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.     

Postbuckling analysis of composite panels with imperfection damage

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to buckling of composite shells is concerned, it is well known that a key step is to investigate the influence of initial geometric imperfection. At present, imperfection sensitivity study of composite shells has not been explored in detail. Thus, the objective of this paper is to present the formulation used in developing a composite shell element and to validate the element from the composite curved panel. The non-linear formulation of the shell element is based on the updated Lagrangian method. The shell element is capable of small strain and large displacement analysis with finite rotations. In order to remove the rigid body rotation, a co-rotational method is used. Subsequently the postbuckling analyses from the modeling of the curved panel with initial imperfection damage are performed to investigate the effect of initial geometric imperfection shape and amplitude. The results are used to estimate imperfection sensitivity for such panels.     

轴心受压CFRP—铝合金组合管弹塑性屈曲性能分析

CFRP管具有轻质高强的特点,适合于建造大跨度空间网格结构,但其破坏呈脆性,且以节点连接破坏为主,不能充分发挥CFRP材料的优点,为此建议将CFRP与铝合金组合形成CFRP-铝合金组合管来改善其受力性能和构件连接性能。首先对CFRP-铝合金组合长管进行了轴心受压稳定试验研究,得到其基本受力性能与破坏模式。利用有限元方法对组合管的特征值屈曲进行分析,研究不同CFRP铺层角度、厚度和顺序的影响。根据特征值屈曲的分析结果,引入初始几何缺陷,对组合管进行了弹塑性屈曲分析,并将分析结果与试验结果进行了对比,确定了有限元分析模型的合理性,进一步研究了不同长细比、铺层角度和厚度对组合管弹塑性稳定性能的影响机理。最后基于试验结果与数值分析结果,通过修正Perry稳定计算公式,得到了CFRP-铝合金组合长管屈曲荷载的计算公式。     

纤维增强复合材料薄壁圆管扭转失效分析

对碳纤维增强树脂基复合材料（CFRP）薄壁圆管的扭转屈曲、失效载荷和失效模式进行了试验和数值模拟。试验观察圆管在扭矩作用下的3种失效模式,分析了不同失效模式的特征和机理。考虑圆柱壳的初始缺陷和非线性屈曲等因素,利用ABAQUS建立了圆管屈曲和损伤的有限元模型。结果表明:屈曲诱发圆管表面微裂纹的产生和扩展,对圆管的失效有着加速作用;扭转失效过程中圆管层间应力较低,层间分层主要由管壁突然的破坏产生;圆柱壳的初始缺陷对屈曲和失效载荷的模拟影响较大,本文通过对比计算结果和试验数据确定了圆管的初始缺陷系数;损伤模型的数值模拟结果与试验数据相一致,验证了有限元模型的有效性。      

基于三维Puck失效准则及唯象模量退化的复合材料臂杆屈曲分析

针对碳纤维增强树脂基复合材料（CFRP）臂杆结构在压缩和扭转载荷条件下屈曲与后屈曲问题,采用三维Puck失效准则和基于唯象分析的模量退化方法,同时考虑层合结构就位效应及沿纤维方向应力对横向强度的影响,建立了一种适用于考虑渐进失效CFRP结构的屈曲分析方法,并通过编写有限元软件ANSYS的USERMAT子程序进行了数值实现。与文献中实验结果的对比表明,上述方法能够分析复合材料结构的渐进失效过程和后屈曲承载特性,预测精度高。进而采用此方法,详细分析了某航天器臂杆结构在承受压缩与扭转载荷条件下的屈曲载荷及后屈曲特性。      

An experimental investigation into the buckling and post-buckling of CFRP shells under combined axial and torsion loading

The results of an experimental study of the buckling and post-buckling behaviour of four unstiffened thin-walled CFRP cylindrical shells are presented. The test equipment allows axial and torsion loading, applied separately and in combination, using a position control mode, and includes a laser scanning system for the measurement in situ of the geometric imperfection as well as of the progressive change in deformations. The results identify the effect of laminate orientation, show that the buckling loads are essentially independent of load sequence and demonstrate that the shells are able to sustain load in the post-buckling field without any damage. The measured data are fundamental for the development and validation of analytical and numerical models and contribute to the definition of applicable strength design criteria of composite cylindrical shells in the post-buckling field, with the final aim of a larger structure weight saving.     

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。     

复合材料圆柱壳的非线性稳定性分析

本文应用能量变分方法,对加筋多层的复合材料圆柱壳,进行了非线性稳定性分析,处理了均匀轴压和横向载荷两种载荷情况。文中用卡门-佟聂耳方程考虑了柱壳失稳时的几何非线性影响,同时通过剪切模量的非线性变化考虑了复合材料的物理并线性影响。本文也分析了初始缺陷对于屈曲特性的影响。文中具体计算了硼/环氧圆柱壳失稳的数值算例。分析和计算表明,材料的剪切非线性和初始缺陷的几何非线性对圆柱壳的屈曲特性有着显著的影响。     

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.     

