# How many termpolynomial is used in the approximation of w for a three noded triangular element with three DOF at each node?

How many termpolynomial is used in the approximation of w for a three noded triangular element with three DOF at each node?

(a) 9-term

(b) 18-term

(c) 6-term

(d) 12-term

This question was addressed to me in examination.

I need to ask this question from Classical Plate Model topic in chapter Bending of Elastic Plates of Finite Element Method

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Right choice is (a) 9-term

To explain I would say: 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.

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