Tension buckling of plate having a hole

Generally, it is believed that buckling of plates never arises under tensile load. However, when a plate has a hole, compression stresses appear locally near the hole under a tensile load, and the compression stress may cause local buckling—so-called tension buckling—of the plate. In this paper, some results of numerical analysis on the tension buckling are presented, and basic behaviour on the tension buckling is discussed.     

Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes

The Finite Element Method (FEM) has been employed to determine the elastic buckling load of uniaxially loaded rectangular perforated plates with length a and width b. Plates with simply supported edges in the out-of-plane direction and subjected to uniaxial end compression in their longitudinal direction are considered. Integer plate aspect ratios, a/b=1, 2, 3 and 4, have been chosen to assess the effect of aspect ratio on the plate buckling load. Two perforation shapes of different sizes are considered; circular, and rectangular with curved corners. The rectangular perforation is oriented such that either its long or its short side is parallel to the longitudinal direction of the plate. The center of perforation was chosen at different locations of the plate. The study shows that the buckling load of a rectangular perforated plate that could be divided into equal square panels is not the same as that of the square panel that contains the perforation when treated as a separate square plate. For rectangular plates, the study recommends not to have the center of a circular hole placed in a critical zone defined by the end half of the outer square panel, to try always to put the hole in an interior panel of the plate, and to have the distance between the edge of a circular hole and the nearest unloaded edge of the plate not less than 0.1b. The study concludes also that the use of a rectangular hole, with curved corners, with its short dimension positioned along the longitudinal direction of the plate is a better option than using a circular hole, from the plate stability point of view.     

钢桥塔内部通行孔选型及有限元分析

钢桥塔内部通行孔对受压壁板力学性能产生不利影响。基于有限元分析,研究不同孔洞形状和孔洞大小对单轴受压开孔板弹性应力分布、弹性屈曲和弹塑性屈曲三方面性能的影响。结果表明:除圆孔外的其他各种孔型板,孔洞形状对开孔板弹性屈曲应力和弹塑性极限强度影响不大,但其对应力集中系数影响较大,其中,圆角矩形孔、长圆形孔和椭圆形孔板的应力集中系数较低。实际情况中,圆角矩形孔和长圆形孔板是钢桥塔内部通行孔的首选。但当孔径较大时,应采取孔洞补强措施来保证大孔径板件的力学性能满足设计要求。     

Vibration, buckling and parametric instability behaviour of plates with centrally located cutouts subjected to in-plane edge loading (Tension or compression)

The vibration, buckling and parameterc instability behaviour of a plate with internal opening subjected to in-plane compressive or tensile periodic edge loading are studied. Different shapes and sizes of the cutout are considered. Compression and tension buckling results are discussed. The vibration analysis for this problem shows that for certain parameters of tensile loading and the opening, the frequency of the plate initially rises' with the load, but then begins to decrease with increasing tension showing the onset of tension buckling. Dynamic instability behaviour of the plate under compressive and tensile loading shows that the instability regions are affected by the size, shape of the opening and the loading parameters. Instability behaviour due to all the parameters are discussed.     

Finite element analysis of linear plates buckling under in-plane patch loading

The elastic buckling load is physically important in design because it is actually the critical step in the changing plate configuration that will eventually lead to complete failure. The present work investigates the problem of linear buckling of simply supported thin plates subjected to patch compression. In order to satisfy the boundary conditions in a rigorous way, the authors chose the finite element method using the exact stress distribution throughout the plate.In the present paper, the stability problem treated using the total energy is briefly outlined. The plate modelling is made by means of an eight noded rectangular element and a reduction of variable strategy is applied to estimate the number of degrees of freedom leading to little or no loss in seeking solution accuracy.The buckling coefficient is determined for different load cases applied to a range of plate with various edge ratios. The achieved results are summarised through different graphs representing variation of the buckling coefficient against the plate ratio for each load case treated. A comparison with previous works is made. Finally, it is shown that the resolution of the plate buckling problem using true stress distribution with the finite element method leads to a good agreement with results previously obtained by means of analytical methods using an exact stress distribution.     

Buckling analysis of stepped plates using modified buckling mode shapes

A new approximate procedure for buckling analysis of simply supported rectangular stepped or perforated plates subjected to uniform edge stresses is formulated. The procedure uses energy method based on modified buckling mode shapes. The change of thickness within a plate is characterized by introducing a stepping index. It is shown that the buckling (vibrational) mode shapes of stepped plates can be predicted by linear combination of various mode shapes of the equivalent flat plates. These buckling mode shapes, in turn, are incorporated to evaluate buckling loads of stepped plates. Some case studies are carried out to demonstrate the accuracy and the versatility of the proposed method by comparing them to the results presented by other researchers.     

