Numerical simulation and constructal theory applied for geometric optimization of thin perforated plates subject to elastic buckling

Abstract

Many elements in engineering are formed by thin plates. Hulls and decks of ships are examples of application. These elements can have holes that serve as inspection port, access or even to weight reduction. The presence of holes causes a redistribution of the membrane stresses in the plate, significantly altering their stability. In this paper the Bejan’s Constructal Theory was employed to discover the best geometry of thin perforated plates submitted to elastic buckling phenomenon. To study this behavior simply supported rectangular plates with a centered elliptical perforation were analyzed. The purpose was to obtain the optimal geometry which maximizes the critical buckling load. For this, the degrees of freedom H/L (ratio between width and length of the plate) and H0/L0 (ratio between the characteristic dimensions of the hole) were varied. Moreover, different values of hole volume fraction ϕ (ratio between the perforation volume and the massive plate volume) were also investigated. A computational modeling, based on the Finite Element Method (FEM), was used for assessing the plate buckling load. The results showed that Constructal Design can be employed not only in the heat transfer and fluid flow problems, but also to define the best shapes in solid mechanics problems.