Optymalne Kształtowanie Pręta Ściskanego Siłą Skierowaną do Bieguna

In the present work the problem has been solved of optimalization of shape of an elastic rod compressed by a force directed towards a constant point the pole, located on the axis of the undeformed rod. On the basis od Chentsov's method which consists of finding the extreme of a functional - the volume of the rod, for a fixed critical force the equation of the bending line of an optimal rod has been derived, valid for three cases: a plane-convergent rod deviating «from the plane» of convergence, a uniformly universally convergent rod and a plane-convergent rod deviating the plane» of convergence. Furthermore the influence of the heterogeneity of Young's modulus on the optimal shape of a rod has been considered and the heterogeneity of an optimal prismatic rod has been round. The profit on material has been calculated, resulting from the substitution of a prismatic rod by an optimal rod bearing the same critical force depending on the position of the pole and a variety of numerical examples are presented. The problem has been solved on the basis of the statical criterion of stability which, due to the «conservativeness» of the load, could be applied for any arbitrary positions of the pole.