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

Abstract

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 ® 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 (ϕ) 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.

Lateral Deflection Behavior of Perforated Steel Plates: Experimental and Numerical Approaches

“…To determine the critical buckling load and the ultimate buckling load of the plates, research has employed numerical simulation. The results showed the direct influence of the perforation ratio H o /L o (with H o being the width and L o the length of the perforation) [5]. The axial buckling of perforated plates reinforced with strips and middle tubes has been reported.…”

Computational Modeling and Constructal Design Theory Applied to the Geometric Optimization of Thin Steel Plates with Stiffeners Subjected to Uniform Transverse Load

“…Nowadays, there are few publications on this topic, but it is possible to cite Bejan and Lorente [33], Bejan et al [54], Lorente et al [55], and Isoldi et al [56] where, by means of analogies among heat transfer, fluid mechanics, and mechanics of materials, it was conceptually proven that the CDM is also applicable in structural engineering problems. There are also works dedicated to investigating the influence of geometric configurations of plates submitted to elastic or elasto-plastic buckling: Isoldi et al [57], Rocha et al [58], Helbig et al [59], Lorenzini et al [60], Helbig et al [61], Helbig et al [62], Da Silva et al [63], and Lima et al [64,65]; while in Cunha et al [66], De Queiroz et al [13], Amaral et al [67], and Pinto et al [68] the influence of geometry of stiffened plates was analyzed when submitted to bending. Finally, Mardanpour et al [69] and Izadpanahi et al [70] applied the CDM in a study about aircraft structures.…”

Constructal design associated with genetic algorithm to minimize the maximum deflection of thin stiffened steel plates

“…To theoretically prove the CD applicability for structural engineering problems, analogies among heat transfer, fluid mechanics, and mechanics of materials were presented in the studies of Bejan and Lorente, 24 Bejan et al, 25 Lorente et al, 26 and Isoldi et al 27 Other approaches that can be considered as related with problems concerned with mechanics of materials are the ones dedicated to the application of CD for optimization of iron and steel manufacturing process. [28][29][30][31] In addition, one can find studies employing CD exclusively to structural engineering problems for the geometric evaluation of perforated steel plates subjected to buckling [32][33][34][35][36][37][38] ; stiffened steel plates subjected to buckling 14,39 ; stiffened steel plates subjected to bending [40][41][42][43]54 ; and aircraft structures. 44,45 Therefore, the present study, by employing an approach that associates the CD method and GA, with the aid of FEM, seeks to find the optimized geometrical configuration that conducts the superior mechanical behavior of simply supported stiffened plates under transverse distributed loading, having the minimization of its maximum out-of-plane displacement as objective function.…”

“…To theoretically prove the CD applicability for structural engineering problems, analogies among heat transfer, fluid mechanics, and mechanics of materials were presented in the studies of Bejan and Lorente, 24 Bejan et al, 25 Lorente et al, 26 and Isoldi et al 27 Other approaches that can be considered as related with problems concerned with mechanics of materials are the ones dedicated to the application of CD for optimization of iron and steel manufacturing process 28‐31 . In addition, one can find studies employing CD exclusively to structural engineering problems for the geometric evaluation of perforated steel plates subjected to buckling 32‐38 ; stiffened steel plates subjected to buckling 14 39 ; stiffened steel plates subjected to bending 40‐43 54 ; and aircraft structures 44,45 …”