国际期刊导读

受压或受弯开孔薄板的弹性屈曲性能 摘要：开发、论证并总结了一组闭合公式,可以估算在弯矩或压力作用下,板的单个或多个开孔对其临界弹性屈曲应力的影响。公式适用于四边简支和三边简支的板（这在设计中又称为加劲板和非加劲板）。由于有限壳单元特征值屈曲分析需要运用商业有限元程序,而这些程序又不是专为结构分析而开发的,不能很方便地用于工程设计,所以可以采用这些公式作为这种屈曲分析方法的简化替代。     

Buckling analysis of skew laminate plates subjected to uniaxial inplane loads

Elastic stability of skew composite laminate plates subjected to uniaxial inplane compressive forces has been studied. The critical buckling loads of the skew laminate plates are carried out by the bifurication buckling analysis implemented in finite element program ABAQUS. The effects of skew angles, laminate layups, plate aspect ratios, plate thicknesses, central circular cutouts, and edge conditions on the buckling resistance of skew composite laminate plates are presented.     

Non-linear analysis of perforated steel plates subjected to localised symmetrical load

Although the literature contains a number of studies which have been developed to describe the non-linear behaviour of ordinary plates, few works are available on perforated plates, and studies on non-linear behaviour of perforated plates under localised symmetrical load are not studied in depth. The aim of this paper is to provide some insights into the elasto-plastic behaviour of plate girder web panels with circular holes under localised symmetrical load.Numerical analyses of square and rectangular perforated plates with centred and eccentric holes were developed. Results provide new insights into post-critical mechanisms in perforated plates subjected to localised loads when the length of the symmetrical compressive load, hole diameter and steel yield limit vary. An increase in the critical slenderness of the plate (a value at which transition from elastic to plastic collapse occurs) and a corresponding reduction in the elastic critical load occur when the dimensions of the hole increase. A further increase in the critical slenderness occurs when the length of the localised load is reduced. High-performance steel may be subject to buckling with a lower possibility of post-critical mechanisms: a reduction in critical slenderness occurs when the steel grade increases. Lastly, numerical analyses of slender and thick perforated plates were developed and their results compared.     

Elastic stability of bi-axially loaded rectangular plates with a single circular hole

The finite-element method has been employed to determine the elastic buckling stresses of a bi-axially loaded perforated rectangular plate with dimensions a and b in the x- and y-directions, respectively. The considered perforation is a single circular hole whose center is located along the longitudinal axis of the plate. The considered plate has simply supported edges in the out-of-plane direction and is subjected to bi-axial uniformly distributed end loads (compressive load σ_x in the x-direction, and compressive or tensile load σ_y in the y-direction). Parameters considered in the study are the plate's aspect ratio a/b, the stress ratio ξ between the applied stresses in the y- and x-directions (ξ=σ_y/σ_x), the circular hole size d and location e_x.The study shows that, in most of the considered cases, the bigger the hole size d, the lesser the plate stability and the lesser the buckling stresses. It also shows that the plate aspect ratios, a/b, between 0.6 and 1.2 should be avoided for plates with large holes and negative ξ, due to the large reduction in the buckling stresses. The hole location should also be selected to be away from the loaded edge of the plate as much as possible (better to have e_x/b>1.0) to increase the buckling stresses and improve stability. The study demonstrates also that the increase in tension in the y-direction in bi-axially loaded plate with large hole (d/b>0.4) reduces its stability. This is in contrary to the expected increase in the stability due to the increase in tension which can be seen clearly in the cases of solid plates and plates with small holes.     

Imperfections in steel girder webs with and without perforations under patch loading

In this paper, the problem of stability of web plates with imperfections, subjected to patch load, is studied. The aim is to give some insights about the best way to take into account real imperfections in non-linear stability analyses of plates with and without perforations. In this context, the study is developed on the basis of the measured imperfections or numerically deriving the deformed model (theoretical imperfections). The influence of the patch load length, out-of-plane imperfection amplitude, dimension and position of the hole on stability behaviour and buckling strength are studied comparing some theoretical deformed configurations corresponding to different modal shapes. The results obtained with a three-dimensional model of the whole real beam with stiffeners, with experimentally measured imperfections, and each corresponding single web panel are compared and discussed obtaining some insights about the accuracy of the simplified (and conservative) model of the single panel.The main insights of this work are as follows. The deformed shape, corresponding to the first buckling mode, can be assumed as the initial configuration of the panels with and without holes to study post-critical behaviour until ultimate condition. The shape of the imperfection does not severely change the critical buckling stress. A longer patch load reduces the ultimate stress in the panel. An initial imperfection amplitude of less than 1% of the height of the panel does not reduce the ultimate load by more than about 5%.     

