Search

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. [ABSTRACT FROM AUTHOR]

Buckling of a column under pre-load restraint has been found to differ from the conventional bifurcation problems and thus requires better understanding. To this end, a simple model consisting of two collinear rigid bars connected by a rotational spring, resting on a smooth surface, loaded by an axial force and restrained by a constant force at the common joint is investigated. The energy method is adopted to establish the equilibrium and stability conditions. The post-buckling response of the simple system indicates that the load-restrained buckling problem is a snap-through problem. The minimum possible buckling force and the buckling force based on the Maxwell construction are found to increase with the restraining force, and can be approximated by power-law functions. It is further shown that an energy barrier exists for the snap-through to occur and the buckling force depends on the perturbation energy. Sensitivity of this system to initial geometric imperfections is also investigated, and an energy barrier is also found to exist for the buckling of systems with imperfection amplitudes smaller than a certain critical value. The characteristic imperfection amplitude depends on the restraining force and, interestingly, transforms the snap-through problem into an eigenvalue problem identical to the conventional one, i.e., the one without imperfection and restraining force. [ABSTRACT FROM AUTHOR]

Buckling of structures under lateral load restraint has been found to differ from the conventional bifurcation problems and cannot be handled with conventional analysis. Towards a better understanding of this type of unconventional buckling problems, this work investigates the upheaval buckling of an elastica resting on a smooth surface and restrained by a lateral constant force. Analytical solutions for the Mode-1 and Mode-2 post-buckling responses and configurations of the elastica are established. Stability of the post-buckling configurations under force-control are investigated via the energy method. An energy barrier is found to exist and the buckling load depends on the restraining force and perturbation energy. The imperfection sensitivity of the system is different from the conventional buckling ones, and a characteristic imperfection is found to exist that can transform a snap-through instability into a bifurcation buckling. As a first attempt to address the problem of flange wrinkling under a constant blank-holding force during the cup-drawing process, the fundamental solutions are extended to study the wrinkling of a shrinking elastic annulus under a constant lateral restraining force. The post-wrinkling responses are established and an energy barrier is found to exist for each wrinkling mode. A characteristic imperfection is also found to exist for each mode, which eliminates the energy barrier and enables bifurcation wrinkling. The linear relationship between the critical restraining force that prevents the wrinkling of the elastic annulus and the imperfection amplitude is established, which is also verified by numerical simulations. This study contributes to a better understanding of load-restrained buckling problems and is expected to shed light on the elastoplastic buckling of plates and shells under lateral load restraints in general, and on the wrinkling of a thin sheet during cup-drawing in particular. [ABSTRACT FROM AUTHOR]