Elasto-plastic buckling of perforated plates under uniaxial compression

Abstract

The finite element method (FEM) has been employed to determine the elasto-plastic buckling stress of uniaxially loaded square and rectangular plates with circular cutouts. Plates with simply supported edges in the out-of-plane direction and subjected to uniaxial end compression in their longitudinal direction are considered. Much attention was placed on studying the elasto-plastic buckling behavior of perforated square plates, since understanding their behavior is the key to understand that of rectangular plates. Curves representing both elastic and elasto-plastic buckling stresses versus the plate slenderness ratio for different grades of steel were plotted in order to determine the governing failure mode as a function of the plate slenderness ratio, which is crucial for the design of such perforated plates. The center of perforation was chosen at different locations along the principal major axis of the plate in order to evaluate the effect of hole location on the failure stress of the plate. The study was extended to discuss the inelastic behavior of rectangular perforated plates with aspect ratio of 2. The study shows that the critical buckling stress for perforated plates always decreases as the plate slenderness ratio increases and that this decrease becomes steeper for large values of plate slenderness ratio, especially for small hole sizes where the failure changes from elasto-plastic into pure elastic. It also concludes that the critical stress decreases as the hole size increases, and that their values depend on the yield point of the steel used, especially for thick plates where the failure becomes elasto-plastic buckling for all hole sizes. The study further concludes that the behavior of perforated rectangular plates with aspect ratio of 2 is similar to that of a square plate with the same perforation and side length equal to the short side of the rectangular plate, but with slightly larger values of the critical failure stresses. Finally, the study recommends avoiding punching the hole near the plate edge since this decreases considerably the critical buckling stress, especially when the failure occurs in the elasto-plastic buckling mode.