Explicit local buckling analysis and design of fiber–reinforced plastic composite structural shapes

Pultruded fiber–reinforced plastic (FRP) composite structural shapes (beams and columns) are thin-walled open or closed sections consisting of assemblies of flat plates and commonly made of E-glass fiber and either polyester or vinylester resins. Due to high strength-to-stiffness ratio of composites and thin-walled sectional geometry of FRP shapes, buckling is the most likely mode of failure before material failure. In this paper, explicit analyses of local buckling of rectangular orthotropic composite plates with various unloaded edge boundary conditions (i.e., (1) rotationally restrained along both unloaded edges (RR), and (2) one rotationally restrained and the other free along the unloaded edges (RF)) and subjected to uniform in-plane axial action at simply-supported loaded edges are first presented. A variational formulation of the Ritz method is used to establish an eigenvalue problem, and explicit solutions of plate local buckling coefficients in term of the rotational restraint stiffness (k) are obtained. The two cases of rotationally restrained plates (i.e., the RR and RF plates) are further treated as discrete plates of closed and open sections, and by considering the effect of elastic restraints at the joint connections of flanges and webs, the local buckling of different FRP shapes under uniform axial compression is studied. The approximate expressions of the rotational restraint stiffness (k) for various common FRP sections are provided, and their application to sectional local buckling predictions is illustrated. The explicit local buckling formulas of rotationally restrained plates are validated with the exact transcendental solutions. The analytical predictions for local buckling of various FRP profiles based on the present discrete plate analysis and considering the elastic restraints of the flange–web connections are in excellent agreements with available experimental results and finite element eigenvalue analyses. A design guideline for local buckling prediction and related performance improvement is proposed. The present explicit formulation can be applied effectively to determine the local buckling capacities of composite plates with elastic restraints along the unloaded edges and can be further used to predict the local buckling strength of FRP shapes.     

GBT formulation to analyse the buckling behaviour of FRP composite open-section thin-walled columns

This paper presents a Generalised Beam Theory (GBT) formulation to analyse the local and global buckling behaviour of FRP (fibre-reinforced polymer) composite thin-walled columns with arbitrary open cross-sections, which takes into account both shear deformation and cross-section deformation effects. After describing the steps and procedures involved in performing the GBT cross-section analysis of an arbitrarily branched composite (laminate plate) thin-walled member, the paper addresses the numerical implementation of the proposed GBT formulation, carried out by means of the finite element method (GBT-based beam element) – particular attention is devoted to the derivation of the element linear and geometric stiffness matrices, which incorporate all the material coupling effects. In order to illustrate the application and capabilities of the proposed formulation and implementation, several numerical results are presented and discussed, dealing with the local and global buckling behaviour of FRP composite I-section columns with different ply orientations and stacking sequences. Taking advantage of the GBT modal features, deep insight is acquired on the complex composite member buckling mechanics, namely those involving bending–torsion or global–local coupling effects. In particular, one investigates the influence of (i) the constitutive assumption regarding the transverse extension occurring in the cross-section composite walls and (ii) the distribution of pre-buckling normal stresses (due to axial compression) on the buckling behaviour of I-section columns. For validation purposes, the above results are compared with values recently reported in the literature and estimates obtained from shell finite element analyses.     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part I: Flexural–torsional stability

In formulating a finite element model for the flexural–torsional stability and 3‐D non‐linear analyses of thin‐walled beams, a rotation matrix is usually used to obtain the non‐linear strain–displacement relationships. Because of the coupling between displacements, twist rotations and their derivatives, the components of the rotation matrix are both lengthy and complicated. To facilitate the formulation, approximations have been used to simplify the rotation matrix. A simplified small rotation matrix is often used in the formulation of finite element models for the flexural–torsional stability analysis of thin‐walled beams of open cross‐section. However, the approximations in the small rotation matrix may lead to the loss of some significant terms in the stability stiffness matrix. Without these terms, a finite element line model may predict the incorrect flexural–torsional buckling load of a beam. This paper investigates the effects of approximations in the elastic flexural–torsional stability analysis of thin‐walled beams, while a companion paper investigates the effects of approximations in the 3‐D non‐linear analysis. It is found that a finite element line model based on a small rotation matrix may predict incorrect elastic flexural–torsional buckling loads of beams. To perform a correct flexural–torsional stability analysis of thin‐walled beams, modification of the model is needed, or a finite element model based on a second‐order rotation matrix can be used. Copyright © 2001 John Wiley & Sons, Ltd.     

