Numerical evaluation of the effect of type and shape of perforations on the buckling of thin steel plates by means of the constructal design method

Abstract

Thin steel plates-with or without cutouts-are structural components largely used in several engineering applications as buildings, bridges, ships, airplanes and automobiles. However, if an axial compressive load is imposed to these panels an undesired instability phenomenon can occur: buckling. At a certain load magnitude the limit stress is reached and the plate suffers lateral displacements (out of plane) indicating the buckling occurrence. In plates an elastic buckling or an elastoplastic buckling can occur, depending on dimensional, constructive or operational aspects. Therefore, in the present work, the Constructal Design method was adopted to investigate the influence of the type and shape of the cutout in the plate buckling. To do so, by means the Finite Element Method (FEM), computational models were developed to simulate the elastic (linear) and elasto-plastic (nonlinear) plate buckling. Square and rectangular thin steel plates, simply supported in its four edges, with a centered cutout, were analyzed, being the objective function to maximize the buckling limit stress, avoiding the plate buckling occurrence. The square and rectangular plates have a ratio H/L (ratio between height and length of the plate) of 0.5 and 1.0, respectively. A value of 0.2 for the cutout volume fraction (ratio between the cutout volume and the total plate volume) was adopted for different types of cutout: diamond, longitudinal hexagonal, transversal hexagonal, elliptical, and rectangular. The cutout shape variations were produced by the H0/L0 degree of freedom (which relates the characteristic dimensions of the cutout). The results showed that the cutout shape variation has a fundamental influence in the plate buckling behavior, determining if the buckling is elastic or elasto-plastic, allowing the definition of a buckling stress limit curve for each studied cutout type. In addition, it was observed that the Constructal Design method conduct to the definition of optimal geometries, reaching buckling stress limit improvements around 100%.

Study About Buckling Phenomenon in Perforated Thin Steel Plates Employing Computational Modeling and Constructal Design Method

“…Thus, giving sequence to Helbig et al (2014) and Lorenzini et al (2016aLorenzini et al ( , 2016b, the main purpose of the present work is to investigate the influence of the size, shape and type of the opening in the elastic and elasto-plastic buckling behavior of a thin steel plate. To do so, computational models developed in the software ANSYS (which is based on the finite element method) were used to numerically predict the elastic critical stress and the elasto-plastic ultimate stress.…”

“…Maiorana et al (2008) and Maiorana et al (2009) focused on the linear and nonlinear finite element analyses of perforated plates subjected to localized symmetrical load. More recently, in Helbig et al (2014) and in Lorenzini et al (2016aLorenzini et al ( , 2016b) the elastic and elastoplastic buckling of perforated plates were analyzed, applying the computational modeling allied to the constructal design method. These last authors investigated the influence of shape and type of centered cutouts in the plate buckling, defining a stress limit curve to avoid the buckling occurrence in each studied case.…”

“…Thereby, combining the elastic and the elasto-plastic behaviors it was possible to define limit stress curves that should not be exceeded to avoid the buckling phenomenon on the studied plates. It is also important to mention that here are considered additional hole sizes and hole types from those used in Helbig et al (2014) and Lorenzini et al (2016aLorenzini et al ( , 2016b.…”

“…Currently only few works employing the constructal design method in structural analysis can be found in literature, however the results presented in these publications show the effectiveness and applicability of the constructal design also in the solid mechanics area. The main works where the constructal design method is applied in the mechanic of materials problems are: Lorente and Bejan (2002), , Rocha et al (2012), Rocha et al (2013a), Helbig et al (2014), and Lorenzini et al (2016aLorenzini et al ( , 2016b.…”

Modelling the Dynamics and Secondary Deformation Behaviour of the Strip with Local Waves in Coiling Process

“…At present, researches on ridge buckles as well as methods for calculating coiling stress and ridge-buckle value are all based on the theory of elasticity. Melfo, Zhu and other scholars have studied the microstructural and temperature features of hot strips that may lead to ridgebuckle defects in thin-rolled steel strip [3][4][5]; Bai supposes that waves are present before coiling and calculates the amount of ridge buckles after the coiling of local waves [6]; Ovesy et al and Lorenzini et al researched the buckling and post-buckling behaviour of moderately thick plates using an exact finite strip [7,8]. In the actual coiling process, the strip exhibits local plastic deformation and there is metal plastic flow if the degree of ridge buckle achieves a certain amount [9].…”