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.     

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δ_max are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.     

初始缺陷对三向张弦梁结构整体稳定性影响研究

三向张弦梁结构是新广州站工程采用的一种新型张弦梁结构,因此有必要对三向张弦梁结构的整体稳定性能进行深入的研究。该文首先对随机缺陷模态法进行了改进,使其更适用于网壳与张弦梁混合结构的缺陷稳定性分析。然后分别采用改进的随机缺陷模态法和一致缺陷模态法对三向张弦梁结构的缺陷稳定性进行了研究。分析结果表明:改进后的随机缺陷模态法更适用于网壳和拱梁混合结构形式的缺陷稳定性分析;缺陷越大,该三向张弦梁结构对缺陷越敏感,整体稳定性能受缺陷的影响越大;与理想结构破坏模式最接近的特征值屈曲模态为最不利的特征值屈曲模态,按此模态施加初始缺陷后的结构承载力最低;按非线性屈曲模态对结构施加缺陷得到的结构极限承载力小于按特征值屈曲模态施加缺陷的情况,与随机缺陷模态法的结果最为接近。     

Isogeometric stability analysis of thin shells: From simple geometries to engineering models

The buckling properties of thin-walled structures are sensitive to different sources of imperfections, among which the geometric imperfections are of paramount importance. This work contributes to the methodology of shell buckling analysis with respect to the following aspects: first, we propose an isogeometric analysis framework for the buckling analysis of shell structures which naturally eliminates the geometric discretization errors; second, we introduce a parameter-free Nitsche-type formulation for thin shells at large deformations that weakly enforces coupling constraints along trimmed boundaries. In combination with the finite cell method, the proposed conceptual modeling and analysis framework is able to handle engineering-related shell structures; and third, we introduce a NURBS modeling of measured geometric imperfection fields, which is much closer to the true imperfection shape compared to the classically used faceted FE models. We demonstrate with a number of benchmark problems and engineering models that our proposed framework is able to fully compete with established and highly sophisticated finite element formulations but at a significant higher level of accuracy and reliability of the analysis results.     

初始缺陷对耐压结构承载性能影响

目的基于有限元方法,通过分析研究深海耐压圆筒结构在不同初始缺陷下的屈曲压力,研究初始缺陷对厚壁圆筒承载极限的影响。方法建立了三维厚壁筒模型,分别研究了圆筒在初始几何缺陷、初始应力缺陷和两种缺陷复合的状态下,结构的承载性能,并将得到的结果与理想状态下的结构作对比。结论结果表明,无论是初始几何缺陷,还是初始应力缺陷,都会降低结构的承载极限。     

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。     

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。     

Buckling analysis of imperfect I-section beam-columns with stochastic shell finite elements

Buckling loads of thin-walled I-section beam-columns exhibit a wide stochastic scattering due to the uncertainty of imperfections. The present paper proposes a finite element based methodology for the stochastic buckling simulation of I-sections, which uses random fields to accurately describe the fluctuating size and spatial correlation of imperfections. The stochastic buckling behaviour is evaluated by crude Monte-Carlo simulation, based on a large number of I-section samples, which are generated by spectral representation and subsequently analyzed by non-linear shell finite elements. The application to an example I-section beam-column demonstrates that the simulated buckling response is in good agreement with experiments and follows key concepts of imperfection triggered buckling. The derivation of the buckling load variability and the stochastic interaction curve for combined compression and major axis bending as well as stochastic sensitivity studies for thickness and geometric imperfections illustrate potential benefits of the proposed methodology in buckling related research and applications.     

考虑节点偏差、杆件缺陷与偏心的单层三向柱面网壳稳定性研究

单层柱面网壳属于缺陷敏感型结构.为了理清节点偏差、杆件缺陷与杆件偏心对其稳定承载能力的影响程度:提出了能同时考虑三种缺陷的力学模型,并详细阐述了各种缺陷的实现方法;深入研究了三种缺陷及其耦合作用对柱面网壳稳定承载能力的影响规律;提出了确定三种缺陷最不利组合形式的方法.主要得出如下结论:柱面网壳稳定承载能力对节点偏差最为...     

Finite element investigations on the dynamic plastic buckling of a slender beam subject to axial impact

The dynamic plastic buckling response of slender beams, with geometric imperfections, subject to an axial impact is modelled by the finite element method. One of the primary objectives for the current study was the development of an accurate numerical model, which was validated by comparison with experimental investigations. A sensitivity analysis was conducted that considered the element aspect ratio, element formulation, constitutive relationship, boundary condition and type of geometric imperfection. The buckling response was defined by a normalized modal parameter as a function of the effective slenderness ratio. The normalized modal parameter accounted for the axial position and amplitude of the transverse peak buckle with respect to the local stiffness characteristics and natural frequency parameters. For the parameters considered, the influence of modelled boundary conditions and element formulation on the computed buckling response was established. In relative terms, the aspect ratio, imperfection model and contact mechanics was of secondary importance on the modal behaviour.     

