 9.1.1 Example 1: Concentrated Force in the Wedge Apex -- 9.1.2 Example 2: Wedge Bending by Uniform Pressure -- 9.2 Complex Representation of a Bi-Harmonic Function -- 9.3 Kolosov Displacement Integral -- 9.4 Action of Concentrated Force -- 9.5 Solution of the First Principal Problem for a Circle -- 9.6 Annex to the Brazilian Test -- References -- 10 Mathematical Structural Imperfections -- 10.1 Mathematical and Physical Theories of Structural Imperfections -- 10.2 Edge Dislocation in an Infinite Body -- 10.3 Mathematical Wedge-Shaped Dislocation -- 10.4 Mathematical Biclination -- 10.5 Flat Dislocation of Somigliana -- 10.6 Somigliana Dislocation in Half-Plane -- 10.6.1 Functions , for the Plane with Dislocation -- 10.6.2 Functions , for a Half-Plane with Dislocation. ; 10.6.3 Calculation of Galin Functions -- 10.6.4 Completion of Problem Solution -- 10.6.5 Addition to Geomechanics -- 10.7 Pair of Fislocations in a Plane -- 10.8 Edge Dislocation in a Half-Plane -- 10.9 Half-Plane with a System of Dislocations -- References -- 11 The Beginning of the Theory of Stability of Equilibrium -- 11.1 Stability and Instability -- 11.2 Work and Classification of Forces -- 11.3 Stability with Conservative and Dissipative Forces -- 11.4 Lyapunov-Chetaev Theorem -- 11.5 Instability in the First Approximation -- 11.6 Critical Load -- 11.7 The Theorem on Stability by the First Approximation -- 11.8 The Raus-Hurwitz criterion -- 11.9 Main Types of Stability Loss -- 11.10 Methods for Determining Critical Load -- 11.11 The Perturbed Motion of the Compressed Rod -- 11.12 Stability Under Non-conservative Load (Example) -- 11.12.1 Equations of Perturbed Motion -- 11.12.2 Area of Valid Stability -- 11.12.3 Investigation of the Value μ, (Formula (11.31)) -- 11.12.4 Investigation of the Effect of Friction -- 11.12.5 The influence of the spacing of the End Masses -- References -- Part II Principal Variants of Mathematical Plasticity Theory -- 12 Origin and Development of Plasticity Theory -- 12.1 Primary Definitions -- 12.2 The Subject and Tasks of the Theory of Plasticity -- 12.3 Early Development Stages of Plasticity Theory -- 12.4 Development of Plasticity Theory in the Twentieth Century -- 12.5 Soviet Period of Plasticity Theory Development -- 12.6 Russian Mechanics in the Post-Soviet Period -- 12.6.1 General Situation and Dangerous Trends -- 12.6.2 Plasticity Theory in Russia in the Post-Soviet Period -- 12.7 Abstract -- References -- 13 Initial Concepts of Plasticity Theory -- 13.1 Second-Rank Tensor in Euclidean Space -- 13.2 Tensors in Plasticity Theory -- 13.3 Decomposition of Stress and Strain Tensors. ; 13.4 Other Invariants in Plasticity Theory -- 13.5 On the Criterion of Similarity of Stress and Strain Deviators -- 13.6 Stress Diagrams and Their Idealization -- References -- 14 On the Plasticity Conditions of an Isotropic Body -- 14.1 General Considerations -- 14.2 General Notes -- 14.3 Tresca Plasticity Condition -- 14.4 Huber-Mises Plasticity Condition -- 14.5 Experimental Study of Elastic-Plastic Materials -- 14.6 Volumetric Elasticity of Materials -- 14.7 Invariant Form of Hooke's Law -- References -- 15 Plasticity Theory of Henky-Nadai-Ilyushin -- 15.1 Laws of Active Elastic-Plastic Deformation -- 15.2 Defining the Universal Hardening Function -- 15.3 Some Properties of the Hardening Function -- 15.4 Another Form of Strain Ratios -- 15.5 Unloading Laws -- 15.6 Work of Stresses, Potential Energy, and Potentials -- 15.6.1 Stress Potential -- 15.6.2 Potential of Strains -- 15.7 Theorem of the Minimal Work of Inner Forces -- 15.8 Lagrange Equilibrium Variation Equation -- 15.9 Setting Boundary Problems of Plasticity Theory -- 15.10 Theorem of Simple Loading -- 15.11 Theorem of Unloading -- References -- 16 Solution of the Simplest Problems for the Strain Theory of Plasticity -- 16.1 Pure Bending of a Straight Beam -- 16.2 Torsion of a Round-Section Beam -- 16.3 Elastic-Plastic Inflation of a Spherical Vessel -- 16.4 Symmetric Strain of a Cylindrical Tube -- 16.5 Torsion of a Beam of Ideally Plastic Material -- 16.5.1 Elastic Torsion: Prandtl Analogy -- 16.5.2 Elastic-Plastic Beam Torsion -- 16.6 Rod of a Variable Section: Method of Elastic Solutions -- 16.6.1 Preparation of Initial Ratios -- 16.6.2 Specification of Problem Setting -- 16.6.3 Algorithm of the Elastic Solutions Method -- References -- 17 Additions and Generalizations to the Strain Theory of Plasticity -- 17.1 Generalizations of Goldenblatt and Prager. ; 17.2 Tensor-Linear Ratios in Plasticity Theories -- 17.3 Vector Representation of Tensors -- 17.4 Transformations of Rotation and Reflection -- 17.5 Ilyushin's Isotropy Postulate -- 17.6 Delay Law -- 17.7 Loading Surface -- 17.8 Drucker Postulate -- 17.9 On the Applicability Limits of the Strain Theory of Plasticity -- References -- 18 Theories of Plastic Yield -- 18.1 General Ratios -- 18.2 Prandtl-Reuss Yield -- 18.3 Saint-Venant-Mises Yield Theory -- 18.4 Plastic Yield in Isotropic Hardening -- 18.5 Handelman-Lin-Prager Plasticity Theory -- 18.6 Yield for Plane Loading Surfaces -- 18.7 Yield for Some Loading Surfaces -- 18.8 Kadashevich-Novozhilov Plasticity Theory -- 18.9 Singular Loading Surfaces -- References -- 19 Other Variants of Plasticity Theories -- 19.1 Batdorf-Budiansky Slip Theory -- 19.2 Two-Dimensional Klyushnikov Model -- 19.3 Endochronic Plasticity Theory -- 19.4 On the Methods of Physical Mesomechanics and Synergetics -- References -- Part III Development of the Slip Concept in Plasticity Theory -- 20 Problem Setting -- 20.1 Initial Concepts and Definitions -- 20.2 Shift Resistance -- 20.3 Slip Synthesis -- 20.4 Definition of Principal Strains -- References -- 21 Strain Specifics of Plastic Bodies -- 21.1 Elongation Diagram of a Plastic Material Specimen -- 21.2 Delay of Yield -- 21.3 Yield Stress and Loading Rate -- References -- 22 Axioms of the Inelastic Body Model -- 22.1 Deformational Softening -- 22.2 Initial Shear Resistance -- 22.3 Function of Elastic Softening -- References -- 23 The Fluidity at the Finite Speed of Loading -- 23.1 Yield Strength at the Final Loading Speed -- 23.2 Defining the Aging Function -- 23.2.1 Example -- 23.3 Components of Deformational Softening -- 23.4 Almost Simple Strain -- References -- 24 Specimen Elongation with Yield Drop -- 24.1 Original Assumption -- 24.2 Occurrence of Non-elastic Strain. ; 24.3 Origins of Boundary Layer Theory.
• Titolo autorizzato: Theory of elasticity and plasticity
• ISBN: 3-030-66622-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910484021503321
• Lo trovi qui: Univ. Federico II