复合材料壁板铺层参数对大展弦比机翼气动弹性优化的影响

开展了大展弦比复合材料机翼气动弹性综合优化设计研究,以复合材料层合板铺层厚度为设计变量,以多种气动弹性约束与强度/应变约束为限制条件对结构进行优化设计,从铺层比例和铺层非均衡两方面分析了蒙皮铺层参数的影响。研究表明: 在满足综合约束的条件下,随着0°铺层比例的增加,翼尖变形略微减小,颤振速度略有下降,副翼效率变化不大; 蒙皮铺层非均衡程度主要影响机翼静气动弹性能,随着蒙皮非均衡引起的机翼刚轴绕翼根向前缘逐渐偏转,翼尖垂直变形变化不明显,但翼尖负扭转变形的绝对值加大,副翼效率下降。     

Global shared-layer blending method for stacking sequence optimization design and blending of composite structures

A global shared-layer blending (GSLB) method is proposed for obtaining manufacturable stacking sequence of composite structures with blending and design rules. The method combines the traditional SLB technique with an evaluation algorithm of spatial variation of panels, where the manufacturability of laminates is enhanced by identifying and minimizing the ply-drops, and controlling the laminate transition drop boundaries. In addition, a blended design scheme is also proposed, which is achieved by using the stacking sequence table technique. A composite wing structure is selected to validate the efficiency and accuracy of the proposed method. Results show that the GSLB method can be used for generating more manufacturable designs of large-scale composite structure with multiple engineering constraints.     

Fracture mechanics and optimization — a useful tool for fibre-reinforced composite design

This paper will demonstrate the application of fracture mechanics and optimization techniques for the optimum design of fibre-reinforced composite laminates (FRC). First, a boundary-value problem of a cracked composite laminate is solved within the framework of linear elastic fracture mechanics (LEFM). The solution relates the stress intensity factor at a crack tip and the crack-induced interfacial stresses to the laminate configuration. These results are then used in two types of the optimum design of fibre-reinforced composite laminates. In the first type of optimum design, namely a crack-insensitive design of the laminate, the crack driving force and interfacial principal tensile stress are both minimized by using single- and multicriterion optimization techniques. The second type of optimum design involves in situ strength design of multidirectional angle-ply laminates. In this case, a set of in situ strength parameters are proposed based on theoretical analysis and experimental observations. This optimization problem is a min {max} one and non-differentiable. A proper treatment of the non-differentiability is introduced and the min {max} optimization problem is converted into a differentiable single-criterion one using the bound-formulation technique. All the optimization problems are solved by non-linear mathematical programming. The results show that optimization can greatly enhance the load carrying capacity of the laminates.     

Optimization of laminated composites subject to uncertain buckling loads

Optimal design of composite laminates under buckling load uncertainty is presented. The laminates are subjected to biaxial compressive loads and the buckling load is maximized under worst case in-plane loading which is computed using an anti-optimization approach. The magnitudes of the in-plane loads are not known a priori resulting in load uncertainty subject to the only constraint that the loads belong to a given uncertainty domain. Results are given for continuous and discrete fibre orientations which constitute the optimization problem coupled to load anti-optimization problem leading to a nested solution method. It is observed that the stacking sequence of a laminate designed for a deterministic load case only differs considerably from that of a robust laminate designed taking load uncertainties into account. Consequently the buckling load carried by a deterministic design is considerably less than the one carried by a robust design when both are subjected to uncertain loads.     

