Elastic buckling of perforated plates under shear

Finite element studies aimed at computing the buckling coefficient for plates containing cut-outs and subjected to shear are reported. The cases considered are:

1. 1. Square and rectangular plates with central circular cut-outs.

2. 2. Square plates with centrally placed rectangular cut-outs.

3. 3. Square plates with eccentrically placed circular cut-outs.

4. 4. Square plates with reinforced circular cut-outs.

5. 5. Square plates with reinforced rectangular cut-outs.

Simply supported plates as well as clamped plates have been studied and approximate formulae for the use of designers have been suggested for the practical cases where the hole dimension is generally not greater than half the width of the plate.     

Free vibration analysis of circular thin plates with stepped thickness by the DSC element method

Novel formulation is presented by using the discrete singular convolution (DSC) for free vibration analysis of circular thin plates with uniform and stepped thickness. Different from the commonly used ones in literature, regularity conditions are not needed at the circular plate center point to avoid singularity. DSC circular and annular thin plate elements are established. For the DSC circular plate element with radius of R₁, the stiffness equation is first formulated in region [−R₁, R₁] with even number of nodes and then reduced to region [0, R₁] by using either symmetric or anti-symmetric conditions. The proposed DSC circular and annular plate elements are used for obtaining frequencies of uniform/stepped circular thin plates or annular thin plates with different boundary conditions. Comparison of the present DSC results to existing analytic and numerical solutions verifies the proposed formulations. The present research extends the DSC method to free vibration of circular thin plates with stepped thicknesses.     

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.     

波形扰动静水压力对圆环平面内稳定性的影响

针对波形扰动静水压力作用下圆环的稳定性问题,采用傅里叶级数逼近圆环平衡微分方程的解,分别求得圆环反对称屈曲、对称屈曲时的临界荷载系数.结果表明:波形扰动荷载参数会引起临界荷载系数的显著变化,最大降幅可达34.0%.     

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。     

A parameter study of the full-range axisymmetric response of uniformly loaded circular plates

Incremental elasto-plastic large deflection equations and their solution via a finite-difference version of the DR-algorithm are outlined as background to a parametric study of the axisymmetric full-range response of uniformly loaded circular plates. Stocky and slender plates with four combinations of flexural and extensional edge conditions are studied. The parametric results for deflections etc. illustrate the limits on the response variation in the full-range regime due to changes in the slenderness as well as the flexural and extensional edge conditions. The results of the study are presented in dimensionless graphical format and, therefore, may be useful in the preliminary design of circular plate structures.     

Solution for large amplitude vibrations of circular plates via modified Berger's approximation

Complex mathematical formulations for the geometrically nonlinear analysis of structural members have been presented by many researchers using the von-Karman strain-displacement relations. Berger proposed a simplifying approximation to take care of the geometric nonlinearity by neglecting the second strain invariant. Although it is a reasonable approximation, it poses problems when applied to circular plates. This is mainly due to the coupling between the radial and circumferential inplane strains, by the radial displacement. In this article, a modification to the Berger's approximation, applicable to the circular plates, is proposed. The main motivation of the present study is to examine how the modified Berger's approximation works in the case of the large amplitude vibrations of circular plates. It is shown that the modified Berger's approximation gives consistently accurate results, for both the simply supported and clamped circular plates, when compared to the classical results.     

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.     

Why local damage increases the buckling load of circular plates

Local material damage is often characterised as degradation of material properties. A recent study has discovered a paradoxical phenomenon that clamped circular plates with a local axisymmetric damage may have a buckling load above that of a corresponding perfect plate. This paper describes a finite element investigation into the buckling behaviour of circular plates with a local axisymmetric damage. The paradoxical results of previous researchers are explained, and observations are made regarding the appropriate modelling of local damage.     

非轴向荷载下开口斜板的弹性屈曲性能

研究非轴向荷载下开口斜板的弹性屈曲性能。研究了长度方向上的非轴向荷载下简支板和固支板的弹性屈曲性能。考虑了两种不同形式的开口;不同尺寸的圆孔和斜孔。采用有限元分析软件ABAQUS。参数分析考虑了斜率、尺寸、形状、开口的位置和板的长宽比。相对于参数分析,以图表的形式给出屈曲系数的影响。     

考虑盾构隧道纵向应力松弛的环缝渗漏水计算分析

为揭示盾构隧道环缝渗漏水演变过程及其影响因素,基于裂缝渗流模型推导盾构隧道管片环缝渗流量计算公式,进一步考虑隧道纵向应力松弛的影响,建立环缝渗漏水演变的时变状态模型,结合算例进行环缝渗漏水演变规律探讨和参数敏感性分析。结果表明,盾构隧道渗漏水量随着环间张开量增大或者外部水头高度的提高而增大,随着环间接头刚度的增大而减小。张开量对环间渗漏水的影响较为敏感,隧道顶部的渗流量始终小于底部。盾构隧道纵向应力越低,隧道渗漏水现象越明显。当纵向应力由3.2MPa衰减为1.2MPa时,渗流量增长为原来的12倍,且不同部位的环间渗流量差距逐渐扩大,隧道底部的渗流量约为顶部的2倍。在隧道纵向应力松弛后,纵向连接螺栓复紧将极大地降低环缝渗漏水量,螺栓复紧导致环缝渗漏量减小为原来的80%,导致纵向应力达到稳定状态后的环缝渗漏量减小至原来的20%以下。工程实践中,应重视盾构隧道纵向应力松弛对衬砌环间防水性能的影响。     

Axi-symmetrical deflection and buckling of circular porous-cellular plate

The main goal of this paper is a solution of the problem of buckling and deflection. A circular porous plate with simply supported edge under radial uniform compression and uniformly distributed load (pressure) is considered. Mechanical properties of the isotropic porous material vary across the thickness of the plate. Middle plane of the plate is its symmetry plane. A field of displacements (geometric model of nonlinear hypothesis) is described. The principle of stationarity of the total potential energy allowed to get a system of differential equations that govern the plate stability. A critical load and a deflection are determined. The results obtained for porous plates are compared to homogeneous circular plates.     

