Engineering Transactions, 19, 1, pp. 65–83, 1971

Optymalne Kształtowanie Sprężysto-Plastycznego Słupa przy Ogólnym Konserwatywnym Zachowaniu się Obciążenia

A. Gajewski
Politechnika Krakowska, Kraków

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.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


N. G. CZENCOW, Stojki najmienszego wiesa, Trudy CAGI, 1936, 265.

A. GAJEWSKI, M. ŻYCZKOWSKI, Optymalne kształtowanie pręta ściskanego silą skierowaną do bieguna, Rozpr. Inż., 17, 2, 299-329, 1969.

A. GAJEWSKI, Pewne problemy optymalnego kształtowania pręta ściskanego silą skierowaną do bieguna, Mech. Teor. i Stos., 8, 2, 159-173, 1970.

A. GAJEWSKI, M. ŻYCZKOWSKI, Optimal design of elastic columns subject to the general conservative behaviour of loading, ZAMP, 21, 5, 806-818, 1970.

A. GAJEWSKI, M. ŻYCZKOWSKI, Optimal design of a column compressed by a subtangential force in the elastic-plastic range, Arch. Mech. Stos., 23, 2, 1971.

Z. KORDAS, Stateczność sprężyście utwierdzonego pręta ściskanego w ogólnym przypadku zachowania się obciążenia, Rozpr. Inż., 11, 3, 435-448, 1963.

W. KRZYŚ, Optymalne kształtowanie z uwagi na stateczność ściskanych slupów cienkościennych o profilu zamkniętym, Zeszyt naukowy Nr 4, Pol. Krakowska 1967.

M. ŁAWRIENTIEW, L. LUSTERNIK, Rachunek wariacyjny, Warszawa 1954.

F. R. SHANLBY, Inelastic column theory, J. Aeron. Sci., 13, 12, 678, 1946.

M. ŻYCZKOWSKI, A. GAJEWSKI, Optimal structural design in non-conservative problems of elastic stability, Proc. IUTAM Symposium on Instability of Continuous Systems, Herrenalb/Karlsruhe 1969 [w druku].