Static deflection of nonlocal Euler Bernoulli and Timoshenko beams by the Castigliano’s theorem

These four mathematica notebooks determine the static deflections of nonlocal beams. A virtual local beam made up of linear elastic material is bent with the superposition of two curvatures. The first curvature is executed by applying the external load, while the second curvature is executed to simulate the nonlocal effects. Thus the final deflection of the virtual local beam is assumed to resemble the deflection of the nonlocal beam. The results matched with a number of previous researchers' established equations for nonlocal beam deflection. This is the first time that the Castigliano's theorem is applied to the static deflection of nonlocal beams.