Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory

Thermal buckling analysis of rectangular composite multilayered plates under uniform temperature rise is investigated using a layerwise plate theory. von Karman strain–displacement equations are employed to account for large deflections occurrence. It is already proven that the layerwise theory results are compatible with the three-dimensional theory of elasticity results. The accuracy of the present results is increased by substituting each layer by many virtual sub-layers. The final governing equations are not simplified or linearized. Material properties are assumed to vary with temperature. Hermitian finite element formulation is used to ensure a C¹ continuity for the lateral deflections. No semi-analytic solution is employed to reduce the problem to an eigenvalue one. Layerwise formulations are usually displacement-based. Therefore, force or moment boundary conditions (e.g. simply supported boundary condition), are approximately satisfied. A FEM algorithm is presented to exactly incorporate the boundary conditions. A proposed numerical scheme and a modified Budiansky instability criterion presented by the author are used to determine the buckling temperature in a computerized solution. Finally, results of the present techniques are compared with the results of the high-order theories presented by some well-known researchers and the influences of various geometric and mechanical properties parameters of the composite plate on the buckling temperature are studied.     

Elastic/plastic buckling of a composite flat plate subjected to uniform edge compression

A theoretical approach, based on the plastic theory, has been developed for studying the elastic/plastic buckling behavior of a simply supported rectangular anisotropic plate subjected to edge compression. The said approach was employed to determine the critical buckling stresses of three different types of fiber reinforced composite plates, namely, carbon epoxy, glass epoxy and boron aluminum plates. Since the proposed approach is for a preliminary prediction of critical buckling loads of composite plates, the results obtained are deemed acceptable compared with those obtained by other authors experimentally.     

Postbuckling behavior of composite plates with through-the-width delaminations

Fiber-reinforced composite materials have been increasingly used over the past few decades in a variety of applications in which a fairly high ratio of stiffness/strength to weight is required. However, these materials are prone to a wide range of defects and damage that can cause significant reductions in stiffness and strength. Delamination is one of the most common failure modes in composite materials which affect the overall stiffness of the structure. In this paper, the compressive behavior of composite laminates with through-the-width delaminations is investigated analytically. The analytical method is based on the CLPT theory, and its formulation is developed on the basis of the Rayleigh–Ritz approximation technique to analyze the bucking and postbuckling behavior of delaminated laminates. The method can handle both local buckling of the delaminated sublaminate and global buckling of the whole plate. Also the three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model. The agreement between the results is very good.     

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.     

Delamination buckling for composite laminated cylindrical shells in Hamilton system

In this article, a semi-analytical three-dimensional model based on the modified Hellinger–Reissner (H–R) variational principle and a nonlinear spring-layer model are presented for the buckling analysis of composite laminated cylindrical shells with a delamination. The method allows the effect of transverse shear deformation in the control equations of the composite laminated structures. In addition, it uses a two-dimensional mesh and can ensure that the number of variables is independent of the layer number. The nonlinear spring-layer model between the exterior and interior sub-laminates ensures the continuity of transverse stresses and displacements in the undelaminated region by specifying infinite values of springs and therefore avoids the possibility of material penetration phenomenon in the delaminated region. As an application of the present method, the influence of the delamination length on the critical buckling loads of delaminated composite laminated stiffened cylindrical shells is investigated.     

叠合梁屈曲的分析与数值研究

根据Euler-Bernouli梁与古典叠合梁理论，提出了一个分析模型，用于获得叠合梁的屈曲荷载，同时，用有限元方法验证了该模型。数值模拟采用8节点壳单元和接触对单元。对铺层方向、排列次序、铺层在宽度方向上的位置、铺层长度以及总层数等参数的影响进行了分析。研究表明，应用R2分析模型给出了比R1更精确的结果；同时发现，重要的表达方式必然包含于反对称次级迭合单元的弯曲刚度阵中；此外，叠合层的长度也影响精确性和分析预测之间的差异。但分析结果和模型值吻合很好。     

Delamination buckling in circular plates

Early studies of delamination buckling in compressively loaded circular plates have been concerned with thin-film and midplane modelling of single delaminations using both linear or nonlinear equations. This paper explores intermediate cases in which the delaminated areas is located between a near surface and midplane condition. The behaviour of the entire plate structure is modelled using nonlinear equations. A numerical integration technique involving the fourth-order Runge-Kutta formula is employed to obtain solutions for the critical buckling load and postbuckling deflections for clamped conditions. These are shown to be dependent upon delamination size and location.     

