The microbuckling failure of Dyneema~? composites under compression

Two grades of Dyneema~?composite laminates with the commercial designations of HB26 and HB50 were cut into blocks with or without an edge crack and compressed in the longitudinal fiber direction. The cracked and uncracked specimens show similar compressive responses including failure pattern and failure load. The two grades of Dyneema~? composites exhibits different failure modes: a diffuse, sinusoidal buckling pattern for Dyneema~? HB50 due to its weak matrix constituent and a kink band for Dyneema~? HB26 due to its relatively stronger matrix constituent. An effective finite element model is used to simulate the collapse of Dyneema~? composites, and the sensitivity of laminate compressive responses to the overall effective shear modulus, interlaminar shear strength, thickness and imperfection angle are investigated. The change of failure mode from kink band to sinusoidal buckling pattern by decreasing the interlaminar shear strength is validated by the finite element analyses.     

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.     

Simplified prediction of the creep buckling of cylinders under external pressure. Part 2: Experimental verification

In this paper, the simplified method, proposed in (Combescure, 1998), for the prediction of creep buckling is compared to experimental results. The model is applied to predict the buckling time of two sets of experiments on cylinders subjected to uniform external pressure. It is shown that the proposed model is satisfactory for this type of prediction: in all cases, the times up to failure predicted by the model are generally lower than the experimental failure times. The model is rather conservative for thicker cylinders. However, it appears that a very detailed geometrical imperfection survey would be necessary if a highly accurate assessement of the creep failure time were sought. It has been observed experimentally that creep buckling is a very dangerous failure mode: nothing seems to happen during a very long “incubation” period but, when the initial imperfection reaches some critical value, buckling then suddenly occurs. For thin cylinders, the level of creep strain at which the instability starts to develop is much lower than the strain at which the tertiary creep initiates; the instability is thus clearly generated from the interaction between the material and the geometrical nonlinearity.     

Behaviour of thick composite tubes considering of delamination

The present paper deals with plane finite element analysis of thick composite tubes. Thick composite tubes are commonly used in marine industry and in deep-water offshore applications. Two kinds of interlaminar delamination type defect in a thick walled cylinder subjected to external pressure were confronted; an annular or ring like delamination and a strip delamination. Two finite element models were developed to predict the strain energy release rate at the delamination fronts. In these models the effects of the processing history of the composite material in the form of a uniform thermal load were also included to simulate the state of the residual stress in the composite. The considered defects are studied by means of the effect of buckling, investigating the annular and the strip delamination buckling, and the subsequent loss of load carrying capacity of the delaminated region.     

基于模态缺陷的受压球壳屈曲特性研究

针对受压球壳非线性屈曲过程,对含初始缺陷受压球壳的稳定性进行研究。根据EN1993-1-6（2007）规范,给出不同制造等级壳体的等效缺陷值计算方法;基于线性特征值分析的模态构型给出初始缺陷的分布。利用非线性有限元弧长法对球壳受压失稳过程进行数值模拟,得到屈曲前后球壳变形情况及全过程载荷-位移曲线。计算一致缺陷模态法和N阶缺陷模态法对应的球壳屈曲临界载荷,结果表明,受压球壳对缺陷较敏感,承载能力随缺陷值增大而降低;一致缺陷模态法计算便捷,在工程应用上具有合理性,N阶缺陷模态法考虑高阶模态缺陷构型,结果更加全面,可以为工程中缺陷结构稳定性设计提供参考。     

Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axial and radial mechanical loads

Buckling and postbuckling analysis is presented for a double-walled carbon nanotube subjected to combined axial and radial loads in thermal environments. The analysis is based on a continuum mechanics model in which each tube of a double-walled carbon nanotube is described as an individual orthotropic shell with presence of van der Waals interaction forces and the interlayer friction is negligible between the inner and outer tubes. The governing equations are based on higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics simulations, and initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, double-walled carbon nanotubes subjected to combined axial and radial mechanical loads under different sets of thermal environments. The results reveal that temperature change only has a small effect on the postbuckling behavior of the double-walled carbon nanotube. The axially-loaded double-walled carbon nanotube subjected to radial pressure has an unstable postbuckling path, and the structure is imperfection–sensitive. In contrast, the pressure-loaded double-walled carbon nanotube subjected to axial compression has a very weak “snap-through” postbuckling path, and the structure is virtually imperfection–insensitive.     

