Consider the plane stress 4-node element shown in the figure. Its global node numbers are shown in the figure with the element connectivity in the table. The coordinates of the nodes in the global \(x y\) coordinate system is shown next to each node. Nodal displacements are given as \(\{\mathbf{q}\}^{\mathrm{T}}=\left\{u_{51}, v_{51}, u_{52}, v_{52}, u_{63}, v_{63}, u_{64}, v_{64}\right\}=\{0,0,0.1,0,0.1,0.1,0,0\}\).

a. Determine the displacement at the point \((x, y)=(0.75,0.75)\) by interpolating the nodal displacements.

b. Compute the Jacobian matrix at the point in (a).

c. Compute strain \(\varepsilon_{y y}\) at the centroid of the element.

64 49 y 63 (0,1) (1,1) 51 (0,0) (1,0) X 52 Element # Local node 1 Local node 2 Local node 3 Local node 4 27 51 52 63 64