Local buckling of grouted and ungrouted internally stiffened double-plate HPS webs

High performance steel (HPS) is rapidly gaining attention as a desirable material for highway bridge girders largely due to its superior toughness properties and high strength. However, the benefits of using steels with nominal yield strengths of 485 MPa (70 ksi) or greater is restricted by factors such as web stability, deflection, and fatigue design limits, which may govern the design and prevent the effective utilization of the material strength. Therefore, new and innovative bridge design concepts are needed to take better advantage of the enhanced properties of HPS. One design innovation that provides a means of optimizing bridge girders for high strength material utilizes I-girders with double web plates. The web is composed of two steel face plates connected internally by continuous longitudinal stiffening elements. The voids between the face plates may be grouted or ungrouted. The stiffeners permit thin webs to be used, while still allowing the material to reach stresses as high as the yield strength without buckling. In the case of grouted webs, composite behavior increases the out-of-plane stiffness of the web, although bond between the two materials may be unreliable. Nevertheless, it is shown that even in a debonded state, the presence of the grout enhances the buckling capacity of the face plates significantly. Using classical plate buckling theory, design criteria are proposed for bend buckling of the web face plates, considering both the grouted and ungrouted cases. As a means of assessing the anticipated behavior of the plates, upper and lower bounds to the buckling strengths are established. In order to evaluate the ability of classical plate theory to predict the buckling of the face plates, tests were conducted on a series of web panels that simulate a portion of a girder web subjected to flexural compressive stresses. Two of the specimens were ungrouted, two were grouted with a cementitious material, and one was grouted with an epoxy grout. It was confirmed that the presence of grout increased the buckling capacity of the face plates and that the improved bond using epoxy grout served to delay buckling as well, although when the bond broke the failure was sudden. The experimentally determined buckling loads are used to validate the theory.     

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.     

The influence of bend–twist coupling on the shear buckling response of thin laminated composite plates

The finite strip method of analysis has been used in this paper to examine the effect of bend–twist coupling on the shear buckling behaviour of laminated composite constructions. The distorted nodal lines of the shear buckling mode and its complex deformation state in general are readily accounted for in the analysis procedure through the multi-term nature of the finite strip buckling displacement field and the appropriate level of structural modelling. The degree of bend–twist coupling in the laminated composite plates is varied by changing the level of anisotropy in the plies and by altering the lay-up configuration of the plies in the laminated stack. Symmetric laminates of a balanced and unbalanced nature are given consideration. It is shown that, for a given degree of anisotropy in the plies of a laminate and for a given laminate thickness, the stacking sequence of the plies significantly alters the degree of bend–twist coupling. The shear buckling performance of composite plates having the same dimensions and being made from the same material are therefore shown in the paper to be quite different. The preclusion of the bend–twist coupling coefficients in the solution procedure of the finite strip method allows the shear buckling orthotropic solution to be determined. Comparisons between the coupled and orthotropic solutions are shown in the paper to be markedly different.     

Non-linear model for stability of thin-walled composite beams with shear deformation

A geometrically non-linear theory for thin-walled composite beams is developed for both open and closed cross-sections and taking into account shear flexibility (bending and warping shear). This non-linear formulation is used for analyzing the static stability of beams made of composite materials subjected to concentrated end moments, concentrated forces, or uniformly distributed loads. Composite is assumed to be made of symmetric balanced laminates or especially orthotropic laminates. In order to solve the non-linear differential system, Ritz's method is first applied. Then, the resulting algebraic equilibrium equations are solved by means of an incremental Newton–Rapshon method. This paper investigates numerically the flexural–torsional and lateral buckling and post-buckling behavior of simply supported beams, pointing out the influence of shear–deformation for different laminate stacking sequence and the pre-buckling deflections effect on buckling loads. The numerical results show that the classical predictions of lateral buckling are conservative when the pre-buckling displacements are not negligible, and a non-linear buckling analysis may be required for reliable solutions.     

