Post-Buckling Behavior of Rectangular Plate under Shear

et al. 2015

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Recently, high strength steel is used increasingly for plates which constitute the frame structures of vehicles. Since these plates become thinner, the buckling on the plates has been recognized as an important issue for automotive industries. For this issue, various methods have been proposed and are currently in practical use. In this paper, regarding bending buckling of box beams which have the rectangular cross-section with four thin plates, we try to derive the buckling stress based on the energy method. The main target of box beams has the aspect ratio of cross-section accompanied with compression buckling in the compressed plate. The bending buckling stress of box beams is derived in two cases of prescribed buckling modes. In first case, it is supposed that the buckling occurs at three sides subjected to compression and bending stresses. In second case, it is supposed that the buckling occurs only at the compression side and forced displacement at two adjacent plates is induced by the compression buckling. And the obtained results of accuracy are compared with the results of buckling eigenvalue analysis using the finite element method (FEM). The results of buckling stress in first case are observed a large difference from FEM results. The reason for this difference is that the buckling deformation assumed for the two surfaces subjected to the bending is much different from FEM results. In second case, the sufficiently practical expression as compared with the FEM results is derived for the buckling stress. So that, the approach shown in this paper is thought to have validity.

“…, 2004, , 2006Karman , 2011, 2012a, 2012b, 2013a, 2013b, 2014a, 2014b4 1 AISI/CARS 2002, 2002, 2014a, 2014b , 2013a, 2014b 1966, Timoshenko, 1961, Ziemian, 2010 ˆc r C e k …”

mentioning

confidence: 99%

Bending buckling of box beam by energy method

et al. 2015

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Elastic flattening of box beams under bending moment (The Brazier effect of rectangular tubes)

et al. 2018

In this study, a formula describing on the flattening phenomenon when a bending moment acts on a box beam was derived considering the cross-sectional deformation. Calculation results obtained using the derived formula were then compared with results acquired using the finite element method (FEM). The case of a bending moment acting on a box beam composed of four thin plates that permits cross-sectional deformation along the longitudinal direction was investigated with the following assumptions: the boundaries of these plates is are simply supported, an equally distributed load acts on these plates, and the width along the neutral line of the plates is retained after deformation. Furthermore, on the basis of the coupling of the deflections of adjacent plates and the thin plate theory, the moment of inertia of cross section was obtained as a function of the curvature of the box beam. A formula relating the bending moment to the curvature is was then derived. Calculation results from this derived formula were compared with FEM results modeling only the cross section using generalized plane strain elements. For box beams with a square cross section, the maximum moments and curvatures calculated from the derived formula were within 5% of the FEM results. This indicates that it is important to consider the reduction in the cross section that accompanies the bending of the plates. Regarding general box beams with a rectangular cross section, the influence of the aspect ratio of the cross section was found to be considerably larger in the FEM results than in the derived formula. The reason for this difference may be that plates do not satisfy the abovementioned assumptions regarding the boundary and load conditions of the plates; however, confirming this remains a task for future work.

Estimation of stresses and displacements of a rectangular plate after compression buckling based on effective width theory by Karman

et al. 2019

In this paper, the equations of in-plane and out-of-plane displacements, in-plane stress distributions, and Mises stress of the rectangular plate after buckling are composed using the well-known buckling deflection shape, based on the plane stress state and the effective width theory by Karman. Equations of in-plane displacement and stress distributions are obtained from the large deflection theory, and the maximum value of out-of-plane displacement is derived by use of Karman's theory. The composed equations are compared with results of the finite element method (FEM) with shell elements. The boundary condition used in FEM is that the in-plane displacement of both long side edges is unconstrained. As a result, the following conclusions were obtained. Among the composed equations, the out-of-plane displacement amplitude and the in-plane compressive displacement are close enough to FEM computation results. Three in-plane stresses near the both long sides show slightly different distributions between composed equations and FEM results. The normal stress distribution of the FEM result fluctuates near the both long side edges, although that distribution by the composed equation indicates the intermediate value of the FEM result, and it was found that the maximum compressive stress appearing at both sides is lower than the one by the FEM result. On the other hand, the Mises stress distribution and its maximum value were close to the FEM results. As factors of these differences, it is considered that the in-plane deflection of the both sides and the out-of-plane displacement shape at larger load are different from the shape used in this paper.