The figure below shows a 4node quadrilateral element in parametric space and in real space where two of the nodes are collapsed or merged to form a triangle.

a. Determine the mapping functions \(x(s, t)\) and \(y(s, t)\).

b. The displacement at the nodes of the element are found to be: \(\left\{u_{1}, v_{1}, u_{2}, v_{2}, u_{3}, v_{3}\right\}=\) \(\{1,0,0,2,0,0\} \times 10^{-3}\) in. Compute the displacement field \(u(s, t)\) and \(v(s, t)\).

c. Compute the Jacobian matrix.

d. Compute the strain in the element. Is this is a constant strain element?

(-1,1) 2 (1,1) 1 (4) 1 (0,0) Physical element x -1 Reference element S