Multiscale Structural Mechanics
John Wiley & Sons Inc (Verlag)
978-1-119-09267-4 (ISBN)
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Multiscale Structural Mechanics: Top-Down Modeling of Composite Structures Using Mechanics of Structure Genome delivers a unified approach to composites modelling based on the concept of structure gene. Dr. Wenbin Yu, distinguished engineer, industry leader, and author, brings together micromechanics and structural mechanics using the Mechanics of Structure Genome. This approach allows multiscale constitutive modelling for general anisotropic and heterogeneous materials and structures without invoking assumptions commonly used in other approaches.
The book introduces readers unfamiliar with vectors and tensors, continuum mechanics, micromechanics, and structural mechanics to the basics of each of these topics. It goes on to bridge the gap between micromechanics and structural mechanics, offering readers multiscale structural models that remain as simple as classical engineering models but with the accuracy expected of more complex theories capturing microstructural details. Specifically, the book offers:
A brief introduction to vectors and tensors, as well as continuum mechanics, classical structural models including kinematics, kinetics, and energetics, and composite materials
Fulsome discussions of the mechanics of structure genome (MSG) and its application to construct multiscale models for beams, plates, shells, and 3D solids
Complete explorations of both micromechanics and structural mechanics, including the theories of beams, plates, and shells
An introduction to the calculus of variations, variational asymptotic method, and their applications to model general anisotropic and heterogeneous materials and structures
Information sufficient to allow readers to construct efficient high-fidelity models for composites using MSG introduced in this book
Detailed discussions of stress and failure analysis of composite laminates
Perfect for graduate students in aerospace, mechanical, and other disciplines making use of anisotropic and heterogeneous materials such as composites, Multiscale Structural Mechanics will also earn a place in the libraries of researchers and engineers in university, government, and industry laboratories who work with composite materials and structures. It is the ideal resource for composites modelling across a wide spectrum of engineering applications.
Wenbin Yu, PhD, is the Milton Clauser Professor of the School of Aeronautics and Astronautics at Purdue University. He obtained his doctorate in Aerospace Engineering from Georgia Tech in 2002. He is Chief Technology Officer of AnalySwift LLC (analyswift.com) and Director of the Composites Design and Manufacturing HUB (cdmhub.org).
List of Figures xv
List of Tables xxi
Foreword xxiii
Preface xxv
Acknowledgments xxxi
Acronyms xxxiii
1 Introduction 1
1.1 Continuum Hypothesis 1
1.2 Isotropic vs. Anisotropic Materials 4
1.3 Homogeneous vs. Heterogeneous Materials 4
1.4 Materials vs. Structures 4
1.5 3D Structures, Plates, Shells, and Beams 6
1.6 Structures, Models, and Assumptions 8
1.6.1 Cauchy Continuum Model 10
1.6.2 Kirchhoff–Love Model 11
1.6.3 Reissner–Mindlin Model 13
1.6.4 Euler–Bernoulli Model 15
1.6.5 Timoshenko Model 17
1.6.6 Vlasov Model 19
1.7 Composite Materials 20
1.8 Benefits of Using Composites 24
1.9 Mechanics of Composite Materials 25
1.10 Challenges for Modeling Composites 26
1.10.1 Anisotropy 26
1.10.2 Heterogeneity 27
1.11 Multiscale Modeling* 28
1.11.1 Bottom-up Multiscale Modeling 28
1.11.2 Top-down Multiscale Modeling 31
1.11.3 Mechanics of Structure Genome 32
1.11.4 Structure Gene and Structure Genome 33
1.11.5 MSG-based Multiscale Structural Modeling 38
Problems 40
