On the Localized Instability of the Free Edge of a Rectangular Plate Supported on Two Opposite Sides under Various Conditions for Securing the Fourth Side

Abstract

The problem of stability of a rectangular plate, freely supported on two opposite sides, the third side of which is free, and the fourth side is either clamped or freely supported, is considered. The plate is compressed by the load applied on the free edge. For both cases of fixing the fourth side of the plate, conditions for the appearance of an instability localized in the vicinity of the free edge were obtained, both for the case of a conservative load and for the case of a tracking load.