Optymalne Kształtowanie Sprężysto-Plastycznego Słupa przy Ogólnym Konserwatywnym Zachowaniu się Obciążenia - Gajewski, A. (Engineering Transactions, 1971)
This paper presents solution of the problem of optimization of rods in the elastic-plastic range as well as in the partially elastic and partially elastic-plastic range compressed by force which, after buckling, changes not only its direction but also its application point. It was assumed, however, that during the buckling the behaviour of the force is conservative (has a potential), which made it possible to base these considerations on a static criterion of stability. It is shown in the paper that in the case of conservative loading the general equation of the deflection line of an optimal rod becomes considerably simplified enabling the obtainment of exact solutions. Accepting the physical laws σ (ε) proposed by W. Krzyś [7], a series of simple solutions is given in Section 5 of the paper for a rod which is entirely in elastic-plastic state, and in Section 6, several solutions are given for cases in which a part of the rod is in elastic state and another part in elastic-plastic state. Figs. show optimal shapes of rods compressed by a force directed to the pole.