Elastic buckling of uniaxially loaded skew plates containing openings

The paper is concerned with elastic buckling behavior of uniaxially loaded skew plates with openings. Simply supported and clamped plates subject to uniaxial compression in the longitudinal direction are studied. Two different shapes of openings, circular and skew of different sizes, are considered. The finite element software package ABAQUS has been employed to analyze the plates. Effects of parameters such as skew angle, size, shape and position of openings and aspect ratio of the plates are examined. Results are presented in the form of plots showing the variation of buckling coefficient against the parameters studied.     

Linear and non-linear behaviour of steel plates with circular and rectangular holes under shear loading

In this work, linear buckling and the non-linear behaviour of steel plates with one perforation subjected to shear loading was studied. The influence of the dimension, position with respect to the two main axes, shape (circular or rectangular) and orientation of a hole with respect to the panel slenderness and aspect ratio were all investigated.In both circular and rectangular holes, the strong influence of hole dimensions on the shear buckling coefficient was observed, and the values of the shear buckling coefficient fell with the plate aspect ratio. Small differences in buckling coefficients were noted in rectangular plates with various hole diameters, and buckling coefficients were practically not influenced by the orientation of the rectangular hole. In both rectangular and circular holes, the coefficient remained constant, regardless of hole position for a given distance from the edge.Linear buckling and non-linear behaviour were compared by observing different shear failure modes for slender and thick perforated plates. Elastic and plastic regions were found, on the basis of critical slenderness, for some common geometries.     

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.     

对带几何缺陷的FGM圆板的非线性热力学后屈曲现象的分析

带有几何缺陷FGM圆板的非线性热力学后屈曲现象是由力学荷载及横向不均匀温度升高导致的。基于组成材料的体积分数导致的能量分布法则,FGM板的材料特性假定在板厚度方向呈梯度变化。根据VonK偄rm偄n平板理论,推导出FGM板在温度荷载作用下的轴对称大变形的计算公式。在此分析中同时考虑了板的几何缺陷。通过运用目标法,解决了那些带有固定边界条件的非线性方程。数值算例中考虑了是否带有几何缺陷、均质或非均质的钢板。带缺陷FGM圆板的后屈曲变形特征曲线根据温度荷载、缺陷参数和体积分数的变化绘制而成。文中同时讨论了荷载参数、材料构成及板的几何缺陷对变形的影响。     

Buckling analysis of thin circular FG plates made of saturated porous-soft ferromagnetic materials in transverse magnetic field

This study presents the buckling analysis of soft ferromagnetic FG circular plates made of poro material. Equilibrium and stability equations of a poro circular plate in transverse magnetic field are derived. This study analyzes the poroelastic instability of clamped edge ferromagnetic plates subjected to magnetic loadings. The geometrical nonlinearities are considered in the Love–Kirchhoff hypothesis sense. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are being investigated.     

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.     

Tragverhalten axial belasteter Stutzen in Kreiszylinderschalen unter Berücksichtigung geometrischer und werkstofflicher Nichtlinearitäten

Axially loaded nozzles in circular cylindrical shells with geometric and physical nonlinearity. The load‐displacement‐relations and the ultimate loads of axially loaded nozzles in circular cylindrical shells are determined by FE‐analyses. These investigations take into account the bi‐linear stress strain behaviour of structural steels and large displacements and instabilities as well. The results which apply for 400 < R/t < 5000 and take into account steel grades up to S690 are presented in graphical form. It is assumed that the thickness t_r of the nozzle is not less than the thickness t of the cylindrical shell. A design rule is given for optimizing the dimensions of pads and insert plates with regard to the effect of the axial load on the nozzle.     

钢环加固圆钢管混凝土柱-RC梁角节点轴压性能有限元分析

针对圆钢管混凝土柱-RC梁角节点,提出了对角节点的节点区采用多段钢环加固的构造方案,并对加固节点模型的轴压性能开展有限元分析研究。通过已有研究成果验证了有限元模型分析方法的可靠性,继而采用ABAQUS有限元分析软件建立152个加固节点模型进行轴压试验模拟。有限元分析结果表明,以多段钢环加强的圆钢管钢筋混凝土柱-RC梁角节点轴压性能优于普通节点,加固节点具有更高的轴压承载力和更好的延性,加固效果明显。参数分析表明：加固角节点的轴压承载力随节点混凝土轴心抗压强度、节点区钢环体积占比和节点区纵筋配筋率的增加而增加;角节点的轴压承载力受梁端剪力影响,较大的梁端剪力可能造成节点延性降低。根据分析结果,建立了节点区采用钢环加固的圆钢管约束混凝土柱-RC梁角节点的轴压承载力算式,供设计该类节点参考。