For the 4node plane stress finite element shown in the figure, finite element computation yields the displacements at the nodes as follows.

a. What is the displacement field \(u(x, y)\) and \(v(x, y)\) within the element?

b. Compute the strain displacement matrix \([\mathbf{B}]\) for this element to express strain as \(\{\boldsymbol{\varepsilon}\}=[\mathbf{B}]\{\mathbf{q}\}\) ?

c. Compute the displacements \((u, v)\) and the strain components at the origin.

d. Show that you can use this element to represent a constant state of strain.

V1 V2 U3 V3 U4 V4 0.005 0.003 0.006 0.005 0.0 0.0 0.0 0.0