Design and evaluation of various section profiles for pultruded deck panels

Local high stresses and buckling may be critical to the composite deck panels with moderately thick walls. Design and evaluation of section profiles for pultruded deck panels with the reduced local stress and improved buckling strength are discussed. The deck panels with several different cross-sectional profiles are assessed based on finite element analysis. The assessment covers the global and local stiffness, the maximum stresses and buckling strength. Compared to the original design, one of the panels with the modified profiles possesses significant improvement in all aspects evaluated. Most profiles provide lower compressive stress and higher local stiffness and significantly higher buckling strength.     

Lateral buckling of pultruded GRP I-section cantilevers

A series of lateral buckling tests on pultruded GRP I-section cantilever beams is described. Comparisons of the theoretical critical loads, determined from approximate formulae and numerical finite element eigenvalue analysis, with the test results are presented. They reveal that linear buckling analysis does not provide an accurate estimate, for use in design, of the maximum tip load that a GRP cantilever may support. It is concluded that both initial deflections and pre-buckling deformations may need to be accounted for in order to model accurately the response of tip loaded pultruded GRP cantilevers.     

Smooth postbuckling stresses by a modified finite element method

Exact postbuckling stresses usually vary fairly smoothly. Unfortunately, finite element postbuckling stresses tend to be much less well behaved. The result is that second order postbuckling constants determined by the finite element method may be highly inaccurate. The reason is that in finite element solutions transverse displacements associated with the buckling fields furnish too rapidly varying postbuckling strain contributions, while the postbuckling axial or membrane displacements contribute strain components that are sufficiently smooth, thus creating an internal postbuckling strain and stress mismatch. The present study suggests a modified finite element method that handles the problem, which is a special example of membrane locking, by introducing the postbuckling strains as independent variables. In general, the method provides rather complicated finite element expressions. However, by a suitable choice of interpolating functions, the resulting finite element equations themselves may be found to be the usual ones, and yet provide smooth postbuckling stresses and therefore good values of the postbuckling constants.     

Buckling Study of Thin‐walled Channel Beams with Double‐box Flanges in Pure Bending

Abstract: This paper provides the results of numerical and experimental investigations of buckling problems of cold‐formed, thin‐walled channel beams with double‐box flanges under pure bending. A local and global buckling analysis is realised numerically with the use of the finite strip method. A local buckling has been experimentally studied and also numerically with the use of the finite element method. Experimental tests of beams subjected to pure bending are conducted. The results of numerical and experimental investigations are presented and compared. A fundamental influence of double‐box flanges on the critical load is shown.     

焊接箱形截面不锈钢柱相关稳定性能分析

采用有限元法对焊接箱形截面不锈钢柱的局部与整体相关稳定性能进行分析,研究利用板件的屈曲后强度,以实现更为经济合理的构件截面设计。建立了可以准确模拟不锈钢非线性材料力学性能、截面焊接残余应力和构件的局部与整体几何初始缺陷等因素的精确有限元数值模型,并依据试验结果对模型的可靠性进行了验证。基于验证可靠的有限元模型,开展了系统参数分析,同时补充了大量的数值计算数据点。根据得到的试验和有限计算结果,对相关稳定承载力的理论计算方法进行了比较分析,表明现有的方法应用较为复杂,而且可能高估构件的相关稳定承载力。针对奥氏体型和双相型两类不锈钢提出了通用的计算修正系数,给出了新的直接强度法计算公式,经试验与有限元计算结果验证,表明其能够准确计算焊接箱形截面不锈钢柱的相关稳定承载力。     

Postbuckling and free vibrations of composite beams

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse deformations of a composite laminated beam accounting for the midplane stretching are derived. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial–integral–differential equation governing the transverse deformations. We find out that the governing equation for the postbuckling of symmetric or asymmetric composite beams has the same form as that of beams made of an isotropic material. Composite beams with fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions are considered. A closed-form solution for the postbuckling deformation is obtained as a function of the applied axial load, which is beyond the critical buckling load. To study the vibrations that take place in the vicinity of a buckled equilibrium position, we exactly solved the linear vibration problem around the first buckled configuration. Solving the resulting eigen-value problem results in the natural frequencies and their associated mode shapes. Both the static response represented by the postbuckling analysis and the dynamic response represented by the free vibration analysis in the postbuckling domain strongly depend on the lay-up of the laminate. Variations of the beam’s midspan rise and the fundamental natural frequency of the postbuckling domain vibrations with the applied axial load are presented for a variety of lay-up laminates. The ratio of the axial stiffness to the bending stiffness was found to be a crucial parameter in the analysis. This control parameter, through the selection of the appropriate lay-up, can be manipulated to help design and optimize the static and dynamic behavior of composite beams.     

