Engineering Transactions, 5, 2, pp. 333-354, 1957

Zastosowanie Niektórych Znanych Metod Przybliżonych do Rozwiązania Zagadnień Płyt Ortotropowych o Dużych Ugięciach

E. Nowiński
Instytut Podstawowych Problemów Techniki PAN

Some problems concerning orthotropic plates with large deflections are solved in an approximate way using the methods proposed by J. Prescott, S.P. Timoshenko and A. and L. Föppl. G.G. Rostovcev's equations and general equations for rectilinearly orthotropic plates are given in rectangular coordinates (Art. 1) and for cylindrically orthotropic plates in polar coordinates (Art. 2). In Art. 3 a circular cylindrically orthotropic plate bent into a portion of a' spherical
surface is considered, and in Art. 4 the same plate simply supported and with the same deflection surface as cylindrically orthotropic plate subjected to uniform load, in the small deflection theory. In Art. 5, J. Prescott's method of pseudo-energy is used reducing the principal system of equations for circular orthotropic plates to the form (5.7) and (5.8). Art. 6 is devoted to a circular cylindrically orthotropic plate on a hinged support and uniformly loaded, with two kinds of approximation: according to (6.1.1) in Sec. 6.1, and according to (6.2.1) in Sec. 6.2. In Art. 7, a solution is obtained for an elliptical rectilinearly orthotropic splate uniformly loaded and resting on a hinged support, by the same method. The same is performed in Art. 8 for a rectangular orthotropic plate with edges fixed in the horizontal plane and loaded as in Art. 7. Art. 9 is devoted to the energy method. Using this method, a solution for a rectangular orthotropic membrane uniformly loaded is obtained in Sec. 9.1, a solution for a similar plate being obtained in Sec. 9.2.

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J. Prescott, Applied Elasticity, New York 1946.

M. T. Huber, Teoria sprezystosci, t. 2, Warszawa 1954.

S. Timoshenko, Theory of Plates und Shells, New York-Londyn 1940.

A. L. FöppI, Drang und Zwang, t. 1, 1924, thum, ros.

S. Way, Proc. 5-th Intern. Congr. Appl. Mech., Cambridge 1938.

Wei-zang Chien, Problem of Large Deflection of Circular Plute, Arch. Mech. Stos. 1 (1956).

II. M. Berger, A New Approach to the Analysis of Large Deflections of Plates, Journ. Appl. Mech. 4 (1955).

S. G. Lechnicki, Anizotropnyje ptastinki, Moskwa-Leningrad 1947.

J. Nowinski, Równania odkształcenia płyt ortotropowych na podstawie nieliniowej teorii sprężystości, Prace Nauk.-Bad. Inst. Techn, Bud., Nr 144, 1952.