含损伤复合材料AGS 板的屈曲特性

采用有限元数值模拟方法, 研究了蒙皮内含分层损伤复合材料格栅加筋板结构(AGS) 的稳定性问题。对蒙皮和肋骨分别采用基于Mindlin 一阶剪切理论的复合材料层合板单元和层合梁单元来模拟, 推导了相应的有限元列式, 并通过坐标变换, 利用蒙皮与肋骨的几何连续条件, 形成了AGS 的单元刚度阵和几何刚度阵, 建立了含损伤AGS 稳定性分析的有限元控制方程。通过典型算例, 研究了压缩载荷作用下, 分层形状、分层大小、分层深度、肋骨的高度和宽度、布置方式等因素对AGS 的稳定性特征的影响。数值结果表明, 含分层损伤的AGS 具有十分复杂的屈曲性态。屈曲临界力和屈曲模式与分层面积、分层形状、分层深度、肋骨的高度和宽度、布置方式和位置均密切相关。      

环加肋圆柱壳屈曲分析的有限条法

导出了有限条法分析环加肋圆柱壳在静水压力作用下总体屈曲的计算格式，将环加肋圆柱壳作为一个构造上的正交各向异性壳处理，推导了考虑环向加肋影响后有限条元的正交各向异性弹性矩阵。对两端简支环加助圆柱壳总体屈曲临界载荷的计算表明，本文方法计算结果与解析解符合良好。有限条法是分析密加肋圆柱壳屈曲问题的有效数值方法。     

Closed-form buckling analysis of stiffened composite plates and identification of minimum stiffener requirements

Longitudinal stiffeners attached to composite plates may significantly increase the overall buckling loads of the resultant stiffened structure. As long as the bending stiffness EI of the stiffener remains beneath some a priori unknown threshold value EI_min (with E being Young’s modulus and I being the bending moment of inertia), the buckling pattern will usually be of a more or less global nature, meaning that both the plate and the stiffener will exhibit some certain buckling modes. Once a threshold value EI_min for the bending stiffness, also called minimum stiffness, is exceeded, the stiffener more or less remains in its original position in the state of the onset of buckling while the buckling pattern of the stiffened plate is dominated by local buckling modes of the plate itself. The knowledge of this minimum bending stiffness EI_min of longitudinal stiffeners of composite plates is of high practical importance and a predominant design criterion and will be considered in this paper. For the basic load cases uniform compression and pure shear and their combination, simple closed-form analytical approaches will be presented which enable a straightforward and quick yet accurate estimation of the buckling loads (compression) and (shear) of stiffened composite plates on the one hand, and the minimum bending stiffness EI_min of the attached stiffeners on the other hand.     

格栅非均匀分布效应对复合材料格栅加筋圆锥壳体稳定性的影响

研究格栅非均匀分布效应对先进复合材料格栅加筋圆锥壳体稳定性的影响。首先,基于格栅间距沿母线方向的变化特征和等效平铺模型推导了格栅加筋圆锥壳体的等效刚度阵。其次,采用Donnell 型扁壳理论推导了在均布外压作用下格栅加筋圆锥壳体稳定性分析的总势能表达式,利用最小势能原理得到了该壳体总体稳定性的临界载荷值,所得计算结果与实验结果十分吻合。最后,通过典型数例参数讨论,说明格栅非均匀分布效应对先进复合材料格栅加筋圆锥壳体稳定性的影响将随底锥角增大而显著。该文将为先进复合材料格栅加筋圆锥壳体的参数优化设计提供一种高效和可靠的分析方法。     

Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened functionally graded thin circular cylindrical shells

This paper is presented to solve the nonlinear buckling and post-buckling problem of functionally graded stiffened thin circular cylindrical shells only under torsion by the analytical approach. The shells are reinforced by rings and stringers attached to their inside and the material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with the geometrical nonlinearity in von Karman sense are derived. Approximate three-term solution of deflection is chosen more correctly and the explicit expression to finding critical load and post-buckling torsional load–deflection curves are given. The effects of various parameters and the effectiveness of stiffeners on the stability of shell are shown.     