Q460高强钢焊接工字形截面单伸臂梁整体稳定性能与设计方法研究

为研究Q460高强钢焊接工字形截面单伸臂梁的整体稳定性能以及完善规范中关于此类构件的设计方法,进行了6根集中荷载作用下Q460高强钢焊接工字形截面单伸臂梁的整体稳定性能试验,测量了试件的初始几何缺陷和截面残余应力。试验结果表明：当单伸臂梁整体失稳的控制梁段位于简支跨时,单伸臂梁的整体稳定承载力随伸臂长度比的增大而减小,截面高宽比较伸臂长度比对单伸臂梁整体稳定承载力的影响更大。在试验基础上,运用有限元程序创建考虑初始几何缺陷和残余应力的有限元模型对试验进行模拟,模拟结果与试验结果吻合良好;基于试验验证的有限元模型,分析荷载形式、荷载比例、简支跨长度、伸臂跨长度和截面高宽比等因素对Q460高强钢焊接工字形截面单伸臂梁整体稳定承载力的影响规律。基于特征值屈曲分析结果,回归出单伸臂梁的弹性屈曲临界弯矩计算公式,并通过对试验结果和有限元参数分析结果的回归提出了Q460高强钢焊接工字形截面单伸臂梁的极限弯矩计算公式。     

Local postbuckling of hat-stringer-stiffened composite laminated plates under transverse compression

In this paper, a closed-form method for the analysis of the local postbuckling behaviour of aircraft panels that are braced by hat-stringers is presented. The stiffened panels are loaded by transverse compression which is a load case that has been treated only scarcely in the open literature, and the corresponding buckling and postbuckling behaviour that eventually leads to failure of the panel is quite different to what is observed when a panel under longitudinal compression is considered. This contribution clarifies that the ultimate load bearing capacity of a stiffened panel with closed-profile stringers under transverse compression is governed by several consecutive stability cases. Firstly a closed-form approximate analysis method for the linear buckling analysis of the skin between two stringers taking the torsional stiffness of the hat-stringers into account is derived (stability case 1). Secondly, a simple Marguerre-type postbuckling analysis method is presented that accounts for the geometrically nonlinear behaviour of the panel skin after buckling (stability case 2) and enables a closed-form analysis of its effective width. Thirdly, the linear buckling analysis is adapted to the analysis of the panel skin under a stringer (stability case 3). It will be shown that stability cases 2 and 3 cannot be treated independently, but have to be considered interactively which necessitates an iterative procedure. The accuracy of the proposed analysis method, relying on the simplifying assumption of a perfectly flat plate rather than considering a cylindrically curved panel is established by comparison with results of accompanying geometrically nonlinear finite element calculations.     

Analysis and design of fiber reinforced plastic composite deck-and-stringer bridges

A comprehensive study on analysis and design of fiber reinforced plastic (FRP) composite deck-and-stringer bridges is presented. The FRP decks considered consist of contiguous thin-walled box sections and are fabricated by bonding side-by-side pultruded thin-walled box beams, which are placed transversely over FRP composite stringers. In this study, we review the modeling and experimental verification of FRP structural beams, including micro/macro-mechanics predictions of ply and laminate properties, beam bending response, shear-lag effect, and local and global buckling behaviors. A simplified design analysis procedure for cellular FRP bridge decks is developed based on a first-order shear deformation macro-flexibility (SDMF) orthotropic plate solution. The present approach can allow the designers to analyze, design and optimize material architectures and shapes of FRP beams, as well as various bridge deck configurations, before their implementation in the field. Experimental studies of cellular FRP bridge decks are conducted to obtain stiffness coefficients, and an example of a cellular FRP deck on optimized winged-box FRP stringers under actual track-loading is presented to illustrate the analytical method. The experimental-analytical approach presented in this study is used to propose simplified engineering design equations for new and replacement highway FRP deck-and-stringer bridges.     

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically non-linear three dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The non-linear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically non-linear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.     

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.     

Non-linear pre-buckling behavior of shear deformable thin-walled composite beams with open cross-section

A kinematic model is presented for thin-walled composite beams able to account for axial force, bending, torsion and warping. Shear deformations on the mid-surface are considered and modeled by means of a polynomial approximation. For this scope appropriate shape functions on the curvilinear abscissa along the cross-section mid-line are introduced.Small strains and moderate rotations are considered over the pre-buckling range.The model allows to predict the static non-linear behavior and the critical loads of composite pultruded beams.A finite element approximation is derived from a variational approach. Some numerical results are also presented revealing the importance of the shear terms on the mechanical response and their effect on the stability of pultruded composite members.     