Localization,delocalization and compression fracture in externally pressurized thick cross-ply (very) long cylindrical shells with material non-linearity: A multi-scale and multi-physics analysis

Compression fracture in carbon fiber reinforced plastics (CFRP) involves multiple physical mechanisms operating at multiple scales ranging from angströms to cms and beyond. First, at the macro/meso-scale, combined effects of modal imperfections, transverse shear/normal deformation along with the non-linear hypo-elastic transverse shear (G_TT) material property on the emergence of interlaminar shear crippling type instability modes, related to the localization (onset of deformation softening), delocalization (onset of deformation hardening) and propagation of mode II compression fracture/damage, in thick imperfect cross-ply very long cylindrical shells under applied hydrostatic pressure, are investigated. The primary accomplishment is the (hitherto unavailable) computation of the layer-wise mode II stress intensity factor, energy release rate and kink crack band-width, under hydrostatic compression, from a non-linear finite element analysis (FEA), using Maxwell’s construction and Griffith׳s energy balance approach. Numerical results include the effects of hypoelastic (G_TT only) material property, on localization and delocalization leading to compression fracture.At the micro-scale, a novel three-dimensional eigenfunction expansion technique, based in part on separation of the cylinder length-variable and partly utilizing a modified Frobenius type series expansion in conjunction with an affine transformation to compute the local stress singularity, in the vicinity of a kinked-fiber/matrix trimaterial junction front. Such computed stress singularities represent a measure of the degree of inherent flaw sensitivity of unidirectional CFRP under compression. Finally, dislocation glide in graphite crystallites plays a dominant role in kink band nucleation and propagation at the nano-meter scale.     

静力预加载环向加筋圆柱壳的轴向流-固冲击屈曲

将初缺陷放大准则应用于静力预加载环向加筋圆柱壳结构受轴向流-固冲击加载作用时的几何非线性动力屈曲研究中。运用Galerkin方法推导出壳体-肋骨系统的动力屈曲控制方程,并且采用Runge-Kutta法进行数值求解。着重分析了静力预加载荷对结构屈曲性态及抗轴向冲击能力的影响。     

Postbuckling of pressure-loaded shear deformable laminated cylindrical panels

IntroductionInrecentyears,fiber_reinforcedcompositelaminatedpanelshavebeenwidelyusedintheaerospace,marine ,automobileandotherengineeringindustries .Theproblemofbucklingandpostbucklingofcylindricalpanelsunderaxialcompressionortorsionhasbeenextensivelystudied .Incontrast,theliteratureoncylindricalpanelsunderpressureloadingisrelativelyspares.Thesestudiesincludealinearbucklinganalysis (Singeretal.[1]) ,anonlinearbucklinganalysi(YamadaandCroll[2 ]) ,anelastoplasticbucklinganalysisusingreducedstif…     

Nonlinear buckling optimization of composite structures considering “worst” shape imperfections

Nonlinear buckling optimization is introduced as a method for doing laminate optimization on generalized composite shell structures exhibiting nonlinear behaviour where the objective is to maximize the buckling load. The method is based on geometrically nonlinear analyses and uses gradient information of the nonlinear buckling load in combination with mathematical programming to solve the problem. Thin-walled optimal laminated structures may have risk of a relatively high sensitivity to geometric imperfections. This is investigated by the concepts of “worst” imperfections and an optimization method to determine the “worst” shape imperfections is presented where the objective is to minimize the buckling load subject to imperfection amplitude constraints. The ability of the nonlinear buckling optimization formulation to solve the laminate problem and determine the “worst” shape imperfections is illustrated by several numerical examples of composite laminated structures and the application of both formulations gives useful insight into the interaction between laminate design and geometric imperfections.     

