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.     

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。     

Analysis for buckling and vibrations of composite stiffened shells and plates

This paper deals with development of triangular finite element for buckling and vibration analysis of laminated composite stiffened shells. For the laminated shell, an equivalent layer shell theory is employed. The first-order shear deformation theory including extension of the normal line is used. In order to take into account a non-homogeneous distribution of the transverse shear stresses a correction of transverse shear stiffness is employed. Based on the equivalent layer theory with six degrees of freedom (three displacements and three rotations), a finite element that ensures C⁰ continuity of the displacement and rotation fields across inter-element boundaries has been developed. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Results of vibration and buckling analysis of stiffened plates and shells are discussed.     

先进复合材料格栅加筋板的总体稳定性分析

通过建立复合材料格栅结构单元的基本力学假设和分析模型, 推导了一种新的等效刚度计算方法, 用于分析复合材料格栅加筋板的总体稳定性。该方法充分考虑了筋条和面板的相互作用和中面偏移效应, 并具有通用性。结合Rayleigh-Ritz能量近似法, 推导出了求解加筋板总体屈曲载荷的通用特征方程; 分析了多种算例, 并与修正平铺法进行了比较, 结果吻合得很好。      

Simultaneous buckling design of stiffened shells with multiple cutouts

Buckling is usually initiated from a local region near the cutout for cylindrical stiffened shells under axial compression, and then the evolution of buckling waves is governed by the combined effects of local and global stiffness, which limit the load-carrying capacity. Therefore, a simultaneous buckling pattern is crucial for improving the structural efficiency. In this study, a multi-step optimization strategy for the integrated design of near and far fields away from cutouts is proposed, and the convergence criterion of buckling optimization is improved as a deformation-based index. The numerical implementation of the asymptotic homogenization method is utilized to construct an efficient finite element model for post-buckling analysis. A 5?m diameter stiffened shell in a launch vehicle demonstrates that the proposed framework can provide a simultaneous buckling design with high structural efficiency in an efficient manner. Both the buckling deformations and stress of the optimum design are more uniform compared to other optimum designs.     

基于分级优化的复合材料带加强筋板屈曲优化

对工程中常用复合材料带加强筋板结构的优化方法进行研究。由于优化变量较多且变量类型涉及离散型和连续型两种类型,因此优化中引入了分级优化方法。在结构质量一定的前提下,确定各加强筋最优的位置、截面尺寸、铺层数及铺层顺序,以提高整体结构的抗屈曲性能。代理层的引入使优化问题可以在先不考虑铺层顺序的情况下对其余变量进行优化,通过析因实验设计方法确定剩余变量中影响结构屈曲载荷的主要变量和次要变量,并分别在第1、2级优化中独立对两类变量进行优化,在优化过程中根据变量的类型及取值范围,对部分变量建立径向基代理模型以提高优化效率。第3级优化采用遗传算法对铺层顺序进行优化。优化结果表明:优化后方案比原方案的抗屈曲能力提高了3.21倍。     

脱胶缺陷尺寸对复合材料加筋板屈曲及后屈曲特性的影响

为确定脱胶缺陷对复合材料加筋板屈曲及后屈曲特性的影响,对含不同脱胶缺陷工型筋条的复合材料加筋板进行了压缩试验研究。结果表明,30 mm和50 mm的缺陷对试验件承载能力影响很小,当缺陷尺寸增至80 mm时,试验件后屈曲承载能力明显下降。借助超声检测技术对缺陷的扩展行为进行了监测,结果表明,当压缩载荷达到破坏载荷的85.3%时,预制缺陷的对角位置处出现扩展迹象。通过影像云纹法获得两半波和三半波失稳模态的形成过程。对失稳模态的监测结果还表明,随缺陷长度增加,该型加筋板的失稳模态从三半波向两半波转换。在试验基础上,利用ABAQUS软件建立有限元（FE）模型,依次进行了屈曲及后屈曲过程的数值模拟。屈曲分析用于获得试验件的失稳载荷及模态,在后屈曲分析中将失稳波形以几何扰动的形式引入FE模型,最终计算结果与试验结果基本吻合,表明该模型可以用于复合材料加筋板屈曲及后屈曲性能的预测。     

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.     

复合材料加筋壁板长桁终止端混合连接设计分析

对缩短胶接面长度以提高起裂载荷的复合材料加筋壁板长桁终止端新型混合连接设计进行了研究。采用经试验验证的有限元方法,对长桁终止端混合连接的传载与失效机制进行分析,并研究了胶接面长度对结构起裂载荷的影响规律。研究结果表明：新型混合连接设计中紧固件提供的法向约束以及剪切载荷传递路径可显著提升终止端结构的起裂载荷,并增强终止端处界面的抑制损伤扩展能力;结构的起裂载荷随着胶接面的缩短而提高;当胶接面前缘退至连接区末排紧固件之后,可避免结构在最终破坏前发生界面失效,结构强度由蒙皮的机械连接强度决定。     

Weight functions for composite repairs to stiffened panels

This paper presents a weight function technique for calculating the stress intensity factors for composite repairs to cracks emanating from an internal notch, corrosion blend out, or a free edge under arbitrary loading in rib stiffened panels. The predictions are compared with both finite element and experimental values. This methodology represents a significant extension to existing assessment and design formulae that are currently limited to the case of uniform loading and flat unstiffened panels.     

