Buckling analysis and design of anisogrid composite lattice conical shells

Composite lattice anisogrid shells have now become a popular choice in many aerospace applications. Their use in various structural components, such as rocket interstages, payload adapters for spacecraft launchers, fuselage components for aerial vehicles, and parts of the deployable space antennas requires the development of more advanced finite-element models and analysis techniques capable of predicting buckling behaviour of these structures under variety of loadings. A specialised finite-element model generation procedure (design modeller) is developed and applied to the buckling analysis of the composite anisogrid conical shells treated as three-dimensional frames composed of the curvilinear ribs made of unidirectional composite material. Featuring a dedicated control procedure for positioning the beam elements, the design modeller enables a close approximation of the original twisted geometry of the curvilinear ribs. The parametric finite-element buckling analyses of the anisogrid conical shells subjected to axial compression, transverse bending, pure bending, and torsion showed the robustness and potential of the modelling approach. It was demonstrated that the buckling resistance can be significantly enhanced by either increasing the stiffness of a few hoop ribs located in the close proximity to the section with the larger diameter, or by introducing the additional hoop ribs in the same part of the conical shell. The effectiveness of the design analyses is demonstrated using particular examples. It has been shown that the resultant optimised designs can produce up to 22% mass savings in comparison with the non-optimised lattice shells.     

复合材料圆柱壳的轴压屈曲失效试验

为了研究高径比大于1的复合材料圆柱壳的轴压屈曲性能及其失效模式,对2组单向纤维圆柱壳和3组外侧环裹环向纤维圆柱壳进行了轴压试验,观察了试件的受力过程和破坏形态,获得了荷载-位移曲线和荷载-应变曲线,利用有限元模型分析了单向纤维圆柱壳两种屈曲形式的破坏机制,对比分析了两种铺层试件的轴压性能。结果表明:单向纤维复合材料圆柱壳出现先纵向劈裂后板壳屈曲和先柱壳屈曲后纵向劈裂的两种破坏模式;外侧环向纤维可改善圆柱壳的轴压性能,屈曲发展有一定的阶段性并表现出延性特征,破坏形式和承载力均较为稳定。     

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.     

Finite-element modelling and buckling analysis of anisogrid composite lattice cylindrical shells

The paper investigates the buckling behaviour of anisogrid composite lattice cylindrical shells under axial compression, transverse bending, pure bending, and torsion. The lattice shells are modelled as three-dimensional frame structures composed of curvilinear ribs subjected to the tension/compression, bending in two planes and torsion. The specialised finite-element model generation procedure (model generator/design modeller) is developed to control the orientation of the beam elements allowing the original twisted geometry of the curvilinear ribs to be closely approximated. The effects of varying the length of the shells, the number of helical ribs and the angles of their orientation on the buckling behaviour of lattice structures are examined using parametric analyses. Buckling of the lattice shells with cutouts is also analysed. The results of these studies indicate that the modelling approach presented in this work can be successfully applied to the solution of design problems.     

纵向稀加筋复合材料园柱层壳的稳定分析

本文引用位移函数,将文献[1]中园柱层壳的经典理论微分方程组转化成一个微分方程式,在此基础上、将W.Nowacki方法[3]推广到复合材料园柱层壳,得到了稀加筋园柱层壳临界载荷的解析解答 给出了算例、若略去筋条时,其数值计算能退化成与文献[1]中相应的数值结果完全一致.      

复合材料波纹夹层圆柱壳设计及轴压性能

结构轻量化是航空航天发展的永恒主题, 波纹夹层圆柱壳作为常见的轻质结构形式, 在航空航天领域具有很大的发展空间。采用模具热压法, 制备出纵向和环向碳纤维复合材料波纹夹层圆柱壳, 其中芯子整体成型, 面板分瓣制备。采用经典板壳屈曲理论, 分析纵向和环向波纹夹层圆柱壳的轴压力学性能, 得到了欧拉屈曲、整体屈曲、局部屈曲和面板压溃4种失效模式下的极限载荷理论公式。绘制出结构的失效机制图, 直观显示出了失效模式与试件尺寸之间的关系。通过对纵向和环向波纹夹层圆柱壳的轴向压缩试验, 获得了结构的载荷-位移曲线及局部屈曲和面板压溃2种失效模式。结果表明:纵向波纹夹层圆柱壳的轴向承载能力及载荷/质量效率优于环向波纹夹层圆柱壳, 在一定范围内增加圆柱壳面板的厚度、减小圆柱壳的高度可提高结构的载荷/质量效率。      

