Mechanics of Composite Materials

EML4230                                                                                                     EML6232


Selected Answers

Answers to Selected Problems in Book




1.1 Introduction

Page 1:  Natural Composites - The Magnificence of Spider Silk

1. 2 Classification

Page 19 : A Polymide Resin: NASA RP46

Pages 24-26: Aramid Fibers - Shear Thickening Fluid

Pages 28-34: Manufacturing of PMCs - Prepreg System for Wind Turbine Blades

Page 36: Sporting Goods - PX Black Materials Technology
Page XX: Application of PMCs - Wind Turbine Blades

Page 34: Application of PMCs - Airline Industry

Page 39: Application of PMCs - Transportation

Page 39: Application of PMCs - Graphite Epoxy Rudder

Page 39: Applications of PMCs - The Oilend Game

Pages 43-44: Metal Matrix Composites - MMC Applications

Page 45: Ceramic Matrix Composites - Aviation

Page 45: Ceramic Matrix Composites - Engines

Page 45: Ceramic Matrix Composites - Insulators

Page 45-46: Ceramic Matrix Composites - Ceramic Brakes

1. 3 Recycling

Page 50-51: Recycling of Composites - Boeing Recycling Composites

1.4 Mechanics Terminology

Page 54: Hybrid Composites - Hybrid Composite Beams

Page XX: Nanocomposites - Nanocomposites and Graphene

Other Videos Related to Introduction to Composite Materials [LINK]

Commercially Available Videos on Composite Materials [LINK]

Free of Charge DOD Composite Materials Handbook [PDF]

FAA AMT Airframe Handbook Volume 2 Chapter 7 on composites [PDF]




Appendix A: Matrix Algebra

Intro to Matrix Algebra [PDF]


Adding Two Matrices [YOUTUBE 4:53]

Subtracting Two Matrices [YOUTUBE 5:34]

Multiplying Two Matrices [YOUTUBE 10:06]


Determinant of a matrix using minors Theory [YOUTUBE 4:41]

Determinant of a matrix using cofactors Theory [YOUTUBE 3:26]

Determinant of a matrix using minors Example [YOUTUBE 6:26]

Determinant of a matrix using cofactors Example [YOUTUBE 5:31] 


A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23]

Writing simultaneous linear equations in matrix form  [YOUTUBE 5:25]


Can we divide two matrices?  [YOUTUBE 5:39] 
Some statements about the inverse of matrices  [YOUTUBE 2:53]

Inverse of matrices Example  [YOUTUBE 3:40]

Using concept of inverse to solve a set of equations  [YOUTUBE 2:27] 

Finding the inverse of a matrix Theory [YOUTUBE 4:32]

Finding the inverse of a matrix Example  [YOUTUBE 7:03] 
Finding the inverse of a matrix by adjoints Theory  [YOUTUBE 2:15]

Finding the inverse of a matrix by adjoints Example  [YOUTUBE 7:19]

Appendix B: Transformation of Stresses and Strains

Transformation of Stresses [LIVESCRIBE 13:55]

2.1 Introduction

Deformations of unidirectional lamina under load  [ PDF]   [PPT]

2.2 Review of Definitions

Review of definitions   [PDF  [PPT]

2.3 Hooke's Law for Different Types of Materials

3D stiffness and compliance matrices   [PDF  [PPT]

2.4 Hooke's Law for a Two Dimensional Unidirectional Lamina

Stiffness and compliance matrices for a unidirectional lamina   [PDF  [PPT]

2.5 Hooke's Law for a Two Dimensional Angle Lamina

Stress-strain relationship for an angle lamina   [PDF  [PPT]

2.6 Engineering Constants of an Angle Lamina

Engineering constants of an angle lamina   [PDF  [PPT]

Problem 2.27 [PDF]

Problem 2.28 [PDF]

Problem 2.29 [PDF]

Problem 2.32 [LIVESCRIBE 9:03]

Background to #2.32: Linear Regression With Zero Intercept: Derivation [YOUTUBE 9:32]

Test problem#3 [problem statement] [LIVESCRIBE Parta 1:34] [LIVESCRIBE Part b 3:08] [LIVESCRIBE Partc 3:46]

2.7 Invariant Form of Stiffness and Compliance Matrices for an Angle Lamina

Invariant form of transformation matrices   [PDF  [PPT]

2.8 Strength Failure Theories of an Angle Lamina.

Maximum stress failure theory   [PDF  [PPT]

Maximum strain failure theory   [PDF  [PPT]

Tsai-Hill failure theory   [PDF  [PPT]

Tsai-Wu failure theory   [PDF  [PPT]

Comparison of failure theories   [PDF  [PPT]

Test problem#4 [problem statement] [LIVESCRIBE 6:53 ]

2.9 Hygrothermal Stresses and Strains in a Lamina

Hygrothermal stresses and strains   [PDF  [PPT]




3.1  Introduction

What is Chapter 3 all about? [LIVESCRIBE 5:49]

Introduction   [PDF  [PPT]

3.2 Volume and Mass Fractions, Density and Void Content

Volume and weight fractions   [PDF  [PPT]

Problem 3.2 [LIVESCRIBE 3:19]

Volume Fraction of Voids  [LIVESCRIBE Part 1  0:51;   LIVESCRIBE Part 2 3:31]

Problem 3.3 [LIVESCRIBE 7:10]

3.3 Evaluation of Four Elastic Moduli

Elastic moduli   [PDF  [PPT]

Problem 3.6 [LIVESCRIBE 5:49]

Derivation of  In-plane Shear Modulus: Halphin Tsai [LIVESCRIBE 6:35]

Why are Halphin-Tsai Equations called SEMI-empirical? [LIVESCRIBE 3:22]

Testing Videos 

3.4 Ultimate Strength of a Unidirectional Lamina

Ultimate strengths of unidirectional lamina   [PDF  [PPT]


3.5 Coefficients of Thermal Expansion

Coefficients of thermal expansion of unidirectional lamina   [PDF  [PPT]

Derivation of Longitudinal Thermal Expansion Coefficient [LIVESCRIBE 8:05]

Derivation of Transverse Thermal Expansion Coefficient [LIVESCRIBE 6:52]

3.6. Coefficients of Moisture Expansion

Coefficient of moisture expansion   [PDF]    [PPT]


4.1 Introduction


4.2 Laminate Code

Objectives and laminate code  [PDF]  [PPT]

4.3 Stress-Strain Relationships for Laminate

Classical lamination theory  [PDF]  [PPT]

Strain to applied load relationship  [PDF]  [PPT]

Laminate analysis theory  [PDF]  [PPT]

Example of laminate analysis  [PDF]  [PPT]

4.4 In-Plane and Flexural Modulus for Laminate

Laminate moduli theory  [PDF]  [PPT]

Laminate moduli example  [PDF]  [PPT]

4.5 Hygrothermal Effects in a Laminate

Thermal load on a laminate  [PDF]  [PPT]


5.1 Introduction


5.2 Special Cases of Laminates

Special cases of laminate  [PDF]   [PPT]

5.3  Failure Criterion for a Laminate

Ply-by-ply failure of laminates [PDF]   [PPT]

5.4 Design of a Laminated Composite

Drive shaft design [PDF]   [PPT] | EXCEL]

Man Made Design: A Few Design Examples [PDF]   [PPT]

Design by Nature Example: Collagen Fiber Angles in Intestines [ABSTRACT]

Design by Nature Example: What We Didn’t Know About Penis Anatomy [VIDEO 11:20]

5.5  Other Mechanical Design Issues

Other mechanical design issues  [PDF]   [PPT]