翼缘加劲的冷弯薄壁型钢受弯构件弹性屈曲应力研究

利用有限条软件CUFSM对普通卷边槽钢和在受压翼缘不同位置设置加劲肋的普通卷边槽钢受弯构件进行了弹性屈曲应力的计算。对计算结果进行比较分析后发现:在受压翼缘的不同位置增设加劲肋对普通卷边槽钢受弯构件弹性局部屈曲应力平均提高了53.15%,而弹性畸变屈曲应力平均提高了7.39%,其中偏向卷边一侧设置加劲肋对构件弹性畸变屈曲应力的提高效果不明显。总体而言,在受压翼缘中间设置加劲肋对提高构件的稳定性能效果最好。     

冲击载荷下复合材料层合杆的动力屈曲

研究复合材料层合杆被一质量块以某一速度沿轴向进行碰撞而导致的动力屈曲现象,采用不同的横向剪切理论,并用差分方法对杆的动力屈曲方程进行求解。文中考察了冲击块质量、初挠度、应力波、横向剪切等因素对临界冲击速度以及屈曲模态的影响。     

The influence of mechanical couplings on the compressive stability of anti-symmetric angle-ply laminates

The compressive stability of anti-symmetric angle-ply laminated plates with particular reference to the degrading influence of membrane–flexural coupling is reported in this paper. The degree of membrane–flexural coupling in the laminated composite plates is varied, essentially, by altering the ply-angle and the number of plies in the laminated stack for a given composite material system. The coupled compressive buckling solutions are determined in the paper using the finite strip method of analysis and the buckling displacement fields of the strip formulation are those which are able to provide zero in-plane normal movement at the edge boundaries of the laminated plates.

Results are given for anti-symmetric angle-ply laminated plates subjected to uniaxial compression and these have been obtained from fully converged finite strip structural models. Validation of the finite strip formulation is indicated in the paper through comparisons with exact solutions where appropriate. Increasing the number of plies in the laminated system is seen to reduce the degree of coupling and the critical stress levels are noted to tend towards the plate orthotropic solutions. The ply-angle corresponding to the optimised buckling stress for any particular laminate is noted in the paper to be influenced by the support boundary conditions at the plates unloaded edges. For any particular laminate the minimum critical buckling stress and corresponding natural half-wavelength of the buckling mode are shown to be highly sensitive to ply-angle variation.

Some post-buckling results are presented in the paper and these have been determined using the finite element method of analysis. The influence of membrane–flexural coupling is shown to be significant throughout the compressive post-buckling history of the laminated plates. The optimised ply-angle with regard to the critical compressive buckling stress of square simply supported anti-symmetric angle-ply laminates is shown to be less effective in the post-buckling range with regard to post-buckled compressional stiffness.     

Finite strip buckling and free vibration analysis of stepped rectangular composite laminated plates

A general spline finite strip method is presented which allows the spline knots to be located arbitrarily along the plate strip and also facilitates the use of analytical integration in evaluating strip properties. The development takes place in the contexts of first‐order shear deformation plate theory and of classical plate theory, and encompasses composite laminated material. The prediction of natural frequencies and buckling stresses of stepped rectangular plates is considered using the new approach in which refinement of knot spacings is used local to a step change. The superstrip concept is used as part of an efficient solution procedure. A number of applications demonstrate the validity and practicability of the developed method. Copyright © John Wiley & Sons, Ltd.     

超高强度钢材焊接截面残余应力分布研究

超高强度钢材(屈服强度≥460MPa)已经在多个钢结构实际工程中得到应用,但关于其构件截面残余应力以及轴心受压整体稳定性的研究还很少。该文总结了国外已有的超高强度钢材焊接截面残余应力的试验测量结果,针对工字形、箱形和十字形三种焊接截面,分析了截面残余压应力与板件宽厚比的关系,并提出了这三种焊接截面超高强度钢材构件残余应力的分布模型和具体计算公式,为研究超高强度钢材受压构件的整体和局部稳定受力特性提供了前提条件。     