Buckling of thin‐walled cylindrical shells under axial compression

Lightweight thin‐walled cylindrical shells subjected to external loads are prone to buckling rather than strength failure. The buckling of an axially compressed shell is studied using analytical, numerical and semi‐empirical models. An analytical model is developed using the classical shell small deflection theory. A semi‐empirical model is obtained by employing experimental correction factors based on the available test data in the theoretical model. Numerical model is built using ANSYS finite element analysis code for the same shell. The comparison reveals that the analytical and numerical linear model results match closely with each other but are higher than the empirical values. To investigate this discrepancy, non‐linear buckling analyses with large deflection effect and geometric imperfections are carried out. These analyses show that the effects of non‐linearity and geometric imperfections are responsible for the mismatch between theoretical and experimental results. The effect of shell thickness, radius and length variation on buckling load and buckling mode has also been studied. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of efficient stiffened shells of revolution

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.     

Optimum structural design of CFRP isogrid cylindrical shell using genetic algorithm

This paper describes an optimum structural design of a CFRP isogrid cylindrical shell using a genetic algorithm (GA). When the CFRP isogrid cylindrical shell receives a prescribed uniaxial compressive load, an objective is to minimize weight of the CFRP isogrid cylindrical shell subjected to the constraint conditions of no buckling and no material failure. The buckling and material failure loads were approximated by a response surface method combined with partitioning of design spaces and these approximated values were used in the process of GA instead of FEM calculations in order to reduce the computational time. Furthermore, the differences from the constraint conditions of the linear or the non-linear (local) buckling loads were also calculated and their results were compared with each other.     

复合材料圆柱壳轴压屈曲性能分析

对完整复合材料圆柱壳轴向压缩性能进行了试验研究,得到了圆柱壳结构的破坏载荷和各测量点的载荷-应变曲线,通过分析得出结构的破坏形式为屈曲破坏。利用ANSYS有限元软件建立了模型,对复合材料圆柱壳进行屈曲分析,将有限元计算的结构变形和屈曲载荷与试验结果进行对比,计算结果与试验结果一致,验证了模型的有效性。利用建立的有限元模型,分析了开口尺寸和铺层角度对含矩形开口的复合材料圆柱壳屈曲载荷的影响。在开口处加装复合材料口盖对结构进行补强,补强后的柱壳结构满足强度设计要求。     

Buckling behavior under radial loading of orthotropic oval cylindrical shells with parabolically varying thickness

In this article, the framework of the Flügge's shell theory, the transfer matrix approach, and the Romberg integration method have been employed to investigate the buckling analysis of a radial loaded oval cylindrical shell with parabolically varying thickness along its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling.     

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically non-linear three dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The non-linear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically non-linear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.     

飞机典型薄壁复合材料夹层结构整体屈曲

为了研究飞机机身无筋无框复合材料典型薄壁夹层结构在型号上应用的可行性,本文采用解析方法、有限元方法和试验方法对蜂窝夹层复合材料结构的面内压缩和剪切整体屈曲开展系统研究。基于经典层合板理论和工程解析方法推导蜂窝夹层复合材料的压缩和剪切屈曲载荷随试验件尺寸的变化规律。依据某型飞机机身典型结构分别设计压缩和剪切试验件尺寸大小、边界条件和加载方式。利用有限元商用软件ABAQUS对试验设计建立虚拟试验分析,对比验证解析方法和有限元方法的一致性。最后通过真实试验方法确定解析方法和有限元方法的有效性,并验证典型薄壁夹层结构的承载能力和破坏模式。结果显示,压缩试验结果失效模式与理论预测一致,故3种方法得到的结构整体失稳载荷相近,验证了理论方法的有效性;剪切试验结果发生局部破坏,故试验结果偏低,但有限元方法与解析方法所得结果一致,解析方法相对保守。     

Optimal laminations of thin underwater composite cylindrical vessels

This paper deals with the optimal design of deep submarine exploration housings and autonomous underwater vehicles. The structures under investigation are thin-walled laminated composite unstiffened vessels. Structural buckling failure due to the high external hydrostatic pressure is the dominant risk factor at exploitation conditions. The search of fiber orientations of the composite cylinders that maximize the stability limits is investigated. A genetic algorithm procedure coupled with an analytical model of shell buckling has been developed to determine numerically optimized stacking sequences. Characteristic lamination patterns have been obtained. FEM analyses have confirmed the corresponding significant increases of buckling pressures with respect to initial design solutions. Experiments on thin glass/epoxy and carbon/epoxy cylinders have been performed. The measured buckling pressures appear to be in good agreement with numerical results and demonstrate the gains due to the optimized laminations.     

