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 |  موضوع: كتاب Finite Element Analysis of Composite Materials Using ANSYS الخميس 18 أبريل 2019, 8:11 pm | |
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أخوانى فى الله
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Finite Element Analysis of Composite Materials Using ANSYS
Second Edition
Ever J. Barbero
ويتناول الموضوعات الأتية :
Contents
Series Preface Xiii
Preface Xv
Acknowledgments Xix
List of Symbols Xxi
List of Examples Xxix
Errata Xxxi
1 Mechanics of Orthotropic Materials 1
1.1 Lamina Coordinate System . 1
1.2 Displacements . 1
1.3 Strain . 2
1.4 Stress . 4
1.5 Contracted Notation . 5
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 9
1.8.1 Traction Continuity . 9
1.8.2 Displacement Continuity . 9
1.9 Compatibility . 10
1.10 Coordinate Transformations . 10
1.10.1 Stress Transformation 13
1.10.2 Strain Transformation 15
1.11 Transformation of Constitutive Equations . 16
1.12 3d Constitutive Equations 17
1.12.1 Anisotropic Material . 18
1.12.2 Monoclinic Material . 19
Viiviii Finite Element Analysis of Composite Materials
1.12.3 Orthotropic Material . 20
1.12.4 Transversely Isotropic Material . 22
1.12.5 Isotropic Material 23
1.13 Engineering Constants 24
1.13.1 Restrictions on Engineering Constants . 28
1.14 From 3d to Plane Stress Equations . 29
1.15 Apparent Laminate Properties . 31
Suggested Problems 33
2 Introduction to Finite Element Analysis 37
2.1 Basic Fem Procedure 37
2.1.1 Discretization . 38
2.1.2 Element Equations 38
2.1.3 Approximation Over an Element 39
2.1.4 Interpolation Functions . 40
2.1.5 Element Equations for a Specific Problem . 42
2.1.6 Assembly of Element Equations . 43
2.1.7 Boundary Conditions 44
2.1.8 Solution of the Equations 44
2.1.9 Solution Inside the Elements 44
2.1.10 Derived Results 45
2.2 General Finite Element Procedure . 45
2.3 Solid Modeling, Analysis, and Visualization 49
2.3.1 Model Geometry . 49
2.3.2 Material and Section Properties . 52
2.3.3 Assembly . 53
2.3.4 Solution Steps 54
2.3.5 Loads . 54
2.3.6 Boundary Conditions 54
2.3.7 Meshing and Element Type . 56
2.3.8 Solution Phase 56
2.3.9 Post-processing and Visualization . 56
Suggested Problems 61
3 Elasticity and Strength of Laminates 63
3.1 Kinematics of Shells . 64
3.1.1 First-order Shear Deformation Theory . 65
3.1.2 Kirchhoff Theory . 69
3.2 Finite Element Analysis of Laminates . 71
3.2.1 Element Types 73
3.2.2 Sandwich Shells 74
3.2.3 Nodes and Curvature 74
3.2.4 Drilling Rotation . 74
3.2.5 a-b-d-h Input Data for Laminate Fea 74
3.2.6 Equivalent Orthotropic Input for Laminate Fea . 77table of Contents Ix
3.2.7 Lss for Multidirectional Laminate Fea 82
3.2.8 Fea of Ply Drop-off Laminates 83
3.2.9 Fea of Sandwich Shells . 87
3.2.10 Element Coordinate System . 88
3.2.11 Constraints 94
3.3 Failure Criteria 100
3.3.1 2d Failure Criteria 101
3.3.2 3d Failure Criteria 103
Suggested Problems 110
4 Buckling 113
4.1 Eigenvalue Buckling Analysis 113
4.1.1 Imperfection Sensitivity . 120
4.1.2 Asymmetric Bifurcation . 121
4.1.3 Post-critical Path 121
4.2 Continuation Methods 126
Suggested Problems 130
5 Free Edge Stresses 133
5.1 Poisson’s Mismatch 134
5.1.1 Interlaminar Force 134
5.1.2 Interlaminar Moment 135
