Elastic stability of orthotropic plates

A semi-numerical method is presented for the analysis of orthotropic rectangular plates subjected to uniform, linearly-varying and partial inplane loads. The solution procedure is based on the classical method of separation of variables. The basic functions are chosen as the eigenfunctions for straight prismatic beams in free vibration. The two-dimensional governing partial differential equation is first reduced to an ordinary differential equation. The classical unidirectional finite difference method is then employed to solve the resulting ordinary differential equation. Results are presented for plates with different edge and loading conditions.     

Effective widths of plates loaded uniaxially

An approximate method for the analysis of axially loaded plates with initial imperfections is presented. Formulae for the computation of effective widths of rectangular plates having nine different combinations of boundary conditions have been derived using the energy method; all the boundary edges are constrained to remain straight in-plane, except when one of the edges is free to wave out-of-plane. Design curves have been presented for each set of support conditions, and these can be employed to obtain solutions within acceptable engineering accuracy for practical structures having small imperfections.     

双向压弯方钢管高强混凝土构件滞回性能试验与分析

进行了4个双向压弯方钢管高强混凝土构件在低周反复荷载作用下的试验研究。试验中的主要参数为轴压比(0.433～0.624)、宽厚比(30和50)和长细比(18.5和25.4)。试验结果表明,随轴压比的提高,构件的承载力和延性降低,随钢管宽厚比的增加,构件的承载力提高;试件的位移延性系数μ=3.63～5.18,抗震性能良好。利用纤维模型法计算了构件的荷载位移滞回曲线,计算结果与试验结果吻合较好。进行了压弯构件的截面参数分析,研究了轴压比、套箍系数、加载角度和荷载类型对构件滞回性能的影响。建立了方钢管混凝土压弯构件的弯矩曲率和荷载位移恢复力模型,基于恢复力模型的计算结果与试验结果吻合较好,可为结构的弹塑性动力分析提供参考。     

傅立叶级数法求解正交各向异性板弯曲问题

用傅立叶级数法分析解决了正交各向异性板各种边界条件的弯曲问题,并结合四边固定板的算例说明了该方法具有计算理论简单,分析易理解,并且计算结果也达到了一定精度的优点.     

Tests on plates loaded in in-plane compression

The paper discusses the difficulties encountered in supporting the edges of plates when they are tested under in-plane compression, and describes a test rig in which this support is achieved using sets of discrete fingers. The results of tests on structural steel plates are given, in which the magnitudes of residual stresses and initial out-of-flatnesses were controlled. These are compared with the results of large-deflection elasticplastic numerical analyses, showing good agreement. Results are also compared with simplified analyses, and with a wide range of design strength data.     

附加集中质量正交各向异性双向连续板结构振动分析

分析了附加集中质量正交各向异性双向连续板结构的振动特性,通过有限傅立叶变换将双向多肋板振动微分方程的解改写为级数形式,通过解附加方程组的方法解出肋梁的约束力和约束力矩与板的相互作用,将其代回原方程得出多肋板的自由振动解,从而可以得到仿真试验模型。     

Accurate discrete modelling of stiffened isotropic and orthotropic rectangular plates

An analytical approach is presented here for simply supported blade-stiffened rectangular plates wherein important non-classical effects such as transverse shear deformation and rotary inertia are carefully accounted for. The analysis differs from full three-dimensional modelling of both the plate and the stiffener in that a plane stress idealization is used to model the kinematics of transverse bending of the stiffener while simple one-dimensional classical models are employed for lateral bending and torsion. Parametric studies are used to highlight the importance of non-classical effects in plate and stiffener kinematics and to finally lead to certain recommendations for accurate modelling of stiffened 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.     

Buckling of orthotropic plates with free and rotationally restrained unloaded edges

Solutions and parametric studies are presented for the buckling of rectangular plates whose axes of material orthotropy coincide with the axes of the plate. The results presented apply to homogeneous orthotropic plates, stiffened orthotropic plates, and laminated composite material plates having flexural orthotropy (i.e. single ply and multiply unidirectional, and symmetric cross-ply composite plates). The plates considered are subjected to uniform uniaxial compression and simply supported on the loaded edges. The boundary conditions are different on the two unloaded edges; one edge being free and the other edge being elastically restrained against rotation. Parametric studies showing the effect of the orthotropic properties of the plate materials, the plate aspect ratio, the rotational restraint of the one unloaded edge and the buckle half-wavelength are discussed. Results in the form of nondimensional buckling curves are given in terms of orthotropy ratios and in terms of properties of common unidirectionally reinforced composite material. The use of the solution in conjunction with experimental data to predict the edge rotational restraint coefficient for thin-walled composite material beams is described.     

Buckling of vibrations of shear-flexible orthotropic plates subjected to mixed boundary conditions

An approximate technique is presented for the analysis of buckling and vibrations of free-form, orthotropic, shear-flexible (‘Mindlin’) plates subject to mixed boundary conditions. The method falls into the category of Rayleigh/ Ritz-techniques; however, by using Lagrangian multipliers to ‘relax’ the geometric boundary conditions, the selection of appropriate trial functions is made considerably simpler. Accuracy and reliability of the proposed technique is demonstrated on the basisof several sample problems.     

Strength of perforated plates subjected to in-plane loading

Finite element solutions for the buckling and geometrically nonlinear elasto-plastic collapse of perforated plates are presented. Triangular elements are used to model the plates and the elasto-plastic stress-strain relationships are based on Ilyushin's approximate area yield function assuming full plastification of the entire thickness of the plate for stress states on the yield surface. Solutions are presented for square plates with central square and circular holes subjected to uniaxial compression, biaxial compression and pure shear, and are shown to be in close agreement with existing approximate and semi-empirical solutions which have been verified by test results.     