复合材料翼面壁板轴压稳定性

基于T型长桁铺层数不同的两块复合材料翼面加筋壁板试件SC-1和SC-2,开展轴压稳定性试验研究,并提出一种预测屈曲载荷及最小后屈曲承载能力的工程分析方法,结合有限元特征值屈曲分析方法、有限元弧长法对试件的屈曲载荷、屈曲模态及后屈曲承载能力进行分析。试验结果表明,铺层数较多的试件SC-1的蒙皮局部屈曲应变较高,壁板也具有更高的屈曲载荷。在后屈曲阶段,SC-2加载到试验屈曲载荷的2.4倍未发生材料破坏和长桁蒙皮间脱粘损伤。工程分析方法和特征值屈曲分析能够准确预测壁板的屈曲载荷,最大误差分别为-9.3%和-2.8%,工程分析得到SC-2的最小后屈曲承载能力为试验屈曲载荷的2.09倍。有限元弧长法分析得到两件试件的屈曲载荷误差均小于1%,并具有壁板轴压屈曲模态预测和变形跟踪能力。      

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.     

Progressive failure analysis for advanced grid stiffened composite plates/shells

A progressive failure methodology is developed to simulate the initiation and propagation of multi-failure modes for advanced grid stiffened (AGS) composite plates/shells on the basis of a stiffened element model. Failures of both skin and ribs are taken into consideration, which are matrix cracking, fiber failure, fiber–matrix shear failure, delamination in skin and fiber failure in rib. All these failures are defined using a set of 2-D stress-based polynomial failure criteria wherein the transverse shear stresses at centroid of the stiffened element are calculated by employing an integrated approach of finite element and finite difference method. Corresponding material and stiffness degradation behavior is introduced after the initiation of individual failure mechanisms. The progressive failure behavior of a composite orthotropic-grid curved panel with a centrally located cutout under compressive load is evaluated using the method.     

Optimal design of general stiffened composite circular cylinders for global buckling with strength constraints

A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.     

Shear buckling of corrugated composite panels

Corrugated composite panels are used in aerospace vehicles primarily because of their ability to withstand higher loads before buckling compared to plain sheets. Shear buckling is one of the important modes of failure. In this paper are presented details of prediction of the shear buckling loads of composite panels having sinusoidal or hat type corrugation. The given panel is idealised as an homogeneous orthotropic plate whose equivalent properties are determined based on the given parameters of the panel. In the analysis Kirchhoff-Love assumptions are used. Two opposite edges of the panel in one direction are assumed to be simply supported and the panel is assumed to be very long in the other direction. Critical buckling loads are obtained using conventional orthotropic plate theory. A large class of 0°/90°/45°-45° lamination schemes leading to quadridirectional, tridirectional and bidirectional T300/N5208 corrugated panels is examined and ranked based on buckling loads. Results indicate that by proper choice of lamination scheme, very significant increases in buckling load compared to the quasi-isotropic case can be obtained. Having the corrugation plane normal to the shorter side is significantly better than having the corrugation plane normal to the longer side. Optimum layup schemes are found for 8, 6, 4 and 2 ply cases.     

Measurement techniques for buckling sensitive composite shells

This paper describes a measurement system that was developed for an experimental study on buckling of glass reinforced composite cylinders. An automated non-contact laser device operating inside the test specimen provided a three dimensional scanning system for measuring the deformation of the shell wall. The measurement system was used to obtain the initial geometric imperfections, as well as the deformation under varying control axial displacement. All loading and data acquisition operations were carried out using advanced computer controlled techniques. Due to the large number of measurements undertaken in each test, data collection was followed by processing and reduction techniques, thus delivering the data in a form suitable for finite element analysis and comparative studies. Typical results are presented in order to demonstrate the reliability, accuracy and versatility of the system.     

Reduced-stiffness method in the theory of buckling of stiffened shells

The reduced-stiffness method is used to establish the lower bounds of buckling loads for stringer- or ring-stiffened cylindrical shells. The numerical results obtained by using this method are compared with the experimental data. We also consider the problem of applicability of the reduced-stiffness method in design practice as well as the prospects for its development and generalization. The present work is a continuation of the review [1]. Translated from Problemy Prochnosti, No. 2, pp. 90–104, March–April, 2000.     

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。