Engineering Transactions, 13, 4, pp. 693-706, 1965

Skończone Odkształcenia Obrotowo-Symetrycznych Powłok w Stanie Błonowym Przy Pewnych Typach Fizycznej Nieliniowości

J. Orkisz
Politechnika Krakowska
Poland

This paper is devoted to the problem of finite deformation of flexible axially-symmetric shells in a membrane state of stress in the case of physical nonlinearity of certain types. The pbysical relations used in the present paper follow from the Nádai-Davis equations. As a result we obtain sets of differential equations describing the behaviour of the shells when both if principal stresses 01 and o2 ale positive and in the «zone of folds», in which the circum-integrated numerically by the Adams method in two differential stress 02 = 0. These equations are integrated numerically by particular cases of a plane membrane and 2 conical shell of variable thickness, The present paper presents some generalization of the works of A, S. GRIGOREV [10, 11] from the viewpoint of the physical type of the body, the existence of tangential load and the variability of the wall thickness in the undefoimed state.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

J. B. ADKINS, R. S. RIVLIN, Large elastic deformations of isotropic materials, IX The deformation of thin shells, Phil. Trans. R. Soc., A 244 (1952), 505-531.

[in Russian]

E. A. DAVIS, Increase of stress with permanent strain and stress-strain relations in the plastic state for copper under combined stresses, Trans. ASME, 65 (1943), s. A-187.

E.A. DAVIS, Yelding and fracture of medium carbon steel under combined stress, J. Appl, Mech., 1 (1945).

[in Russian]

[in Russian]

[in Russian]

A. E. GREEN, J. E. ADKINS, Large elastic deformations and non-linear continuum mechanics, Oxford University Press, 1960.

[in Russian]

[in Russian]

A.S. GRIGORIEV, The stress state and the carrying capacity of flexible plates and shells at Jarge deformations, North-Holland Publ. Co., Amsterdam, PWN, Warszawa 1964, repr. Non-classical Shell Problems, Proc. IASS Symp., Warsaw, Sept. 1963.

[in Russian]

[in Russian]

[in Russian]

W. T. LANKFORD, E. SEIBELL, Some problems in unstable plastic flow under biaxial tensions, Metals Technol., August 1947.

[in Russian]

Z. MARCINIAK, Analiza stateczności cienkościennej powłoki walcowej poddanej rozciąganiu w stanie plastycznym, Rozpr. Inzyn., 10 (1959).

A. NADAI, Theory of flow and fracture of solids, New York-Toronto-London 1950.

[in Russian]

J. ORKISZ, Problem odciążenia obrotowo-symetrycznych powłok w stanie błonowym przy dużych odkształceniach niesprężystych, Mech. Teoret. Stos., 1, 3 (1965).

[in Russian]

F. OTTO, R. TROSTEL, Zugbeanspruchte Konstruktionen, Ullstein Fachverlag, Frankfurt-Berlin 1962.

R. S. RIVLIN, Some topics in finite elasticity, Struct. Mech., Oxford 1960.

L. TRELOAR, The physics of rubber elasticity, Oxford 1948. 25. N.A. WEIL, Tensile instability of thin-walled cylinders of finite length, Int. J. Mech. Sci., Pergamon Press Ltd, 5, 1963, 487-506.

[in Russian]