考虑荷载偏心的梯形波纹腹板工字梁弯矩修正因子

对不同荷载偏心和端部约束条件下梯形波纹腹板工字梁的弯矩修正因子进行研究。通过有限元屈曲分析获取弯曲修正因子。采用梁单元、新横截面属性公式及新梯形波纹腹板工字梁翘曲常数,建立有限元程序。将弯矩修正因子的理论结果与软件ABAQUS的壳单元模拟结果进行对比。以波纹形式和长度为参数,进行了大量有限元分析。通过数值研究,对理论结果进行验证,并将SSRC规范中的弯矩修正因子与有限元结果对比。将SSRC规范中弯矩修正因子Cb改进为Cb,c,提高了侧向畸变屈曲强度的准确性。     

正八边形钢板腹梁弯曲性能试验研究

基于蜂窝钢梁外观,提出了一种新型空腹式钢结构主梁——正八边形钢板腹梁。借鉴蜂窝钢梁挠度计算中费氏空腹桁架理论,推导了该结构在弯曲荷载作用下的挠度变形公式,并通过有限元方法进行了验证。进一步地,为了研究该结构的弯曲性能,根据《公路钢结构桥梁设计规范》(JTG D64-2015)要求,设计了1根缩尺模型试件,通过两点加载方式对其变形能力、应变特点和破坏方式进行了试验研究。采用通用有限元软件ABAQUS 2017建立了该结构非线性有限元分析模型,并将试验结果与有限元模拟结果进行了对比研究。结果表明:对于腹板非连续的正八边形钢板腹梁,采用费氏空腹桁架理论提出的结构挠度计算公式具有较好的精度;通过静载弯曲试验发现,正八边形钢板腹梁发生破坏时,顶板纯弯段区域出现了局部屈曲现象,同时腹板发生屈曲变形;经过合理设计的正八边形钢板腹梁在弯曲荷载作用下具有较好的抗弯性能。     

切口梁弯扭屈曲承载力参数分析

利用有限元方法,对切口梁进行弯扭屈曲分析。研究表明:切口长度、切口高度、梁的跨度对切口梁弯扭屈曲承载力有着重要的影响。与试验结果的对比验证了计算结果的准确性和适用性。根据有限元数据结果,提出了切口梁整体稳定系数计算公式。     

工字形截面楔形梁的侧向屈曲:新理论

针对工字形截面楔形梁的侧向屈曲提出了一个全新的理论。在工字形截面楔形梁的分析中首先采用线性分析,其中梁的两个翼缘和腹板的变形能力根据薄壁构件的基本假定决定。随后,基于屈曲分析的经典变分原理,提出该梁侧向屈曲分析中的总势能。利用该理论计算出楔形悬臂梁和工字形简支梁的侧向屈曲荷载,并将其与分别采用2个壳单元和2个梁单元建模的有限元分析结果对比。这2个梁单元模型分别代表了利用柱状梁单元和典型楔形梁理论的等效方法。对比显示:按照新提议的方法计算出来的总势能要比按以往方法计算出来的数值更精确,这表示新提议的理论要优于以往的理论。同时发现,利用柱状梁的等效法来计算楔形梁的屈曲荷载可能会得出不可靠的结果。     

切口梁弯扭屈曲承载力参数分析

利用有限元方法,对切口梁进行弯扭屈曲分析.研究表明:切口长度、切口高度、梁的跨度对切口梁弯扭屈曲承载力有着重要的影响.与试验结果的对比验证了计算结果的准确性和适用性.根据有限元数据结果,提出了切口梁整体稳定系数计算公式.     