2 Mathematical Preliminaries 43
2.1 Scalars, Vectors, and Tensors 43
2.2 Cartesian Coordinate System 44
2.3 Index Notation 44
2.3.1 Free Index 45
2.3.2 Dummy Index 46
2.3.3 Kronecker Symbol and Permutation Symbol 47
2.3.4 Differentiation Using Index Notation 48
2.4 Vectors 48
2.4.1 Three Ways to Express a Vector 48
2.4.2 Determinant Expressed Using the Permutation Symbol 50
2.4.3 Vector Calculus 51
2.5 Transformation Between Different Coordinate Systems 52
2.5.1 Transformation for Base Vectors 52
2.5.2 Transformation for General Vectors 54
2.5.3 New Coordinate System Defined by Three Points 55
2.6 Second-order Tensors 55
2.6.1 Second-order Tensors and Their Coordinate Transformation 55
2.6.2 Basic Operations of Second-order Tensors 56
2.6.3 Principal Values and Directions of Second-order Tensors 57
2.6.4 Polar Decomposition Theorem 59
2.7 Quotient Rule and Higher-order Tensors 60
2.8 Special Tensors 61
2.9 Isotropic Tensors 62
2.10 Tensor Calculus 62
2.11 General Coordinate Systems* 63
2.11.1 General Coordinate Systems 63
2.11.2 Cylindrical Coordinate Systems 64
2.11.3 Spherical Coordinate Systems 67
2.11.4 Strain Field of a Toroidal Tube 70
2.12 Calculus of Variations* 73
2.12.1 Differential vs. Variational Statements 73
2.12.2 Unconstrained Stationary Problems 73
2.12.3 Constrained Stationary Problems—Lagrange Multiplier Method 74
2.12.4 Stationary Values of Functionals 76
2.12.5 Calculus of Variations 77
2.12.6 Boundary Conditions 80
2.12.7 Subsidiary Conditions 81
2.12.8 Functionals of Higher Derivatives and Multiple Functions 83
2.12.9 Transform from Differential Statements to Variational Statements 85
2.12.10 Ritz Method 85
2.12.11 Kantorovich Method 86
2.12.12 Galerkin Method 87
2.12.13 Variational Asymptotic Method 89
Problems 94
3 Theory of Anisotropic Elasticity 103
3.1 Kinematics 103
3.1.1 Material Point, Configuration, Displacement, Deformation, and Motion 104
3.1.2 Deformation Gradient Tensor 104
3.1.3 Green–Lagrange Strain Tensor 105
3.1.4 Infinitesimal Strain Tensor 106
3.1.5 Engineering Notation and Coordinate Transformation 107
3.1.6 Compatibility Equations 108
3.2 Kinetics 109
3.2.1 The State of Stress at a Point 109
3.2.2 Engineering Notation and Coordinate Transformation 111
3.2.3 Equilibrium Equations 112
3.3 Constitutive Relations 114
3.3.1 The Need for Constitutive Relations 114
3.3.2 Strain Energy Density and Elasticity Tensor 114
3.3.3 Stiffness Matrix and Its Transformation 116
3.3.4 Compliance Matrix and Engineering Constants 118
3.3.5 Material Symmetry 120
3.3.6 Constitutive Relations Including Temperature and Moisture Effects 135
3.3.7 Plane Stress Reduced Constitutive Relations 138
3.4 Theory of Linear Elasticity 147
3.5 Boundary Conditions and Continuity Conditions 149
3.6 A Few Anisotropic Elasticity Problems 151
3.6.1 Off-axis Composite Specimens 151
3.6.2 Three-point Bend Test 157
3.6.3 Cylindrical Bending of Laminated Plates 165
3.7 Variational Principles for Anisotropic Elasticity* 173
3.7.1 Principle of Virtual Work 173
3.7.2 Principle of Minimum Total Potential Energy (PMTPE) 174
Problems 176
4 Micromechanics 187
4.1 Introduction 187
4.2 Microstructures and Their Idealizations 188
4.3 Volume Average 192
4.4 Effective Stiffness and Compliance 192
4.5 Voigt and Reuss Rules of Mixtures 193
4.5.1 Composites Made of General Anisotropic Constituents 193
4.5.2 Composites Made of Orthotropic Constituents 195
4.5.3 Composites Made of Isotropic Constituents 196
4.5.4 Unidirectional Fiber-reinforced Composites 198
4.5.5 Effective CTEs According to Rules of Mixtures 201
4.6 Hybrid Rules of Mixtures 202
4.6.1 Effective Properties of UDFRCs 203
4.6.2 Effective 3D Properties of Laminates 206
4.7 Macro and Micro Coordinates* 209
4.8 Average Stress Theorem* 210
4.9 Average Strain Theorem* 211
