Table of Contents      


1

Introduction

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

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

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

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

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

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

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

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