运用MFD方法对以屈曲为破坏标准的叠层复合板进行最优化设计

对给定平面内静力荷载作用下,以屈曲为破坏机制的简支叠层复合板进行最优化设计。目标函数是使得叠层板的屈曲荷载达到最大,纤维方向为设计变量。有限元分析中应用了一阶剪切变形理论。优化设计中考虑了弯扭力偶的作用,同时采用了以Matlab和Golden Section法编制的计算机程序进行计算。对宽厚比、纵横比、层数、各向异性材料、荷载比(Ny/Nx)等材料特性中其他一些不确定因素进行了对比和分析。     

Stability of variable thickness shear deformable plates—first order and high order analyses

This work presents analysis of the buckling loads for thick elastic rectangular plates with variable thickness and various combinations of boundary conditions. Both the first order and high order shear deformation plate theories have been applied to the plate's analysis. The effects of higher order non-linear strain terms (curvature terms) are considered as well. The governing equations and the boundary conditions are derived using the principle of minimum of potential energy. The solution is obtained by the extended Kantorovich method. This approach is combined with the exact element method for the stability analysis of compressed members with variable cross-section, which provides for the derivation of the exact stiffness matrix of tapered strips including the effect of in-plane forces. The results from the two shear deformation theories are compared with those obtained by the classical thin plate's theory and with published results.     

考虑基坑围护桩约束和层状地基效应的高层建筑基础沉降实例分析

深圳地区某一高层建筑基坑采用排桩支护,筏板基础,沉降计算时考虑了基坑围护桩对地基土侧向变形的约束效应,并采用更适合于层状地基的Burmister理论计算地基附加应力,计算值比用Boussinesq理论计算的小,因此适当降低了分层总和法中沉降计算经验系数ys的取值,使计算得到的沉降量大大低于传统分层总和法的计算值。通过与实测的沉降数据对比,证明这样设计是科学合理的。     

Optimum design of laminated composite plates to maximize buckling load using MFD method

This paper presents optimal design of simply supported laminated composite plates subject to given in-plane static loads for which the critical failure mode is buckling. The objective function is to maximize the buckling load capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used for the finite element analysis. In this paper, the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used as an optimization method. Also, computer programs are coded in MATLAB and Golden Section method is adapted in this program for the optimal design of laminated plates for maximum buckling load. The effect of width-to-thickness ratio, aspect ratio, number of layers, material anisotropy, load ratios (N_y/N_x), uncertainties in material properties and functionally graded materials on the results is investigated and compared.     

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.     

钢-竹组合工字形柱轴压性能试验研究

为研究钢-竹组合工字形轴心受压构件性能,设计制作了18根工字形柱试件,以含钢率与长细比为基本参数,对其进行了轴压试验,观测了试件的破坏形态和变形特征,分析了各参数对试件轴压性能的影响规律,得到了组合柱在轴压荷载作用下的荷载-位移关系,基于钢材与竹材本构关系使用纤维模型法推演了荷载-位移全过程曲线.通过分析组合柱的屈服条...     

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.     

半离散法分析薄壁柱的畸变屈曲

采用广义梁理论(GBT)的耦合差分方程解决了半离散法分析薄壁柱的畸变屈曲问题。作者近期发表的两篇文章对类似GBT的新型半离散分析方法进行了阐述。对横截面进行离散分析,寻找沿梁变化的解析解。采用新方法,利用齐次和非齐次方程建立确定梁全部变形的一般GBT方程并求解,从而使GBT的(复杂)变形方程变形为可降阶的微分方程。提出的半离散方法在广义梁理论(GBT)基础上增加了用于柱的失稳分析和失稳形态识别的几何刚度因素。通过势能的变化并在梁理论中引入约束条件,对初始应力下建立的GBT齐次微分方程进行修正,以分析其变形特性。对简支梁梁端施加横向位移和轴力,建立GBT初始应力方程,通过该方程寻求失稳的解决方法。根据已知的边界条件,利用三角函数关系式和求解特征值的方法求解这些可降阶的微分方程,使得屈曲形态和相关特征值与分叉荷载因素相符。因此,无需通过模态分解,可由耦合的GBT方程直接求得屈曲形态的解析解。通过实例分析了柱的整体失稳、屈曲变形和局部纵弯失稳,以及如何将新方法用于描述特征曲线和弹性屈曲曲线。将该方法的分析结果与ABAQUS、GBTUL和CUFSM软件的分析结果进行对比,验证了该方法的正确性。     

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.