Uzupełnienie Równań Technicznej Teorii Powłok
The solution of the shell is reduced to that of a set of two equations (4.18) of which the form resembles those of Vlasov engineer's theory of shells.
For circularly cylindrical shells these equations reduce to the equation proposed by Morley, [4]. The accuracy of this equation is verified by comparing it with Flügge's equation for the Cylindrical shell, very good agreement being found. For shells with double curvature the results obtained by means of the equations proposed are confronted with those of the Vlasov engineer's theory. Relatively large differences are observed. However, they decrease with increasing curvature radius and with incerasing quantity n of the Fourier expansion of the external load.
References
[in Russian]
[in Russian]
L.H. DONNELL, Stability of thin Walled Tubes under Tortion, N.A.C.A., Report No. 479 (1933).
L.S.D. MORLEY, An Improvement on Donnell's Aproximation for Thin-Walled Circular Cylinders, J. Mech. App. Math., 12 (1959), 89.
N.J. HOFE, The Accuracy of Donnells Equations, J. App. Math., 22 (1955), s. 329.
V. V. NOVOZHILOV, The Theory of Thin Shells, Groningen, English translation, 1959.
[in Russian]
W. FLÜGGE, Statik und Dynamik der Scholen, Berlin 1957.
S. LUKASIEWICZ, Uproszczone rozwiązanie powłok pierścieniowych o podwójnej krzywiźnie, Arch. Bud. Maszyn, 4 (1961), s. 427.
D. S. HOUGHTON, D.J. JOHNS, A Compasison of the Characteristic Equations in the Theory of Circular Cylindrical Shells, Aeronautical quart. 12 (1961), s. 228-236.