Right option is (c) It’s an incomplete third order polynomial

Explanation: Several C1 rectangular and triangular plate bending elements with (w, \(\frac{dw}{dx}\),\(\frac{dw}{dy}\)) or with (w,\(\frac{dw}{dx}\),\(\frac{dw}{dy}\),\(\frac{d^2w}{dy^2}\)) as the degrees of freedom at each node exists in the literature. A triangular element with three nodes, with (w, \(\frac{dw}{dx}\),\(\frac{dw}{dy}\)) at each node, requires the 9-term (n=9) polynomial approximation of w, i.e., w=a1+a2x+a3y+a4xy+a5x^2+a6y^2+a7(x^2y+xy^2)+a8x^3+a9y^3. This is an incomplete third-order polynomial because x^2y and y^2x do not vary independently. We note from the equation that w varies as a cubic along with any line x=constant or y=constant.