5.2 Coefficient of Mutual Influence . 141
5.2.1 Interlaminar Stress Due to Mutual Influence 143
Suggested Problems 147
6 Computational Micromechanics 151
6.1 Analytical Homogenization . 152
6.1.1 Reuss Model . 152
6.1.2 Voigt Model 153
6.1.3 Periodic Microstructure Model . 153
6.1.4 Transversely Isotropic Averaging 154
6.2 Numerical Homogenization . 157
6.3 Global-local Analysis 172
6.4 Laminated Rve 175
Suggested Problems 178
7 Viscoelasticity 179
7.1 Viscoelastic Models 181
7.1.1 Maxwell Model 181
7.1.2 Kelvin Model . 182
7.1.3 Standard Linear Solid 183
7.1.4 Maxwell-kelvin Model 183
7.1.5 Power Law 184
7.1.6 Prony Series . 184x Finite Element Analysis of Composite Materials
7.1.7 Standard Nonlinear Solid 185
7.1.8 Nonlinear Power Law 186
7.2 Boltzmann Superposition 187
7.2.1 Linear Viscoelastic Material . 187
7.2.2 Unaging Viscoelastic Material 189
7.3 Correspondence Principle 190
7.4 Frequency Domain 191
7.5 Spectrum Representation 192
7.6 Micromechanics of Viscoelastic Composites 192
7.6.1 One-dimensional Case 192
7.6.2 Three-dimensional Case . 193
7.7 Macromechanics of Viscoelastic Composites 197
7.7.1 Balanced Symmetric Laminates . 197
7.7.2 General Laminates 197
7.8 Fea of Viscoelastic Composites . 198
Suggested Problems 204
8 Continuum Damage Mechanics 207
8.1 One-dimensional Damage Mechanics 208
8.1.1 Damage Variable . 208
8.1.2 Damage Threshold and Activation Function 210
8.1.3 Kinetic Equation . 211
8.1.4 Statistical Interpretation of the Kinetic Equation . 212
8.1.5 One-dimensional Random-strength Model 213
8.1.6 Fiber Direction, Tension Damage 218
8.1.7 Fiber Direction, Compression Damage . 222
8.2 Multidimensional Damage and Effective Spaces 226
8.3 Thermodynamics Formulation 228
8.3.1 First Law . 228
8.3.2 Second Law 230
8.4 Kinetic Law in Three-dimensional Space 235
8.4.1 Return-mapping Algorithm . 238
8.5 Damage and Plasticity 244
Suggested Problems 245
9 Discrete Damage Mechanics 249
9.1 Overview . 250
9.2 Approximations 254
9.3 Lamina Constitutive Equation . 256
9.4 Displacement Field 256
9.4.1 Boundary Conditions for ?t = 0 258
9.4.2 Boundary Conditions for ?t 6= 0 259
9.5 Degraded Laminate Stiffness and Cte . 260
9.6 Degraded Lamina Stiffness 261
9.7 Fracture Energy . 262table of Contents Xi
9.8 Solution Algorithm 263
9.8.1 Lamina Iterations 263
9.8.2 Laminate Iterations . 264
Suggested Problems 271
10 Delaminations 273
10.1 Cohesive Zone Method 276
10.1.1 Single Mode Cohesive Model 278
10.1.2 Mixed Mode Cohesive Model 281
10.2 Virtual Crack Closure Technique 290
Suggested Problems 295
A Tensor Algebra 297
A.1 Principal Directions of Stress and Strain 297
A.2 Tensor Symmetry . 297
A.3 Matrix Representation of a Tensor . 298
A.4 Double Contraction 299
A.5 Tensor Inversion . 299
A.6 Tensor Differentiation 300
A.6.1 Derivative of a Tensor 300
A.6.2 Derivative of the Inverse of a Tensor 301
B Second-order Diagonal Damage Models 303
B.1 Effective and Damaged Spaces . 303
B.2 Thermodynamic Force Y 304
B.3 Damage Surface 306
B.4 Unrecoverable-strain Surface 307
C Software Used 309
C.1 ANSYS Mechanical Apdl 309
C.1.1 ANSYS Usermat, Compilation and Execution . 311
C.2 Bmi3 . 314
C.2.1 Stand-alone Bmi3 314
C.2.2 Bmi3 Within ANSYS . 314
References 31
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