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 |  موضوع: كتاب Finite Element Analysis of Composite Materials Using Abaqus الأربعاء 21 أغسطس 2024, 2:38 am | |
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أحضرت لكم كتاب
Finite Element Analysis of Composite Materials Using Abaqus
Ever J. Barbero
و المحتوى كما يلي :
Contents
Series Preface xiii
Preface xv
Acknowledgments xix
List of Symbols xxi
List of Examples xxix
1 Mechanics of Orthotropic Materials 1
1.1 Lamina Coordinate System . 1
1.2 Displacements . 1
1.3 Strain . 2
1.4 Stress . 3
1.5 Contracted Notation . 4
1.5.1 Alternate Contracted Notation . 5
1.6 Equilibrium and Virtual Work . 6
1.7 Boundary Conditions . 8
1.7.1 Traction Boundary Conditions . 8
1.7.2 Free Surface Boundary Conditions . 8
1.8 Continuity Conditions 8
1.8.1 Traction Continuity . 8
1.8.2 Displacement Continuity . 9
1.9 Compatibility . 9
1.10 Coordinate Transformations . 10
1.10.1 Stress Transformation 12
1.10.2 Strain Transformation 14
1.11 Transformation of Constitutive Equations . 15
1.12 3D Constitutive Equations 17
1.12.1 Anisotropic Material . 18
1.12.2 Monoclinic Material . 19
1.12.3 Orthotropic Material . 20
1.12.4 Transversely Isotropic Material . 21
1.12.5 Isotropic Material 23
viiviii Finite Element Analysis of Composite Materials
1.13 Engineering Constants 24
1.13.1 Restrictions on Engineering Constants . 27
1.14 From 3D to Plane Stress Equations . 29
1.15 Apparent Laminate Properties . 30
Suggested Problems 32
2 Introduction to Finite Element Analysis 35
2.1 Basic FEM Procedure 35
2.1.1 Discretization . 36
2.1.2 Element Equations 36
2.1.3 Approximation over an Element 37
2.1.4 Interpolation Functions . 38
2.1.5 Element Equations for a Specific Problem . 40
2.1.6 Assembly of Element Equations . 41
2.1.7 Boundary Conditions 42
2.1.8 Solution of the Equations 42
2.1.9 Solution Inside the Elements 42
2.1.10 Derived Results 43
2.2 General Finite Element Procedure . 43
2.3 Solid Modeling, Analysis, and Visualization 46
2.3.1 Model Geometry . 47
2.3.2 Material and Section Properties . 57
2.3.3 Assembly . 61
2.3.4 Solution Steps 63
2.3.5 Loads . 63
2.3.6 Boundary Conditions 65
2.3.7 Meshing and Element Type . 68
2.3.8 Solution Phase 70
2.3.9 Post-processing and Visualization 73
Suggested Problems 89
3 Elasticity and Strength of Laminates 91
3.1 Kinematic of Shells 92
3.1.1 First-Order Shear Deformation Theory . 93
3.1.2 Kirchhoff Theory . 97
3.1.3 Simply Supported Boundary Conditions 99
3.2 Finite Element Analysis of Laminates . 100
3.2.1 Element Types and Naming Convention 101
3.2.2 Thin (Kirchhoff) Shell Elements 104
3.2.3 Thick Shell Elements . 104
3.2.4 General-purpose (FSDT) Shell Elements 104
3.2.5 Continuum Shell Elements 105
3.2.6 Sandwich Shells 106
3.2.7 Nodes and Curvature 106
3.2.8 Drilling Rotation . 106Table of Contents ix
3.2.9 A, B, D, H Input Data for Laminate FEA . 107
3.2.10 Equivalent Orthotropic Input for Laminate FEA . 113
3.2.11 LSS for Multidirectional Laminate FEA 119
3.2.12 FEA of Ply Drop-Off Laminates 129
3.2.13 FEA of Sandwich Shells . 139
3.2.14 Element Coordinate System . 150
3.2.15 Constraints 159
3.3 Failure Criteria 163
3.3.1 2D Failure Criteria 163
3.3.2 3D Failure Criteria 166
3.4 Predefined Fields . 171
Suggested Problems 173
4 Buckling 177
4.1 Eigenvalue Buckling Analysis 177
4.1.1 Imperfection Sensitivity . 183
4.1.2 Asymmetric Bifurcation . 183
4.1.3 Post-critical Path . 184
