Use Matlab, program up an ABD calculator which can calculate the ABD matrix of n$-$layer composite laminate with a given lay$-$up$.$Apply your ABD calculator to the following cases:

$1.$Quasi$-$isotropic laminate: consisting of lamina with layup $[$theta$,$theta $+60,$theta $+120\backslash (]\_\{2\}\backslash )$

$2.$Symmetric laminate: For every ply above the laminate midplane, there is an identical ply $($material and orientation$)$an equal distance below the midplane. $($make up your own symmetric layup.$)$

$3.$Balanced laminate: For every ply at $\backslash ($a$+\backslash$theta $\backslash )$orientation$,$ there is another ply at the $\backslash (-\backslash$theta $\backslash )$orientation somewhere in the laminate. $($make up your own balanced layup.$)$

$4.$Discuss the characteristic of the ABD matrices obtained for each type of layup.

Assume all layers are made of the same graphite$-$epoxy material $($as shown in the table below$)$and have equal thickness of $0\mathrm{.}02$inches$.$