Dynamic buckling of a laminated composite stringer–stiffened cylindrical panel

The present study deals with the “dynamic buckling” of a laminated composite stringer–stiffened curved panel. The “dynamic buckling”, in the present study, is concerned with the unbounded lateral response of the panel, which is subjected to an axial impact load.In reinforced panels with widely spaced adequately stiff stringers, the structure may pass through two major states before its total collapse: buckling of the panel skin between stiffeners and buckling of the stiffeners themselves. This study focuses on the lowest buckling load of the stringer–stiffened panel, which is, buckling of the panel skin between stiffeners.The analysis of the laminated composite stringer–stiffened cylindrical panel was performed by using the commercial ANSYS finite element software. The model simulates the structure and its associated boundary conditions. The boundary conditions simulate the stringer–stiffened cylindrical panel as a part of a fuselage. The static buckling analysis was performed using the eigenvalue buckling approach to determine the static critical load. Modal analysis was used to calculate the first natural frequency and corresponding mode shape of the structure. Nonlinear transient dynamic analysis was used to determine the dynamic critical load. In the transient dynamic analysis the Newmark method with the Newton–Raphson scheme were used.In the present study, the equation of motion approach was applied. By this approach, the equations of motion were numerically solved for various load parameter values (loading amplitude and loading duration) to obtain the system response. Special attention was given to the neighborhood of loading durations corresponding to the period of the lowest bending frequency of the skin.For each load duration, the dynamic buckling load was calculated using a load versus lateral displacement curve generated by the ANSYS code.The results were plotted on a dynamic load amplification factor (DLF) graph. The DLF is defined, as the ratio of the dynamic buckling to the static buckling of the panel. For loading periods in the neighborhood of the lowest natural frequency of the panel, the DLF was less than unity. It means that, for those particular loading periods, the dynamic buckling load is lower than the static one.     

On the free vibrations of grid-stiffened composite cylindrical shells

A unified analytical approach is applied for investigating the vibrational behavior of grid-stiffened composite cylindrical shells considering the flexural behavior of the ribs. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of the shell in order to obtain the equivalent stiffness parameters of the whole panel. The stiffeners are modeled as a beam and considered to support shear loads and bending moments in addition to the axial loads. Therefore, the corresponding stiffness terms are taken into consideration while obtaining the stiffness matrices due to the stiffeners. Theoretical formulations are based on first-order shear deformation shell theory, which includes the effects of transverse shear deformation and rotary inertia. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes’ transformation. In order to validate the obtained results, a 3-D finite element model is also built using ABAQUS CAE software. Results obtained from two types of analyses are compared with each other, and good agreement has been achieved. Furthermore, the influence of variations in the shell thickness and changes of the boundary conditions on the shell frequencies is studied. The results obtained are novel and can be used as a benchmark for further studies.     

Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading

This article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element with C⁰ continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate.     

Nonlinear Response of Imperfect Eccentrically Stiffened Ceramic-Metal-Ceramic Sigmoid Functionally Graded Material (S-FGM) Thin Circular Cylindrical Shells Surrounded on Elastic Foundations Under Uniform Radial Load

This article researches nonlinear response of imperfect eccentrically stiffened symmetric FGM thin circular cylindrical shells with ceramic-metal-ceramic layers, which are symmetric through the middle surface by Sigmoid-law distribution (S-FGM) and have stiffeners surrounded on elastic foundations under uniform radial load. The Donnell classical shell theory, stress function, and Galerkin method are used for investigation of the nonlinear stability of the S-FGM shell. The obtained results show the effects of the stiffeners, elastic foundations, mechanical load, and material parameters on the nonlinear buckling response of symmetric S-FGM circular cylindrical shells.     

Investigations on Buckling Behaviour of Laminated Curved Composite Stiffened Panels

In Industrial applications structural efficiency is primary concern, this brings about the need of strong and lightweight materials. Due to their high specific strength, fibre reinforced polymers find wide application in these areas. Panels made of composite materials are widely used in aerospace structures, automobile, civil, marine and biomedical industries because of their good mechanical properties, impact resistance, excellent damage tolerance and also low fabrication cost. In this Paper, buckling and post-buckling analysis was performed on composite stiffened panel to obtain the critical load and modes of failures, with different parameters like ply-orientation, different composite materials, and stiffeners and by changing the number of stiffeners was derived. To analyze the post buckling behaviour of composite stiffened panels the nonlinear finite element analysis is employed and substantial investigations are undertaken using finite element (FE) model. Effect of critical parameters on buckling behaviour is studied and parametric studies were conducted with analytical tool to understand the structural behaviour in the post buckling range.     

Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of functionally graded stiffened thin circular cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach. Shells are reinforced by closely spaced rings and stringers in which material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical shell theory with von Karman geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method with three-term solution of deflection, the closed form to find critical torsional load and post-buckling load–deflection curves are obtained. The effects of temperature, stiffener, foundation, material and dimensional parameters are analyzed.     

基于变环肋间距的碳纤维/环氧树脂复合材料格栅加筋截顶圆锥壳体稳定性

研究均布外压作用下具有非均匀特征的碳纤维/环氧树脂复合材料格栅加筋（AGS）圆锥壳体构型优化。首先,充分考虑复合材料格栅圆锥壳体中格栅非均匀分布造成结构小端材料利用不充分问题,提出变环肋铺设间距的优化分布方式,使格栅在截顶圆锥壳体结构上小端疏大端密。之后,基于考虑格栅非均匀分布及变环肋间距铺设特征的等效刚度模型,并采用最小势能原理得到环肋铺设优化后的AGS圆锥壳体临界载荷值解析式。针对典型锥壳的有限元验证表明解析算法的误差在1%左右,证实了本文提出的分析方法的可靠性和有效性。最后,通过对环肋间距优化圆锥壳体的参数分析,发现优化环肋分布方式可以使AGS锥壳结构的外压稳定性大幅上升。本文研究内容为碳纤维/环氧树脂复合材料AGS圆锥壳体的优化设计提供了一种具有较高承载力的构型,并为此类结构的计算提供了解析算法。     