复合材料双曲率壳屈曲和后屈曲的非线性有限元研究

基于 ABAQUS软件分析平台 , 采用非线性有限元法研究了横向载荷作用下复合材料双曲率壳的屈曲和后屈曲行为。通过在有限元模型中引入 Tsai2Wu失效准则 , 预测了复合材料双曲率壳的初始失效及渐进破坏过程 , 数值结果和试验数据吻合较好 , 表明了该模型的合理有效性 , 并详细讨论了各种参数对屈曲和后屈曲行为的影响。经分析复合材料双曲率加筋壳在均布压载和剪力联合作用下的屈曲和后屈曲行为 , 得到了屈曲载荷的拟合曲线 , 研究表明顺剪力的存在有利于提高屈曲载荷。     

The buckling of composite stiffened plates with some emphasis on the effects of fibre orientation and on loading configuration

The bucking characteristics of some composite stiffened plates are determined in this paper using a finite strip approach. The finite strip formulation is able to predict the complex buckling modes associated with in-plane shear loading and the method of approach can allow for other loading configurations whose associated pre-buckling stresses are not so obviously realised.

Two loading conditions have essentially been considered in the paper, that of in-plane shear and that of partial edge loads being reacted by shear. The strip displacement fields before and after buckling are represented by algebraic polynomials across the strip and trigonometric functions along the strip length. The inclusion of sufficient harmonics in the appropriate displacement representations thus allows the distorted nodal lines of the shear buckling mode and the complex pre-buckled stresses associated with partial edge loads to be determined with relative ease.     

竖向槽钢加劲钢板剪力墙剪切屈曲

对设置多道竖向闭口加劲肋的钢板剪力墙的剪切屈曲进行了有限元弹性屈曲分析,得到了剪切应力随加劲肋抗弯和加劲肋抗扭刚度变化曲线,以加劲板临界应力等于小区格按简支计算的剪切屈曲应力为条件,得到了双面加劲肋的门槛刚度。刚度小于门槛刚度时给出了剪切屈曲临界应力与加劲肋刚度的关系;将双面加劲同单面加劲、交错单面加劲两种情况进行比较,得出了后两者的门槛刚度放大系数。与数值结果比较表明：公式具有良好精度且偏安全。     

基于弯曲刚度最大分层临界载荷的层压板局部屈曲预测

提出了一种预测含特定分层损伤层压板发生局部屈曲时整体应变的方法。认为含分层子板的局部屈曲载荷由其弯曲刚度最大的分层决定, 因而含有相同最大弯曲刚度分层的不同子板具有相同的屈曲载荷。在已知弯曲刚度最大分层的屈曲载荷的情况下, 根据层压板的轴向刚度公式, 计算出发生局部屈曲时弯曲刚度最大的分层与完好的基板分别承受的载荷, 即得到总载荷, 进而得到层压板的整体应变。用ABAQUS有限元分析软件建立含分层损伤的层压板模型, 使用准静态加载进行了多种分层深度和分层位置下的局部屈曲仿真, 所得局部屈曲载荷符合上述推论。用所提方法预测发生局部屈曲时的整体应变, 结果与有限元结果吻合较好, 此方法可用于建立分层参数识别的参照样本库。     

Nonlinear failure prediction of concrete composite columns by a mixed finite element formulation

This study focuses on developing a mixed frame finite element formulation of reinforced concrete and FRP composite columns in order to give more accuracy not only to predict the global behavior of the structural system but also to predict the local damage in the cross-section. A hypo-elastic constitutive law of concrete is presented under the basis of a three-dimensional stress state in order to model the compressive behavior of confined concrete wrapped with FRP jackets. To predict the nonlinear load path-dependent confinement model of FRP-confined concrete, the strength enhancement of concrete was determined by the failure surface of concrete in a tri-axial stress state, and its corresponding peak strain was computed by the strain-enhancement factor proposed in this study. The behavior of FRP jacket was modeled using the two-dimensional classical lamination theory. The flexural behavior of concrete and composite members was defined using a nonlinear fiber cross-sectional approach. The results obtained by developed mixed finite element formulation were verified with the experiments of concrete composite columns and also were compared with a displacement-based finite element formulation. It is shown that the proposed formulation gives e more accurate results in the global behavior of the column system as well as in the local damage in the column sections.     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