含单分层损伤复合材料层合梁的动力屈曲研究

采用有限差分（FDM）方法求解了含初始缺陷和单个分层损伤复合材料层合梁的轴向刚性质量块撞击的脉冲动力屈曲问题。基于Hamilton原理导出了考虑所有惯性影响以及一阶横向剪切变形（FSDT）影响时单个分层损伤复合材料梁的非线性动力屈曲控制方程；采用B—R准则判断梁动力屈曲时刻，同时确定刚性质量块的临界冲击速度。重点研究脱层、冲击速度、初始几何缺陷等因素对复合材料层合梁脉冲动力屈曲的影响。     

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.     

Thermal Postbuckling of Imperfect Shear-Deformable Laminated Plates on Two-Parameter Elastic Foundations

Thermal postbuckling analysis is presented for a simply supported, shear-deformable composite laminated plate subjected to uniform or nonuniform parabolic temperature loading and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Reddy's third-order shear-deformation plate theory with von Karman nonlinearity is used. The governing equations also include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, plate aspect ratio, fiber orientation, thermal load ratio, and initial geometric imperfections, is studied. Typical results are presented in dimensionless graphical form.     

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。     

受轴压黏弹性层合圆柱壳的极值点蠕变失稳

基于Donnell薄壳理论, 采用准弹性方法, 分析了含初始几何缺陷黏弹性层合圆柱壳极值点形式的延迟失稳特征。由轴向缩短量的突然增加定义失稳临界时间, 对玻璃纤维/环氧树脂层合圆柱壳进行了数值计算。结果表明: 圆柱壳存在临界时间趋于无穷的持久临界荷载; 表征延迟失稳程度的瞬时弹性临界荷载与持久临界荷载之差值随着初始几何缺陷的增加而减小; 边界条件、 铺设方式对延迟失稳的影响机制可通过对应弹性层合圆柱壳的缺陷敏感性分析来考察。      

Postbuckling Analysis of Shear-Deformable Composite Laminated Plates on Two-Parameter Elastic Foundations

Postbuckling analysis is presented for a simply supported, shear-deformable, composite laminated plate subjected to uniaxial compression and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Two cases of in-plane boundary conditions are considered. The formulations are based on Reddy’s higher-order shear-deformation plate theory, including plate–foundation interaction. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, the character of the in-plane boundary conditions, plate aspect ratio, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical thin shell of finite length subjected to compressive axial loads and in thermal environments. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of axially-loaded, perfect and imperfect, cylindrical thin shells with two constituent materials and under different sets of thermal environments. The effects played by temperature rise, volume fraction distribution, shell geometric parameter, and initial geometric imperfections are studied.     

非加劲板抗剪极限承载力

重点研究了板的初始几何缺陷、残余应力、高厚比及边长比等影响因素与抗剪极限承载力的关系,推导出铰接刚性边界焊接板抗剪承载力计算公式。研究表明,初始几何缺陷分布模态、大小和残余应力对板的抗剪极限承载力的影响程度可以忽略不计,从而大大地简化了抗剪板承载力的计算;在经过大量塑性塑动后,较小高厚比受剪板的屈曲后强度有一定的提高,而薄板基本保持不变。     

Static and dynamic snap-through of orthotropic spherical caps

This paper presents the results of a study on the axisymmetric snap-through buckling of orthotropic shallow spherical shells subjected to a total-area uniform pressure. Both static and dynamic buckling of the orthotropic caps are investigated according to the classical thin shell theory and Reissener's shallow shell assumptions.

To take moderate rotation and initial imperfection into account, a set of nonlinear differential governing equations is derived in terms of the mid-surface displacement and a stress function.

Two types of imperfection, and damping (in the dynamic case) are included to simulate real structures. It is seen that imperfections play an important role in the reduction of buckling loads for both static and dynamic analyses. Damping, on the other hand, increases the dynamic buckling load. The finite difference scheme is applied to represent spatial and time derivatives, and the block elimination method is used to solve the resulting difference equations.     

Local Buckling Delamination of a Rectangular Sandwich Plate Containing Interface Embedded Rectangular Cracks and Made From Elastic and Viscoelastic Materials

A three-dimensional buckling delamination problem for a rectangular sandwich plate made from elastic and viscoelastic materials is studied. It is supposed that the plate contains interface embedded rectangular cracks and that the edge-surfaces of these cracks have initial infinitesimal imperfections. The evolution of these initial imperfections with an external bi-axial compressed force (for the case where the materials of the layers of the plate are elastic) or with duration of time (for the case where the materials of the layers of the plate are viscoelastic) is investigated. The corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model with the use of three-dimensional geometrically nonlinear field equations of the theory of viscoelastic bodies. This problem is solved by employing boundary form perturbation techniques, Laplace transform and FEM. According to the initial imperfection criterion, the values of the critical parameters are determined. Numerical results on the critical force and critical time are presented and discussed. In particular, it is established that the values of the critical forces obtained for the buckling delamination around the rectangular embedded interface cracks are significantly greater than those obtained for the corresponding edge and band cracks.