4.2 Continuation Methods 187
Suggested Problems 192
5 Free Edge Stresses 195
5.1 Poisson’s Mismatch 196
5.1.1 Interlaminar Force 196
5.1.2 Interlaminar Moment 197
5.2 Coefficient of Mutual Influence . 204
5.2.1 Interlaminar Stress due to Mutual Influence 207
Suggested Problems 212
6 Computational Micromechanics 215
6.1 Analytical Homogenization . 216
6.1.1 Reuss Model . 216
6.1.2 Voigt Model 217
6.1.3 Periodic Microstructure Model . 217
6.1.4 Transversely Isotropic Averaging 218
6.2 Numerical Homogenization . 220
6.3 Local-Global Analysis 238
6.4 Laminated RVE 241
Suggested Problems 247
7 Viscoelasticity 249
7.1 Viscoelastic Models 251
7.1.1 Maxwell Model 251
7.1.2 Kelvin Model . 252
7.1.3 Standard Linear Solid 253x Finite Element Analysis of Composite Materials
7.1.4 Maxwell-Kelvin Model 253
7.1.5 Power Law 254
7.1.6 Prony Series . 254
7.1.7 Standard Nonlinear Solid 256
7.1.8 Nonlinear Power Law 256
7.2 Boltzmann Superposition 258
7.2.1 Linear Viscoelastic Material . 258
7.2.2 Unaging Viscoelastic Material 259
7.3 Correspondence Principle 260
7.4 Frequency Domain 261
7.5 Spectrum Representation 262
7.6 Micromechanics of Viscoelastic Composites 262
7.6.1 One-Dimensional Case 262
7.6.2 Three-Dimensional Case . 264
7.7 Macromechanics of Viscoelastic Composites 269
7.7.1 Balanced Symmetric Laminates . 269
7.7.2 General Laminates 269
7.8 FEA of Viscoelastic Composites . 269
Suggested Problems 280
8 Continuum Damage Mechanics 283
8.1 One-Dimensional Damage Mechanics 284
8.1.1 Damage Variable . 284
8.1.2 Damage Threshold and Activation Function 286
8.1.3 Kinetic Equation . 287
8.1.4 Statistical Interpretation of the Kinetic Equation . 288
8.1.5 One-Dimensional Random-Strength Model 289
8.1.6 Fiber-Direction, Tension Damage 294
8.1.7 Fiber-Direction, Compression Damage . 300
8.2 Multidimensional Damage and Effective Spaces 304
8.3 Thermodynamics Formulation 305
8.3.1 First Law . 306
8.3.2 Second Law 307
8.4 Kinetic Law in Three-Dimensional Space 313
8.4.1 Return-Mapping Algorithm . 316
8.5 Damage and Plasticity 322
Suggested Problems 324
9 Discrete Damage Mechanics 327
9.1 Overview . 328
9.2 Approximations 332
9.3 Lamina Constitutive Equation . 333
9.4 Displacement Field 334
9.4.1 Boundary Conditions for ΔT = 0 335
9.4.2 Boundary Conditions for ΔT ∕= 0 336Table of Contents xi
9.5 Degraded Laminate Stiffness and CTE . 337
9.6 Degraded Lamina Stiffness 338
9.7 Fracture Energy . 339
9.8 Solution Algorithm 340
9.8.1 Lamina Iterations 340
9.8.2 Laminate Iterations . 340
Suggested Problems 351
10 Delaminations 353
10.1 Cohesive Zone Method 356
10.1.1 Single Mode Cohesive Model 358
10.1.2 Mixed Mode Cohesive Model 361
10.2 Virtual Crack Closure Technique 371
Suggested Problems 375
A Tensor Algebra 377
A.1 Principal Directions of Stress and Strain 377
A.2 Tensor Symmetry . 377
A.3 Matrix Representation of a Tensor . 378
A.4 Double Contraction 379
A.5 Tensor Inversion . 379
A.6 Tensor Differentiation 380
A.6.1 Derivative of a Tensor with Respect to Itself . 380
A.6.2 Derivative of the Inverse of a Tensor with Respect to the Tensor 381
B Second-Order Diagonal Damage Models 383
B.1 Effective and Damaged Spaces . 383
B.2 Thermodynamic Force Y 384
B.3 Damage Surface 386
B.4 Unrecoverable-Strain Surface 387
C Software Used 389
C.1 Abaqus . 389
C.1.1 Abaqus Programmable Features . 391
C.2 BMI3 . 393
References 395
Index 407
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