冲击后含损伤复合材料格栅加筋板的后屈曲

采用数值分析方法研究了冲击后含损伤的复合材料格栅加筋板的后屈曲特性。基于Mindlin 一阶剪切理论和Von Karman 大挠度理论, 建立了冲击后蒙皮内含分层损伤复合材料格栅加筋板后屈曲分析的有限元方法; 分析中同时考虑了蒙皮和肋骨中纤维断裂、基体开裂等损伤累积造成的刚度的退化和蒙皮分层子板间的闭合接触效应, 为含损伤复合材料格栅加筋板的后屈曲特性研究提供了一种有效的数值分析方法。分析结果表明, 蒙皮分层面积较大时, 格栅加筋板出现蒙皮分层上子板的局部屈曲后仍然具有较强的继续承载能力, 而在后屈曲分析中, 应考虑损伤累积对格栅加筋结构承载能力的影响; 采用非线性虚拟界面元可成功处理分层子板间的闭合接触效应。      

A Novel Threshold Accelerometer With Postbuckling Structures for Airbag Restraint Systems

Based on the postbuckling theory of large deflection beams, the nonlinear stiffness of a postbuckling beam is deduced and in agreement with the results of buckling experiments. Then, a novel post machined threshold accelerometer is designed, which consists of eight oblique post beams with an inertial mass in the middle to ensure its single moving direction and an electrical contact part fabricated on the bottom of the inertial mass. The threshold accelerometer is an integration of a threshold sensor and an inertial driven actuator used in airbag restraint systems. When the acceleration reaches the threshold, the beams buckle and close the threshold accelerometer, and when it gets down to be a certain value, the accelerometer opens quickly under the effect of the elastic force developed by the postbuckling beams. Compared with the design models of other threshold accelerometers with linear beam structures, the nonlinear postbuckling beams are introduced as threshold sensing elements. A number of design factors such as the air film damping and the contact force are taken into full consideration, thus establishing the dynamic equation of the accelerometer under coupled forces. The dynamical simulation for the strong nonlinear system with elliptic integrals indicates its good threshold characteristic and high contact reliability. The threshold accelerometer responds within 4 ms when it is triggered by a threshold acceleration ac = 20 g, and cuts off quickly when the cutoff acceleration is under ad = 5 g. Meanwhile, the unstable contact time is only 0.02 ms for the contact force to reach 50 mN, which guarantees the contact resistance to be less than 20 mOmega. With the results of the dynamic simulation, supported by previous buckling experiments, the accelerometer can provide accurate threshold sensing without false actuations under interferences outside, especially electromagnetic and vibration interferences, and hence their wide applications in safe-arming systems.     

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。     

Simultaneous buckling design of stiffened shells with multiple cutouts

Buckling is usually initiated from a local region near the cutout for cylindrical stiffened shells under axial compression, and then the evolution of buckling waves is governed by the combined effects of local and global stiffness, which limit the load-carrying capacity. Therefore, a simultaneous buckling pattern is crucial for improving the structural efficiency. In this study, a multi-step optimization strategy for the integrated design of near and far fields away from cutouts is proposed, and the convergence criterion of buckling optimization is improved as a deformation-based index. The numerical implementation of the asymptotic homogenization method is utilized to construct an efficient finite element model for post-buckling analysis. A 5?m diameter stiffened shell in a launch vehicle demonstrates that the proposed framework can provide a simultaneous buckling design with high structural efficiency in an efficient manner. Both the buckling deformations and stress of the optimum design are more uniform compared to other optimum designs.     

Surface stress effects on the critical buckling strains of silicon nanowires

The objective of this paper is to quantify how nanoscale surface stresses impact the critical buckling strains of silicon nanowires. These insights are gained by using nonlinear finite element calculations based upon a multiscale, finite deformation constitutive model that incorporates nanoscale surface stress and surface elastic effects to study the buckling behavior of silicon nanowires that have cross sectional dimensions between 10 and 25 nm under axial compressive loading. The key finding is that, in contrast to existing surface elasticity solutions, the critical buckling strains are found to show little deviation from the classical bulk Euler solution. The present results suggest that accounting for axial strain relaxation due to surface stresses may be necessary to improve the accuracy and predictive capability of analytic linear surface elastic theories.     

Mixed state-vector finite element analysis for a higher-order box beam theory

If thin-walled closed beams are analyzed by the standard Timoshenko beam elements, their structural behavior, especially near boundaries, cannot be accurately predicted because of the incapability of the Timoskenko theory to predict the sectional warping and distortional deformations. If a higher-order thin-walled box beam theory is used, on the other hand, accurate results comparable to those obtained by plate finite elements can be obtained. However, currently available two-node displacement based higher-order beam elements are not efficient in capturing exponential solution behavior near boundaries. Based on this motivation, we consider developing higher-order mixed finite elements. Instead of using the standard mixed formulation, we propose to develop the mixed formulation based on the state-vector form so that only the field variables that can be prescribed on the boundary are interpolated for finite element analysis. By this formulation, less field variables are used than by the standard mixed formulation, and the interpolated field variables have the physical meaning as the boundary work conjugates. To facilitate the discretization, two-node elements are considered. The effects of interpolation orders for the generalized stresses and displacements on the solution behavior are investigated along with numerical examples.     

复合材料加筋圆拱壳的失稳特性分析

本文应用增量形式的拉格朗日列式法对其有纵横加筋的迭层圆拱壳在均布载荷作用下的稳定性进行了非线性有限元分析。文中应用Sander 壳体理论及横向剪切的影响, 推导了矩形壳元及与该壳元变形相协调的直梁元和曲梁元的切线刚度矩阵。编制了FORTRAN 计算程序。计算并分析了加筋拱壳的局部及整体失稳过程。