Vibration and buckling of plates with mixed boundary conditions

This paper deals with the vibration or buckling of thin plates with either mixed boundary conditions or discontinuous boundary conditions using the spline element method.

To demonstrate the accuracy of the method, several examples are solved, and results are compared with those obtained by other numerical methods. The effects of partial rotational constraints and angles of skew on frequencies and buckling loads of isotropic skew plates are also 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.     

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.     

Local buckling of steel plates in concrete-filled thin-walled steel tubular beam-columns

The availability of high strength steels and concrete leads to the use of thin steel plates in concrete-filled steel tubular beam-columns. However, the use of thin steel plates in composite beam-columns gives a rise to local buckling that would appreciably reduce the strength and ductility performance of the members. This paper studies the critical local and post-local buckling behavior of steel plates in concrete-filled thin-walled steel tubular beam-columns by using the finite element analysis method. Geometric and material nonlinear analyses are performed to investigate the critical local and post-local buckling strengths of steel plates under compression and in-plane bending. Initial geometric imperfections and residual stresses presented in steel plates, material yielding and strain hardening are taken into account in the nonlinear analysis. Based on the results obtained from the nonlinear finite element analyses, a set of design formulas are proposed for determining the critical local buckling and ultimate strengths of steel plates in concrete-filled steel tubular beam-columns. In addition, effective width formulas are developed for the ultimate strength design of clamped steel plates under non-uniform compression. The accuracy of the proposed design formulas is established by comparisons with available solutions. The proposed design formulas can be used directly in the design of composite beam-columns and adopted in the advanced analysis of concrete-filled thin-walled steel tubular beam-columns to account for local buckling effects.     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

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。     

薄壁钢管混凝土梁-柱的钢板局部屈曲分析

高强钢和混凝土的应用,使得薄钢板开始应用在填充混凝土的钢管梁柱中。然而,在组合梁柱中薄钢板的应用可能会增加局部屈曲,这将减弱这些构件的强度和延性性能。通过有限元分析方法,分析了在填充混凝土的薄壁钢管梁-柱中钢板的临界局部屈曲和局部屈曲后性能。运用几何和材料非线性分析来研究在压力和平面内弯曲作用下钢板中的临界局部和后张局部屈曲强度。非线性分析中考虑了钢板的初始几何缺陷和残余应力,材料屈服和应变硬化。基于非线性有限元分析结果,本文提出一组设计公式,以确定这种组合梁柱的临界局部屈曲和钢板的极限强度。此外,还提出在不均匀压力作用下,钢板极限强度设计中有效宽度的计算公式。这一组设计公式可以直接用于组合梁-柱的设计和考虑局部屈曲作用后的薄壁钢管混凝土梁-柱分析。     

Local–global mode interaction in stringer-stiffened plates

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global buckling mode and the strongly stable local buckling mode is highlighted. Highly unstable post-buckling behaviour and a progressively changing wavelength in the local buckling mode profile are observed under increasing compressive deformation. The analytical model is compared against both physical experiments from the literature and finite element analysis conducted in the commercial code Abaqus; excellent agreement is found both in terms of the mechanical response and the predicted deflections.     

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam-column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.     

梁腹板在弯、剪及局压复合应力作用下的屈曲分析

前钢结构设计规范(GBJ17-88)中有关梁腹板局部稳定的计算公式来源于无限弹性完善板假定,一方面与构件的实际工作状况有一定出入,导致计算结果有时会偏于不安全;另一方面又与有关钢梁在弯曲正应力作用下的强度计算公式(考虑截面部分进入塑性)不相协调。针对《钢结构设计规范》(GB50017-2003)中变动较大的该部分设计内容,本文考虑不同的几何参数及弯、剪、局压多种应力组合工况对梁腹板屈曲临界应力的影响,对修订后的梁腹板横向加劲区格在复合应力作用下的临界应力相关公式进行了大量的有限元分析与计算;重点考察了梁腹板的弹塑性屈曲性态及规范(GB50017-2003)中相关公式所具有的设计安全度。在此基础上,提出相关的设计建议,供规范修订及进一步的研究参考。     

Experimental verification of an inelastic plate theory based on plastic flow theory

The paper aims to verify a recently proposed inelastic plate theory by Becque (2010) [1]. In a first part, the theory is revisited and some necessary corrections to the derivation are presented.A total of 486 data points pertaining to the local buckling of aluminium and stainless steel plates and plate assemblies were collected from literature in order to be compared to the predictions of the theory. For plates with straightforward boundary conditions (either simply supported edges or free edges), the theoretical buckling load was obtained by solving Becque's differential equation analytically or numerically. For plate assemblies with less obvious boundary conditions, including plain channels, lipped cannels, Z- and H-sections, the buckling load was obtained by employing an inelastic semi-analytical finite strip method based on Becque's differential equation. Including all data points, the average ratio of the predicted buckling load to the experimentally measured buckling load was 0.98 with a standard deviation of 0.069, thus confirming the proposed theory.     

