Engineering Transactions, 20, 3, pp. 389–407, 1972

Równania Teorii Dużych Ugięć Powłok Plastycznych

M. Duszek
Instytut Podstawowych Problemów Techniki, Warszawa
Poland

The paper is aimed at the determination of the equations of the theory of plastic, incompressible shells, account being taken of the geometry changes produced by plastic deformation. Using the Lagrangean description (referred to the initial configuration) a systematic classification of the stress­strain relations has been done, their form being specified in dependence of the shell geometry assumed and of the admissible values of the individual displacement vector components.
The estimation of the generalized variables and the equilibrium equations are then discussed, as also the principles of formulation of the yield conditions in the theory of large deflections.
Finally, the fundamental relations concerning certain particular cases of cylindrical and spherical shells are given.

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References

W. T. KOITER, On the nonlinear theory of thin elastic shells, Proc. Kon. Ned. Ak. Wet., B 69, 1-54, 1966.

W. T. KOITER, A consistent first approximation in the general theory of thin elastic shells, Proc. IUTAM Symp. Theory Thin Shell, (Delf 1959) North Holland, 12- 33, Amsterdam 1960.

F. JOHN, Estimates for the derivatives of the stresses in a thin shell and interior shell equations, Comm. Pure Appl. Math. 18, 235 -267, 1965.

J. L. SANDERS, Nonlinear theories for thin shells, Quart. Appl. Math., 21,21 - 36, 1963.

P. M. NAGHDI, Foundations of elastic shell theory, Progress in Solid Mechanics, 4, 1-90, North Holland, Amsterdam 1963.

Cz. WOŹNIAK, Nieliniowa teoria powłok, PWN, Warszawa 1966.

P. G. HODGE, Jr., Plastic analysis of rotationally symmetric shells, Prentice Hall, Englewood Cliffs, N. J. 1963.

M, DUSZEK, A. SAWCZUK, O związkach podstawowych teorii powłok plastycznych, Rozpr. Inżyn., 18, 715-732, 1970.

Ю. P. Лепик, Равновесие упруго-пластических и жестко-пластических пластин и оболочек, Инж, Жури., 4, 601 -616, 1964.

Z. WASZCZYSZYN, Obliczanie skończonych ugięć sprężysto-plastycznych płyt i powłok obrotowo­symetrycznych. Polit. Krak., Kraków 1970.

A. SAWCZUK, Lagrangean formulation of large deflection theory for plastic shells, Bull. Acad. Polon. Sci., serie Sci. Techn., 19, 6, 1971.

Y. C. FUNG, Fundations of solid mechanics, Prentice-Hall, Englewood Cliffs, N. J. 1965.

L. J. HART-SMITH, The linear and non-linear equilibrium equations for thin elastic shells according to the Kirchhoff-Love hypotheses, Int. J. Mech. Sci., 12, 1-16, 1970.

W. T. KOITER, Comment on: The linear and non-linear equilibrium equations for thin elastic shells according to the Kirchhoff-Love hypotheses, Int. J. Mech. Sci., 12, 1970.

W. Z. CHIEN, The intrinsic theory of thin shells and plates, Quart. Appl, Math., 1, 297 -327, 1944.

H. L. DONNELL, General thin shell displacement – strain relations, Proc. 4th U.S. Nat. Congr. Appl. Mech., 1962 ASME, 529–536, New York 1963.

M. DUSZEK, Plastic analysis of cylindrical shells subjected to large deffections, Arch. Mech. Stos., 18, 599–614, 1966.

M. DUSZEK, Plastic analysis of shallow spherical shells at moderately large deflections IUTAM Symposium Theory Thin Shells, (Copenhagen 1967), Springer 374–388, Berlin 1969.

M. DUSZEK, A. SAWCZUK, Load-deflexion relations for rigid-plastic cylindrical shells beyond the incipient collapse load, Int. J. Mech. Sci., 12, 839–848, 1970.

R. H. LANCE, J. E. SOECHTING, A displacement bounding principle in finite plasticity, Int. J. Solid Structures, 6, 1103–1118, 1970.

A. SAWCZUK, Zagadnienia teorii umiarkowanie dużych ugięć powłok sztywno-plastycznych, Mech. Teoret. Stos., 9, 335–354, 1971.

M. ARCISZ, J. RYCHLEWSKI, Lagrangean description of plane plastic flow, Bull. Acad. Polon. Sci., Serie Sci. Tech., 17, 1969.

А. А. Колесников, установлению пределов применимости уравнений Кармана изгиба пластин, Расчет Пространственных Конструкций, выл. VII, 1962.

E. REISSNER, Rotationally symmetric problems in the theory of thin plastic shells, Proc. 3-rd U. S. Nat. Congress of Appl. Mech. 1958.

Ю. P. Лепик, Большие прогибы жестко-пластической цилиндрической оболочки под действием впутренного давления, VI Всесоюзная Конф; по теорий оболочек и пластинок, 1966.