Interlaminar shear strength of cloth-reinforced composites

A test specimen to define the interlaminar shear strength of cloth-reinforced composite materials is developed. The specimen is a hollow circular cylinder which is subjected to torsion. The experiment is employed for the determination of the warp-normal shear strength of a graphite-fiber carbon-matrix composite material. It is demonstrated that the proper failure mode takes place, while the problems associated with the use of strain gages on this porous material, nonlinearity, difference in tension and compression properties, and the influence of clamping effects are all discussed. The proposed experiment appears to be ideally suited to study the interlaminar shear response of cloth-reinforced composites.     

Thermal postbuckling analysis of moderately thick plates

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.     

Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses

The available accurate shell theories satisfy the interlaminar transverse stress continuity conditions based on linear strain-displacement relations. Furthermore, in majority of these theories, either influence of the transverse normal stress and strain or the transverse flexibility of the shell has been ignored. These effects remarkably influence the non-linear behavior of the shells especially in the postbuckling region. Furthermore, majority of the buckling analyses performed so far for the laminated composite and sandwich shells have been restricted to linear, static analysis of the perfect shells. Moreover, almost all the available shell theories have employed the Love-Timoshenko assumption, which may lead to remarkable errors for thick and relatively thick shells. In the present paper, a novel three-dimensional high-order global-local theory that satisfies all the kinematic and the interlaminar stress continuity conditions at the layer interfaces is developed for imperfect cylindrical shells subjected to thermo-mechanical loads.In comparison with the layerwise, mixed, and available global-local theories, the present theory has the advantages of: (1) suitability for non-linear analyses, (2) higher accuracy due to satisfying the complete interlaminar kinematic and transverse stress continuity conditions, considering the transverse flexibility, and releasing the Love-Timoshenko assumption, (3) less required computational time due to using the global-local technique and matrix formulations, and (4) capability of investigating the local phenomena. To enhance the accuracy of the results, compatible Hermitian quadrilateral elements are employed. The buckling loads are determined based on a criterion previously published by the author.     

Enhanced generalised beam theory buckling formulation to handle transverse load application effects

This work deals with the development, finite element implementation and application of a generalised beam theory (GBT) formulation intended to analyse the localised, local, distortional and global buckling behaviour of thin-walled steel beams and frames subjected to transverse loads applied at various member cross-section points (away from its shear centre). In order to take into account the effects stemming from the transverse load position, the GBT buckling formulation must incorporate geometrical stiffness terms stemming from either (i) the internal work of the pre-buckling transversal normal stresses (“exact” formulation) or (ii) the external work of the applied transverse loads (approximate/simplified formulation). After presenting the main concepts and procedures involved in the development of the above “exact” and simplified formulations, the paper addresses the corresponding numerical implementations. Then, in order to illustrate their application and capabilities, as well as the limitations of the simplified formulation, various numerical result sets are presented and discussed. The accuracy of the GBT-based results is assessed through the comparison with “exact” values, yielded by rigorous shell finite element analyses carried out in the code Ansys.     

The Shallow Arch—General Buckling,Postbuckling, and Imperfection Analysis∗

A general discussion of the behavior of the shallow circular arch is presented. It is shown that, irrespective of specific loading or boundary conditions, it is possible to arrive at general conclusions regarding buckling, postbuckling, and imperfection sensitivity. General methods of analysis are established which lead to the determination of points of bifurcation and of postbuckling paths under symmetric loads. Modifications accounting for antisymmetric load components are introduced, with special emphasis on their asymptotic and limit load effect.

A typical numerical example is carried through in detail. The solution is “exact” in the sense of shallow arch theory. Its asymptotic behavior conforms to the asymptotic theory of Koiter.     