圆孔蜂窝梁的弯扭屈曲分析

为了对纯弯状态下圆孔蜂窝梁的弯扭屈曲进行研究,将蜂窝梁翼缘和腹板分离,采用有限元软件ANSYS对蜂窝梁开圆孔腹板进行侧向纯弯分析,由挠度-刚度关系反算侧向刚度,得出开孔腹板相对于实心腹板的刚度折减系数ky。考虑开孔腹板的径高比和距高比,经拟合给出了刚度折减系数ky的计算公式,用该系数对蜂窝梁的自由扭转刚度进行修正,代入实腹工字截面梁弯扭屈曲临界弯矩计算公式,得到蜂窝梁的相应计算公式。最后利用该公式分别对不同跨度、不同孔况的简支蜂窝梁在纯弯状态下的弯扭屈曲临界弯矩进行计算,并与有限元分析结果进行对比。分析结果表明,修正后的临界弯矩计算公式具有较高精度。     

纯弯曲蜂窝梁弯扭屈曲的有限元分析

为了研究蜂窝梁纯弯状态下的弯扭屈曲,笔者利用有限元软件ANSYS对两种不同截面的H形钢梁在纯弯曲时的弹性弯扭屈曲临界弯矩进行了分析,对所得到结果与理论公式计算的结果进行了比较,结果吻合的较好,这表明所选单元及计算方法的正确性。根据这一结果,笔者认为蜂窝梁在纯弯曲时的弹性弯扭屈曲临界荷载也可以采用该软件进行模拟分析。然后,对开孔率相同跨度不同以及跨度相同度开孔率不同的蜂窝梁进行了计算,并对计算结果与原型钢进行了比较分析。分析结果表明,蜂窝梁的弯扭屈曲临界弯矩略高于原型钢钢梁,其值随着开孔率的逐渐增加而降低,但是开孔率的影响并不十分明显。     

纯弯曲蜂窝梁弯扭屈曲的有限元分析

为了研究蜂窝梁纯弯状态下的弯扭屈曲，笔者利用有限元软件ANSYS对两种不同截面的H形钢梁在纯弯曲时的弹性弯扭屈曲临界弯矩进行了分析，对所得到结果与理论公式计算的结果进行了比较，结果吻合的较好，这表明所选单元及计算方法的正确性。根据这一结果，笔者认为蜂窝梁在纯弯曲时的弹性弯扭屈曲临界荷载也可以采用该软件进行模拟分析。然后，对开孔率相同跨度不同以及跨度相同度开孔率不同的蜂窝梁进行了计算，并对计算结果与原型钢进行了比较分析。分析结果表明，蜂窝梁的弯扭屈曲临界弯矩略高于原型钢钢梁，其值随着开孔率的逐渐增加而降低，但是开孔率的影响并不十分明显。     

考虑剪切变形影响的空间管桁架组合梁挠度计算与分析

为研究新型空间管桁架组合结构的变形特点,将空间管桁架组合梁弯曲受力行为分解为等效空腹虚拟梁的弯曲作用和腹杆组成的虚拟桁架作用。利用虚功原理建立了考虑空腹式腹杆剪切变形影响的挠度计算公式,并采用模型梁加载试验与有限元分析法对计算挠度进行了对比分析。结果表明:剪切变形产生的挠度为计算总挠度的52%,为弯曲作用产生的计算挠度的1.07倍;在各级荷载作用下,考虑剪切变形影响的计算挠度与试验、有限元结果吻合较好,平均偏差分别为5%和2%,试验值与有限元计算值的平均偏差为2%;实测结果验证了计算公式的正确性和有限元模型的合理性。文中建立的挠度计算公式为此类结构在弹性状态时的挠度计算提供了一种准确的简化计算方法。     

铝合金梁弯扭稳定系数的试验研究及数值分析

本文依托国家标准《铝合金结构设计规范》编制研究项目,采用数值分析与试验相结合的手段研究了铝合金梁弯扭稳定系数的计算问题。首先根据铝合金材料的Ramberg-Osgood本构关系,近似地将梁屈曲时截面边缘纤维的切线模量应用于全截面,由此得出无缺陷铝合金梁弯扭稳定系数的计算式;接着采用有限元数值模拟技术,应用壳板单元结合材料的随动强化模型,并同时考虑构件的初始缺陷,对强硬化和弱硬化合金分别拟合出Perry-Robertson形式的铝合金梁弹塑性弯扭屈曲稳定系数计算公式;最后,针对梁弯扭屈曲时侧向扭转的特点,合理设计了一套试验装置,并进行了铝合金拉伸力学性能的测定和10根跨中受集中力作用的简支工字梁弯扭屈曲承载力的测定,通过与试验结果的比较,验证了拟合公式的正确性。     

