Elastic stability of infinite strips

Abstract

In this paper some elastic stability problems are solved for infinitely long, rectangular, isotropic plates, simply supported at the long edges. The problem is solved when the same arbitrarily prescribed distribution of normal stress is applied to each long edge, with no stresses and normal displacement at infinity. The extensional deformation of the middle surface during buckling is neglected; this leads to an underestimation (at most of the order of 10%) of the critical forces, but is unlikely to influence the general conclusions. A strain-energy method of analysis is used. The critical stress distributions are shown to be given by the eigenvalues of an ordinary differential equation, or, alternatively, of an integral equation. The general problem is then specialized to that of sets of concentrated normal forces, and to that of a normal force distributed uniformly over a finite length of each long edge; some numerical results are given for these cases. In the first of these problems there is negligible error in treating pairs of concentrated forces individually when they are separated by distances greater than twice the plate width. In the second problem there is little change in the critical stress when the length of edge stressed exceeds four times the plate width; also, if the length of edge stressed is less than one-quarter of the plate width, the distributed force required to produce instability does not differ appreciably from the concentrated force required to produce instability.