Optimal shape of the rotating nano rod

Abstract

By using a Pontryagin's principle, we study the optimal shape of a rotating nano rod and determine the optimal cross-section that is stable against buckling due to centrifugal forces. We generalize the results of the earlier studies focused on the constant cross-sectional area of nano rods. The problem of the optimal shape of a Bernoulli–Euler rotating rod is analyzed first. The optimal nano rod with fixed volume was found to have larger critical rotation speed than the optimally shaped Bernoulli–Euler rod with the same volume. Similarly, for fixed rotational speed, the optimally shaped nano rod was found to have smaller volume than the optimally shaped Bernoulli–Euler rod.