For a simple three-noded triangular element, show explicitly that differentiation of Eq. (6.2.47) indeed results in Eq.

Question:

For a simple three-noded triangular element, show explicitly that differentiation of Eq. (6.2.47) indeed results in Eq. (6.2.48); that is, substitute the expression for [B] and the plane stress condition for [D] into Eq. (6.2.47), and then differentiate πp with respect to each nodal degree of freedom in Eq. (6.2.47) to obtain Eq. (6.2.48).