{"product_id":"analysis-of-engineering-structures-and-material-behavior-9781119329077","title":"Analysis of Engineering Structures and Material","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAnalysis of Engineering Structures and Material Behavior    Professor Josip Brniae, D. Sc.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrequently Used Symbols and the Meaning of Symbols xv\u003c\/p\u003e \u003cp\u003ePrincipal SI Units and the US Equivalents xxiii\u003c\/p\u003e \u003cp\u003eSI Prefixes, Basic Units, Physical Constants, the Greek Alphabet xxv\u003c\/p\u003e \u003cp\u003eImportant Notice Before Reading the Book xxvii\u003c\/p\u003e \u003cp\u003ePreface xxix\u003c\/p\u003e \u003cp\u003eAbout the Author xxxi\u003c\/p\u003e \u003cp\u003eAcknowledgements xxxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Task of Design and Manufacture 1\u003c\/p\u003e \u003cp\u003e1.2 Factors that Influence the Design of Engineering Structures 1\u003c\/p\u003e \u003cp\u003e1.3 The Importance of Optimization in the Process of Design and the Selection of Structural Materials 3\u003c\/p\u003e \u003cp\u003e1.4 Commonly Observed Failure Modes in Engineering Practice 4\u003c\/p\u003e \u003cp\u003e1.5 Structures and the Analysis of Structures 5\u003c\/p\u003e \u003cp\u003eReferences 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Stress 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Definition of Average Stress and Stress at a Point 7\u003c\/p\u003e \u003cp\u003e2.2 Stress Components and Equilibrium Equations 8\u003c\/p\u003e \u003cp\u003e2.2.1 Stress Components 8\u003c\/p\u003e \u003cp\u003e2.2.2 Equilibrium Equations 9\u003c\/p\u003e \u003cp\u003e2.3 Stress Tensor 10\u003c\/p\u003e \u003cp\u003e2.3.1 Mean and Deviatoric Stress Tensors 10\u003c\/p\u003e \u003cp\u003e2.4 States of Stress 12\u003c\/p\u003e \u003cp\u003e2.4.1 Uniaxial State of Stress 12\u003c\/p\u003e \u003cp\u003e2.4.2 Two-dimensional State of Stress 14\u003c\/p\u003e \u003cp\u003e2.4.3 Three-dimensional State of Stress 18\u003c\/p\u003e \u003cp\u003e2.4.3.1 Stress on an Arbitrary Plane 20\u003c\/p\u003e \u003cp\u003e2.4.3.2 Stress on an Octahedral Plane 21\u003c\/p\u003e \u003cp\u003e2.4.3.3 Principal Stresses and Stress Invariants 22\u003c\/p\u003e \u003cp\u003e2.5 Transformation of Stress Components 24\u003c\/p\u003e \u003cp\u003eReferences 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Strain 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definition of Strain 29\u003c\/p\u003e \u003cp\u003e3.1.1 Some Properties of Materials Associated with Strain 30\u003c\/p\u003e \u003cp\u003e3.1.1.1 Poisson’s Ratio 30\u003c\/p\u003e \u003cp\u003e3.1.1.2 Volumetric Strain 30\u003c\/p\u003e \u003cp\u003e3.1.1.3 Bulk Modulus 31\u003c\/p\u003e \u003cp\u003e3.1.1.4 Modulus of Elasticity 32\u003c\/p\u003e \u003cp\u003e3.1.1.5 Shear Modulus (Modulus of Rigidity) 32\u003c\/p\u003e \u003cp\u003e3.2 Strain–Displacement Equations 33\u003c\/p\u003e \u003cp\u003e3.3 Strain Tensors 35\u003c\/p\u003e \u003cp\u003e3.3.1 Small Strain Tensor 35\u003c\/p\u003e \u003cp\u003e3.3.2 Finite Strain Tensor 38\u003c\/p\u003e \u003cp\u003e3.3.3 Mean and Deviatoric Strain Tensors 40\u003c\/p\u003e \u003cp\u003e3.3.4 Principal Strains and Strain Invariants 41\u003c\/p\u003e \u003cp\u003e3.3.4.1 Strain Tensor 41\u003c\/p\u003e \u003cp\u003e3.3.4.2 Deviatoric Strain Tensor 42\u003c\/p\u003e \u003cp\u003e3.4 Transformation of Strain Components 43\u003c\/p\u003e \u003cp\u003e3.4.1 Mohr’s Circle 44\u003c\/p\u003e \u003cp\u003e3.5 Strain Measurement 44\u003c\/p\u003e \u003cp\u003eReferences 48\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Mechanical Testing of Materials 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Material Properties 51\u003c\/p\u003e \u003cp\u003e4.2 Types of Material Testing 52\u003c\/p\u003e \u003cp\u003e4.3 Test Methods Related to Mechanical Properties 52\u003c\/p\u003e \u003cp\u003e4.4 Testing Machines and Specimens 52\u003c\/p\u003e \u003cp\u003e4.4.1 Static Tensile Testing Machine and Specimens 52\u003c\/p\u003e \u003cp\u003e4.4.2 Impact Testing Machine and Specimens 54\u003c\/p\u003e \u003cp\u003e4.4.3 Hardness Testing Machine 54\u003c\/p\u003e \u003cp\u003e4.4.4 Fatigue Testing Machines 56\u003c\/p\u003e \u003cp\u003e4.5 Test Results 56\u003c\/p\u003e \u003cp\u003e4.5.1 Static Tensile Test Results 56\u003c\/p\u003e \u003cp\u003e4.5.1.1 Engineering Stress–Strain Diagram 56\u003c\/p\u003e \u003cp\u003e4.5.1.2 Creep Diagram\/Curve 62\u003c\/p\u003e \u003cp\u003e4.5.1.3 Relaxation Diagram\/Curve 62\u003c\/p\u003e \u003cp\u003e4.5.2 Dynamic Test Results 63\u003c\/p\u003e \u003cp\u003e4.5.2.1 Tensile, Flexural and Torsional Test Results 63\u003c\/p\u003e \u003cp\u003e4.5.2.2 Toughness Test Results 64\u003c\/p\u003e \u003cp\u003e4.5.2.3 Fracture Toughness Test Results 64\u003c\/p\u003e \u003cp\u003eReferences 64\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Material Behavior and Yield Criteria 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Elastic and Inelastic Responses of a Solid 67\u003c\/p\u003e \u003cp\u003e5.2 Yield Criteria 67\u003c\/p\u003e \u003cp\u003e5.2.1 Ductile Materials 71\u003c\/p\u003e \u003cp\u003e5.2.1.1 Maximum Shear Stress Criterion (Tresca Criterion) 71\u003c\/p\u003e \u003cp\u003e5.2.1.2 Distortional Energy Density Criterion (von Mises Criterion) 74\u003c\/p\u003e \u003cp\u003e5.2.2 Brittle Materials 76\u003c\/p\u003e \u003cp\u003e5.2.2.1 Maximum Normal Stress Criterion 76\u003c\/p\u003e \u003cp\u003e5.2.2.2 Maximum Normal Strain Criterion 76\u003c\/p\u003e \u003cp\u003eReferences 78\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Loads Imposed on Engineering Elements 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Axial Loading 79\u003c\/p\u003e \u003cp\u003e6.1.1 Normal Stress 81\u003c\/p\u003e \u003cp\u003e6.1.2 The Principal Stress 82\u003c\/p\u003e \u003cp\u003e6.2 Torsion 85\u003c\/p\u003e \u003cp\u003e6.2.1 Elastic Torsion – Shear Stress and Strain Analysis 86\u003c\/p\u003e \u003cp\u003e6.2.1.1 Prismatic Bars: Circular Cross-section 86\u003c\/p\u003e \u003cp\u003e6.2.1.2 Prismatic Bars: Noncircular Cross-section 95\u003c\/p\u003e \u003cp\u003e6.2.1.3 Thin-walled Structures 96\u003c\/p\u003e \u003cp\u003e6.2.2 Warping (Distortion) of a Cross-section 101\u003c\/p\u003e \u003cp\u003e6.2.3 Inelastic Torsion and Residual Stress 103\u003c\/p\u003e \u003cp\u003e6.2.3.1 Residual Stress 105\u003c\/p\u003e \u003cp\u003e6.3 Bending 109\u003c\/p\u003e \u003cp\u003e6.3.1 Beam Supports, Types of Beams, Types of Loads 109\u003c\/p\u003e \u003cp\u003e6.3.2 Internal Forces – Bending Moments (Mf), Shear Force (Q), Distributed Load (q) 111\u003c\/p\u003e \u003cp\u003e6.3.3 Principal Moments of Inertia of an Area (I1, I2) and Extreme Values of Product of Inertia (Ixy) of an Area 112\u003c\/p\u003e \u003cp\u003e6.3.3.1 Axes Parallel to the Centroidal Axes 114\u003c\/p\u003e \u003cp\u003e6.3.3.2 Rotation of the Coordinate Axes at the Observed Point (Rotated Axes) 115\u003c\/p\u003e \u003cp\u003e6.3.4 Symmetrical Bending 116\u003c\/p\u003e \u003cp\u003e6.3.4.1 Pure Bending 116\u003c\/p\u003e \u003cp\u003e6.3.4.2 Nonuniform Bending 122\u003c\/p\u003e \u003cp\u003e6.3.5 Nonsymmetrical Bending 126\u003c\/p\u003e \u003cp\u003e6.3.6 Loading of Thin-walled Engineering Elements; Shear Center 133\u003c\/p\u003e \u003cp\u003e6.3.6.1 Shear Center 134\u003c\/p\u003e \u003cp\u003e6.3.7 Beam Deflections 136\u003c\/p\u003e \u003cp\u003e6.3.8 Bending of Curved Elements 140\u003c\/p\u003e \u003cp\u003e6.4 Stability of Columns 149\u003c\/p\u003e \u003cp\u003e6.4.1 Critical Buckling Force in the Elastic Range 150\u003c\/p\u003e \u003cp\u003e6.4.1.1 Pin-ended Columns 150\u003c\/p\u003e \u003cp\u003e6.4.1.2 Columns with Other End Conditions 153\u003c\/p\u003e \u003cp\u003e6.4.2 Critical Buckling Stress in the Elastic Range 155\u003c\/p\u003e \u003cp\u003e6.4.3 Buckling – Plastic Range 156\u003c\/p\u003e \u003cp\u003e6.4.3.1 Local Buckling of the Column 157\u003c\/p\u003e \u003cp\u003e6.5 Eccentric Axial Loads 159\u003c\/p\u003e \u003cp\u003e6.5.1 Eccentric Axial Load Acting in a Plane of Symmetry 159\u003c\/p\u003e \u003cp\u003e6.5.2 General Case of an Eccentric Axial Load 161\u003c\/p\u003e \u003cp\u003eReferences 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Relationships Between Stress and Strain 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Fundamental Considerations 167\u003c\/p\u003e \u003cp\u003e7.2 Anisotropic Materials 169\u003c\/p\u003e \u003cp\u003e7.3 Isotropic Materials 171\u003c\/p\u003e \u003cp\u003e7.3.1 Determination of Hooke’s Law – Method of Superposition 175\u003c\/p\u003e \u003cp\u003e7.3.2 Engineering Constants of Elasticity 178\u003c\/p\u003e \u003cp\u003e7.4 Orthotropic Materials 180\u003c\/p\u003e \u003cp\u003e7.5 Linear Stress–Strain–Temperature Relations for Isotropic Materials 184\u003c\/p\u003e \u003cp\u003eReferences 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Rheological Models 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 189\u003c\/p\u003e \u003cp\u003e8.2 Time-independent Behavior Modeling 190\u003c\/p\u003e \u003cp\u003e8.2.1 Elastic Deformation Modeling 190\u003c\/p\u003e \u003cp\u003e8.2.1.1 Hooke’s Element (H Model) 190\u003c\/p\u003e \u003cp\u003e8.2.2 Deformation Modeling after the Elastic Limit 192\u003c\/p\u003e \u003cp\u003e8.2.2.1 Saint Venant Element (SV Model) 192\u003c\/p\u003e \u003cp\u003e8.2.2.2 Saint Venant Element–Spring\/(SV–Spring) 192\u003c\/p\u003e \u003cp\u003e8.2.2.3 Saint Venant Element | Spring−Spring\/(SV | Spring−Spring) 