A thin rectangular plate is subjected to plane stress conditions. The displacement field of the

plate is given by the following functions:

$u(x,y)=0\mathrm{.}002x^2+0\mathrm{.}003xy$

$v(x,y)=0\mathrm{.}001y^2+0\mathrm{.}004xy$

Here

$u(x,y)$ is the displacement in the x $-$direction $($in meters$),$

$v(x,y)$ is the displacement in the y $-$direction $($in meters$)$

$x$ and $y$ are the coordinates in meters

Given, the plate is made of steel $($Young$\text{'}$s modulus $E=200$GPa and Poisson's ratio $v=0\mathrm{.}3),$

calculate:

a$)$ the normal and shear strain components

b$)$ the normal and shear stress components