In the next two problems, we receive an order from our partner aircraft manufacturing company,

to design and fabricate a composite plate. In Problem $1$ we design and fabricate the composite,

and in Problem $2$ we test the quality of fabricated product.

$1.$ We decide to use continuous AS$-4$ carbon fiber reinforced epoxy $(3501-6)$ according to their

needs. The fiber volume ratio is $60\%,$ and there is no void in the composite. Note that in this

problem the analysis is simplified in $2$D $($only in $1-2$ plane$).(30)$

$(1)$ First of all, use the table of constituents $($fiber and matrix$)$ below to determine the density of

composite, Young$$s modulus $1,2,$ Poisson$$s ratio $12$ and shear modulus G$12$ for the composite

using the rule of mixture. $($Hint: use parallel and series models, while you need to choose which

one to use for the specific engineering constant$)(10,2$ for each$)$

$(2)$ Using the results from $(1),$ write down the macroscopic compliance matrix. Note: plane stress

assumption is used in $2$D$,$ and hence the matrix should be $33.(10+2,2$ for each$)$ Draw a picture

to demonstrate the stress $($normal and shear stress$)$ that a $2$D lamina is undertaking. $(5)$

$(3)$ How many independent components exist in the compliance matrix? $(3)$

In the next two problems, we receive an order from our partner aircraft manufacturing company,

to design and fabricate a composite plate. In Problem $1$ we design and fabricate the composite,

and in Problem $2$ we test the quality of fabricated product.

We decide to use continuous AS$-4$ carbon fiber reinforced epoxy $(3501-6)$ according to their

needs. The fiber volume ratio is $60\%,$ and there is no void in the composite. Note that in this

problem the analysis is simplified in $2$D $($only in $1-2$ plane$).(30\text{'})$

$(1)$ First of all, use the table of constituents $($fiber and matrix$)$ below to determine the density of

composite, Young's modulus E$\_(1),$E$\_(2),$ Poisson's ratio v$\_(12)$ and shear modulus G$\_(12)$ for the composite

using the rule of mixture. $($Hint: use parallel and series models, while you need to choose which

one to use for the specific engineering constant$)(10\text{'},2\text{'}$ for each$)$

$(2)$ Using the results from $(1),$ write down the macroscopic compliance matrix. Note: plane stress

assumption is used in $2$D$,$ and hence the matrix should be $3$x$3.(10+2^(\text{'}),2^(\text{'})$ for each'$)$ Draw a picture

to demonstrate the stress $($normal and shear stress$)$ that a $2$D lamina is undertaking. $(5\text{'})$

$(3)$ How many independent components exist in the compliance matrix? $(3\text{'})$