For a four noded quadrilateral elements, In u^T=[u.v]^T the displacement elements can be represented as u=N₁q₁+N₂q₃+ N₃q₅+ N₄q₇
v= N₁q₂+N₂q₄+ N₃q₆+ N₄q₈
then the shape function can be represented as _____
a) \(N=\left[\begin{array}{ |c c c c}q_1 & q_5 \\ q_2 &q_6\\q_3 &q_7\\q_4 & q_8\end{array}\right]\)
b) \(N=\begin{bmatrix}q_1 &q_3 &q_5 &q_7 \\ q_2 &q_4&q_6&q_8\end{bmatrix}\)
c) \(N=\begin{bmatrix}q_1 \\ q_2\end{bmatrix}\)
d) \(N=\begin{bmatrix}N_1 & 0 & N_3 & 0&N_5&0&N_7 & 0 \\ 0 & N_2 &0 &N_4&0&N_6&0&N_8\end{bmatrix}\)

Answer: d
Explanation: Displacement function in FEM. When the nodes displace, they will drag the elements along in a certain manner dictated by the element formulation. In other words, displacements of any points in the element will be interpolated from the nodal displacements, and this is the main reason for the approximate nature of the solution.