Thickness optimization of circular annular plate at buckling

This work deals with thickness optimization of a circular annular plate at buckling. The plate is loaded with uniform, axially symmetric, in-plane loads on the inner and outer edge. The variable thickness of the plate is approximated by a function of radial coordinates and design variables. An optimization problem is defined to find optimal sets of design variables which maximize buckling loads at constant weight/volume of the plate. The required buckling loads are determined according to the standard linear buckling equations, and the material is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model is considered. Optimal thickness functions are determined for different support and load cases and the numerical results show that buckling loads can be increased significantly.     

Buckling of imperfect functionally graded plates under in-plane compressive loading

Buckling behavior of rectangular functionally graded plates with geometrical imperfections is studied in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive loading. Simultaneous solving of the stability and compatibility equations in conjunction with the equilibrium equations leads to the buckling relation of the plate. The critical buckling load of a sample plate is obtained and compared for different geometrical ratios. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates.     

An analytical study on post-buckling behaviour of imperfect sandwich panels subjected to uniform thermal stresses

The governing equations for determining thermal buckling of imperfect sandwich plates are developed using the large deflection theory and considering first shear deformation principles. The equations are then solved via an analytical method comprising infinite summation of trigonometric series and defining in-plane and out-of-plane displacement. After verification of the proposed method and convergence studies, the effects of parameters like plate aspect ratio, material properties and layer setting angles on buckling stress and the post-buckling path are studied. Numerical results show that the number of trigonometric terms does not affect the buckling thermal stress or the post-buckling path of sandwich plates having face layer setting angles less than 15°. Results also show that the buckling stress and post-buckling path for complementary layer setting angles are similar and that the rate of variation of bifurcation points for different face layer setting angles of sandwich panels strongly depend on material properties, especially on the face and core stiffness. Furthermore, for aspect ratios greater than five, buckling thermal stress remains about constant.     

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.     

交叉加劲钢板剪力墙弹性屈曲研究

用有限元方法对交叉加劲钢板剪力墙的弹性屈曲性能进行了研究,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比等对弹性屈曲系数k的影响,同时与十字加劲板的抗剪屈曲性能进行了对比。研究结果表明,设置交叉加劲肋能显著提高钢板剪力墙的弹性屈曲荷载;屈曲系数k随着墙板边长比、高厚比以及加劲肋宽厚比的增大而趋于减小;本文给出的交叉加劲板弹性屈曲系数k的计算公式与有限元法的结果较吻合。     

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.     

Buckling optimization of variable thickness prismatic folded plates

This paper deals with the structural shape optimization of prismatic folded plates under buckling load consideration. Buckling loads are determined using linear, quadratic and cubic, variable thickness, C(0) continuity, Mindlin-Reissner finite strips. The whole structural optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, semi analytical sensitivity analysis and mathematical programming algorithm. The objective is either the maximization of the critical buckling load or minimization of the cross-section of the prismatic folded plate with constraints on the volume and buckling loads. Several examples are included to illustrate various features of the optimization algorithm, including plates and stiffened panels.     

开口肋加劲板屈曲模态与临界屈曲应力分析

为更好掌握开口肋加劲板的设计计算方法,采用弹性稳定分析方法,对无纵向和横向加劲肋的四边简支板、纵向加劲肋等间距布置的四边简支加劲板、纵向和横向加劲肋等间距布置的加劲板进行屈曲模态和临界屈曲应力分析。结果表明:对于四边简支板或四边简支加劲板,临界屈曲应力与板宽、板长和板厚均有关,减小板宽和板长以及增大板厚可提高临界屈曲应力;随着加劲肋刚度比的变化,四边简支加劲板一般表现出3种屈曲模态,模态1为加劲肋与被加劲板共同发生整体屈曲,模态2为在加劲肋处形成波节,加劲肋与被加劲板发生屈曲,模态3为加劲肋为刚性加劲肋,不会发生失稳,只有被加劲板发生局部失稳;临界屈曲应力随加劲肋刚度比的增大而增大,模态1增大幅度最大,模态2次之,模态3逐步趋于定值。     