Multi-material topology optimization of laminated composite beam cross sections

This paper presents a novel framework for simultaneous optimization of topology and laminate properties in structural design of laminated composite beam cross sections. The structural response of the beam is evaluated using a beam finite element model comprising a cross section analysis tool which is suitable for the analysis of anisotropic and inhomogeneous sections of arbitrary geometry. The optimization framework is based on a multi-material topology optimization model in which the design variables represent the amount of the given materials in the cross section. Existing material interpolation, penalization, and filtering schemes have been extended to accommodate any number of anisotropic materials. The methodology is applied to the optimal design of several laminated composite beams with different cross sections. Solutions are presented for a minimum compliance (maximum stiffness) problem with constraints on the weight, and the shear and mass center positions. The practical applicability of the method is illustrated by performing optimal design of an idealized wind turbine blade subjected to static loading of aerodynamic nature. The numerical results suggest that the proposed framework is suitable for simultaneous optimization of cross section topology and identification of optimal laminate properties in structural design of laminated composite beams.     

Optimal design of variable fiber spacing composites for morphing aircraft skins

Morphing aircraft concepts aim to enhance the aircraft performance over multiple missions by designing time variant wing configurations. The morphing concepts require wing skins that are flexible enough to allow large in-plane stretching and high bending stiffness to resist the aerodynamic loads. In this study, an optimization problem is formed to enhance the in-plane flexibility and bending stiffness of wing skins made of composite laminate. Initially, the optimal fiber and elastomer materials for highly flexible fiber reinforced elastomer laminates are studied using materials available in the literature. The minor Poisson’s ratio of the laminate is almost zero for all the fiber and elastomer combinations. In the next stage, the effects of boundary conditions and aspect ratio on the out-of-plane deflection of the laminate are studied. Finally, an optimization is performed to minimize the in-plane stiffness and maximize the bending stiffness by spatially varying the volume fraction of fibers of a laminate. The optimization results show that the in-plane flexibility and bending stiffness of the laminate with a variable fiber distribution is 30–40% higher than for the uniform fiber distribution.     

Optimisation of blended bistable laminates for a morphing flap

Multistable composites offer significant deformations in stable shapes, and, this makes them interesting for morphing applications. Moreover, bistable laminates can be manufactured to have variable angle tows (VATs) in a ply using a tow-steering technique to ensure continuity of fibres over the planform of the laminates and, in doing so, may impart additional structural strength due to load path continuity along-with the prospect of easier integration with the major structure by blending lay-ups across components. The use of ant colony systems as an optimisation concept has been implemented, incorporating the feedback from the finite element analysis to identify blended VAT (equivalent) bistable laminate for a morphing flap application. Proof-of-concept is demonstrated by manufacture of VAT (equivalent) laminates. Presented research findings highlight the potential of blended bistable laminates, developed through optimisation based design methodology, for morphing applications.     

Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

A partial mixed finite element (FE)–state space method (SSM) semi-analytical approach is presented for the static analysis of piezoelectric smart laminate composite and functionally graded material (FGM) plates. Hence, using the Hamiltonian formalism, the three-dimensional piezoelectricity equations are first worked so that a partial mixed variational formulation, which retains the translational displacements, electric potential, transverse stresses, and transverse electric displacement as primary variables, is obtained; this allows, in particular, straightforward fulfillment of the electromechanical continuity constraints at the laminate interfaces. After an in-plane FE discretization only, the problem is first reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved using the symplectic approach; then, the multilayer solution is reached via the SSM propagator matrix. The proposed methodology is finally applied to the static analysis of piezoelectric-cross-ply hybrid laminated composite and FGM plates. In a comparison with open literature, available tabulated results show good agreements, thus validating the proposed approach.     

Design of multifunctional structure with embedded electronic circuitry using composite laminate optimization techniques

This research investigates the optimization of a multifunctional structure with embedded electronic circuitry, following traditional composite laminate optimization methods. A heavily ‘de-featured’ finite element model provides thermal and mechanical analyses of the structure. The model places point heat sources at the surface component locations, and the optimization problem enforces strain constraints at these locations. A simple problem seeks the least-mass I-beam whose shear web contains a simple circuit, subject to strength and strain constraints. A second problem finds the lowest mass unmanned aerial vehicle (UAV) wing box configuration containing embedded circuitry subject to strength, deflection and strain constraints under two load cases. Sequential unconstrained minimization techniques and sequential quadratic programming perform the optimization; combinatorial methods are computationally impractical. Despite the model de-featuring and the use of calculus-based methods, the problem requires significant computational effort. The surface-component strain constraints result in structures with more mass than those without surface components.     