192\u003c\/p\u003e \u003cp\u003e8.3 Time-dependent Behavior Modeling 194\u003c\/p\u003e \u003cp\u003e8.3.1 Newton Element (N Model): Linear Viscous Dashpot Element 195\u003c\/p\u003e \u003cp\u003e8.3.2 Maxwell Model (M = H−N) 195\u003c\/p\u003e \u003cp\u003e8.3.2.1 Generalized Maxwell Model 197\u003c\/p\u003e \u003cp\u003e8.3.3 Voigt-Kelvin Model (K = H | N) 198\u003c\/p\u003e \u003cp\u003e8.3.3.1 Generalized Voigt–Kelvin Model 199\u003c\/p\u003e \u003cp\u003e8.3.4 Standard Linear Solid Model (SLS) 200\u003c\/p\u003e \u003cp\u003e8.3.5 Voigt–Kelvin−Hooke’s Model (K−H) 201\u003c\/p\u003e \u003cp\u003e8.3.6 Burgers’ Model 202\u003c\/p\u003e \u003cp\u003e8.4 Differential Form of Constitutive Equations 205\u003c\/p\u003e \u003cp\u003eReferences 207\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Creep in Metallic Materials 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 209\u003c\/p\u003e \u003cp\u003e9.2 Plastic Deformation – General 211\u003c\/p\u003e \u003cp\u003e9.2.1 Slip 211\u003c\/p\u003e \u003cp\u003e9.2.2 Cleavage 212\u003c\/p\u003e \u003cp\u003e9.2.3 Twinning 213\u003c\/p\u003e \u003cp\u003e9.2.4 Grain Boundary Sliding 213\u003c\/p\u003e \u003cp\u003e9.2.5 Void Coalescence 214\u003c\/p\u003e \u003cp\u003e9.3 The Creep Phenomenon and Its Geometrical Representation 214\u003c\/p\u003e \u003cp\u003e9.3.1 Creep Deformation Maps and Fracture Mechanism Maps 216\u003c\/p\u003e \u003cp\u003e9.3.1.1 Creep Deformation Mechanisms 216\u003c\/p\u003e \u003cp\u003e9.3.1.2 Fracture Micromechanisms and Macromechanisms 220\u003c\/p\u003e \u003cp\u003e9.3.1.3 Creep Fracture Mechanisms 221\u003c\/p\u003e \u003cp\u003e9.3.2 Short-time Uniaxial Creep Tests, Creep Modeling and Microstructure Analysis 223\u003c\/p\u003e \u003cp\u003e9.3.2.1 Short-time Uniaxial Creep Tests 223\u003c\/p\u003e \u003cp\u003e9.3.2.2 Creep Modeling 225\u003c\/p\u003e \u003cp\u003e9.3.2.3 Microstructure Analysis – Basic 227\u003c\/p\u003e \u003cp\u003e9.3.3 Long-term Creep Behavior Prediction Based on the Short-time Creep Process 228\u003c\/p\u003e \u003cp\u003e9.3.3.1 Extrapolation Methods 230\u003c\/p\u003e \u003cp\u003e9.3.3.2 Time–Temperature Parameters 231\u003c\/p\u003e \u003cp\u003e9.3.4 Multiaxial Creep 232\u003c\/p\u003e \u003cp\u003e9.4 Relaxation Phenomenon and Modeling 234\u003c\/p\u003e \u003cp\u003eReferences 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Fracture Mechanics 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 239\u003c\/p\u003e \u003cp\u003e10.2 Fracture Classification 240\u003c\/p\u003e \u003cp\u003e10.3 Fatigue Phenomenon 242\u003c\/p\u003e \u003cp\u003e10.3.1 Known Starting Points 242\u003c\/p\u003e \u003cp\u003e10.3.2 Stress versus Life Curves (σ–N\/S–N), Endurance Limit 242\u003c\/p\u003e \u003cp\u003e10.4 Linear Elastic Fracture Mechanics (LEFM) 248\u003c\/p\u003e \u003cp\u003e10.4.1 Basic Consideration 248\u003c\/p\u003e \u003cp\u003e10.4.2 Crack Opening Modes 251\u003c\/p\u003e \u003cp\u003e10.4.2.1 Stress Intensity Factor (K\/SIF) 252\u003c\/p\u003e \u003cp\u003e10.4.2.2 Plastic Zone Size around the Crack Tip 260\u003c\/p\u003e \u003cp\u003e10.4.2.3 Plastic Zone Shape around the Crack Tip 263\u003c\/p\u003e \u003cp\u003e10.5 