Conclusions
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1.
The method of subregions. first used for the design of circular flexible plates free at the contour, yields results sufficiently accurate for practical purposes.
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2.
Formula (6) is recommended for use instead of the formulas given in design handbooks.
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3.
Stresses must be calculated not only at section ξ=0, and ξ=1, but also at section ξ=ξ0 where the positive flexural stress is maximal. For this one may use the coefficients γ found on the graph in Fig. 1.
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Literature Cited
B. M. Broude, “Nonlinear problems in the theory of plates and their role in structural design,” in: Summer-Session Study Course on Physical and Geometrical Problems in the Theory of Plates and Shells [in Russian]. Izd. Akad. Nauk ÉstSSR. Tartu (1966), pp. 42–46.
L. Collatz, Numerical Treatment of Differential Equations, 3rd ed., Springer-Verlag (1966).
M. S. Kornishin, Nonlinear Problems in the Theory of Plates and Shallow Shells and Methods of Their Solution [in Russian], Izd. Nauka, Moscow (1964).
I. A. Birger and Ya. G. Panovko (editors), Strength-Stability-Vibrations [in Russian], Vol. 1, Izd. Mashinostroenie, Moscow (1968).
Additional information
Ukrainian Institute of Hydraulic Engineers, Rovno. Translated from Prikladnaya Mekhanika, Vol. 12, No. 7, pp. 106–109, July, 1976.
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Kraiterman, B.L., Maksimova, I.I. Design formulas for flexible plates not clamped at the contour. Soviet Applied Mechanics 12, 719–721 (1976). https://doi.org/10.1007/BF00882757
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DOI: https://doi.org/10.1007/BF00882757