单层网壳结构稳定性分析方法研究

为了准确地分析具有初始几何缺陷的单层网壳结构整体稳定性,运用随机缺陷模态法、一致缺陷模态法和N阶特征缺陷模态法,对4个不同矢跨比的K8型单层网壳进行了近1300例弹塑性荷载-位移全过程分析,探讨不同分析方法的合理性和可行性。研究表明:随机缺陷模态法能较为科学地评估初始几何缺陷对结构稳定性的影响,但计算量较大;对稳定承载力系数样本进行统计特性分析时,空间样本数量n不应小于100;运用随机缺陷模态法确定网壳结构最终的稳定承载力系数时,建议采用“3σ”原则;采用最低阶屈曲模态模拟初始几何缺陷分布,求得的稳定承载力并非最不利,其保证率得不到有效保证;N阶特征缺陷模态法能够通过较少的计算量,得到满足“3σ”原则要求的稳定承载力,并能较为合理、安全地评估网壳结构的稳定性能;在运用N阶特征缺陷模态法时,建议N=20。     

考虑杆件初弯曲的网壳弹塑性稳定性的弱形式求积元分析

初始缺陷是影响网壳稳定性的主要因素之一。技术规程建议的一致缺陷模态法综合考虑了结点的位置偏差与杆件的初弯曲,但现有计算方法难于便捷地单独全面体现初弯曲的影响。该文基于几何精确梁理论构造了一种弱形式求积元模型。通过引入纤维模型模拟材料非线性,结合柱面弧长法实现了对空间曲梁结构的弹塑性大位移分析,通过算例验证了提出模型的有效性。该模型构建不需具体指定位移形函数,避免了使用有限元软件中的复杂建模过程。运用该模型计算了几类典型网壳在杆件初弯曲方向随机分布,不同弯曲挠度下的极限承载力。计算结果表明,在现有钢结构生产工艺下杆件初弯曲的缺陷对于网壳稳定性的影响较小,不起控制作用。通过与一致缺陷模态法的计算结果和空间网格结构技术规程计算的承载力进行对比,对规范的承载力计算公式提出了考虑特殊网壳形式及材料屈服强度的改进建议。     

基于反演推定的空间结构随机缺陷传播法

在空间结构施工过程监测和检测评估等工作中,需依据部分已测节点几何位形推断结构全部节点几何位形。该文提出随机缺陷传播算法,建立几何位置偏差在节点之间的传播法则,利用有限已知节点几何位形偏差反演推定空间结构整体几何缺陷,进而确定结构整体几何位形,并用随机偏差理论证明所生成的结构随机缺陷服从正态分布。对一个缩尺K6单层网壳模型进行实测和稳定分析,结果表明:相对于随机缺陷法和一致缺陷模态法,采用随机缺陷传播法生成的结构几何缺陷与实测几何缺陷接近,据此计算得到的极限承载力更接近结构承载力理论值。基于随机缺陷传播法得到的空间结构整体稳定极限荷载因子中位数,可作为结构的实际极限承载能力代表值。     

初始几何缺陷模式对单层球面网壳抗震性能的影响

为探索地震作用下单层网壳的最不利初始几何缺陷分布模式,对施加四种初始几何缺陷的单层球面网壳分别开展了抗震性能研究。参照相关文献选取一致缺陷模态一、一致缺陷模态二,特征值缺陷及一阶振型缺陷四种典型的初始几何缺陷分布模式,并介绍了四种初始几何缺陷模式的理论计算公式及施加于理想网壳的方法;通过有限元建模分析,考察了施加四种初始几何缺陷模式后单层网壳的变形及自振频率变化;分别对跨度为100 m和其它不同参数的单层球面网壳施加上述四种初始几何缺陷模式、并分别输入七条选取于唐山地震主震实测三向地震动记录开展动力时程分析,考察四种初始几何缺陷模式对单层网壳动力工作性能及承载能力的影响。结果显示,对于矢跨比为1/3的单层球面网壳,施加一致缺陷模态一后网壳的最大节点位移值较大;其它参数的单层球面网壳,施加了特征值初始几何缺陷模式后网壳的最大节点位移值较大。该研究可对单层网壳开展动力工作性能分析及结构设计考虑地震作用时最不利初始几何缺陷模式的选取提供参考。     