Investigations on imperfection sensitivity and deduction of improved knock-down factors for unstiffened CFRP cylindrical shells

In the field of aerospace engineering but also in the fields of civil and mechanical engineering the industry demands for significantly reduced costs for development and operating. Reduction of structural weight at safe design is one avenue to achieve this objective. In many cases it results in thin-walled structures, which are prone to buckling if subjected to compression or shear. The presented paper is based on a recent European Space Agency (ESA) study, conducted at DLR Braunschweig, on Probabilistic Aspects of Buckling Knock-Down Factors and contributes to this goal by striving for an improved buckling knock-down factor (the ratio of buckling loads of imperfect and perfect structures) for unstiffened CFRP cylindrical shells. Buckling tests and buckling simulations were performed to investigate the imperfection sensitivity and to validate the applied simulation methodologies. Test results as well as deterministic and probabilistic buckling simulation results are presented and compared. Finally, improved knock-down factors are deduced and discussed.     

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.     

Delamination growth in long composite tubes under external pressure

Delamination growth is a phenomenon known to reduce the integrity of laminated composite structural elements and may lead to premature failures. In the present study, state of the art procedures of delamination growth analysis are overviewed. The energy release rate calculation is formulated for composite delaminated tubular cross sections and specialized to a finite element model for delamination buckling and growth analysis of long laminated composite tubes taking into account initial geometric imperfections, large deformations, contact between delamination faces and material degradation. It is, then, used to study the potential of delamination growth in a hybrid composite tube. Parametric studies are conducted to assess the effects of delamination length, location and geometric imperfection on growth.     

球面网壳最不利几何缺陷的凸集和概率模型

该文提出了一种使用凸集模型确定单层球面网壳最不利初始几何缺陷的有效方法。初始几何缺陷的模拟使用前N阶线性屈曲模态的线性组合,其大小为随机变量,在N维欧氏空间中的椭球集合上变化,结构的非线性屈曲极限承载力表示为这些随机变量的函数,该文方法可以替代计算昂贵的概率方法研究缺陷敏感性结构。通过蒙特卡罗方法验证了凸集模型所得结果的正确性,该文计算采用ANSYS参数化设计语言二次开发实现。     

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.     

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.     

Dynamic buckling of metal matrix composite plates and shells under cylindrical bending

A micro-to-macro analysis is offered to investigate the dynamic response and buckling of metal matrix composite cylindrical shells and plates under cylindrical bending. The micromechanical analysis relies on the elastic fibers and inelastic matrix material properties, and provides the bulk behavior of the metal matrix composite at room and elevated temperatures. The macromechanical analysis employs the classical and higher order plate theories in conjunction with a spatial finite difference and temporal Runge-Kutta integrations to provide the dynamic response of the structure. The effects of the metallic matrix inelasticity, material rate sensitivity, shear deformation, fiber orientation, and initial geometrical imperfection on the behavior of the metal matrix composite structures are studied.     

Axial capacity and crushing behavior of metal–fiber square tubes – Steel,stainless steel and aluminum with CFRP

Composite metal-carbon fiber reinforced polymer (CFRP) tubes combine the benefits of the high strength to weight ratio of the fiber/resin composite and the stable, ductile plastic collapse mechanism of the metal, to form a composite tube with high strength and energy absorption capability. This paper investigates the axial capacity and crushing behavior of square hollow section (SHS) tubes composed of composite steel-CFRP, stainless steel-CFRP and aluminum-CFRP. Experiments of tubes with different metal SHS geometries and two different matrix layouts of carbon fibers are described, and a general theory to predict the compression buckling, axial capacity, axial collapse and mean crush load of metal–fiber square tubes is developed and validated against the experimental results. It is shown that carbon fiber may be successfully externally bonded to metal SHS, and such application may be provided to improve the performance of existing structures, or to design new structures with enhanced strength-weight and energy absorption-weight ratios. Comparisons are made between the performance of the different types of metals, SHS geometries and carbon fiber matrix layouts.     

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。     

Optimisation of geometrically non-linear composite structures based on load–displacement control

A design optimisation methodology for beam reinforced composite structures with non-linear geometric behaviour is proposed. The formulation involves displacement, stresses, buckling and size constraints. The Newton–Raphson iterative procedure and the arc-length method are used for tracing equilibrium path and later updating the buckling load and the first ply failure load. The proposed sensitivity analysis model is based on an approach of the adjoint variable method for structures with non-linear geometric behaviour. The optimal design performs on a multilevel scheme based on structural efficiency maximisation exploring the anisotropic properties of the composites and weight minimisation using the ply thickness and the cross-section variables of the stiffeners. To demonstrate the applicability of the proposed developments, optimisation problems considering first ply failure and buckling conditions are presented.     

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。