An 8node element is shown in the figure in the parametric space.

a. Derive the shape functions for this element.

b. If in the real \((x, y)\) space, an element of this type is square and has side length of \(5 \mathrm{~m}\), write the Jacobian matrix for this element. Assume that the edges of the element are parallel or perpendicular to the \(x\) and yaxis and that the midedge nodes are at the midpoint of the edge. Hint: You do not need the shape functions.

c. What is the order of Gauss quadrature that is appropriate to evaluate the stiffness matrix of this element? Will this integration be exact for the element described in (b) using this order of quadrature. Explain.

4 (-1,1) 8 1 (-1,-1) t 7 (1,1) 5 (1,-1) 3 3 S 6 (2