Elastic stability of uniformly compressed plates perforated in triangular patterns

Critical elastic buckling load of uniformly compressed isotropic plates perforated in equilateral triangular patterns was investigated using FEM. Stiffened and unstiffened square and rectangular elements with wide ranges of hole diameter-to-spacing ratio and plate slenderness were studied. The effect of perforations on the critical elastic buckling load was determined. Design formulas for predicting critical elastic buckling stress based on reduction coefficient approach and equivalent thickness approach were developed using multiple nonlinear regression analysis of FEM results. The obtained critical elastic buckling stress reductions and developed formulas were verified by comparison with results available in literature and with an extensive database of FEM results.     

Strengthening of perforated plates under uniaxial compression: Buckling analysis

This paper focuses on the cutout-strengthening of perforated steel plates subjected to uniaxial compressive loads. The square plates considered each has a centrally placed circular hole and four simply supported edges in the out-of-plane direction. Four types of stiffeners named ringed stiffener (RS), flat stiffener (FS), longitudinal stiffener (LS) and transverse stiffener (TS) are mainly discussed. The finite element method (FEM) has been employed to analyse the elastic and elasto-plastic buckling behaviors of strengthened and unstrengthened perforated plates. The results show that the strengthened perforated plates have higher buckling strengths than those of the unstrengthened ones, while the elevations in elastic buckling stress and elasto-plastic ultimate strength are closely related to stiffener types (i.e., RS, FS, LS and TS) as well as plate geometric parameters (i.e., a plate slenderness ratio and a hole diameter ratio). Furthermore, comparisons of strengthening efficiency considering the variations of buckling stress with stiffener weight are carried out, and recommendations on the most efficient cutout-strengthening methods for the uniaxially compressed perforated square plates with centric circular holes are proposed.     

受压波纹板组局部相关屈曲特性研究

拱型波纹钢屋盖结构是一种典型的冷弯薄壁结构,其波纹截面板组的宽厚比远远超过有关规范宽厚比限值的上限要求,结构的极限承载能力既取决于其整体稳定承载能力也取决于其局部相关屈曲承载能力。本文根据拱型波纹钢屋盖结构的成型特点和受力特性,建立了波纹槽形截面板组局部相关屈曲分析的有限元模型,对不同宽厚比的受压波纹槽形截面板组的局部相关屈曲特性进行了理论计算,并与同形状同尺寸平板槽形截面板组的屈曲特性进行了比较分析。研究结果表明,如同平板板组一样,波纹板组也可能发生局部相关屈曲,但其板组屈曲半波长要受制于小波纹的几何尺寸,即屈曲半波应位于波形构造的波节点之间或波峰、波谷之间,而平板槽形截面板组的屈曲波长则可以自由调节,这点与平板板组的屈曲特性存在明显的差异。并且波纹的存在对板组屈曲性能有显著提高。理论研究与相应的试验研究符合很好。     

Finite element analysis of local buckling behavior of steel plates in concrete-filled double steel plate composite shear walls

采用ABAQUS有限元软件对双钢板-混凝土组合剪力墙中外包钢板的局部屈曲行为进行了有限元模拟,分析外包钢板在轴压作用下的局部屈曲和屈曲后的受力性能。共开展了15个模型的有限元分析,模型的变化参数包括钢板的宽厚比和对拉钢筋的列数。分析结果表明：对于列间距和行间距相同的对拉钢筋布置方案,钢板局部屈曲始终发生在相邻两对拉钢筋之间;钢板发生屈曲后,与屈曲位置相邻的对拉钢筋承受较大的拉力,且对拉钢筋拉力随着对拉钢筋间距的减小而增大;增加对拉钢筋列数和减小钢板宽厚比可有效改善外包钢板的局部稳定性能,提高钢板的承载能力和变形能力;相比点约束,线约束对钢板局部屈曲的约束更为有效;无对拉钢筋模型、单列对拉钢筋模型和双列对拉钢筋模型达到屈服强度（345MPa）所需的最小宽厚比分别为25、30和37.5。     

Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements

Buckling of plates with arbitrarily oriented, sniped stiffeners is studied. The main objective is to present and validate an approximate, semi-analytical computational model for such plates subjected to in-plane loading. Estimation of the buckling strength is made using the von Mises’ yield criterion for the membrane stress as the strength limit. The formulations derived are implemented in a Fortran computer code, and numerical results are obtained for a variety of plate and stiffener geometries. The model may handle complex plate geometries, by using inclined stiffeners to enclose irregular plate shapes. The method allows for a very efficient analysis. Relatively high numerical accuracy is achieved with low computational efforts. The results are, in most cases, found to be conservative compared to fully nonlinear finite element analysis results.     

Experimental investigation on the behavior of corrugated steel shear wall subjected to the different angle of trapezoidal plate

Studies on corrugated steel shear walls (CSSWs) generally indicate noticeable increase of energy absorption, as well as increasing shear buckling capacity of corrugated plates being more likely rather than the flat plates. In this paper, the effect of variation in the angle of trapezoidal plate on the behavior of CSSWs has extensively been investigated. Three specimens of CSSW with 1 story and single bay in half scale are tested under cyclic load. The observations of experiment do indicate that stress concentration has been increased in the corner of subpanels, by increasing of the corrugation angle. Development of the tensile field and wall yield and damage depends on the geometry of the plate. By increasing the corrugation angle, the stiffness and energy dissipation decrease; in addition, large loss of strength takes place. Comparing the numerical and experimental results indicates that for a closer look at behavior of trapezoidal CSSWs, fracture mechanics, fatigue, and damping of materials should be considered by numerical analysis.     

Buckling of cracked functionally graded plates under tension

Buckling of functionally graded cracked plates under tension has not been investigated so far. In this paper critical buckling load of functionally graded plates containing a crack has been obtained using classical plate theory through the finite element method. Displacement in vicinity of crack tips has been approximated using previous solutions related to bending of cracked plates. Effect on buckling of plate under uni-axial and bi-axial tension of different parameters, such as plate dimensions and material properties, are studied. Results show that the critical load decreases as material gradient index increases, while bi-axial loading leads to higher critical loads compared to uni-axial case.     

Buckling of centerline-stiffened plates subjected to uniaxial eccentric compression

A solution for the elastic buckling of flat rectangular plates with centerline boundary conditions subjected to non-uniform in-plane axial compression is presented. The loaded edges are simply supported, the non-loaded edges are free, and the centerline is simply supported with a variable rotational stiffness. The Galerkin method is used to establish an eigenvalue problem and a series solution for plate buckling coefficients is obtained by using combined trigonometric and polynomial functions that satisfy the boundary conditions. It is demonstrated that the formulation approaches the classical solution of a plate with a clamped edge as the variable rotational stiffness is increased. The variation of buckling coefficient with aspect ratio is presented for various stress gradient ratios. The coupling between plate aspect ratio, centerline rotational stiffness, and gradient of applied compressive stress is illustrated and discussed. The solution is applicable to stiffened plates and I-shaped beams that are subjected to biaxial bending or combined flexure and torsion, and is important to estimate the reduction in elastic buckling capacity due to stress gradient.     

Experimental study of low yield point steel gusset plate connections

Concentrically braced frames have been used widely in the seismic-resistant design of steel building structures. During earthquake excitation, the braces of the concentrically braced frame are subjected to recursive tensile and compressive forces. The compressive strength of the brace is usually less than its tensile strength because of the buckling of the brace, and this may degenerate the seismic resistance capacity of the braced frame. In this reported research, an alternative design concept that adopts the weak gusset plate-strong brace is examined. The gusset plate is designed to yield prior to the buckling of the brace. Low yield point (LYP) steel is selected for the gusset plate. The LYP steel possesses low yield strength and high elongation capacity. A series of experimental studies was carried out to examine the LYP steel gusset plates under cyclic loads. It is found that adding slot-type restrainers (STR) to the LYP steel gusset plate greatly enhances the seismic resistance of the gusset plate. The proposed LYP steel gusset plate with an STR is able to provide similar strengths under tensile and compressive loads. The energy dissipation capacity of the gusset plate is also increased substantially. Based on this study, suggestions are made for the design of LYP gusset plates.