1 |
Introduction |
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1.1 | Introduction to Composite Materials | ||
1.1.1 | Classification of Composite Materials | ||
1.1.2 | Fiber-Reinforced Composite Materials | ||
1.2 | Properties of Laminated Composites | ||
1.2.1 | Material Orthotropy | ||
1.2.2 | Rule of Mixtures, Complementation, and Interaction | ||
1.2.3 | Laminate Definition | ||
1.3 | Design of Composite Laminates | ||
1.3.1 | Historical Perspective | ||
1.3.2 | Material-Related Design Issues | ||
1.4 | Design Optimization | ||
1.4.1 | Mathematical Optimization | ||
1.4.2 | Stacking Sequence Optimization | ||
2 |
Mechanics of Laminated Composite Materials |
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2.1 | Governing Equations for Elastic Medium | ||
2.1.1 | Strain-Displacement Relations | ||
2.1.2 | Stress-Strain Relations | ||
2.1.3 | Equilibrium Equations | ||
2.2 | In-Plane Response of Isotropic Layer(s) | ||
2.2.1 | Plane Stress | ||
2.2.2 | Single Isotropic Layer | ||
2.2.3 | Symmetrically Laminated Layers | ||
2.3 | Bending Deformations of Isotropic Layer(s) | ||
2.3.1 | Bending Response of a Single Layer | ||
2.3.2 | Bending Response of Symmetrically Laminated Layers | ||
2.3.3 | Bending-Extension Coupling of Unsymmetrically Laminated Layers | ||
2.4 | Orthotropic Layers | ||
2.4.1 | Stress-Strain Relations for Orthotropic Layers | ||
2.4.2 | Orthotropic Layers Oriented at an Angle | ||
2.4.3 | Laminates of Orthotropic Plies | ||
2.4.4 | Elastic Properties of Composite Laminates | ||
2.5 | Properties of Laminates Made of Sublaminates | ||
3 |
Hygrothermal Analysis of Laminated Composites |
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3.1 | Hygrothermal Behavior of Composite Laminates | ||
3.1.1 | Temperature and Moisture Diffusion in Composite Laminates | ||
3.1.2 | Hygrothermal Deformations | ||
3.1.3 | Residual Stress | ||
3.1.4 | Hygrothermal Laminate Analysis and Hygrothermal Loads | ||
3.1.5 | Coefficients of Hygrothermal Laminate Expansion | ||
3.2 | Laminate Analysis for Combined Mechanical and Hygrothermal Loads | ||
3.3 | Hygrothermal Design Considerations | ||
4 |
Laminate In-Plane Stiffness Design |
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4.1 | Design Optimization Problem Formulation | ||
4.1.1 | Design Formulation of In-Plane Stiffness Problem | ||
4.1.2 | Mathematical Optimization Formulation | ||
4.2 | Graphical Solution Procedures | ||
4.2.1 | Optimization of Orientations of Layers | ||
4.2.2 | Graphical Design of Coefficients of Thermal Expansion | ||
4.2.3 | Optimization of Stack Thicknesses | ||
4.3 | Dealing with the Discreteness of the Design Problem | ||
5 |
Integer Programming |
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5.1 | Integer Linear Programming | ||
5.2 | In-Plane Stiffness Design as a Linear Integer Programming Problem | ||
5.3 | Solution of Integer Linear Programming Problems | ||
5.3.1 | Enumeration | ||
5.3.2 | Branch-and-Bound Algorithm | ||
5.4 | Genetic Algorithms | ||
5.4.1 | Design Coding | ||
5.4.2 | Initial Population | ||
5.4.3 | Selection and Fitness | ||
5.4.4 | Crossover | ||
5.4.5 | Mutation | ||
5.4.6 | Permutation, Ply Addition, and Deletion | ||
5.4.7 | Computational Cost and Reliability | ||
6 |
Failure Criteria for Laminated Composites |
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6.1 | Failure Criteria for Isotropic Layers | ||
6.1.1 | Maximum Normal Stress Criterion | ||
6.1.2 | Maximum Strain Criterion | ||
6.1.3 | Maximum Shear Stress (Tresca) Criterion | ||
6.1.4 | Distortional Energy (von Mises) Criterion | ||
6.2 | Failure of Fiber-Reinforces Orthotropic Layers | ||
6.2.1 | Maximum Stress and Maximum Strain Criteria | ||
6.2.2 | Tsai-Hill Criterion | ||
6.2.3 | Tsai-Wu Criterion | ||
6.3 | Failure of Laminated Composites | ||
6.3.1 | Failure under In-Plane Loads | ||
6.3.2 | Failure under Bending Loads | ||
7 |
Strength Design of Laminates |
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7.1 | Graphical Strength Design | ||
7.1.1 | Design for Specified Laminate Strain Limits | ||
7.1.2 | Design of Laminates with Two-Fiber Orientations | ||
7.1.3 | Design of Multiple-Ply Laminates with Discrete Fiber Orientations | ||
7.2 | Numerical Strength Optimization Using Continuous Variables | ||
7.2.1 | Strength Design with Thickness Design Variables | ||
7.2.2 | Strength Design with Orientations Angle Design Variables | ||
7.3 | Numerical Strength Optimization Using Discrete Variables | ||
7.3.1 | Integer Linear Programming for Strength Design | ||
7.3.2 | Genetic Algorithms for Strength Design | ||
8 |
Laminate Design for Flexural and Combined Response |
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8.1 | Flexural Response Equations | ||
8.2 | Stiffness Design by Miki's Graphical Procedure | ||
8.2.1 | Linear Problems | ||
8.2.2 | Changes in Stacking Sequence | ||
8.2.3 | Nonlinear Problems | ||
8.3 | Flexural Stiffness Design by Integer Linear Programming | ||
8.3.1 | Ply-Identity and Stack-Identity Design Variables | ||
8.3.2 | Stiffness Design with Fixed Thickness | ||
8.3.3 | Buckling Load Maximization with Stiffness and Strength Constraints | ||
8.3.4 | Stiffness Design for Minimum Thickness |