A generalised effective width method for plates loaded in compression

In recent years there have been a number of notable theoretical studies which have provided extensive load-shortening curves for rectangular plates loaded in compression along their transverse edges. These studies have provided engineers with a clear understanding of the effects which initial out-of-plane deformations and residual stresses have upon the behaviour of plates loaded in compression. The present paper shows how the information provided by these load-shortening curves can be utilised to provide effective width expressions. This will enable this latest research information to be incorporated in those existing design methods which utilise an effective width approach.One important benefit of the present study is that whereas earlier effective width formulae only provided information on the load-carrying capacity of a plate up to its peak load, the proposed method enables the post peak load behaviour of a compressed plate to be readily calculated.     

正交异性闭口加劲板的承载力分析理论及试验研究

加劲板的局部稳定是正交异性扁平钢箱梁结构设计中的一个关键问题,我国桥梁设计规范没有这方面的规定。为了解决正交异性扁平钢箱梁结构中闭口加劲板的稳定极限承载力计算问题,以适应我国目前钢桥应用日益广泛的需要,在总结中外学者研究成果和国内外设计规范的基础上,提出一种计算闭口加劲板稳定承载力的计算理论,该理论计入材料非线性、几何非线性、初始几何缺陷、焊接残余应力等4种不利影响,并对加劲板结构的初始几何缺陷大小的取值以及残余应力分布模式进行讨论。为了验证理论的正确性、把握闭口加劲板结构的屈曲特性,设计3种不同结构布置的6块闭口加劲板结构进行稳定承载力模型试验,得到加劲板的破坏形态、极限荷载大小以及荷载-位移关系曲线。试验结果与理论分析结果吻合较好,这表明该理论可用于对闭口加劲板的极限承载力计算。     

Effects of anchoring tensile stresses in axially loaded plates and sections

Thin-walled compression members are commonly designed on the assumption that the loaded edges remain straight. Under this assumption, tensile stresses develop in the most flexible parts of the component plates at advanced local buckling deformation, and thus are assumed to be ‘anchored’ at the ends. However, current design rules for plate elements, such as the Winter formulae, are partly based on tests in which the load was applied by use of rigid platens that did not permit tensile stresses to develop. There exists an apparent inconsistency between the assumption of straight loaded edges and the use of a design curve calibrated from tests in which the loaded edges of component plates may not have remained straight.This paper addresses this apparent inconsistency by comparing finite element solutions for the conditions of straight loaded edges and loading by use of a contact surface between the plate edge and a non-deformable rigid body end platen, where there is no constraint for the plate edge to remain in contact with the rigid body. Solutions are provided for a single half-wavelength of unstiffened and stiffened plate elements simply supported along three and four edges, respectively. The effect of multiple half-wavelengths is also investigated, as is the effect of interaction between elements in practical sections comprising stiffened and unstiffened elements.     

基于马尔可夫链的钢箱梁正交异性板疲劳状态分析

为对正交异性板U肋的剩余强度退化规律进行研究,引入马尔可夫过程理论,以特大跨径钢箱梁悬索桥--西堠门大桥为工程背景展开研究。首先分析西堠门大桥钢箱梁长期应变监测数据的时频特征,应用小波分析分离出环境温度变化所引起的桥面板结构应力波动,再对小波变换系数在不同尺度上选择合适的阈值来消除由环境随机激励和测量噪声引起的低幅值应力变异;采用雨流计数法对车辆荷载作用下的应变监测数据进行统计分析,得到疲劳应力范围并设定6个疲劳应力区间;然后由U肋对接部位的典型S-N曲线计算得到其强度从初始状态至最终状态的转移概率,并根据Palmgren-Miner线性疲劳累积损伤理论构造出连接部位易损点区域强度演变的状态转移概率矩阵;最后利用初始状态的概率分布向量和状态转移概率矩阵,得出大桥运营阶段不同时刻对应的剩余强度值,给出U肋连接部位的强度退化轨迹。结果表明：所建立的疲劳状态分析模型可以考虑构件强度退化过程中各状态的相关性,能够根据车流量变化来预测正交异性板U肋疲劳状态随桥梁服役时间的变化规律,从而可实现钢箱梁正交异性板U肋的服役性能评估。     

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.     

Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading

This paper derives the similitude invariants and scaling laws for buckling of polar orthotropic annular plates subjected to radial compressive load and torsional load. The similitude transformation is applied to the governing differential equation directly resulting in a scaling law for buckling load of annular plates and the similarity conditions between a model and a prototype. The scaling law is verified by a series of numerical tests using the solutions from the Ritz method as the theoretical solutions. For complete similitude cases, the buckling loads obtained from the scaling laws are identical to those of the theoretical solution. Since the derived scaling law is independent of the boundary conditions, it is valid for any pairs of model and prototype on the condition that they have identical boundary condition. Therefore, buckling behaviors of the prototype with complicated boundary conditions, of which a theoretical solution is not available, can be predicted from the experimental result on the model. Partial similitude model or scaling law for a pair of model and prototype without complete similarity is also investigated. The partial similarity model is not recommended for polar orthotropic materials, however it demonstrated good estimations for isotropic materials.     

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.     

Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria

In this paper a simple method of deriving lower bound limit loads for thin plates is presented. This method is based on the method of elastic compensation, an iterative elastic technique, which has recently been extended to allow the analysis of structures using thin shell finite element analysis using generalised yield criteria. Here the method is modified to allow analysis of plates, including the effects of transverse shear. The elastic compensation method, combined with generalised yield criteria, is implemented using the finite element numerical analysis technique. Convergence studies are carried out and limit loads are obtained for a range of geometries, boundary conditions and loading. The calculated limit loads are compared with results available in the literature and with new elasto-plastic results and show that the method can be used to quickly obtain practical results.