Finite element analysis of composite materials using ANSYS

Designing structures using composite materials poses unique challenges, especially due to the need for concurrent design of both material and structure. Students are faced with two options: textbooks that teach the theory of advanced mechanics of composites, but lack computational examples of advanced analysis, and books on finite element analysis that may or may not demonstrate very limited applications to composites. But there is a third option that makes the other two obsolete: Ever J. Barbero's Finite Element Analysis of Composite Materials Using ANSYS®, Second Edition.

The Only Finite Element Analysis Book on the Market Using ANSYS to Analyze Composite Materials .

By layering detailed theoretical and conceptual discussions with fully developed examples, this text supplies the missing link between theory and implementation. In-depth discussions cover all of the major aspects of advanced analysis, including three-dimensional effects, viscoelasticity, edge effects, elastic instability, damage, and delamination. This second edition of the bestseller has been completely revised to incorporate advances in the state of the art in such areas as modeling of damage in composites. In addition, all 50+ worked examples have been updated to reflect the newest version of ANSYS. Including some use of MATLAB®, these examples demonstrate how to use the concepts to formulate and execute finite element analyses and how to interpret the results in engineering terms. Additionally, the source code for each example is available to students for download online via a companion website featuring a special area reserved for instructors. Plus a solutions manual is available for qualifying course adoptions.

Cementing applied computational and analytical experience to a firm foundation of basic concepts and theory, Finite Element Analysis of Composite Materials Using ANSYS, Second Edition offers a modern, practical, and versatile classroom tool for today's engineering classroom.

Author Notes

Ever J. Barbero holds a BSME-BSEE from Universidad Nacional de Río Cuarto, Argentina and a Ph.D from Virginia Polytechnic Institute and State University, Blacksburg, USA. He is ASME and SAMPE fellow, a professor at West Virginia University, Morgantown, USA, and honorary professor at Universidad Nacional de Trujillo, Peru. Holder of two US patents, author of over 100 peer-reviewed publications, and recipient of numerous teaching and research awards, he is recognized internationally for his work on material models for composite materials.

