Constructal Design for the ultimate buckling stress improvement of stiffened plates submitted to uniaxial compressive load

Several engineering structures used in civil, aeronautical and, mainly, naval and offshore industries consist of steel stiffened panels formed by beams welded into thin plates. These beams are called stiffeners, being arranged longitudinally and/or transversely aiming to increase the mechanical strength of the plate. So, it is desirable to obtain an optimal geometric configuration for these structures which maximizes its ultimate buckling stress. In this context, it has been used the Constructal Design Method associated with the Exhaustive Search technique and the Finite Element Method (by ANSYS software) in a geometric optimization study of plates with stiffeners subjected to elasto-plastic buckling. Initially, it was adopted a simply supported thin plate without stiffeners (called reference plate), using its ultimate buckling stress as a reference value for the study. After that, part of its volume has been transformed into stiffeners, which were incorporated into the plate. For this, the volume fraction (phi) parameter, which represents the ratio of the volume of stiffeners (V-s) and the total volume of the structural element plate/stiffeners (V-T), has been adopted, without varying the final volume of the plate. Moreover, the number of longitudinal (N-ls) and transverse (N-ts) stiffeners, as well as the ratio between the height of the stiffener and its thickness (h(s)/t(s)), were considered as degrees of freedom. The study considered two total steel volume values V-T1 = 0.040 m(3) and V-T2 = 0.028 m(3 ) The results indicated that the variation of the geometrical configuration significantly affects the mechanical behavior of stiffened panels under buckling. Therefore, it was possible to determine the optimum geometry that leads to a maximized ultimate buckling stress, near the yield strength of the material. The stiffened plates with volume V-T1 did not present relevant improvements if compared with the reference plate, since the optimal geometry achieved an improvement of 7.38% concerning the ultimate buckling stress of the reference plate. On the other hand, the study of the plates with volume V-T2 showed significant improvements in the value of the ultimate buckling stress, so that the optimized geometric configuration among all analyzed geometries reached an improvement of 88.50% when compared with the ultimate buckling stress of the reference plate.