Numerical buckling analysis of thin steel plates with centered hexagonal perforation through constructal design method

Slenderness is a remarkable geometrical characteristic of thin steel plates. When a slender plate is subjected to an axial compression loading, a mechanical behavior called buckling can occur, causing an out-of-plane displacement. This instability phenomenon can be divided into elastic buckling (linear) and elasto-plastic buckling (nonlinear), depending on dimensional, constructive, or operational aspects. Moreover, in several practical situations, it is necessary to provide holes on thin steel plates, causing stress redistribution and changes in its buckling behavior. The present work purposes a buckling study in square and rectangular plates, simply supported, with two different centered perforations types: longitudinal hexagonal and transverse hexagonal. Numerical simulation, using the ANSYS((R)) software, was employed to determine the critical buckling load and the ultimate buckling load of the plates. The constructal design method was applied, allowing evaluating the variation effect of the degree of freedom H-0/L-0 (being H-0 the width and L-0 the length of the perforation) on the plate's mechanical buckling behavior. The hole volume fraction (phi) was another considered parameter, corresponding to cutouts of 10%, 15%, 20%, and 25% of the total plate volume. The results showed the direct influence of the H-0/L-0 ratio on the buckling type, allowing the definition of a buckling stress limit curve for each cutout type and hole volume fraction. Besides, the constructal design method, associated with the exhaustive search technique, enabled to define the optimized geometric configuration for each hole type that conducted the plate to a maximized mechanical performance.