侧边边界条件对复合材料加筋板轴压载荷下屈曲和后屈曲性能的影响

为研究侧边边界条件对复合材料加筋板压缩稳定性能的影响,首先采用有限元软件对压缩载荷作用下的复合材料加筋板进行建模数值计算,得到加筋板在侧边简支和自由2种边界条件下的屈曲载荷和形式,然后采用工程计算方法对加筋板轴压承载能力进行了估算,参考计算结果,分别对侧边有支持和侧边自由2组加筋板进行轴向压缩试验,分析侧边边界条件对试验件的屈曲形式、屈曲载荷以及后屈曲破坏过程的影响。试验结果表明：侧边支持条件会影响加筋板的屈曲形式和破坏形式。对于侧边有支持的试验件,屈曲后整体变形较小,筋条的压缩断裂是主要的破坏形式;而侧边自由的试验件屈曲后会逐渐出现整体弯曲变形,变形引起的筋条脱粘和弯曲断裂则是主要的破坏形式,且筋条脱粘会显著降低结构的承载能力。有限元计算结果与试验结果较吻合,验证了有限元模型的合理性。采用工程计算方法对侧边有支持的加筋板承载能力进行估算具有较好的精度。     

用于AGS结构分析的混合法

结合均匀化模型和加筋单元模型构造了一种混合模型用来分析复合材料格栅加筋板/壳结构（AGS）。所构造的加筋单元模型是一种高性能协调转角独立加筋板壳单元,保持了肋骨和蒙皮位移场的协调性,同时还满足肋骨和蒙皮具有独立转动条件,该单元中肋骨的方向和位置任意。混合法具有精度高、速度快等特点。通过典型算例讨论了肋骨间距和高度对均匀化模型计算结果精度的影响,通过对带孔复合材料AGS板孔边特殊点应力值的分析证明了混合法的有效性。      

考虑脱粘的复合材料加筋板屈曲后屈曲及承载能力数值分析

建立了复合材料层合加筋壁板的屈曲后屈曲有限元分析模型。该模型采用界面单元以有效模拟筋条和壁板之间的连接界面, 连接界面和复合材料层板分别采用Quads和Hashin失效准则作为失效判据, 引入材料刚度退化模型, 采用非线性有限元方法, 研究了复合材料加筋壁板在压缩载荷下的前后屈曲平衡路径及破坏过程。数值分析结果与实验结果吻合良好, 证明了该方法的合理有效性。详细探讨了筋条尺寸及界面单元强度等参数对加筋壁板屈曲后屈曲行为及承载能力的影响规律, 研究表明增加筋条截面惯性矩及筋条密度在一定程度上能有效提高加筋板的屈曲载荷与极限强度, 筋条密度增加到一定程度会引起结构破坏形式由失稳破坏?湮顾跗苹? 界面强度与铺层方式对极限强度有重要影响, 界面脱粘是引起加筋板最终破坏的重要因素。      

Optimum buckling design of composite stiffened panels using ant colony algorithm

Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions.     

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.     

复合材料加筋圆拱壳的失稳特性分析

本文应用增量形式的拉格朗日列式法对其有纵横加筋的迭层圆拱壳在均布载荷作用下的稳定性进行了非线性有限元分析。文中应用Sander 壳体理论及横向剪切的影响, 推导了矩形壳元及与该壳元变形相协调的直梁元和曲梁元的切线刚度矩阵。编制了FORTRAN 计算程序。计算并分析了加筋拱壳的局部及整体失稳过程。      

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

Buckling of folded plate structures subjected to partial in‐plane edge loads by the FSDT meshfree Galerkin method

This paper presents a meshfree Galerkin method that is based on the first‐order shear deformation theory (FSDT) to study the elastic buckling behaviour of stiffened and un‐stiffened folded plates under partial in‐plane edge loads. The un‐stiffened folded plates are modelled as assemblies of flat plates. The stiffness and initial stress matrices of the flat plates are derived by the meshfree Galerkin method. A treatment is implemented to modify the stiffness and initial stress matrices, and the matrices are then superposed to obtain the stiffness and initial stress matrix of the entire folded plate. The analytical process for stiffened folded plates is similar, except that the effects of the stiffeners must be taken into account. Because no mesh is required, the proposed method is superior for studying problems that would involve remeshing in the finite element method. Several examples are employed to show the convergence and accuracy of the proposed method. The results obtained show good agreement with the results computed from the finite element analysis software ANSYS. Copyright © 2005 John Wiley & Sons, Ltd.