Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually.     

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.     

MT300/KH420碳纤维/聚酰亚胺树脂复合材料层合圆柱壳高温承载性能

基于Donnell-Mushtali近似理论及热弹性理论,考虑结构热变形和材料高温性能衰减等温度影响因素,对MT300/KH420碳纤维/聚酰亚胺树脂复合材料圆柱壳在常温、420℃及周向210~420℃不均匀温度场等热载工况下的承载性能进行了理论分析。并引入一阶屈曲模态缺陷作为几何初始扰动,利用ABAQUS,采用非线性显式动力学方法完成对MT300/KH420复合材料圆柱壳在以上热载工况下的轴压稳定性有限元仿真计算,计算结果与理论分析较为一致。设计并开展MT300/KH420复合材料圆柱壳力-热载荷联合轴压试验,获得圆柱壳在以上热载工况下的破坏载荷和破坏模式。研究表明:高温工况下,力学性能衰减和温场不均匀引起的结构热变形是影响MT300/KH420复合材料圆柱壳轴向失稳载荷的主要因素。      

Buckling of moderately thick laminated cylindrical shells: a review

The present paper is a review article on the problem of buckling of moderately thick, laminated, composite shells subjected to destabilizing loads. The loads consist of uniform axial compression, uniform lateral pressure and torsion applied individually or in combination. In all the works reported in the literature, the analysis is based on higher-order shear deformation (HOSD) shell theory and/or first-order shear deformation (FOSD) shell theory with or without a shear correction factor. Results obtained by these two shell theories and by employing classical thin shell theory are compared to determine the range of applicability of each in predicting critical conditions. The effect of stacking sequence, radius-to-thickness ratio and length-to-radius ratio is assessed. Typical numerical results are presented in tabular form. Moreover, some limited results, which are based on limit point analysis are also presented (imperfection sensitivity studies).     

On the analysis of the buckling behaviour of laminated composite plates and shells

In general, plates and shells out of composite laminates are more susceptible to transverse shear than those out of homogeneous isotropic material. By means of different shear flexible theories the effect on buckling and postbuckling behaviour is studied. It turns out that there is a rather limited range of plates where the transverse shear is of considerable influence. Results obtained with Mindlin- or Reissner-type theories prove almost as adequate as those obtained with Reddy's theory. For the buckling analysis of shells the Kirchhoff–Love theory is precise enough. Snap-through buckling and imperfection sensitivity appear in composite shells, too, especially if they are optimized with respect to high bifurcation buckling loads.     

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.     

Finite element buckling analysis of rotationally periodic laminated composite shells

A finite element (FE) buckling analysis of rotationally periodic laminated composite shells is performed in this paper. Because the buckling mode of such structures is characterized as rotationally periodic, a corresponding FE buckling analysis scheme is proposed to reduce the computational expenses. Moreover, a new kind of relative degrees‐of‐freedom element is developed, which can be connected to other solid elements with ease and can yield satisfactory results with a relatively coarse FE mesh. Numerical results of two laminated cylindrical shells subjected to lateral pressure are compared with theoretical ones. The good agreement of them shows the validity of this new computational strategy. Finally, a practical structure is analysed to demonstrate the advantage of this method. Copyright © 2001 John Wiley & Sons, Ltd.     

Hybrid stress finite element model for non-linear shell problems

The present paper describes a hybrid stress finite element formulation for geometrically non-linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger-Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi-field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non-linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton-Raphson iteratioin. Numerical examples presented in the paper include complete snap-through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non-linear shell problems of high complexity.     

复合材料层合扁锥壳的冲击屈曲

研究了计及横向剪切的对称铺设正交异性复合材料层合扁锥壳在三角脉冲载荷作用下的非线性动力屈曲问题；通过在复合材料层合扁锥壳非线性稳定性的基本方程中增加横向转动惯量项并引入三角脉冲冲击力，得到了层合扁锥壳的冲击控制方程，采用Galerkin方法得到以顶点挠度表达的冲击响应方程，并用Runge—Kutta方法进行数值求解，应用B—R准则确定冲击屈曲的临界荷载；讨论了壳体几何参数、物理参数和边界条件对复合材料层合扁锥壳冲击屈曲的影响。     

The non-linear buckling analysis of cross-ply laminated orthotropic truncated conical shells

In this study, the non-linear buckling behavior of cross-ply laminated orthotropic truncated conical shells under axial load has been investigated. The basic relations of the cross-ply laminated orthotropic truncated conical shells are derived using the von Karman–Donnell-type of kinematic non-linearity. Then modified Donnell type non-linear stability and compatibility equations are obtained and are solved. Finally, the influences of the number and ordering of layers and the variations of the conical shell characteristics on the non-linear axial buckling load are investigated. Comparison with available results is satisfactorily good.     

具有夹层的正交异性复合材料圆锥壳体的非线性轴对称屈曲分析

研究均布载荷作用下边缘可移夹支具有正交异性复合材料表层和软夹心的夹层圆锥壳非线性轴对称屈曲问题.利用变分原理导出具有正交各向异性表层夹层圆锥壳在均匀外压作用下的非线性轴对称屈曲问题的基本方程,采用修正迭代法[8]求得了可移夹支边界条件下壳体临界屈曲载荷的解析表达式,对几种典型的纤维增强复合材料表层夹层圆锥壳给出了数值结果和图表,讨论了几何参数和物理参数对临界屈曲载荷的影响。     

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。     

复合材料迭层板壳有限单元法现状分析

本文从剖析单元构成因素的角度出发,综合评述了目前用于复合材料板壳结构分析的各种有限单元,分析了这些单元的特点及其适用范围,并说明Mindlin类等参板壳单元广泛应用迭层板壳的原因以及存在问题、解决办法。还深入地讨论了杂交单元应用至迭层板壳计算的优点。     

Modal validation of a set of C0-compatible composite shell finite elements

This paper presents efficient C⁰-compatible finite elements for modelling laminated composite shells under free vibrations. Derived from the first-order shear deformation theory (equivalent single-layer laminate model), the elements are well adapted for evaluating the global dynamic response (natural frequencies and mode shapes) of moderately thick multilayered shells. The components of their structural matrices are based on an exact integration per layer, which results in a higher solution accuracy than with standard explicit through-the-thickness schemes. The described finite element formulation, which can be easily implemented in commercial finite element codes, is next validated by means of several experimental modal test cases on thin to relatively thick plates or shells.     

Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method

Hygrothermal stresses due to the change in environmental condition may induce buckling and dynamic instability in the composite shell structures. In the present investigation, the hygrothermoelastic buckling behavior of laminated composite shells are numerically simulated using geometrically nonlinear finite element method. The orthogonal curvilinear coordinate is used for modeling a general doubly curved deep or shallow shell surface. The geometrically nonlinear finite element formulation is based on general nonlinear strain–displacement relations in the orthogonal curvilinear coordinate system. The present theory can be applicable to thin and moderately thick shells. The mechanical linear and nonlinear stiffnesses, and the nonmechanical nonlinear geometric stiffness matrices and the hygrothermal load vector are presented. It is also observed that during the present numerical solution of nonlinear equilibrium equation, in order to construct the nonlinear stiffness matrices for the first load step, the initial deformation can be assumed as zero or any computer generated small random number or the properly scaled fundamental buckling mode shape. To verify the present formulations and finite element code, the present results are compared well with those available in the open literature. Parametric studies such as thickness ratio and shallowness ratio on buckling are performed for spherical, truncated conical and cylindrical composite shell panels. The buckling behavior and deflection shapes are characterized by multiple wrinkles along unreinforced direction at higher moisture concentrations or temperature rise.     

Efficient modelling of delamination buckling in composite cylindrical shells under axial compression

Composite cylindrical shells and panels are widely used in aerospace structures. These are often subjected to defects and damage from both in-service and manufacturing events. Delamination is the most important of these defects. This paper deals with the computational modelling of delamination in isotropic and laminated composite cylindrical shells. The use of three-dimensional finite elements for predicting the delamination buckling of these structures is computationally expensive. Here combined double-layer and single-layer of shell elements are employed to study the effect of delamination on the global load-carrying capacity of such systems under axial compressive load. It is shown that through-the-thickness delamination can be modelled and analysed effectively without requiring a great deal of computing time and memory. A parametric study is carried out to study the influence of the delamination size, orientation and through-the-width position of a series of laminated cylinders. The effect of material properties is also investigated. Some of the results are compared with the corresponding analytical results. It is shown that ignoring the contact between the delaminated layers can result in wrong estimations of the critical buckling loads in cylindrical shells under compressive load.     

Optimum design for buckling of plain and stiffened composite axisymmetric shell panels/shells

The buckling of plain and discretely stiffened composite axisymmetric shell panels/shells made of repeated sublaminate construction is studied using the finite element method. In repeated sublaminate construction, a full laminate is obtained by repeating a basic sublaminate, which has a smaller number of plies. The optimum design for buckling is obtained by determining the layup sequence of the plies in the sublaminate by ranking, so as to achieve maximum buckling load for a specified thickness. For this purpose, a four-noded 48-dof quadrilateral composite thin shell element, together with fully compatible two-noded 16-dof composite meridional and parallel circle stiffener elements are used.     

Benchmark three-dimensional elasticity solutions for the buckling of thick orthotropic cylindrical shells

Benchmark solutions to the problem of buckling of orthotropic cylindrical shells, which are based on the three-dimensional theory of elasticity, are presented in this review article. It is assumed that the shell is under external pressure or axial compression or a combination of these loadings. These solutions provide a means of accurately assessing the limitations of the various shell theories in predicting critical loads. A comparison with some classical shell theories shows that the classical shell theories may produce, in general, highly non-conservative results on the critical load of composite shells with thick construction. One noteworthy exception: the Timoshenko shell buckling equations produce conservative results under pure axial compression.     

Performance of a fiber reinforced polymer web core skew bridge superstructure. Part I: field testing and finite element simulations

An analytical method is presented to investigate hydrothermal effects on locally buckling for an elliptical delamination near the surface of cylindrical laminated shells. The critical strain of non-linear buckling for a locally elliptic delamination of cylindrical laminated shells is obtained by considering transverse displacements of the elliptically sub-laminated shells. The stacking sequence of sub-laminated shells may be multilayer and asymmetric. The geometrical axis of sub-laminated shells may be arbitrary. The Young's modulus and the thermal and humidity expansion coefficients of the material are considered as functions of temperature change in base-laminated shells. The critical strains of locally buckling for cylindrical laminated shells subjected to hydrothermal effects are extracted for different stacking sequences, and different radii of base-laminated shells, by applying Rayleigh–Ritz method based on second variation of potential energy. From results carried out, it is found that the critical strain from the non-linear buckling for a locally elliptic delamination near the surface of a cylindrical laminated shell presents a lower value than that from linear considerations.     

Experimental Investigations of Compressed Sandwich Composite/Honeycomb Cylindrical Shells

This article explains in some details the behaviour of thick, deep cylindrical sandwich panels subjected to compressive loads. In general, experimental results indicated that two different forms of failure have been observed – the first corresponds to the overall buckling and the second to the facesheet wrinkling. The obtained experimentally damages of shells are verified and validated with the use of the FE analysis, 2-D and 3-D both in the linear and non-linear approach. The unidirectional strain gauges were applied to detect the initiation of the overall buckling mode.