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.
Elastoplastic buckling of circular annular plates under uniform in-plane loading
Abstract This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J 2 flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.
Buckling of a thin annular plate under uniform compression
thin rods, is solved. The analysis yields a set of stability criteria involving the system parameters such as the body moments of inertia, the length and mass distribution of the elastic rods, the lowest natural frequencies of the rods, and the satellite spin velocity. The power of the method is illustrated by the relative ease with which closed-form stability criteria are derived and by the amount of information which can be extracted from their ready physical interpretation. In particular, the analysis shows that, for stability, the spinning motion is to be imparted about the axis of maximum moment of inertia. This is the well-known "greatest moment of inertia" requirement. Moreover, the initial spin velocity flc should not be merely lower than the first natural frequencies Aiu and Air associated with the transverse vibration of the rods (as the frequency of simple harmonic excitation of the rods should be if resonance is to be prevented), but the ratios Os/AiM and fi./Ai,, are dictated by the system parameters. Of course, for very stiff rods the natural frequencies AI« and AIV may be sufficiently high that the satisfaction of criteria (40) is ensured. References