采用等效有限元模型的复合材料机翼结构优化

在机翼设计过程中,将等效有限元模型(EFEM)方法应用于考虑静力学和动力学要求的机翼结构优化。提出了"三步走"的结构优化策略,将一个多变量的复杂优化问题转换为一系列少变量的简单优化问题,对某支线客机的复合材料机翼进行了优化设计。首先以位移、静强度和颤振速度作为约束条件对机翼复合材料铺层比例进行优化;然后以静强度和结构稳定性作为约束,以最小化结构质量和结构效率作为优化目标,对各翼肋之间的加强壁板进行优化设计;最后再以位移和颤振速度为约束,对机翼结构总体刚度进行优化设计。结果表明:EFEM方法具有快速建模和计算量少的优点,采用"三步走"优化策略具有更高的效率,适用于初步机翼结构优化设计。     

基于轻量化目标的发射箱纤维增强材料铺层设计

目的以某型发射箱复合材料箱体为对象,探讨复合材料箱体的纤维增强材料铺层设计方法。方法以箱体质量为控制为目标,运用复合材料层合板力学理论结合有限元分析方法进行纤维增强材料铺层计算。结果将纤维的体积分数控制在43.6%,箱体玻璃纤维布铺层总数量为10层,可实现箱体的质量控制目标为(23±1)kg。结论获得的纤维增强材料铺层方式可有效保证箱体的质量一致性和尺寸控制要求。     

Design optimization of composites using genetic algorithms and failure mechanism based failure criterion

In this paper, minimum weight design of composite laminates is presented using the failure mechanism based (FMB), maximum stress and Tsai–Wu failure criteria. The objective is to demonstrate the effectiveness of the newly proposed FMB failure criterion (FMBFC) in composite design. The FMBFC considers different failure mechanisms such as fiber breaks, matrix cracks, fiber compressive failure, and matrix crushing which are relevant for different loading conditions. A genetic algorithm is used for the optimization study. The Tsai–Wu failure criterion over predicts the weight of the laminate by up to 86% in the third quadrant of the failure envelope compared to FMB and maximum stress failure criteria, when the laminate is subjected to compressive–compressive loading. It is found that the FMB and maximum stress failure criteria give comparable weight estimates. The FMBFC can be considered for use in the strength design of composite structures.     

A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

Non‐linear dynamic stability analysis of composite laminates under periodic in‐plane compressive loads

This work deals with the investigation of the non‐linear instability behaviour of the composite laminates subjected to periodic in‐plane/axial load, through the finite element formulation with dynamic response analysis. Here, C¹ eight‐noded shear‐flexible plate element, based on a new kind of kinematics which allows to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate, is employed. The non‐linear governing equations obtained are solved using the Newmark direct integration method coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the dynamic stability such as existence of beats, their dependency on the forcing frequency, and the typical character of vibrations in the different regions. Numerical results are also presented to highlight the influence of ply‐angle and lay‐up of the laminate on dynamic stability behaviour of the composite laminates. Copyright © 1999 John Wiley & Sons, Ltd.     

Probabilistic optimal design of laminates using improved particle swarm optimization

A new approach to the particle swarm optimization (PSO) is proposed for the solution of non-linear optimization problems with constraints, and is applied to the reliability-based optimum design of laminated composites. Special mutation-interference operators are introduced to increase swarm variety and improve the convergence performance of the algorithm. The reliability-based optimum design of laminated composites is modelled and solved using the improved PSO. The maximization of structural reliability and the minimization of total weight of laminates are analysed. The stacking sequence optimization is implemented in the improved PSO by using a special coding technique. Examples show that the improved PSO has high convergence and good stability and is efficient in dealing with the probabilistic optimal design of composite structures.     