随机缺陷模态法在弦支穹顶稳定性计算中的应用

初始几何缺陷对弦支穹顶的稳定性能有较大的影响。在结构整体稳定性计算中,利用随机缺陷模态法为结构施加合理的初始几何缺陷是该文的主要研究目的。首先采用一致缺陷模态法,在不同初始几何缺陷下,对肋环2型弦支穹顶结构进行稳定性能分析,然后讨论随机缺陷模态中方差的取值方法,并利用该方法对肋环2型弦支穹顶结构进行了210种不同初始几何缺陷下的稳定性能分析,两种分析方法所施加缺陷的最大值均为结构跨度的1/300。分析结果表明:结构的初始几何缺陷对结构的稳定性能影响较大,考虑初始几何缺陷后结构稳定性能为完善结构的50%左右,且采用一致缺陷模态法时也需通过考虑不同缺陷分布形式的多次计算才能合理评估结构的稳定性能,建议在跨度较大、较为复杂的结构中采用随机模态法来考虑初始几何缺陷对结构稳定性能的影响。     

基于改进的同伦随机有限元法的随机参数结构弹性稳定性分析

结构参数的不确定性将对结构稳定性产生不可忽视的影响，实现随机结构屈曲荷载与屈曲模态的高效高精度求解和统计分析，对结构设计与安全评估有重要意义。该文基于随机残差最小化法改进现有的同伦随机有限元法，并利用新方法高效高精度地求解了大变异随机参数结构的屈曲特征值和屈曲模态。将随机参数结构的屈曲特征值和屈曲模态以同伦级数的形式表达，并给出了同伦级数中任意阶系数的显式递推表达式；在此基础上，定义了关于弹性屈曲方程近似解的随机残余误差，通过使该随机残余误差最小化，得到了优化的随机屈曲特征值和屈曲模态的同伦级数展开表达式。该文提出的改进的同伦随机有限元法能够实现同伦级数展开的自动寻优，有效避免了现有同伦随机有限元法(HSFEM)计算精度易受样本选点影响的缺点。当随机参数变异性较大时，随着级数展开阶数的增加，该文方法计算结果除了能保持良好的收敛性外，相比于HSFEM具有更好的稳定性，而摄动随机有限元法则可能出现发散现象；与蒙特卡洛模拟法相比，新方法具有很高的求解效率。通过强非线性函数算例以及变截面轴心受压杆和框架结构的弹性稳定性分析说明了该文方法的有效性。     

张弦梁平面外弹性稳定性能研究

无平面外支撑的张弦梁在平面内受荷过程中可能发生平面外失稳。该文首先将张弦梁的平面外失稳分为索撑体系的失稳和张弦梁整体失稳,并采用平衡法和能量法对索撑体系的稳定性进行研究;其次对于张弦梁平面外整体失稳,指出将撑杆和拉索的作用等效为集中力、提取钢梁进行稳定设计的方法并不安全;该文采用Ritz法建立张弦梁的势能方程,结合势能驻值原理,得到张弦梁在全跨均布荷载和纯弯荷载下的平面外弹性屈曲荷载,结果与有限元吻合较好。该文得到的张弦梁平面外屈曲荷载计算公式对其平面外稳定设计具有参考作用。     

考虑杆件失稳的网壳结构稳定分析方法

网壳结构在整体失稳之前可能存在杆件失稳, 但目前网壳稳定分析中大多没有考虑杆件失稳问题。该文通过引入杆件初始缺陷的方法研究杆件失稳对网壳结构整体稳定性的影响。首先讨论了单根杆件的单元划分数量、缺陷形式和缺陷幅值的确定方法, 进而分析网壳结构单根杆件失稳后的内力变化及对网壳整体稳定性的影响。算例分析表明:网壳整体稳定分析中可通过对杆件施加初始缺陷有效地考虑杆件失稳的影响;对整体失稳前存在杆件失稳的网壳结构, 有必要引入杆件缺陷考虑杆件失稳的影响, 不考虑杆件失稳会过高估计结构的承载能力。最后提出了网壳结构稳定分析的合理计算流程, 与试验结果的比较表明该文方法合理、有效。     