Series Preface	p. xiii
Preface	p. xv
Acknowledgments	p. xix
List of Symbols	p. xxi
List of Examples	p. xxix
Errata	p. xxxi
1 Mechanics of Orthotropic Materials	p. 1
1.1 Lamina Coordinate System	p. 1
1.2 Displacements	p. 1
1.3 Strain	p. 2
1.4 Stress	p. 4
1.5 Contracted Notation	p. 5
1.5.1 Alternate Contracted Notation	p. 5
1.6 Equilibrium and Virtual Work	p. 6
1.7 Boundary Conditions	p. 8
1.7.1 Traction Boundary Conditions	p. 8
1.7.2 Free Surface Boundary Conditions	p. 8
1.8 Continuity Conditions	p. 9
1.8.1 Traction Continuity	p. 9
1.8.2 Displacement Continuity	p. 9
1.9 Compatibility	p. 10
1.10 Coordinate Transformations	p. 10
1.10.1 Stress Transformation	p. 13
1.10.2 Strain Transformation	p. 15
1.11 Transformation of Constitutive Equations	p. 16
1.12 3D Constitutive Equations	p. 17
1.12.1 Anisotropic Material	p. 18
1.12.2 Monoclinic Material	p. 19
1.12.3 Orthotropic Material	p. 20
1.12.4 Transversely Isotropic Material	p. 22
1.12.5 Isotropic Material	p. 23
1.13 Engineering Constants	p. 24
1.13.1 Restrictions on Engineering Constants	p. 28
1.14 From 3D to Plane Stress Equations	p. 29
1.15 Apparent Laminate Properties	p. 31
Suggested Problems	p. 33
2 Introduction to Finite Element Analysis	p. 37
2.1 Basic FEM Procedure	p. 37
2.1.1 Discretization	p. 38
2.1.2 Element Equations	p. 38
2.1.3 Approximation over an Element	p. 39
2.1.4 Interpolation Functions	p. 40
2.1.5 Element Equations for a Specific Problem	p. 42
2.1.6 Assembly of Element Equations	p. 43
2.1.7 Boundary Conditions	p. 44
2.1.8 Solution of the Equations	p. 44
2.1.9 Solution Inside the Elements	p. 44
2.1.10 Derived Results	p. 45
2.2 General Finite Element Procedure	p. 45
2.3 Solid Modeling, Analysis, and Visualization	p. 49
2.3.1 Model Geometry	p. 49
2.3.2 Material and Section Properties	p. 52
2.3.3 Assembly	p. 53
2.3.4 Solution Steps	p. 54
2.3.5 Loads	p. 54
2.3.6 Boundary Conditions	p. 54
2.3.7 Meshing and Element Type	p. 56
2.3.8 Solution Phase	p. 56
2.3.9 Post-Processing and Visualization	p. 56
Suggested Problems	p. 61
3 Elasticity and Strength of Laminates	p. 63
3.1 Kinematics of Shells	p. 64
3.1.1 First-Order Shear Deformation Theory	p. 65
3.1.2 Kirchhoff Theory	p. 69
3.2 Finite Element Analysis of Laminates	p. 71
3.2.1 Element Types	p. 73
3.2.2 Sandwich Shells	p. 74
3.2.3 Nodes and Curvature	p. 74
3.2.4 Drilling Rotation	p. 74
3.2.5 A-B-D-H Input Data for Laminate FEA	p. 74
3.2.6 Equivalent Orthotropic Input for Laminate FEA	p. 77
3.2.7 LSS for Multidirectional Laminate FEA	p. 82
3.2.8 FEA of Ply Drop-Off Laminates	p. 83
3.2.9 FEA of Sandwich Shells	p. 87
3.2.10 Element Coordinate System	p. 88
3.2.11 Constraints	p. 94
3.3 Failure Criteria	p. 100
3.3.1 2D Failure Criteria	p. 101
3.3.2 3D Failure Criteria	p. 103
Suggested Problems	p. 110
4 Buckling	p. 113
4.1 Eigenvalue Buckling Analysis	p. 113
4.1.1 Imperfection Sensitivity	p. 120
4.1.2 Asymmetric Bifurcation	p. 121
4.1.3 Post-Critical Path	p. 121
4.2 Continuation Methods	p. 126
Suggested Problems	p. 130
5 Free Edge Stresses	p. 133
5.1 Poisson's Mismatch	p. 134
5.1.1 Interlaminar Force	p. 134
5.1.2 Interlaminar Moment	p. 135
5.2 Coefficient of Mutual Influence	p. 141
5.2.1 Interlaminar Stress due to Mutual Influence	p. 143
Suggested Problems	p. 147
6 Computational Micromechanics	p. 151
6.1 Analytical Homogenization	p. 152
6.1.1 Reuss Model	p. 152
6.1.2 Voigt Model	p. 153
6.1.3 Periodic Microstructure Model	p. 153
6.1.4 Transversely Isotropic Averaging	p. 154
6.2 Numerical Homogenization	p. 157
6.3 Global-Local Analysis	p. 172
6.4 Laminated RVE	p. 175
Suggested Problems	p. 178
7 Viscoelasticity	p. 179
7.1 Viscoelastic Models	p. 181
7.1.1 Maxwell Model	p. 181
7.1.2 Kelvin Model	p. 182
7.1.3 Standard Linear Solid	p. 183
7.1.4 Maxwell-Kelvin Model	p. 183
7.1.5 Power Law	p. 184
7.1.6 Prony Series	p. 184
7.1.7 Standard Nonlinear Solid	p. 185
7.1.8 Nonlinear Power Law	p. 186
7.2 Boltzmann Superposition	p. 187
7.2.1 Linear Viscoelastic Material	p. 187
7.2.2 Unaging Viscoelastic Material	p. 189
7.3 Correspondence Principle	p. 190
7.4 Frequency Domain	p. 191
7.5 Spectrum Representation	p. 192
7.6 Micromechanics of Viscoelastic Composites	p. 192
7.6.1 One-Dimensional Case	p. 192
7.6.2 Three-Dimensional Case	p. 193
7.7 Macromechanics of Viscoelastic Composites	p. 197
7.7.1 Balanced Symmetric Laminates	p. 197
7.7.2 General Laminates	p. 197
7.8 FEA of Viscoelastic Composites	p. 198
Suggested Problems	p. 204
8 Continuum Damage Mechanics	p. 207
8.1 One-Dimensional Damage Mechanics	p. 208
8.1.1 Damage Variable	p. 208
8.1.2 Damage Threshold and Activation Function	p. 210
8.1.3 Kinetic Equation	p. 211
8.1.4 Statistical Interpretation of the Kinetic Equation	p. 212
8.1.5 One-Dimensional Random-Strength Model	p. 213
8.1.6 Fiber Direction, Tension Damage	p. 218
8.1.7 Fiber Direction, Compression Damage	p. 222
8.2 Multidimensional Damage and Effective Spaces	p. 226
8.3 Thermodynamics Formulation	p. 228
8.3.1 First Law	p. 228
8.3.2 Second Law	p. 230
8.4 Kinetic Law in Three-Dimensional Space	p. 235
8.4.1 Return-Mapping Algorithm	p. 238
8.5 Damage and Plasticity	p. 244
Suggested Problems	p. 245
9 Discrete Damage Mechanics	p. 249
9.1 Overview	p. 250
9.2 Approximations	p. 254
9.3 Lamina Constitutive Equation	p. 256
9.4 Displacement Field	p. 256
9.4.1 Boundary Conditions for ¿T = 0	p. 258
9.4.2 Boundary Conditions for ¿T ≠ 0	p. 259
9.5 Degraded Laminate Stiffness and CTE	p. 260
9.6 Degraded Lamina Stiffness	p. 261
9.7 Fracture Energy	p. 262
9.8 Solution Algorithm	p. 263
9.8.1 Lamina Iterations	p. 263
9.8.2 Laminate Iterations	p. 264
Suggested Problems	p. 271
10 Delaminations	p. 273
10.1 Cohesive Zone Method	p. 276
10.1.1 Single Mode Cohesive Model	p. 278
10.1.2 Mixed Mode Cohesive Model	p. 281
10.2 Virtual Crack Closure Technique	p. 290
Suggested Problems	p. 295
A Tensor Algebra	p. 297
A.1 Principal Directions of Stress and Strain	p. 297
A.2 Tensor Symmetry	p. 297
A.3 Matrix Representation of a Tensor	p. 298
A.4 Double Contraction	p. 299
A.5 Tensor Inversion	p. 299
A.6 Tensor Differentiation	p. 300
A.6.1 Derivative of a Tensor	p. 300
A.6.2 Derivative of the Inverse of a Tensor	p. 301
B Second-Order Diagonal Damage Models	p. 303
B.1 Effective and Damaged Spaces	p. 303
B.2 Thermodynamic Force Y	p. 304
B.3 Damage Surface	p. 306
B.4 Unrecoverable-Strain Surface	p. 307
C Software Used	p. 309
C.1 ANSYS Mechanical APDL	p. 309
C.1.1 ANSYS USERMAT, Compilation and Execution	p. 311
C.2 BMI3	p. 314
C.2.1 Stand-Alone BMT3	p. 314
C.2.2 BMI3 within ANSYS	p. 314
References	p. 317
Index	p. 329

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