$(3\mathrm{.}1)$ You are developing a plane stress element which can have variable Young's modulus, $E,$ based on values prescribed at the nodes of the element. Such elements are used to model "functionally graded materials". Note that this means the $D$ matrix is a polynomial function of the spatial coordinates $x,y($of the same degree as the displacement field$).$ How many Gaussian quadrature points should be used to fully integrate the stiffness of elements with $2,3,$ and $4$ nodes per edge, respectively $($shown at right$)?$