Optymalne Kształtowanie Przekroju Pręta Cienkościennego Jednocześnie Skręcanego i Zginanego

The paper is devoted to the problem of optimum design of the profile of a thin-walled bar. This profile is determined in plane polar coordinates by the functions ϱ (θ) and g (θ) (the radius and the thickness of the wall, Fig. 1).
These functions are interrelated by means of the condition of equal strength (1.1), so that the problem is formulated, finally, as an isoperimetric problem of the variational calculus with one unknown function, with the condition of minimum cross-sectional area, that is for minimum weight. The Euler-Langrange equation is solved by means of the small parameter method. The influence of bending on the optimum form of the twisted bar is the only studied. The stability condition of the wall is considered additionally on the grounds of the linear theory of shell stability. The resulting form of the profile is determined by Eqs. (3.38)1 and (3.38)2 and the minimum cross-sectional area - by Eq. (3.38)3. A numerical example is given for the ratio of moments Mg/Ms = 0,5.