Suppose a large rectangular prism is made of an elastic material with E $=80$ MPa $($note: MPa not GPa$)$ and $=0\mathrm{.}4$ and has dimensions Lx $=1$m$,$ Ly $=1$m$,$ and Lz $=2$m$,$ extending from one corner at the origin to an opposite corner at $($Lx$,$Ly$,$Lz$).$ The prism$$s z $=0$ surface is fixed and it is initially put into pure shear static equilibrium by applying surface stresses to cause an internal shear stress vector of$,$ and THEN given an additional $40$ kPa of axial tensile z$-$stress on its $+$z surface.

a$)$ Ignoring anchor effects and assuming stress & strain are uniform, produce a plot of x displacement vs$.$ z$-$position along the line from $($x$,$y$,$z$)=($Lx$,$Ly$,0)$ to $($Lx$,$Ly$,$Lz$),$ assuming the point $($Lx$/2,$Ly$/2,0)$ is fixed.

b$)$ Use FlexPDE to model the beam and determine the real displacement along this line $($i$.$e$.,$ including anchor effects$)$ and plot both together with a FlexPDE elevation plot.