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.     

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。      

Computational strategy for multiobjective optimization of composite stiffened panels

This paper presents a multiobjective optimization methodology for composite stiffened panels. The purpose is to improve the performances of an existing design of stiffened composite panels in terms of both its first buckling load and ultimate collapse or failure loads. The design variables are the stacking sequences of the skin and of the stiffeners of the panel. The optimization is performed using a multiobjective evolutionary algorithm specifically developed for the design of laminated parts. The algorithm takes into account the industrial design guidelines for stacking sequence design. An original method is proposed for the initialization of the optimization that significantly accelerates the search for the Pareto front. In order to reduce the calculation time, Radial Basis Functions under Tension are used to approximate the objective functions. Special attention is paid to generalization errors around the optimum. The multiobjective optimization results in a wide set of trade-offs, offering important improvements for both considered objectives, among which the designer can make a choice.     

考虑屈曲的复合材料加筋壁板铺层顺序优化

提出了一种考虑屈曲的复合材料加筋壁板铺层顺序优化方法。基于复合材料加筋壁板屈曲载荷求解的能量法,系统推导了轴压载荷作用下复合材料加筋壁板蒙皮、筋条局部屈曲载荷的显示表达式,考虑了加筋壁板各板元之间的弹性支持作用及筋条下缘条的影响,引入工程法求解了加筋壁板整体屈曲载荷。基于国产自主结构分析软件HAJIF中的复合材料铺层工程数据库,以铺层参数为中间变量,利用本文提出的复合材料加筋壁板屈曲载荷求解方法,构建了考虑屈曲的复合材料加筋壁板铺层顺序优化设计流程并完成程序实现,将最小二乘法用于最优铺层顺序与工程铺层数据库的匹配。相比于传统有限元计算方法,本文提出的复合材料加筋壁板屈曲载荷求解方法具备较好的求解精度及求解效率。复合材料加筋壁板优化算例表明,采用本文提出的加筋壁板屈曲载荷分析及其优化方法,在结构重量不变的前提下,屈曲载荷提高约17%,且铺层顺序优化结果可直接从铺层工程数据库中提取并用于工程实际。      

复合材料帽型加筋板轴压试验及承载能力预测

随着复合材料的广泛使用,复合材料帽型加筋板在飞机结构上的使用也越来越多。为研究复合材料帽型加筋板承受轴向压缩的能力,首先对不同蒙皮半径、蒙皮厚度及长桁间距的复合材料帽型加筋板进行了轴压试验,得到了局部屈曲载荷、破坏载荷与加筋板曲率系数、长桁间距的关系,然后,通过引入曲率修正系数,修正了现有加筋板屈曲载荷的工程估算公式;最后,利用分段处理法结合有效宽度概念改进了加筋板轴压极限承载的工程算法。结果表明:帽型复合材料加筋板局部屈曲载荷及最终破坏载荷与曲率系数正相关;改进的方法能对复合材料加筋板的极限承载进行准确预测。所得结果表明该方法为复合材料加筋板结构设计及载荷估算提供了一种新方法,具有一定的工程应用价值。      

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。     

复合材料加筋板屈曲/后屈曲分析的应用

研究了复合材料加筋板翼面结构稳定性问题,分析了加筋板在压缩和剪切等载荷作用下的稳定性安全裕度。利用计算复合材料加筋板屈曲及后屈曲承载能力的方法,验证复杂受载情况下结构的稳定性。验证对象是一个优化后的满足强度、刚度和工艺制造要求的复合材料机翼。该机翼在各种载荷工况下的内力分布情况由MSC.NASTRAN分析得到,通过本文提出的方法得到每块蒙皮的稳定性承载能力。然后给出复合材料层合板在复杂载荷下的屈曲及后屈曲安全裕度的计算准则,验证优化后的机翼加筋板是否满足稳定性设计要求。该方法可作为约束集成到结构优化系统平台中。     

Single-mode solution for post-buckling analysis of composite panels with elastic restraints loaded in compression

A closed-form solution is obtained to determine the buckling and post-buckling behavior of elastically restrained composite panels under compressive loading. The approach allows to study the response of stiffened panels undergoing local buckling modes, taking into account the restraints provided by the stiffeners to the rotation of the skin edges. The panels are modeled as thin plates referring to Marguerre type equations together with classical lamination theory. The equations are written in non-dimensional form, allowing for the study of a wide class of orthotropic laminates. The problem is formulated in terms of out of plane displacement, represented with a single-mode approximation, and Airy stress function. The compatibility equation is solved exactly, while the method of Galerkin is applied to impose the equilibrium. The buckling load, the out of plane displacement at different load levels, and the post-buckling stiffness are derived and compared with finite element analyses, revealing good accuracy. Sensitivity analyses are also performed obtaining design charts.     