Buckling failure analysis of all-terrain crane telescopic boom section

In this research work, a nonlinear structure analysis by the finite element analysis (FEA) was carried out to investigate the failure reason of an all-terrain crane telescopic boom. An overall simplified model consisting of telescopic boom and luffing jib was established by beam element, and analyzed using geometric nonlinear static method. A local detailed model consisting of the 4th and 5th telescopic boom section (TBS) was established by shell and solid element, and analyzed using geometric nonlinear and contact nonlinear static method. The result of the overall simplified model FEA indicated that the boom strength met the design criteria, and the 5th TBS of local detailed model occurred stress wrinkle.Structure experiment was designed based on the boom load characteristics in accident and analyzed using nonlinear static method and explicit dynamic method; the connection of load, boom buckling failure and stress wrinkle was studied. The result indicated that the accident was caused by elastic buckling. When the telescopic boom stress state changed from continuous state to wrinkle state, the buckling occurred. So the critical buckling state characteristic was stress wrinkle.     

A comparative study on the elastic-plastic collapse strength of initially imperfect deep spherical shells

A finite difference method for the large deformation elastic-plastic analysis of spherical caps is applied to predict the collapse strength of initially imperfect deep spherical shells. Twelve uniformly loaded hemispherical shell models with flat spots at their apex are analysed. For each model, a number of shallow spherical regions containing the flat spot are selected from its domain. One of these selected shallow regions yields a minimum buckling pressure; this minimum value is taken as the theoretical buckling load for the shell model under consideration. Present solutions are in good agreement with existing experimental and empirical results. The good comparison suggests that initially imperfect deep spherical shells may be analysed by using a much simpler mathematical model—the spherical cap—and thus the analytical cost may be greatly reduced. This also demonstrates that the collapse of imperfect spherical shells is primarily a local phenomenon and therefore dependent on local geometry. Consequently, the presence of initial imperfections must be fully taken into consideration in any large deformation inelastic buckling analysis before such analysis can be expected to quantitatively predict the collapse strength of practical shell structures.     

斜直井内钻柱的非线性螺旋屈曲

基于最小位能原理,研究了斜直井内钻柱的非线性螺旋屈曲问题。利用圆柱面坐标系,使接触非线性问题简化成了纯几何非线性问题。对于上端周向自由,下端铰支的钻柱,用Rayleigh-Ritz法得到了有一定横向载荷作用时,确定螺旋屈曲临界载荷无量纲形式的非线性积分方程。应用符号运算软件Maple10,对具体的工程算例进行了求解。研究发现:该文的计算结果与已有的实验结果吻合,说明钻柱的螺旋屈曲问题是非线性问题,同时也证实了该文的非线性算法的有效性。该方法可用于求解斜直井内的钻柱屈曲问题。     

Flexural-torsional buckling of pultruded fiber reinforced plastic composite I-beams: experimental and analytical evaluations

In this paper a comprehensive experimental and analytical approach is presented to study flexural-torsional buckling behavior of full-size pultruded fiber-reinforced plastic (FRP) I-beams. Two full-size FRP I-beams with distinct material architectures are tested under midspan-concentrated loads to evaluate their flexural-torsional buckling responses. To monitor rotations of the cross-section and the onset of critical buckling loads, transverse bars are attached to the beam crosssection and are subsequently connected to LVDTs; strain gages bonded at the edges of the top flange are also used. The analysis is based on energy principles, and the total potential energy equations for the instability of FRP I-beams are derived using nonlinear elastic theory. The equilibrium equation in terms of the total potential energy is solved by the Rayleigh-Ritz method, and simplified engineering equations for predicting the critical flexural-torsional buckling loads are formulated. A good agreement is obtained between the experimental results, proposed analytical solutions and finite-element analyses. Through the combined experimental and analytical evaluations reported in this study, it is shown that the testing setup used can be efficiently implemented in the characterization of flexural-torsional buckling of FRP shapes and the proposed analytical design equations can be adopted to predict flexural-torsional buckling loads.     

Buckling of a composite cantilever circular cylindrical shell subjected to uniform external lateral pressure

In this paper a solution is presented for a buckling problem formulated for the cantilever circular cylindrical composite shell subjected to uniform external lateral pressure. The edge of the shell is fully clamped at one end of the cylinder and is free at the open section of the other end. An analytical formula for critical pressure has been derived using the generalised Galerkin method. The approach is illustrated by the buckling analyses of composite, orthotropic and isotropic shells. The results are verified using the finite-element method. It has been shown that the analytical solution provides an accurate estimate of the critical load and does not involve any computationally expensive procedures. This is particularly useful in the design optimisation of composite structures.