The Effect of Opening on Elastic Buckling of Plates Subjected to Unidirectional Compression Load

This paper has investigated the effect of hole shape, hole size and hole position on elastic buckling of square perforated plates by using the finite element method. According to the effect law of these three geometric factors on buckling bearing capacity, buckling coefficient was obtained by data fitting. The results show that: The plate with circular perforation has the greatest buckling bearing capacity of the three perforation shape plate; When the center perforations have the same area, the relationship between buckling coefficient and perforation size is exponential for the plate with circular hole or square hole, the relationship between buckling coefficient and perforation size is biquadratic for the plate with triangular hole and the greater the perforation size is, the less the buckling bearing capacity will be; For the plate with uniform circular perforation size, The relationship of buckling coefficient and the spacing between perforation center and structure center is quadratic and the greater the spacing is, the less the buckling bearing capacity will be. The results in this paper provide reference for perforation design of plate. Introduction The plates are often used as the main components of structures such as aircraft wing, ship decks and hulls, platforms on oil rigs, and so on. Take account of access for inspection, maintenance, or simply weight loss, openings in such plates may be required. However, the presence of such openings in plate elements leads to change in stress distribution within the member and variations in buckling characteristics of the plate element [1] In the case that the plates are subjected to axial compression load, the stress and deformation around the opening increases and the buckling bearing capacity decreases, which make them prone to instability or buckling. The impact of geometric imperfection factors on the structural buckling bearing capacity is relatively complicated, it’s too difficult to accurately calculate buckling load by analytic method. With the development of Numerical Simulation Technology, scholars lay emphasis on solving buckling problem of perforated plate by Finite Element Method. Maiorana et al. [2] analyzed linear buckling of plates with circular and rectangular perforations in various positions subjected to axial compression and bending moment by FEM. EI-Sawy et al.[4] analyzed the effect of the plates aspect ratio, the stress ratio between the applied stresses in the yand x-directions, the circular perforation size and location on the elastic buckling stresses of a bi-axially loaded perforated rectangular plate. V.V. Degtyarev et al. [6] investigated the effect of perforations on the critical elastic buckling load and developed design formulas for predicting critical elastic buckling stress based on reduction coefficient approach and equivalent thickness approach using multiple nonlinear regression analysis of FEM results. Because of the limitation of Numerical Simulation Technology such as control parameters, mesh density and so on, the calculation results will appear error. Therefore, the results need to compared with the test result which can verify its accuracy. M. Shariati et al. [7] investigated buckling and post-buckling of steel thin-walled semi-spherical shells under different loadings, both experimentally and numerically. Rahmans et al. [8] studied the buckling load of plate with crack subjected to compression load, in which the effect of crack length, orientation, thickness of plate and aspect ratio were considered, both experimentally and numerically. Kabir M.Z. et al. [9] analyzed the effect of opening orientation and opening size on buckling bearing capacity. Applied Mechanics and Materials Submitted: 2014-05-14 ISSN: 1662-7482, Vol. 574, pp 127-132 Accepted: 2014-05-15 doi:10.4028/www.scientific.net/AMM.574.127 Online: 2014-07-18 © 2014 Trans Tech Publications, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69874386, Pennsylvania State University, University Park, USA-20/09/16,21:16:06) Literature search revealed minimal documentation of empirical equations incorporated with comprehensive geometric imperfection factors. In this paper, elastic buckling of square perforated plates by using the finite element method were investigated, in which the effects of perforation shape, perforation size and perforation position were considered. Empirical equations that relevant to these geometric imperfection factors by data fitting of buckling coefficient were attained. The aim is to give some practical indications on the best hole shape, hole size and hole position of the perforation in plates, when axial compression acts on the plate. Theory Basis For the square plate whose side length is a and thickness is t, it subjects to uniform load Pcr under the boundary conditions shown in Fig. 1. Buckling load of simply supported plates subjected to uniform compression is analytically determined by solving the well known Eq. (1). Fig. 1. The boundary condition and load of square plate 2 4 cr 2 0 w D w P x ∂ ∇ + = ∂ . (1) With the following boundary conditions When / 2, / 2 x a a = − , 0 w = 2 2 / 0 w x ∂ ∂ = When / 2, / 2 y a a = − , 0 w = 2 2 / 0 w y ∂ ∂ = The deflect equation has the form 1 1 sin sin 2 2 mn m n m x m y w A a a π π ∞ ∞