具有初始几何缺陷加劲板的动态屈曲

针对工程中常用的加劲板,研究了动态屈曲的求解方法。将加劲板分为母板与加劲肋两个部分考虑,其中母板按经典薄板理论计算,加劲肋视为Euler梁。假定加劲板的位移,利用Hamilton原理结合系统能量和振型叠加法建立了加劲板的动态屈曲特征方程。最后,选择四边简支加劲板进行数值分析,分析中考虑初始几何缺陷的影响,并讨论了初始几何缺陷、加劲肋的数量及其刚度的变化对动态屈曲临界荷载的影响。结果表明：一阶模态的初始几何缺陷对加劲板的临界荷载影响很大,而增加加劲肋的数量及其刚度可以提高加劲板的抗动态屈曲能力。研究结果也为加劲板的结构设计方法提供一定的参考。     

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.     

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.     

复合材料翼面壁板剪切稳定性

基于长桁铺层数不同的两块复合材料翼面T型加筋壁板试件SS-1和SS-2开展剪切稳定性试验。试件SS-1和SS-2的L型层合板铺层分别为11层和14层,腹板铺层分别为22层和28层,缘条铺层分别为15层和18层。采用提出的工程方法进行壁板的剪切屈曲应变分析,方法中考虑了长桁尺寸和铺层数的影响,并应用有限元弧长法进行试件屈曲载荷、后屈曲承载能力及剪切屈曲模态分析。试验结果表明,屈曲发生之前试件蒙皮处于均匀纯剪切应变状态,后屈曲阶段试件发生了长桁-蒙皮脱粘破坏失效,长桁铺层数较多的试件SS-2具有更高的屈曲载荷和蒙皮局部屈曲应变。工程方法计算得到试件SS-1和SS-2的剪切屈曲应变相对于试验结果的误差分别为–14.9%和–9.2%。有限元弧长法分析得到试件SS-1的屈曲载荷和屈曲应变误差分别为1.9%和2.7%,且剪切屈曲模态与试验结果一致。弧长法对不同长桁铺层数的研究结果表明,长桁铺层较少时,壁板发生整体失稳的材料破坏,而长桁铺层数较多时,更容易发生长桁与蒙皮的脱粘失效。      

翼肋支撑对复合材料加筋板轴压性能的影响

为确定翼肋支撑对复合材料加筋板轴压性能的影响,对施加翼肋支撑前后的复合材料工型加筋板和帽型加筋板进行压缩试验和数值模拟研究。轴压试验中,通过应变计和影像云纹法实时监测试验件的失稳载荷及失稳模态,通过断面观测分析结构损伤破坏机制。基于ABAQUS软件建立有限元模型模拟加筋板屈曲及后屈曲过程,通过失稳节线及反节线上的应力分布变化分析加筋板破坏机制。计算结果与试验结果相吻合,表明翼肋支撑对不同筋条加筋板失稳模态有影响但均不改变结构失稳载荷,位于节线上的翼肋支撑对工型加筋板破坏载荷影响较小,但位于反节线上的翼肋支撑使帽型加筋板的承载能力提高了26.2%。试验件失稳后应力向反节线上筋条蒙皮界面集中,过高的应力导致界面脱粘,使得结构集中在反节线上破坏。      

Buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads using lamination parameters

The buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads of axial compression and torsion are examined on the basis of Flügge’s theory. In the buckling analysis of long laminated composite cylindrical shells, 12 lamination parameters are introduced and used as design variables for layup optimization. Applying a variational approach, the feasible region in the design space of the 12 lamination parameters is numerically obtained. The buckling characteristics are discussed in the design space of the 12 lamination parameters. In the layup optimization, the optimum lamination parameters for maximizing the buckling loads and the laminate configurations for realizing the optimum lamination parameters are determined by mathematical programming methods. It is found that in case of combined loads of axial compression and torsion, the optimum laminate configurations are unsymmetric.     

Positioning of Embedded Optical Fibres Sensors for the Monitoring of Buckling in Stiffened Composite Panels

A numerical/experimental study on the monitoring of the skin buckling phenomenon in stiffened composite panels by embedding optical fibres is presented in this paper. A numerical procedure has been introduced able to provide the most efficient embedded optical fibre path (with minimum length) fulfilling the grating sensors locations and directions requirements whilst satisfying specific embedding/integrity constraints for the optical fibre. The developed numerical procedure has been applied to a stiffened composite panel under compression load. The best location and direction of the grating sensors and the optimal optical fibre path for the monitoring of the skin buckling phenomenon have been found by performing respectively non-linear FEM analyses and optimization analyses. The procedure has been validated by means of an experimental testing activity on a stiffened panel instrumented with embedded optical fibres and back-to-back strain gauges which have been positioned according to the numerically estimated grating sensors locations and directions.     

