The effect of two isolated forces on the elastic stability of a flat rectangular plate

Abstract

1. Introduction and summary. The problem of the elastic stability of a simply supported rectangular plate, compressed by two equal and opposite forces acting in the plane of the plate (see Fig. 1), was first attempted by A. Sommerfeld, and later by S. Timoshenko. The former produced a solution which in a later paper he admitted to be liable to very considerable error, while the latter constructed a solution by means of the well-known strain-energy method. In many problems this method gives results in very close agreement with those obtained in a more rigorous manner, but, in the particular case considered here, it appeared likely that the error would be appreciable owing to the underlying assumption that the only stresses in the plate occurred along the common line of action of the two external forces.