Elastic–Plastic Fracture Mechanics (EPFM) 266\u003c\/p\u003e \u003cp\u003e10.5.1 The J Integral 267\u003c\/p\u003e \u003cp\u003e10.6 Experimental Determination of Fracture Toughness 270\u003c\/p\u003e \u003cp\u003e10.6.1 Test Specimens: Shapes, Dimensions, Orientations and Pre-cracking 271\u003c\/p\u003e \u003cp\u003e10.6.1.1 Shapes and Dimensions of the Specimens 271\u003c\/p\u003e \u003cp\u003e10.6.1.2 Orientation of a Specimen Made from Base Material 272\u003c\/p\u003e \u003cp\u003e10.6.1.3 Fatigue Pre-cracking 274\u003c\/p\u003e \u003cp\u003e10.6.2 Fracture Toughness, KIc and the K–R Curve 274\u003c\/p\u003e \u003cp\u003e10.6.2.1 R-curve (K–R Curve) 274\u003c\/p\u003e \u003cp\u003e10.6.2.2 Plane Strain Fracture Toughness (KIc) Testing 277\u003c\/p\u003e \u003cp\u003e10.6.3 Fracture Toughness JIc and the J–R Curve 279\u003c\/p\u003e \u003cp\u003e10.6.3.1 R-curve (J–R Curve) 279\u003c\/p\u003e \u003cp\u003e10.6.3.2 Fracture Toughness ( JIc) Determination\/Testing 280\u003c\/p\u003e \u003cp\u003e10.7 Charpy Impact Energy Testing 284\u003c\/p\u003e \u003cp\u003e10.8 Crack Propagation 288\u003c\/p\u003e \u003cp\u003e10.8.1 Introduction 288\u003c\/p\u003e \u003cp\u003e10.8.2 Fatigue Crack Growth 289\u003c\/p\u003e \u003cp\u003e10.8.2.1 The Paris Equation 294\u003c\/p\u003e \u003cp\u003e10.8.2.2 The Walker Equation 296\u003c\/p\u003e \u003cp\u003e10.8.2.3 The Forman Equation 297\u003c\/p\u003e \u003cp\u003e10.8.2.4 The Forman–Newman–de Koning Equation 297\u003c\/p\u003e \u003cp\u003e10.8.3 Creep Crack Growth 297\u003c\/p\u003e \u003cp\u003e10.8.4 Life Assessment of Engineering Components 298\u003c\/p\u003e \u003cp\u003e10.8.4.1 Constant Amplitude Loading 298\u003c\/p\u003e \u003cp\u003e10.8.4.2 Variable Amplitude Loading 298\u003c\/p\u003e \u003cp\u003e10.8.5 Crack Closure 299\u003c\/p\u003e \u003cp\u003e10.8.5.1 Elber Crack Closure Phenomenon 299\u003c\/p\u003e \u003cp\u003e10.8.6 A Brief Review of Testing of Unnotched, Axially Loaded Specimens 301\u003c\/p\u003e \u003cp\u003eReferences 309\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 The Finite Element Method and Applications 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Finite Element Method (FEM) in the Analysis of Engineering Problems 313\u003c\/p\u003e \u003cp\u003e11.1.1 Applications of FEM 313\u003c\/p\u003e \u003cp\u003e11.1.2 The Advantages of Using the FEM 314\u003c\/p\u003e \u003cp\u003e11.1.3 A Brief Overview of the Historical Development of the FEM 314\u003c\/p\u003e \u003cp\u003e11.2 Linear Analysis of Structural Behavior 315\u003c\/p\u003e \u003cp\u003e11.2.1 Formulations of Equilibrium Equations 316\u003c\/p\u003e \u003cp\u003e11.2.1.1 Variational Formulation of the Finite Element (Equilibrium) Equation 318\u003c\/p\u003e \u003cp\u003e11.2.2 Structures 334\u003c\/p\u003e \u003cp\u003e11.2.3 Finite Elements 334\u003c\/p\u003e \u003cp\u003e11.2.4 Shape Functions – Cartesian and Natural (Dimensionless) Coordinate Systems 334\u003c\/p\u003e \u003cp\u003e11.2.4.1 Cartesian Coordinate System 335\u003c\/p\u003e \u003cp\u003e11.2.4.2 Natural (Dimensionless) Coordinate System 341\u003c\/p\u003e \u003cp\u003e11.2.5 One-dimensional Finite Elements 347\u003c\/p\u003e \u003cp\u003e11.2.5.1 Basic 1-D Finite Elements 347\u003c\/p\u003e \u003cp\u003e11.2.5.2 Finite Elements of Higher Order 359\u003c\/p\u003e \u003cp\u003e11.2.6 Two-dimensional Finite Elements 363\u003c\/p\u003e \u003cp\u003e11.2.6.1 Basic 2-D Finite Elements 367\u003c\/p\u003e \u003cp\u003e11.2.6.2 Finite Elements of Higher Order 376\u003c\/p\u003e \u003cp\u003e11.2.6.3 Transformation Procedure for the Finite Element Equation 378\u003c\/p\u003e \u003cp\u003e11.2.7 Three-dimensional Finite Elements 379\u003c\/p\u003e \u003cp\u003e11.2.7.1 Basic 3-D Finite Elements 381\u003c\/p\u003e \u003cp\u003e11.2.7.2 Finite Elements of Higher Order 388\u003c\/p\u003e \u003cp\u003e11.2.8 Isoparametric Finite Elements 393\u003c\/p\u003e \u003cp\u003e11.2.8.1 Introduction 393\u003c\/p\u003e \u003cp\u003e11.2.8.2 Isoparametric Representation 395\u003c\/p\u003e \u003cp\u003e11.2.9 Bending of Elastic Flat Plates 398\u003c\/p\u003e \u003cp\u003e11.2.9.1 Deformation Theories for Elastic Plates 398\u003c\/p\u003e \u003cp\u003e11.2.9.2 Finite Elements Based on Kirchhoff Plate Theory 407\u003c\/p\u003e \u003cp\u003e11.2.10 Basics of Dynamic Behavior of Elastic Structures 410\u003c\/p\u003e \u003cp\u003e11.2.10.1 Mass Matrix of the Finite Element 413\u003c\/p\u003e \u003cp\u003e11.2.10.2 Free, Undamped Vibrations of Constructions – Eigenvalues 414\u003c\/p\u003e \u003cp\u003e11.3 A Brief Introduction to Nonlinear Analysis of Structural Behavior 421\u003c\/p\u003e \u003cp\u003e11.4 Metal-forming Processes – Brief Overview 422\u003c\/p\u003e \u003cp\u003e11.4.1 Introduction 422\u003c\/p\u003e \u003cp\u003e11.4.2 Classification, Variables and Characteristics of Metal-forming Processes 423\u003c\/p\u003e \u003cp\u003e11.4.2.1 Comparison of Hot and Cold Working Processes in Terms of Working Temperature, Shaping Force and Achieved Material Properties 428\u003c\/p\u003e \u003cp\u003e11.4.3 Basic Settings Related to the Theory of Metal-forming Processes 429\u003c\/p\u003e \u003cp\u003e11.4.3.1 Strain-rate Tensor and Data Relating to Yield Criteria 430\u003c\/p\u003e \u003cp\u003e11.4.3.2 Virtual Work-rate Principle 433\u003c\/p\u003e \u003cp\u003e11.4.3.3 The Prandtl–Reuss Equations 433\u003c\/p\u003e \u003cp\u003e11.4.3.4 The Governing Equations of Plastic Deformation 437\u003c\/p\u003e \u003cp\u003e11.4.3.5 Shape Functions 437\u003c\/p\u003e \u003cp\u003e11.4.3.6 Strain-rate Matrix 438\u003c\/p\u003e \u003cp\u003e11.5 The Application of the Finite Element Method in Structural Analysis 438\u003c\/p\u003e \u003cp\u003e11.5.1 One-dimensional Finite Elements: Finite Element Analysis of Truss Structure Deformation 439\u003c\/p\u003e \u003cp\u003e11.5.2 Two-dimensional Finite Elements: J Integral Calculation 443\u003c\/p\u003e \u003cp\u003e11.5.3 Special Two-dimensional Finite Elements in Shear Stress Analysis 447\u003c\/p\u003e \u003cp\u003e11.5.3.1 Introduction 447\u003c\/p\u003e \u003cp\u003e11.5.3.2 Application of General Quadrilateral Finite Elements 450\u003c\/p\u003e \u003cp\u003eReferences 451\u003c\/p\u003e \u003cp\u003eIndex 453\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e","brand":"John Wiley \u0026 Sons 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