一种基于复合材料加筋板结构效率的稳定性优化方法

提出一种以承载效率最高作为目标的新设计方法, 对复合材料加筋板的承载能力进行优化。讨论了不同压缩与弯曲刚度的匹配模式与加筋板临界失稳载荷的关系。将全局失稳载荷、局部失稳载荷与静载荷的接近程度作为结构承载效率的量化标准, 通过静载荷的控制, 使结构的稳定性向着效率最高的方向优化。以宏观的加筋板压缩与弯曲刚度参数作为设计变量, 构建了一种可用于结构效率优化的代理模型, 避免了局部最优点的出现, 更便于数值寻优。通过有限元分析验证, 优化后壁板的临界失稳载荷与所施加的静载荷基本一致, 反映出较高的效率, 从而验证了该方法的可靠性。      

Buckling of open-section bead-stiffened composite panels

Stiffened panels are structures that can be designed to efficiently support in-plane compression, bending, and shear loads. Although the stiffeners are usually discrete elements which are fastened or bonded to a flat or continuously curved plate, manufacturing methods such as thermoforming allow integral formation of the stiffeners in a panel. Such a configuration offers potential advantages in terms of a reduced number of parts and manufacturing operations. For thermoplastic composite panels stiffened by integrally formed open-section beads, the effects of bead spacing and bend cross-section geometry on the initiation of buckling under uniaxial compression and uniform shear loading were investigated. Finite elements results for a range of stiffened panel sizes and bead geometries are presented and compared with approximate closed-form solutions based on an effective flat plate size. Experimental verification of analytical predictions for one of the shear panels and one of the compression panels is described. Compensation of the forming tool to reduce the degree of initial curvature of the panels was found to be necessary.     

Weight optimal design of lateral wing upper covers made of composite materials

The present investigation is devoted to the development of a new optimal design of lateral wing upper covers made of advanced composite materials, with special emphasis on closer conformity of the developed finite element analysis and operational requirements for aircraft wing panels. In the first stage, 24 weight optimization problems based on linear buckling analysis were solved for the laminated composite panels with three types of stiffener, two stiffener pitches and four load levels, taking into account manufacturing, reparability and damage tolerance requirements. In the second stage, a composite panel with the best weight/design performance from the previous study was verified by nonlinear buckling analysis and optimization to investigate the effect of shear and fuel pressure on the performance of stiffened panels, and their behaviour under skin post-buckling. Three rib-bay laminated composite panels with T-, I- and HAT-stiffeners were modelled with ANSYS, NASTRAN and ABAQUS finite element codes to study their buckling behaviour as a function of skin and stiffener lay-ups, stiffener height, stiffener top and root width. Owing to the large dimension of numerical problems to be solved, an optimization methodology was developed employing the method of experimental design and response surface technique. Optimal results obtained in terms of cross-sectional areas were verified successfully using ANSYS and ABAQUS shared-node models and a NASTRAN rigid-linked model, and were used later to estimate the weight of the Advanced Low Cost Aircraft Structures (ALCAS) lateral wing upper cover.     

A parametric study of skin laminates used in the composite layup of large-scale wind turbine blades

To reach an optimal design solution for the composite layup of large-scale wind turbine blades, subjected to various design load conditions, while, fulfilling numerous design requirements, is a challenging task to accomplish. Since, a large-scale blade is a slender beam structure, therefore, its thin composite layup can be assumed to be under plane stress condition. Consequently, a parametric study of the skin laminates used in the blade composite layup, is conducted to explore and identify the possible design improvements. The results show that the use of off-axis fiber angles of the skin laminate lower than the conventional 45° are more favorable to achieve higher laminate stiffness, strength, bucking stability, fatigue resistance, and bend-twist coupling value, thereby, demonstrating the potential improvements to the existing composite layup design of large-scale wind turbine blade.     

Calculation of the collapse load of an axially compressed laminated composite stringer-stiffened curved panel–An engineering approach

The effective width method that is widely applied for the analysis of isotropic planar stringer-stiffened panels has been extended to laminated composite stringer-stiffened circular cylindrical panels. The approach was modified and adapted to handle curved composite structures.

Panels stiffened by blade type stiffeners, J-form stiffeners and T-form stiffeners were considered in the present study. Bending buckling of the stiffeners, their torsional buckling, combined bending and torsion buckling and local buckling of the stringers were accounted for in the investigation. Using the proposed extended effective width method, a MATLAB based software code TEW¹ was developed and implemented. To validate this code, predictions obtained by it were compared with experimental results and with finite element calculations. Good agreement between the present proposed method, experiments and finite element simulations was found, thus yielding an efficient, simple to apply and fast engineering code to be used in design and optimization stages.