Finite element formulation for inflatable beams

The discretized nonlinear equations for bending and buckling of inflatable beams are written by use of the virtual work principle with Timoshenko's kinematics, finite rotations and small strains. The linearized equations around a pre-stressed reference configuration are then deduced, giving rise to a new inflatable beam finite element. The stiffness matrix contains the shear coefficient and the internal pressure. Use is made of the particular 3-node beam element to investigate the bending and the buckling of a cantilever beam, the deflection of a pinched torus and the buckling of a torus submitted to a radial compressive force. The numerical results obtained with the beam element are shown to be close to analytical and three-dimensional (3D) membrane finite element results. The validity of the numerical results is discussed, in connection with the concepts of the crushing force or the wrinkling pressure of the inflated beam.     

Bending and buckling of inflatable beams: Some new theoretical results

The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.     

Deflections of highly inflated fabric tubes

Inflatable beams made of modern textile materials with important mechanical characteristics can be inflated at high pressure. The aim of the paper is to present experimental, analytical and numerical results on the deflections of highly inflated fabric tubes submitted to bending loads. Experiments are displayed and we show that tube behaviour looks like that of inflatable panels (Thin-Walled Struct. 40 (2002) 523–536). Equilibrium equations are once again written in the deformed state to take into account the geometrical stiffness and the following forces. The influence of the shear stress cannot be neglected and Timoshenko’s beam theory is used. A new inflatable tube theory is established and simple analytical formulas are given for a cantilever-inflated tube. Comparisons between analytical and experimental results are shown. A new inflatable finite tube element is constructed by use of algebraic operations, because the compliance matrix of the cantilever beam is not symmetric. Comparisons between experimental, analytical and numerical results prove the accuracy of this beam theory and on this new finite element for solving problems on the deflections of highly inflated tubes.     

Inflation and bending of an orthotropic inflatable beam

An inflatable beam is an airtight structure made of a soft technical fabric and subjected to an internal pressure which gives it a final cylindrical shape, a pre-stress in the membrane and a bearing capacity. Against all appearances, it is not a standard beam and it requires a specific formulation in order to take account of the internal pressure which plays a key role in its mechanical response.This work deals with inflatable beams made of orthotropic materials. The first part of the paper is concerned with the inflation of the membrane tube, an important stage which is often neglected so far in the literature. As preliminaries of the bending problem studied in the next part of the paper, the constitutive law related to the inflated state of the tube – not the natural state – is investigated. It will be shown that the constitutive law related to the inflated pre-stressed state is not the same as the constitutive law related to the natural state. Expressions of the material coefficients involved in the former constitutive law will be established from the material coefficients defined on the natural reference configuration which are the only ones supposed to be known. The second part of the paper deals with the bending of the inflatable beam. The Timoshenko beam kinematics will be chosen because of the significant shear effect in the tube wall and the problem will be formulated in finite deformations in order to account for all the nonlinear effects, in particular the action due to the internal pressure which is a follower load. The nonlinear system of equations obtained will then be linearized around the pre-stressed configuration and will result in a more tractable linear system. The proposed formulation allows a comprehensive study of the influence of the internal pressure on the geometry and material properties of orthotropic inflatable beams. The analytical results will be compared with numerical results obtained from a nonlinear membrane finite element code.     

Deflections of inflatable fabric panels at high pressure

Inflatable structures made of modern textile materials with important mechanical characteristics can be inflated at high pressure (up to a several hundreds of kPa). They can be used as strong building elements thanks to their mechanical strength. The aim of the paper is to present experimental and analytical studies on the behaviour of inflated fabric panels at high pressure and submitted to bending loads. It is shown that inflatable structures cannot be viewed as ordinary plates or beams, because their deformation pattern is quite different. Experiments show that their behaviour depends on the applied load, the inflation pressure, and the constitutive law of the fabrics. Equilibrium equations are written in the deformed state to take into account the influence of geometrical stiffness and the following forces. A Timoshenko’s beam theory must be used because sections of the panels do not satisfy the usual Bernoulli’s beam theory. A new inflatable beam theory is developed. Wrinkling loads are derived from equilibrium equations. Deflections satisfy the fact that the compliance of the inflatable panel is the sum of the beam compliance and of the yarn compliance. Comparisons between the results of our modelling and experimental results are shown and prove the accuracy of this theory on the mechanical strength of inflatable structures at high pressure.     