Thermal postbuckling of laminated composite skew plates with temperature-dependent properties

Thermal postbuckling and consequently, the role of temperature dependence of material properties on the thermal postbuckling behavior of laminated composite skew plates have not been addressed in literature. Hence, this problem is investigated here. The plate governing equations are based on the first-order shear deformation theory (FSDT) and the geometrical nonlinearity is modeled using Green’s strain tensor in conjunction with the von Karman assumptions. Since the problem is geometrically and physically nonlinear, the differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the critical temperature (bifurcation point) and consequently the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated skew plates. After validating the formulation and the method of solution, the effects of temperature dependence of the material properties on the postbuckling characteristic of laminated skew plates with different skew angle, boundary conditions, length-to-thickness ratio, number of layers and ply layout are investigated.     

Inelastic buckling analyses of beams, columns and plates using the spline finite strip method

A method of inelastic buckling analysis of thin-walled structural members and plates is described. The method is based on the spline finite strip method of structural analysis. The analysis takes into account the non-linear material stress-strain properties, strain hardening and residual stresses. The plastic theories used in the study are the flow theory of plasticity and the deformation theory of plasticity. The method of inelastic buckling analysis is applied to a variety of instability problems including plates, cold-formed columns, hot-rolled columns and welded tee section beams. The buckling modes and loads computed are compared with theoretical values and test results.     

Inelastic restrained distortional buckling of continuous composite T-beams

This paper develops a method of inelastic buckling analysis of thin-walled sections to study buckling characteristics of single span and two-span composite T-section beams in the inelastic range of structural response. The method is based on a bubble-augmented spline finite strip method, developed elsewhere by the authors, and confirmed as both accurate and efficient for the elastic buckling analysis of thin-walled structural members and plates. The method admits both flexural and membrane buckling deformations and it allows for consideration of structures with intermediate supports and a variety of boundary conditions that may be prescribed at the ends of plate assembly. The analysis includes the so-called Tendon Force Concept developed at Cambridge University for residual stresses caused by the process of fabrication, and the non-linear stress-strain properties of the structural steel from which the joist section is made. The inelastic restrained distortional buckling (RDB) of continuous composite T-section beams under transverse loading and moment gradient is investigated, and conclusions are drawn that address the influence of geometry, residual stresses, member length, the rigid restraint provided by the concrete and the degree of reinforcement in the concrete element.     

Thermal buckling load optimization of laminated composite plates

In this study, the applicability of the Modified Feasible Direction (MFD) method on the thermal buckling optimization of laminated plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. For this purpose, a program based on FORTRAN is used for the optimization of laminated plates. Finally, the effect of aspect ratio, antisymmetric lay-up, boundary condition, material anisotropy, ratio of coefficients of thermal expansion, and hybrid laminates on the results is investigated and the results are compared.     

复合材料层合板的热屈曲荷载的优化设计

对均布温度荷载作用下，复合材料层合板的热屈曲荷载最优化设计采用的改进可行方向法进行研究。目标函数可使层合板临界温度最大化，将纤维方向设为设计变量，数学公式中采用了一阶剪切变形理论。为此，采用一个基于FORTRAN的计算机程序来进行层合板的优化。最后，分析了长宽比、反对称铺层、边界条件、材料各向异性、热膨胀比例系数和复合层合板对研究结果的影响，并将结果进行对比。     

T形截面板件的局部稳定性

根据《钢结构设计规范》(GBJl7-88),对一边自由、一边与其他板件相连的板件的宽厚比限值来校核由H型钢剖分的T形截面腹板的宽厚比,会很多截面都不满足要求,这使得H型钢的推广应用非常不利。本文对T形截面腹板的宽厚比从板件相互约束的角度进行了研究,提出了相应的宽厚比限值计算公式,供规范修订和工程应用时参考。     

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.