The displacement field in a material is:

$u=A(3x-y),v=Ax{y}^2$

a$)$ Calculate the strains $,$ and $($:${}_{xy}\}$ as function of $x,y$ and $A.$

b$)$ Sketch the deformations of a differential $($tiny$)$ square around the point $(1,1).$ Assume $A$ is a positive constant.

c$)$ Assuming plane stress, calculate the stresses and the out$-$of$-$plane strain at the point $(1,1)$ if $A=0\mathrm{.}01,E=100,v=0\mathrm{.}1.$

d$)$ Assuming plane strain, calculate the out$-$of$-$plane stress at the point $(1,1)$ if $A=0\mathrm{.}01,E=100,v=0\mathrm{.}1.$