A general strategy for the optimal design of composite laminates by the polar-genetic method

The object of the present work is the development and application of a totally general approach to optimal design of composite laminates where all the required properties for the laminate are explicitly expressed as criteria of the optimisation process. Our formulation is in the form of a highly non-linear and non-convex single- or multi-objective optimisation problem subject to equality and inequality constraints. We show here applications to the design of maximum stiffness, maximum buckling load, maximum eigenfrequencies, maximum strength as well as combinations of the afore mentioned criteria; all types of elastic symmetries can also be taken into account. In order to keep the same greatest generality in solving our optimisation problem, we developed an evolved version of the genetic algorithm BIANCA for the design of composite laminates. We show here a number of numerical solutions found using BIANCA.     

复合材料翼面结构带位移约束的优化设计

本文对复合材料航空翼面结构进行了满足位移及工艺尺寸要求的最小重量设计,用多项式模拟复合材料蒙皮各个铺层的厚度采用有限元法做结构分析,用可行方向法求解优化问题.设计变量取为多项式的系数及其他有限单元的厚度或截面积,通过变量成组减小问题的规模.文中对一个复合材料盒段,一个复合材料机翼进行了优化设计,得到了较好的结果.      

Design optimization framework for tiltrotor composite wings considering whirl flutter stability

This paper constructs the design optimization framework for the composite wing of a tiltrotor aircraft based on the Korea Aerospace Research Institute (KARI) Smart Unmanned Aerial Vehicle (SUAV) TRS4 model. The present optimal design attempts to find the cross-section layout that minimizes the structural weight of a composite wing, while satisfying a series of design constraints. The framework consists of various analysis and design tools that include a 2-D beam cross-section analysis, a whirl flutter analysis, and a 3-D strain/stress analysis under the worst wing-loading case. The variation of wing sectional properties of tiltrotor aircrafts in the course of design optimization greatly affects the whirl flutter stability and shows considerable influence on the structural integrity of the wing. In the design framework, the whirl flutter stability is analysed by the nonlinear flexible multibody analysis code DYMORE and the structural integrity is investigated using a MATLAB-based 3-D strain analysis module along with the previous load analysis result. The MATLAB is used to conduct the optimization with a gradient-based optimizer and integrate all of the design and analysis tools. The nonlinear constraints associated with the aeroelastic stability and the structural integrity are also considered. For optimal design examples using the developed framework, a simplified cross-section model based on the KARI SUAV TRS4 composite wing is considered as an initial model. Design optimization examples are investigated to show the validity of the proposed framework and to illustrate the reduction of the structural weight of the composite wing. It is observed that weight reductions of wing structures by 26% and 40% are achieved, while maintaining the whirl flutter stability margins.     

基于几何因子的复合材料气动弹性剪裁设计

实现了基于几何因子的复合材料层合板建模,解决了几何因子与Natran的参数输入问题,并根据工艺约束中的最小铺层比例对几何因子可行空间进行了推导补充。在此基础上,提出了一种基于几何因子和Nastran的复合材料气动弹性剪裁优化设计方法。首先以总厚度和几何因子作为设计变量以及以Nastran作为求解器,以强度、刚度、颤振和发散速度以及几何因子相关性约束作为约束条件进行结构寻优,得到最优的铺层总厚度和几何因子。其次,以最优几何因子作为目标,进行铺层结构逆问题求解,约束条件为复合材料铺层工艺约束。因几何因子为铺层厚度和铺层顺序的表达式,与传统的多级优化相比,以几何因子作为设计变量可以避免铺层厚度和铺层顺序的解耦,进而获得更大的设计空间,且得到的铺层结构可以满足工艺约束。最后,对一矩形悬臂复合材料层合板进行剪裁设计,使得铺层结构满足气动弹性约束且质量最小。结果显示,运用该优化方法可以得到质量更小且满足工艺约束的铺层结构。