Experimental investigation of composite shear walls under shear loadings

One of the efficient methods for improving the seismic behaviour of high-rise buildings is using Composite Steel Plate Shear Wall (CSPSW). In this paper, extensive experimental studies of one and three-story CSPSWs with the scale of 1:3 and 1:4, together with stress equations of each element are reported. The experimental results indicate that this system has reliable behaviour if the columns have high bending stiffness. Also bolts spacing to plate thickness ratio has direct relationship with system ductility. However, plate yield load has an inverse relationship with this ratio. In this system, plate stiffening requirement is obtained with minimum reinforcement for reinforced concrete, though for damage prevention high strength concrete is preferred. Also, the results show a good agreement for the recommended values of (b/t) by an AISC code for preventing plate buckling.     

Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory

The third-order shear deformation theory of Reddy and collocation with radial basis functions is used to predict the buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse strains through the thickness of the plate. It is shown that the collocation method with radial basis functions produces highly accurate critical buckling loads and modes.     

全受压和局部边缘受压下有裂纹薄板屈曲的试验和数值研究

受压下薄钢板经常发生屈曲失效,尤其当薄钢板存在一些如开口和裂纹等缺陷时。这种失效模式先于强度失效。给出了轴压下有裂纹板的屈曲荷载的试验结果和数值结果。为此,采用1200A铝合金制作成矩形板,且板的中心有斜裂缝。在试验和数值研究中,分析了裂缝的长度和方向、板的厚度和长宽比的影响。对两种不同的支撑形式和荷载条件(如:局部边缘荷载和支撑)的影响进行研究。最后,将试验结果与数值结果进行对比。     

Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading

Buckling failure is a common occurrence in thin plates under compression loading, in particular when there are some imperfections such as openings and cracks. This form of failure can often precede strength failure. In this paper, experimental and numerical studies on the critical buckling load of cracked plates subjected to axial compression is carried out. For this purpose, the rectangular plates made by 1200A aluminum alloy with central inclined crack are considered. The effects of crack length and orientation, thickness of plates and plate aspect ratio are investigated experimentally and numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading such as partial edge acting forces and supports. Finally, the results of experiments are compared with the results of numerical methods.     

基于高阶剪切变形理论及径向基函数的各向同性叠合板的屈曲分析

基于三阶剪切变形理论及径向基函数,预测弹性板的临界荷载。该理论说明了沿钢板厚度方向的横向应力呈抛物线分布的原因。结果表明:径向基函数能精确地预测钢板的临界荷载和失效模式。     

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.     

Analytical demonstrations to assess residual bearing capacities of steel plate girder ends with stiffeners damaged by corrosion

Many field surveys depict that steel plate girder ends tend to corrode due to the leakage of water from construction joints and/or detention of rain water near bearing regions. In many cases, buckling failures of plate girders were observed due to the excessive loss of material at the bottom portion of bearing stiffeners. In this study, the effect on the buckling strength of steel plate girder due to the corrosion damage at bearing stiffeners was investigated. Full-scale experimental tests were performed on two plate girder ends to determine the bearing capacity. Bearing capacity and failure modes were also verified by numerical analyses. Initial imperfections and welding residual stresses were also taken into account in analytical models. The simulation of the model was extended to the various corrosion damages, considering different damaged heights and thicknesses of the bearing stiffener near weld seam. All results were plotted in terms of remaining bearing capacity versus damage thickness ratio keeping the damage height of the stiffener constant. In this study, a damage parameter Reduced Thickness Ratio was used to assess the ultimate capacity and buckling of steel plate girder end with various corrosion levels.     