轴压作用下矩形开口圆柱壳的稳定性

利用数值方法系统研究带矩形开口的薄壁圆柱壳的稳定性能．对矩形开口的周向角度、高度、轴向位置、开口数量等几何参数进行比较分析,并考察两类几何初始缺陷对结构稳定性的影响．分析表明,影响矩形开口圆柱壳轴压下稳定性的主要因素是周向开口角度,屈曲荷载随开口角度的增大而线性下降,而开口高度及开口的轴向位置对屈曲荷载的影响很小．此外,矩形开口圆柱壳对以特征值屈曲模态分布的初始缺陷并不敏感,但对周向轴对称凹陷十分敏感．     

某大跨度网壳结构的稳定性分析

稳定性分析是网壳结构,特别是单层网壳结构设计中的关键问题。该文以某大跨度球类馆为工程实例,采用非线性有限元法针对承载力计算时的11种工况进行整体稳定计算,考虑了材料和几何非线性,对实际工程进行了第一类和第二类稳定分析,其中,第二类稳定分析采用截面边缘纤维屈服准则,该文给出了两种典型工况的第一类稳定屈曲模态和两类稳定系数。结果表明:该网壳结构的第一类稳定符合相关规范的要求;其第二类稳定性较差。因此,第二类稳定分析应该受到重视。     

模态缺陷条件下复合材料柱形壳屈曲特性

为了开展多模态缺陷条件下复合材料柱形壳的屈曲特性研究,进行了理想柱形壳在轴压工况下的线性屈曲分析,得出前50阶屈曲失稳模式,即模态缺陷;基于弧长法研究不同模态缺陷条件下复合材料柱形壳的非线性屈曲特性;将有限元分析结果、NASA SP-8007规范计算结果与Bisagni试验结果作对比分析。结果表明:对于轴压柱形壳屈曲问题,第1阶模态缺陷不是最差缺陷,在第1阶模态缺陷条件下求出的非线性屈曲载荷比试验值高出较多;高阶模态缺陷条件下的复合材料柱形壳非线性屈曲计算结果与试验结果最为吻合,两者相差较少;屈曲载荷下降受缺陷形状、幅值双重影响,复合材料柱形壳屈曲计算需考虑多模态问题;NASA求出的屈曲载荷非常保守,低于试验值较多,用NASA方法进行复合材料柱形壳的设计,往往会导致结构笨重、材料浪费、性能降低。     

The use of initial imperfection approach in design process and buckling failure evaluation of axially compressed composite cylindrical shells

Thin-walled cylindrical shells are susceptible to buckling failures caused by the axial compressive loading. During the design process or the buckling failure evaluation of axially-compressed cylindrical shells, initial geometric and loading imperfections are of important parameters for the analyses. Therefore, the engineers/designers are expected to well understand the physical behaviours of shell buckling to prevent unexpected serious failure in structures. In particular, it is widely reported that no efficient guidelines for modelling imperfections in composite structures are available. Knowledge obtained from the relevant works is open for updates and highly sought. In this work, we study the influence of imperfections on the critical buckling of axially compressed cylindrical shells for different geometries and composite materials (Glass Fibre Reinforced Polymer (GFRP), Carbon Fibre Reinforced Polymer (CFRP)) and aluminium using the finite element (FE) analysis. Two different imperfection techniques called eigenmode-affine method and single perturbation load approach (SPLA) were adopted. Validations of the present results with the published experimental data were presented. The use of the SPLA for introducing an imperfection in axially compressed composite cylindrical shells seemed to be desirable in a preliminary design process and an investigation of a buckling failure. The knockdown factors produced by the SPLA were becoming attractive to account for uncertainties in the structure.     

