Engineering Transactions, 21, 2, pp. 347-360, 1973

Obliczanie Pozakrytycznych Ugięć Sprężysto-Plastycznych Płyt Kołowych

Z. Waszczyszn
Politechnika Krakowska, Instytut Mechaniki Budowli, Kraków

The fundamental set of equations of large deflections of elastic-plastic shells presented in earlier papers by the author [10, 11] is adapted for the evaluation of post-critical states of circular plates
under radial pressure uniformly distributed along the contour. The problem is formulated as an initial and boundary value problem, described by an uncoupled system of differential equations. Considered are sandwich plates made of clastic-plastic material with a combined, kinematic-iso- tropic hardening rule given by the constitutive equations of the plastic flow theory (2.5). The fundamental set of Eqs. (2.10) is solved by means of the semi-inverse method proposed in [11]. In the present paper the detailed algorithm intended for a computer is discussed, particular attention being paid to passive processes (local unloading) occuring in the plate. The algorithm ls verified on the example of a simply supported plate. It is found that, similarly to the case of elastic plates, a boundary layer is formed exhibiting large values of circumferential stresess, while around the center of the plate a region of tensile stresses appears. The results are compared with those obtained in [5, 9] for a perfectly rigid-plastic material. The method of inversion of physical relations and certain numerical data are presented in the Appendix.

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J. C. GERDEEN, F.A. SIMENON, D. I. HUNTER, Large deflection analysis of elastic-plastic shells using numerical integration, ATAA Journal, 9, 8, 1012 -I018, 1971.

K. O. FRIEDRICHS, J. J. STOKER, Buckling of the circular plate beyond the critical thrust, J. Appl. Mech., 9, 1, 7 - 14, 1942.

A. KALNINS, J. F. LESTINGI, On nonlinear analysis of shells of revolution, J. Appl. Mech., 34, 1, 59 - 64, 1967.

J. R. LEPIK, O rawnowiesii gibkich plastinok za priedielom uprugosti, 21, 6, 833 - 842, 1957.

J. R. LEPIK, K osiessimetricznomu izgibu kruglych zestko-plasticzeskich plastin, Inz. Zurnał-Mech. Tw. Tieła, 4, 104 - 110, 1966.

P. V. MARCAL, C. E. TURNER, Numerical analysis of the elastic-plastic behaviour of axisymmetrically loaded shells of revolution, J. Mech. Engng. Sci., 5, 3, 232 - 237, 1963.

P. V. MARCAL, Lurge deflection analysis of elastic-plastic plates and shells, Proc. First Intern. Conf. on Pressure Vessel Technology, P.I, Design and Analysis, ASME, 75 - 87, 1969.

E. P. POPOV, S. YAGHMAI, Linear and nonlinear static analysis of axisymmetric loaded thin shells of revolution, Proc. First Intern. Conf. on Pressure Vessels Technology, P. I, Design and Analysis, ASME, 234 - 237, 1969.

A. N. SHERBOURNE, Collapse of rigid-plastic circular plate in uniform compression, J. Mech. Engng Sci., 2, 2, 133 - 142, 1961.

Z. WASZCZYSZYN, Obliczanie skończonych ugięć sprężysto-plastycznych płyt i powłok obrotowo-symetrycznych, Zeszyty Naukowe Polit. Krak., 3, 1970.

Z. WASZCZYSZYN, Calculation of sandwich shells of revolution at large elastic-plastic deflections, Arch. Mech. Stosy 24, 3, 483 498, 1972.

Z. WASZCZYSZYN, Poslekriticzeskoje rawnowiesije krugowoj idiealizirowannoj plastinki za priedielom uprugosti, Inz. Zurnal-Mech. Tw. Tieła [w druku].