Stability of Board with Discontinuous Support on Perimeter

Huber (1923) was the first to analyse the scheme partially fixed elastically on the perimeter of an isotropic board, subject to shearing (Huber 1923). He proposed to adopt the function of a curved shaped board in the following form:

nx ny n ( a

w = A sin sin sin x — y. (7.178)

b b a b

This equation does not satisfy the border conditions for free support and gives a finite value of the moment on the perimeter. Therefore, when calculating the energy of buckling board AU and work of external forces AW, the sought critical edge load is obtained, expressed in the form

Nr = 4n2 D (b + – + . (7.179)

The application of an orthotropic board in a discontinuous manner (discreet) corresponds to the scheme of fixing the rear wall to the body using stables or bolts. Korolew (1970) dealt with the stability of such a board, at the mentioned support conditions, noting that, during the course of normal load of the furniture body, the protuberances of the rear wall assume the form of oblique waves. In this case, for the equation of a buckling surface, fulfilling all the border conditions, the following function should be adopted:

w =A(1 — co-F^)). (7.180)

By substituting this expression to the differential equation of a sheared shield and specifying the number of oblique buckling waves for conditions of minimum kinetic energy loading the furniture body, we get the following equation: