A cantilever beam can be analyzed using the three different finite element models shown in the figure.

a. Rank these three models based on which one you expect to give results closest to the analytic solution for the displacement at the tip of the beam (point of application of load). Give a brief explanation for the ranking you assign.

b. Plot the normal stress distribution you expect to compute at a section near the center of the beam for each model. Explain why you expect these plots.

(a) 4-Node Quadrilateral Plane stress elements (b) JNV NV 3-Node Triangular Plane stress elements (c) A single 2-Node Hermite beam element