4.10 Hill–Mandel Macro-homogeneity Condition* 213
4.11 Computational Homogenization* 216
4.11.1 Representative Volume Element Analysis 216
4.11.2 Mathematical Homogenization Theory 220
4.11.3 Mechanics of Structure Genome 224
4.11.4 Theoretical Connections of RVE Analysis, MHT, and MSG 228
Problems 229
5 Composite Plate Models 233
5.1 Introduction 233
5.2 Composite Laminates 234
5.3 Why Composite Plate Theories? 236
5.4 Kirchhoff–Love Model Derived Using the Newtonian Method 238
5.4.1 Kinetics 238
5.4.2 Kinematics 243
5.4.3 Elastic Constitutive Relations 248
5.4.4 3D Stresses and Strains 251
5.4.5 Thermoelastic Constitutive Relations 255
5.4.6 Thermal Stresses 259
5.4.7 Symmetric Laminates 262
5.4.8 Balanced Laminates 267
5.4.9 Cross-ply Laminates 268
5.4.10 Quasi-isotropic Laminates 269
5.4.11 [±45] s Laminates 272
5.4.12 Plates with Reference Surface Not at the Middle Plane 274
5.4.13 Kirchhoff–Love Model and Boundary Conditions 276
5.4.14 An Example of Composite Laminate Using CLT 278
5.4.15 Kirchhoff–Love Model Derived Using the Variational Method* 284
5.5 Reissner–Mindlin Model* 288
5.5.1 Reissner–Mindlin Model Derived Using the Newtonian Method 289
5.5.2 Reissner–Mindlin Model Derived Using the Variational Method 290
5.6 MSG-based Composite Plate Models* 292
5.6.1 Kirchhoff–Love Model Derived Using MSG 293
5.6.2 Reissner–Mindlin Model Derived Using MSG 295
Problems 298
6 Composite Beam Models* 301
6.1 Introduction 301
6.2 Ad Hoc Methods 303
6.2.1 Kinematic Assumptions 303
6.2.2 Stress Assumption 307
6.2.3 Newtonian Method 308
6.2.4 Variational Method 316
6.3 Beam Models Derived Using MSG 319
6.3.1 Euler–Bernoulli Model for Isotropic Homogeneous Beams 319
6.3.2 Euler–Bernoulli Model for Composite Beams 323
6.3.3 Timoshenko Model for Composite Beams 325
6.4 A Few Composite Beam Problems 328
6.4.1 Static Behavior of Cantilever Composite Beams Under Tip Loading Using the Euler–Bernoulli Model 329
6.4.2 Static Behavior of Composite Beams Using the Timoshenko Model 330
6.4.3 Static Behavior of Composite Beams with Discrete Reference Lines Using the Timoshenko Model 332
Problems 334
7 Mechanics of Structure Genome* 337
7.1 Introduction 338
7.2 Kinematics 339
7.2.1 Coordinate Systems 339
7.2.2 Undeformed and Deformed Configurations 340
7.2.3 Strain Field 342
7.3 Variational Statement for SG 349
7.4 MSG Illustrated 353
7.4.1 MSG-based Cauchy Continuum Model 353
7.4.2 MSG-based Kirchhoff–Love Plate Model 355
7.4.3 MSG-based Euler–Bernoulli Beam Model 357
7.5 Numerical Examples 359
7.5.1 Cross-ply Laminate 359
7.5.2 Sandwich Beam with Periodically Varying Cross-sections 365
7.5.3 Sandwich Panel with a Corrugated Core 366
Problems 368
8 Failure of Composite Materials 371
8.1 Introduction 371
8.1.1 Basic Types of Failure 371
8.1.2 Challenges for Failure Analysis of Composites 372
8.1.3 Stress, Stiffness, and Strength 373
8.2 Failure Criteria for Isotropic Materials 374
8.2.1 Maximum Normal Stress (Strain) Criterion 374
8.2.2 Maximum Shear Stress (Strain) Failure Criterion 377
8.2.3 Mises Failure Criterion 379
8.3 Failure Criteria for Orthotropic Materials 382
8.3.1 Maximum Stress (Strain) Criterion 383
8.3.2 Tsai–Hill Failure Criterion 385
8.3.3 Tsai–Wu Failure Criterion 391
8.3.4 Hashin Failure Criterion 395
8.4 Strength Ratio 399
8.5 Failure Envelope 403
8.6 Progressive Failure Analysis 406
8.7 Nonlocal Approach for Computing Strength 408
Problems 409
References 413
Index 421
| Erscheinungsdatum | 15.07.2019 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 170 x 244 mm |
| Themenwelt | Technik ► Bauwesen |
| ISBN-10 | 1-119-09267-1 / 1119092671 |
| ISBN-13 | 978-1-119-09267-4 / 9781119092674 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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