Question

u=u[x(e,n),y(e,n)] and v=v[x(e,n),y(e,n)] Using the chain rule of partial derivatives, we get Jacobian of the transformation, J. The relation between area (A) of 2D three noded triangular element and Jacobian is given by _____

(a) A=1*|detJ|

(b) A=(1/3)*|detJ|

(c) A=0.5*|detJ|

(d) A=2*|detJ|

The question was posed to me during an internship interview.

I want to ask this question from Boundary Value Problems in chapter Single Variable Problems of Finite Element Method

Answer 1

The correct answer is (c) A=0.5*|detJ|

Easy explanation: For a 2D three noded triangular element area A=(0.5)*|(x1-x3)*(y2-y3)-(x2-x3)*(y1-y3)|. Using the chain rule of partial derivatives, we get Jacobian of the transformation, J=\(\begin{pmatrix}x1-x3&x2-x3\\y1-y3&y2-y3\end{pmatrix}\). Then detJ=(x1-x3)*(y2-y3)-(x2-x3)*(y1-y3) and in terms of detJ

A=A=0.5*|detJ|