刚性外筒内不同厚度圆柱形内筒的弹性屈曲分析

塑性管道内管被广泛应用于修复损坏的刚性管道。在之前的分析中,一般简化地认为内管是等厚度的。然而,在正常使用中,由于腐蚀性液体或气体的腐蚀,会造成内管厚度不均。论述了在外部流体压力作用下不同厚度圆柱体形管道内管的弹性屈曲的分析结果。根据最小势能理论得出了分析结果,并与有限元数值分析结果进行了对比。结果显示,有限元的分析结果与最小势能理论分析结果较好地吻合。分别对最小势能理论分析结果和有限元分析结果进行了讨论,并与其他理论得出的结果进行了对比。当内管厚度是常数时,本分析结果就简化为Glock的经典结论。     

Local buckling restraint condition for core plates in buckling restrained braces

Buckling Restrained Braces (BRBs) are commonly used as bracing elements in seismic zones. A key limit state governing BRB design is to prevent flexural buckling. However, when the wall thickness of the steel tube restrainer is relatively small compared to the cross-section of the core plate, the restraint conditions against the local buckling of the core plate can be critical for the stability and strength of the BRB. In this study, cyclic loading tests and numerical analyses of BRBs were carried out using various tube restrainer configurations to investigate the influence of local buckling of the restrainer on BRB strength and ductility.     

The wall–frame and the steel–concrete interactions in composite shear walls

The nonlinear pushover analyses of 24 composite steel plate shear walls (CSPSWs), 24 corresponding steel plate shear walls (SPSWs), and 24 corresponding frames are conducted. CSPSWs have different aspect ratios and infill steel plate thicknesses. The study aims to understand the wall–frame and steel–concrete interactions. The infill steel plate thickness and aspect ratio of CSPSW are the main parameters of the study. In CSPSWs, the percentage of absorbed shear forces by the infill composite wall is always greater than the infill plate of its corresponding SPSW. The percentage of shear in the composite wall is constant at the initial stage of loading up to a drift of 0.15–0.2%. By increasing the drift, the shear yielding of steel plate leads to a reduction of the shear force absorption. The reduction continues until the bulk of shear stiffness of CSPSW is provided by the frame. At the beginning of lateral loading, steel–concrete interactions increase until shear yield of steel plate. Following this stage, a sudden decrease takes place in shear force absorption of reinforced concrete (RC) panel. The reason is that, at the lower drifts, the steel plate has a tendency for elastic buckling, which is prevented by the RC panel. Finally, the shear force absorption remains approximately constant in the RC panel.     

Interactive local buckling and limiting slenderness of T-strut stem

This paper presents in the first place an analytical solution by energy approach to the interactive buckling of plate elements of T-sections subject to axial compression. The critical stress obtained is then compared to that of the strut buckling torsionally with respect to its shear center and the identity of these two stresses is revealed. Further analysis shows that stem buckling stress is always larger than the flexural-torsional buckling stress in the case when the strut is not restrained by any other member. A limiting depth-thickness ratio of the stem is derived on the basis of a plate element with one longitudinal edge built-in and the other free. Finally, the relevant provision in the Chinese code for design of steel structures is introduced.     

Frictional behavior of planar and rough granite fractures subjected to normal load oscillations of different amplitudes

The dynamic frictional behaviors of natural discontinuities (joints, fractures, faults) play an important role in geohazards assessment; however, the mechanisms of the dynamic fault weakening/strengthening are still unclear. In this paper, a dynamic shear box was used to perform direct shear tests on saw-cut (planar) and natural (rough) granite fractures, with different normal load oscillation amplitudes. Based on the recorded shear forces and normal displacements, the shear forces, apparent friction coefficients and normal displacements are found to change periodically with oscillated normal loads and are characterized by a series of time shifts. The observed changing patterns are similar for the rough and planar fractures. Compared with the test data under constant normal load (CNL), small/large normal load oscillation amplitude enhances/reduces the peak shear strength, with a critical point. The magnitude of critical normal load oscillation for the rough fractures is smaller than the planer fractures. The results imply that dynamic fault weakening/strengthening can be achieved by both normal load oscillation amplitudes and slip surface topography. The rough fractures with larger normal oscillation amplitude can easily cause frictional weakening under stress disturbance.