A Contribution to the stability of stiffened plates under uniform compression

Abstract

The first part of the paper presents an extensive literature review of the research done on stability of stiffened plates under uniform compression. The methods developed to predict the overall buckling load are first presented. The common methods and idealization to predict the local buckling load of stiffened plates are also discussed. The philosophies of the various techniques developed to compute the ultimate strength of the structure are then described. Finally, the optimization approaches developed for minimum weight design of the structure are presented. In the second part of the paper, theoretical formulations for the stability analysis of stiffened plates under uniform compression are presented. As a first stage, the governing differential equations for eccentric stiffening are derived. The transition to the orthotropic plate equation is shown through a simplifying assumption. It will be shown that for eccentric stiffening, three coupled differential equations need to be solved, while for concentric stiffening only Huber differential equation need to be considered. Then, an alternative energy-based approach is described for stability analysis of multi-stiffened plates under uniform compression. The structure is idealized as assembled plate and beam elements and rigidity connected at their junctions. The strain energy components for the plate and the stiffener elements are then derived in terms of the out-of- and in-plane displacement functions and sequential quadratic programming is then used to find the buckling load of the structure for given plate/stiffener geometric proportions. Efficiency of the method is compared with the finite element method. Finally, extensive results are presented to investigate the buckling behavior of multi-stiffened plates. The transition from the various buckling modes is shown by changing the plate/stiffener geometric parameters for various concentric and eccentric stiffening configurations. Influence of stiffener spacing, in-plane boundary condition on the buckling load is also highlighted. Using these results guidelines are proposed for efficient design of stiffened plates.