Task to possible reduction of the maximum deflection of circular section rod under the influence of centralized force

A round rod of variable cross-section is considered, to which a centralized force is applied. An optimization problem is stated for obtaining such a regularity of transverse section variability, for which the value of maximum deflection of the rod would be the least. The case of pin-jointing of the rod was considered and the problem was solved by means of variational method. An analytical solution to this problem was obtained, according to which the corresponding plots of unknown functions were constructed.