$(3\mathrm{.}4)$ The weak form for a $2-$dimensional Kirchhoff $($classical$)$ plate is given by the following expression:

${\displaystyle \underset{A}{\overset{\phantom{}}{}}}($:$[w_{,},w_{,yy},w_{,xy}]$:$)D^b\{[w_{,}],[w_{,yy}],[w_{,xy}]\}dA={\displaystyle \underset{A}{\overset{\phantom{}}{}}}(w)pdA$

in which $p(x,y)$ is the distributed load and the matrix $D^b$ is a constant matrix containing the material parameters. What is the regularity$/$smoothness of an admissible finite element approximation for this problem? Suggest an element that satisfies these requirements $($how many nodes, what order polynomial$($s$),$ what nodal DOF's$).$