含轴对称初始缺陷的具有正交各向异性表层的夹层圆柱壳的非线性屈曲

夹层圆柱壳具有很高的结构效能。在许多工程结构中被广泛采用。本文研究分析了含有轴对称初始缺陷的夹层圆柱壳在轴压下的非线性屈曲问题。该夹层壳具有正交各向异性表层和各向同性可承剪的夹心．利用Stein的前屈曲一致理论得出了前屈曲挠度随轴向载荷及缺陷参数的变化情况，运用Galerkin法导出了屈曲控制方程，并进行了数值计算，得到了屈曲载荷、缺陷幅值、缺陷波数、夹心模量等参量之间的关系．结果表明与壳体实际屈曲模态相同的初始缺陷具有很大的危害性，可以通过增加壳体表层的轴向弹性模量或优化夹心的有关参数等途径来提高屈曲载荷，改善壳体屈曲性能。     

局部轴压下圆柱壳的失稳分析

本文用传递矩阵法在初始缺陷法的概念下对圆柱壳的一端有四个类似集中力的局部轴压作用下的失稳问题进行了研究。     

Asymptotic analysis of the non-linear behavior of long anisotropic tubes

An asymptotically correct beam model is obtained for a long, thin-walled, circular tube with circumferentially uniform stiffness (CUS) and made of generally anisotropic materials. By virtue of its special geometry certain small parameters cause unusual non-linear phenomena, such as the Brazier effect, to be exhibited. The model is constructed without ad hoc approximations from 3D elasticity by deriving its strain energy functional in terms of generalized 1D strains corresponding to extension, bending, and torsion. Large displacement and rotation are allowed but strain is assumed to be small. Closed-form expressions are provided for the 3D non-linear warping and stress fields, the 1D non-linear stiffness matrix and the bending moment–curvature relationship. In bending, failure could be caused by limit-moment instability, local buckling or material failure of a ply. A procedure to determine the failure load is provided based on the non-linear response, neglecting micro-mechanical failure modes, post-failure behavior, and hygrothermal effects. Asymptotic considerations lead to the neglect of local shell interlaminar and transverse shear stresses for the thin-walled configuration. Results of the theory are illustrated for a few symmetric, antisymmetric angle-ply and unsymmetric layups and show that some previously published theories are not asymptotically correct.     

Nonlinear interaction of geometrical and material properties in sandwich beam instabilities

The first part of this paper is dedicated to the analytical and numerical characterization of local and global sandwich beam instabilities in a perfect linear framework. Analytical loads are extracted from an original unified model and used to understand in depth, through a parametric study, the role played by each geometrical and material parameter in the development of global as well as local instabilities. Also, the effects of the combinations of these characteristics is used to draw precious design indications. A low CPU time-consuming simplified model is then built and assessed. Critical loads and wavelengths computed from this model are shown to correlate very well with analytical predictions. It is established that this first approach is essential in order to lead to more detailed investigations in a numerical nonlinear framework which is the aim of the second part. The first geometrical nonlinear investigations in which linear elastic materials are considered permit to isolate sandwich configurations developing super- or sub-critical post-buckling behaviours. As a general trend, unstable behaviours are rather related to the occurrence of geometrical localizations along the beam. This is illustrated by the drastic effects of the so-called interactive buckling onto the whole stiffness of the sandwich beam. Moreover, it is shown that sandwiches are very sensitive towards imperfection sizes and forms. Eventually, an elastoplastic constitutive law is introduced for the core. It is demonstrated that plastic flow and strain localization in the core, combined with the occurrence of instabilities, are associated with a drastic drop in the global beam stiffness and with a strong decrease of the maximum limit load for some cases. The phenomenon of shear crimping is also observed which can be assimilated to a post-bifurcated development of the global buckling mode.     

Buckling driven debonding in sandwich columns

A compression loaded sandwich column that contains a debond is analyzed using a geometrically non-linear finite element model. The model includes a cohesive zone along one face sheet/core interface whereby the debond can extend by interface crack growth. Two geometrical imperfections are introduced; a global imperfection of the sandwich column axis and a local imperfection of the debonded face sheet axis. The model predicts the sandwich column to be very sensitive to the initial debond length and the local face sheet imperfection. The study shows that the sensitivity to the face sheet imperfection results from two mechanisms: (a) interaction of local debond buckling and global buckling and (b) the development of a damaged zone at the debond crack tip. Based on the pronounced imperfection sensitivity, the author predicts that an experimental measurement of the strength of sandwich structures may exhibit a large scatter caused by geometrical variations between test specimens.