Free vibration analysis of inflatable beam made of orthotropic woven fabric

The free vibration of inflatable beams was studied using the dynamic stiffness method. A 3D Timoshenko beam with a homogeneous orthotropic woven fabric (OWF) was considered. Using the usual total Lagrangian form of the virtual work principle, the model took the geometric nonlinearities and the inflation pressure follower force effect into account. The nonlinear equilibrium equations were then linearized around the prestressed reference configuration. The exact dynamic stiffness matrix was developed by directly solving the governing differential equations of a 3D loaded inflatable beam in a free vibration. The effects of the inflation pressure, fabric mechanical properties and the boundary conditions on the natural frequencies and mode shapes of the inflatable beams were demonstrated. The proposed model was validated favorably through its comparison with a 3D thin shell finite element model and an isotropic fabric model found in the literature.     

Analytical buckling analysis of an inflatable beam made of orthotropic technical textiles

An analytical approach was considered to study the buckling and the behavior of an inflatable orthotropic beam subjected to uniform compression loads under different boundary conditions. In order to assess the stability of inflatable structures, it is necessary to evaluate the critical load of the inflatable components in their pressurized configurations. First, a 3D inflatable orthotropic beam model based on the Timoshenko's kinematics was briefly introduced: the nonlinearities (finite rotation, follower forces) were included in this model. The nonlinear equilibrium equations were derived from the total Lagrangian form of the virtual work principle: the linearized equations were then obtained. By solving these linearized equations, an analytical expression of the critical buckling load was obtained. This critical buckling load was investigated through several load cases with several boundary conditions. The discrepancy due to the orthotropic character between the present model and the isotropic models found in the literature was evaluated, as well as the influence of the inflation pressure and the fabric mechanical properties on the value of critical load. The buckling mode shapes were also determined. To check the limit of validity of the results, the wrinkling load was also presented in every case.     

Wrinkling prediction of cylindrical and conical inflated cantilever beams under torsion and bending

The combined load case of bending and torsion of a cantilever inflated beam is a load case that has not been studied extensively. When a series of inflated beams is placed parallel to each other as can be the case for an inflatable wing, each beam experiences a combination of torque and bending. A theoretical model already exist for such a load case but it is limited to membrane like materials. This paper deals with beams made of materials that need to be treated like a shell. It requires a modification for the wrinkling load due to solely bending and solely torsion. Semi-empirical expressions for both cases are presented for both cylindrical and conical shaped beams.     

Bending and optimisation of an inflated braided beam

Two braided inflatable beams have been made that differ in the number of axial fibres that are placed parallel to the length, and in the angle at which the bias fibres are placed. Each beam consists of a silicone rubber bladder, two end caps and a dry carbon fibre braid placed over the silicone bladder. Experimental and theoretical analysis of the beams have been revealed that due to bending, the beams initially deflect in a linear manner like the Euler–Bernoulli beam model predicts. Once the stress in the axial fibres becomes zero, wrinkling occurs resulting in a significant loss of bending stiffness. The two beams that were tested were optimised for minimum deflection at a constant volume of fibres. The stiffest design has the maximum possible amount of fibres in parallel to the beam.     

Nonlinear theory of non-uniform torsion of thin-walled open beams

A nonlinear theory of non-uniform torsion based on finite displacements is developed. Expressions for the finite nonlinear strains in Lagrangian coordinates and the Kirchhoff stresses for thin-walled open beams are presented. Using the principle of stationary total potential, the dual forms of the beam equilibrium equations are derived. For conservatively loaded thin-walled open beams a static stability criterion, based on the positive definiteness of the second variation of the total potential, is presented. The criterion developed takes into account the effects of changes in beam geometry such as initial bending curvature, prior to instability.