Problem $1$:

Design $($determine the relative amount of fiber and matrix$)$ the lightest $($i$.$e$.$ minimum amount of

fibers$)$ a unidirectionial graphite fiber reinforced epoxy lamina that meets the following

minimum stiffness requirements and report the actual predicted values for your final lamina

design:

$E_1=160$GPa,$E_2=14$GPa,$v_{12}=0\mathrm{.}23,G_{12}=5$GPa

Useful isotropic constituent material properties: T$-300$ Graphite fiber modulus: $228$ GPa $,$ Epoxy

modulus: $3\mathrm{.}5$ GPa $,$ fiber Poisson's ratio $=0\mathrm{.}2,$ matrix Poisson's ratio $=0\mathrm{.}35.$

Problem $2$:

Use Halpin$-$Tsai to calculate $G_{12}$ for a graphite$/$epoxy orthotropic lamina with $60\%$ fiber volume

fraction and compare with the answer from the Lecture $6$ example.

Graphite fibers: $E=228$GPa,$v=0\mathrm{.}2$

Epoxy: $E=3\mathrm{.}5$GPa,$v=0\mathrm{.}35$

Problem $3$:

Design an orthotropic lamina $($i$.$e$.$ find $V_f)$ to have a $0$ CTE in the fiber direction given the

following properties:

Fiber Modulus $=228$GPa

Matrix Modulus $=10$GPa

Fiber CTE $=-0\mathrm{.}5{10}^{-6}\frac{m}{m}\frac{?}{C}$

Matrix CTE $=15{10}^{-6}\frac{m}{m}\frac{?}{C}$