The elastic stability of a long and slightly bent rectangular plate under uniform shear

Abstract

1—The problem of the elastic stability of a plane rectangular plate when subjected to uniform shear has been approximately solved for various conditions (Cox 1933; Timoshenko 1936). In the case of an indefinitely long strip an exact solution has been found (Southwell and Skan 1924), but it appears that no attempt has been made to investigate what happens if the plate is no longer plane. It is accordingly the object of this paper to consider the stability of a long strip, slightly curved, when its two side edges are subjected to uniform shear. 2—In what follows we assume that the thickness and curvature of the plate are constant, and that the edges of the plate are two generators and two lines of curvature. It is, moreover, further assumed that the plate is thin as in all similar stability problems, and that it is of such length that the boundary conditions over the two curved ends can be ignored.