THE INFLUENCE OF SMALL STRENGHTENINGS AND WEAKENINGS ON LOAD CARRYING CAPICITY OF PLATES
Lower quality plates are often manufactured by cutting or stamping sheet metal produced by cold rolling and delivered in rolls. This sheet metal cannot be ideally straightened and its thickenss is often not equal to the nominal thickness. Due to the manufacturing technology and the straightening process, places of unequal thickness can be observed in the direction of rolling, i.e. at right angle to the edge of the roll. The load carrying capacity of a square plate depends on the angle at which it is cut out from such a sheel metal plate or on the direction of strengthening or weakening with respect to the loaded edge. The paper gives an estimation of the influence of small strengthenings and weakenings on the stability of a square plate. Strengthenings and weakenings were studied with respect to the angle they form with the loaded edge. It was found that small strengthenings and weekenings forming a right angle with the loaded edge do not affect its stability. However, strengthenings and weakenings forming any other angle with the loaded edge may importantly lower the buckling stability of the plate.
Buckling of plates with strengthenings
This paper studies the buckling behaviour of simply supported square plates, which have weakening or strengthening bands. The weakening/strengthening bands are equally spaced and their thickness is either decreased or increased. The analysis assumes that the stress state in the plate before and during the buckling process remains in the elastic range. Two cases of plate loading are studied, one with compressive forces and one with tangential forces. The buckling coefficients are calculated for different numbers and thicknesses of strengthening/weakening bands. The thickness of strengthening/weakening bands and the thickness of the remaining plate is varied so that the volume/weight of the plate remains constant. In one case it is found that the buckling load at constant weight of the plate can be increased by 118% if an optimal ratio of the thickness of strengthening bands and the thickness of the remaining plate is used.
Elastoplastic buckling of rectangular plates in biaxial compression/tension
Abstract This paper examines the elastoplastic buckling of a rectangular plate, with various boundary conditions, under uniform compression combined with uniform tension (or compression) in the perpendicular direction. The analysis is based on the standard linear buckling equations and material behaviour is modelled by the small strain J2 flow and deformation theories of plasticity. A detailed parametric study has been made for Al 7075 T6 over a range of plate geometries (a/b=0.25–4,a/h≈20–100) and with three sets of boundary conditions (four simply supported boundaries and the symmetric combinations of clamped/simply supported sides). For sufficiently thin plates we recover with both theories the classical elastic results. However, for thicker plates there is a remarkable difference in the buckling loads predicted by these two theories. Apart from the expected observation that deformation theory gives lower critical stresses than those obtained from the flow theory, we report on the existence of an optimal loading path for the deformation theory model. Buckling loads attained along the optimal path—specified by particular compression/tension ratios—are the highest possible over the entire space of loading histories. By contrast, no similar optimum has been found with the flow theory. This discrepancy in the buckling behaviour, obtained from the two competing plastic theories, provides a possibly new illustration of the plastic buckling paradox.