Numerical analysis and experimental correlation of composite shell buckling and post-buckling

This paper deals with the buckling and post-buckling behaviour of carbon fibre reinforced plastic cylindrical shells under axial compression. The finite element analysis is used to investigate this problem and three different types of analysis are compared: eigenvalue analysis, non-linear Riks method and dynamic analysis. The effect of geometric imperfection shape and amplitude on critical loads is discussed. A numerical–experimental correlation is performed, using the results of experimental buckling tests. The geometric imperfections measured on the real specimens are accounted for in the finite element model. The results show the reliability of the method to follow the evolution of the cylinder shape from the buckling to the post-buckling field and good accuracy in reproducing the experimental post-buckling behaviour.     

电除尘器壳体墙板立柱结构体系缺陷敏感性研究

电除尘器是用于消除大气烟尘的重要环保设备,壳体是其中最重要的工艺部分。壳体墙板为加劲钢板,与立柱连续焊接连接,组成共同承载的结构体系。壳体承受的横向荷载为负压与风荷载,作用在墙板上,壳体承受的竖向荷载主要作用在立柱上。墙板的初始缺陷会影响立柱的承载能力。该文通过非线性有限元方法,研究不同缺陷幅值时,完善结构极值点变形缺陷模态、完善结构非线性分岔点变形缺陷模态、特征值屈曲缺陷模态、墙板正弦波形缺陷模态以及墙板安装过程中的焊接收缩残余变形与残余应力对立柱承载力的影响。当缺陷幅值一定时,各种初始几何缺陷形式中,以完善结构的极值点变形缺陷模态为最不利。墙板安装过程中的焊接收缩引起的残余应力对于立柱承载是有利的,但是提高承载力很小。随着焊接收缩量的增大,残余应力值增大,同时考虑残余应力和残余变形影响得到的立柱承载力比仅考虑残余变形得到的承载力的增加量变大。     

Stimulating Equivalent Geometric Imperfections for the Numerical Buckling Strength Verification of Axially Compressed Cylindrical Steel Shells

A geometrically and materially nonlinear analysis with imperfections included (GMNIA) is currently the most sophisticated and perspectively the most accurate method of a numerical buckling strength verification. By this way, equivalent geometric imperfections, which have to cover the influence of all deviations from the nominal data of the resistance parameters, are fundamental. The problem of consistent equivalent geometric imperfections includes the problems of their shape and size. It is recommended to start from the failure modes of the perfect structure in order to get imperfection patterns, which are unfavourable with respect to buckling resistance, relevant referring to manufacture and easy to use. The influence of the imperfection length is not sufficiently attended in the present design codes. It is proposed to use the full wave length of the ideal ring buckling mode as the imperfection length of the equivalent geometric imperfection for the basic buckling case of the axially compressed cylindrical shell. Finally, proposals are made for consistent equivalent geometric imperfection amplitudes of this buckling case.     

The dynamic elastic buckling of a circular arch with finite displacements and initial imperfections

The equilibrium equations for elastic circular arches are established using the principle of virtual work. The nonlinear partial differential equations of motion are solved using a finite difference method (Park's method for time difference). The dynamic stability of a hinged and a clamped elastic circular arch with a uniform step load is analysed with finite deformations and initial geometric imperfections. Results show that the buckling mode varies with the value of the arch half angle, θ₀. The boundary condition and initial imperfection amplitude also effect the buckling mode. A nearly perfect arch usually buckling with a “direct” buckling form, while an imperfect arch with an “indirect” buckling form. The effect of θ₀ on the ratio p_d/p_s (p_d is the dynamic critical load and p_s the static critical load) is shown for different initial imperfections and different boundary conditions.     

Effects of thickness and modal imperfection amplitude on elastic collapse pressure of a cross-ply imperfect ring

Effects of thickness and modal imperfection amplitude on mode 2 elastic collapse pressures of thin, moderately thick and thick cross-ply perfect and imperfect rings are investigated in detail. A recently developed nonlinear resonance (eigenvalue) based semi-analytical solution technique is employed here for computation of the elastic mode 2 collapse pressures of thin to thick cross-ply rings, weakened by modal or harmonic type imperfections. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the perfect/imperfect cross-ply ring. Interesting and hitherto unavailable numerical results pertaining to the effects of thickness and amplitude of modal imperfection on the hydrostatic collapse pressures of imperfect cross-ply rings and comparison with their perfect counterparts are also presented.