Q420高强度等边角钢轴压构件整体稳定性能设计方法研究

为研究Q420高强度等边角钢轴压构件的整体稳定受力性能与设计方法, 该文采用有限元软件ANSYS建立数值模型, 并经与试验结果对比验证后进行了大量参数分析, 研究了构件几何初始缺陷、残余应力和钢材屈强比对该类轴压构件整体稳定性能的影响, 分析了已有设计方法的适用性。结果表明, 构件初始缺陷对其稳定性能的影响与构件长细比及失稳模态有关, 残余应力的影响与构件长细比有关, 钢材屈强比的影响较小。基于数值计算结果建议了Q420高强度等边角钢轴压构件考虑板件局部屈曲相关作用的整体稳定设计方法, 为补充和完善我国钢结构设计规范提供了参考, 同时也有利于促进高强度钢材在我国钢结构工程中的应用。     

On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method

This paper augments bubble functions to the ordinary spline finite strip method in order to calculate the elastic local buckling coefficients of plates and plate structures. The results show that the use of bubble functions improves significantly the convergence of the spline finite strip method in terms of the strip subdivision, and therefore leads to smaller storage requirements for the global stiffness and stability matrices, and faster eigenvalue extraction. Benchmark numerical investigations are presented, including the study of plates with different boundary conditions under uniaxial and biaxial stresses, plates with different aspect ratios under shear, and a stiffened panel under combined shear and compression that has been studied elsewhere. These studies demonstrate that by implementation of the bubble functions, rapid convergence of the solution is obtained. The formulation is ideal for analysing local buckling under a variety of boundary and loading conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

环加肋圆柱壳屈曲分析的有限条法

导出了有限条法分析环加肋圆柱壳在静水压力作用下总体屈曲的计算格式，将环加肋圆柱壳作为一个构造上的正交各向异性壳处理，推导了考虑环向加肋影响后有限条元的正交各向异性弹性矩阵。对两端简支环加助圆柱壳总体屈曲临界载荷的计算表明，本文方法计算结果与解析解符合良好。有限条法是分析密加肋圆柱壳屈曲问题的有效数值方法。     

冷弯薄壁型钢卷边槽形截面构件畸变屈曲承载力计算方法研究

基于能量法对冷弯薄壁型钢卷边槽形截面的弹性畸变屈曲应力进行了推导分析,得到相应畸变屈曲半波长、畸变屈曲应力以及稳定系数计算公式。通过与有限条法进行对比分析,表明推导出的畸变屈曲应力计算方法具有较高的精度和较好的适用性。在此基础上,建立了冷弯薄壁型钢卷边槽形截面部分加劲板件弹性局部和畸变屈曲稳定系数的统一计算公式。最后通过算例分析,验证了该文提出方法的合理性和适用性,相对于中国现行《冷弯薄壁型钢结构技术规范》能够更加准确的计算部分加劲板件的屈曲稳定系数及卷边槽形截面构件的稳定承 载力。     

板件中间V形加劲复杂卷边槽钢轴压构件的稳定性能研究

分别采用有限条数值解法和手算方法对16根轴压简支试件的弹性局部、畸变屈曲临界应力进行了计算,对比了数值解法与手算方法的计算结果,验证了手算方法求解弹性稳定临界应力的有效性。研究了V形加劲复杂卷边槽钢轴压构件的弹性稳定性能。研究表明:V形加劲肋的存在对轴压试件的弹性局部屈曲临界应力影响显著,但对弹性畸变屈曲临界应力影响较小,减小翼缘板件的宽厚比能明显提高截面的弹性畸变屈曲临界应力。     

Flexural-Torsional Buckling and Vibration Analysis of Composite Beams

In this paper the general flexural-torsional buckling and vibration problems of composite Euler-Bernoulli beams of arbitrarily shaped cross section are solved using a boundary element method. The general character of the proposed method is verified from the formulation of all basic equations with respect to an arbitrary coordinate system, which is not restricted to the principal one. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. It is subjected to a compressive centrally applied load together with arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting problems are (i) the flexural-torsional buckling problem, which is described by three coupled ordinary differential equations and (ii) the flexural-torsional vibration problem, which is described by three coupled partial differential equations. Both problems are solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the method can treat composite beams of both thin and thick walled cross sections taking into account the warping along the thickness of the walls. The proposed method overcomes the shortcoming of possible thin tube theory (TTT) solution, which its utilization has been proven to be prohibitive even in thin walled homogeneous sections. Example problems of composite beams are analysed, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. Moreover, useful conclusions are drawn from the buckling and dynamic response of the beam.