Constructal Design

Numerical ANALYSIS of PERFORATED steel plates subjected to ELASTIC AND ELASTO-PLASTIC buckling BY MEANS THE coNSTRUCTAL DESIGN METHOD

Caio Cesar Cardoso da Silva

Elizaldo Domingues dos Santos

Mauro de Vasconcellos Real

Liércio André Isoldi

Universidade Federal do Rio Grande (FURG) – Programa de Pós-Graduação em Engenharia Oceânica (PPGEO)

Itália Ave. km 8, 96203-900, Rio Grande, Rio Grande do Sul, Brazil.

[e-mail]        

[e-mail]  

[e-mail]

[e-mail]

Daniel Helbig

Luiz Alberto Oliveira Rocha

Universidade Federal do Rio Grande do Sul – Programa de Pós-Graduação em Engenharia Mecânica

Sarmento Leite St. nº 425, 90050-170, Porto Alegre, Rio Grande do Sul, Brazil.

[e-mail]

[e-mail]

Abstract. Steel plates are structural elements widely employed in several mechanical engineering applications. It is well known that if an axial compressive load is imposed to these plates an undesired instability phenomenon can occur: buckling. At a certain load magnitude a limit stress is reached and the plate suffers lateral displacements (out of plane) indicating the buckling occurrence. In plates an elastic buckling or an elasto-plastic 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 perforations in the plate buckling. To do so, using the ANSYS® software, which is based on the finite element method (FEM), computational models were developed to tackle with the elastic (linear) and elasto-plastic (nonlinear) plate buckling. Square and rectangular thin steel plates, simply supported along its four edges, with a centered perforation, were analyzed, being the objective function to maximize the buckling limit stress, avoiding the plate buckling occurrence. The square and rectangular plates have H/L (ratio between width and length of the plate) of 1.0 and 0.5, respectively. A value of 0.15 for the cutout volume fraction (ratio between the cutout volume and the total plate volume) was considered for different types of cutout: elliptical, rectangular, hexagonal and diamond. The cutout shape variations were promoted 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 to define a buckling stress limit curve for each perforation type. In addition, it was observed that the Constructal Design method conducts to the definition of optimal geometries and dimensions of the cutouts.

Keywords: Buckling, Constructal Design, ANSYS®, Finite Element Method, Numerical Simulation.

1. INTRODUCTION

In several practical applications it is necessary to provide cutouts in plate structures to allow access for services or inspection and even aesthetics purposes, as well as to reduce the structure self-weight. The presence of a hole in a plate panel changes the stress distribution within the member, alters its elastic buckling and post-buckling characteristics and generally reduces its ultimate load carrying capacity. The performance of a plate containing an opening is influenced by the nature of the applied stress (e.g. compressive, tensile, shear, etc.), besides the type, size and location of the hole (Narayanan, 1984).

There are several works dedicated to the study of the elastic (linear) buckling (e.g.: El-Sawy and Nazmy, 2001; El-Sawy and Martini, 2007; Rocha et al., 2012; Rocha et al., 2013; Isoldi et al., 2013) as well as to the analysis of the elasto-plastic buckling (e.g.: Paik et al., 2001; El-Sawy et al., 2004; Kumar et al., 2007; Helbig et al., 2013; Helbig et al., 2014). Considering the publications above one can note the fundamental importance of the study and understanding of the mechanical behavior of perforated steel plates subjected to buckling in structural engineering, especially if the goal is to improve the performance of these structural elements. Therefore, the main objective of this work is numerically investigate the influence of the  hole type and shape in the behavior of buckling perforated steel plates, in order to improve its mechanical behavior. The Constructal Design method is used in order to guarantee an adequate and consistent comparison among the studied cases. The objective function is to maximize the compressive stress, avoiding the plate buckling occurrence. To do so, it was considered a hole volume fraction (ratio between the hole and the volume of the total volume of the plate) of 0.15, for different cutout types: elliptical, rectangular, diamond, longitudinal hexagonal and transversal hexagonal. The shape of these perforations can vary by means the ratio H0/L0, which relates the characteristics dimensions of each hole. Besides, two ratios between the plate width (H) and the plate length (L) were studied: H/L = 0.5 and H/L = 1.0, with a plate thickness (t) of 10 mm and keeping constant the total volume of the plate. Besides, in all studied cases, the plate is simply supported along its four edges and has a centered perforation. A constraint which limits a minimal distance of 100 mm from the plate edges to the hole edges is also employed.

1. BUCKLING AND POSTBUCKLING OF PLATES

Buckling is an instability phenomenon that can occur if a slender and thin-walled plate (plane or curved) is subjected to axial compression. At a certain critical load, the plate will suddenly buckle in the out-of-plane transverse direction. However, plate buckling has a post-critical load-carrying capacity that enables for additional loading after elastic buckling has occurred. A plate is in that sense inner statically indeterminate, which makes the collapse of the plate not coming when elastic buckling occurs, but instead later, at a higher loading level reached in the elasto-plastic buckling. This is taken into consideration in the ultimate limit state design of plates because the elastic buckling does not restrict the load carrying capacity to the critical buckling stress, instead the maximum capacity consists of the two parts: the buckling load added to the additional post-critical load (Åkesson, 2007). In other words, when a load level called critical (Pcr) is achieved the plate is subjected to the elastic buckling, however the ultimate loading capacity (Pu) of plates is not restricted to the occurrence of elastic buckling.