a) Use a computer program to plot the shape functions N1, N2, N3, N4 over 0 Sx SL for the two-node beam element that we developed in class (you can assume L-1 to make plotting easy) b) Perform calculations to show that the interpolation functions Ni, N2, N3, N4 for the 2-node beam element influence only the corresponding DOF when evaluated at the corresponding nodes. (i.e show that N-1, N2-0,N3-0,N40 and dNodV2-1dN-odN, en evaluated at node 1. Show the similar behavior for node 2) c) Show that the interpolation functions allow for rigid body translation i.e. N1 N3 1) dx dx dx a) Use a computer program to plot the shape functions N1, N2, N3, N4 over 0 Sx SL for the two-node beam element that we developed in class (you can assume L-1 to make plotting easy) b) Perform calculations to show that the interpolation functions Ni, N2, N3, N4 for the 2-node beam element influence only the corresponding DOF when evaluated at the corresponding nodes. (i.e show that N-1, N2-0,N3-0,N40 and dNodV2-1dN-odN, en evaluated at node 1. Show the similar behavior for node 2) c) Show that the interpolation functions allow for rigid body translation i.e. N1 N3 1) dx dx dx