Duże ugięcia sprężyście nieliniowych membran kołowych

Elastically nonlinear circular membranes in the range of large deflections

The problem solved in the present paper is that of an elastically and geometrically nonlinear circular membrane hinged along the edge and subjected to the action of uniform pressure. This problem was also considered for primary creep by Odqvist, who did not satisfy, however, the compatibility condition in a clear manner.

The solution of the present author is based on the method of power series as applied to the set of fundamental equations for a circular membrane: the compatibility equation and the equilibrium equation. Recurrence equations are given for the coefficients of the series, of which three are actually determined. Approximate values of deflection at the centre are given in function of the pressure and the exponent of physical nonlinearity. The influence of the latter is represented in the form of graphs for successive approximations bounded from below by the value for a perfectly plastic membrane. In the particular case of a physically linear material the results are in agreement with the solutions of other authors.