Aircraft morphing wing design by using partial topology optimization

A morphing wing concept has been investigated over the last decade because it can effectively enhance aircraft aerodynamic performance over a wider range of flight conditions through structural flexibility. The internal structural layouts and component sizes of a morphing aircraft wing have an impact on aircraft performance i.e. aeroelastic characteristics, mechanical behaviors, and mass. In this paper, a novel design approach is proposed for synthesizing the internal structural layout of a morphing wing. The new internal structures are achieved by using two new design strategies. The first design strategy applies design variables for simultaneous partial topology and sizing optimization while the second design strategy includes nodal positions as design variables. Both strategies are based on a ground structure approach. A multiobjective optimization problem is assigned to optimize the percentage of change in lift effectiveness, buckling factor, and mass of a structure subject to design constraints including divergence and flutter speeds, buckling factors, and stresses. The design problem is solved by using multiobjective population-based incremental learning (MOPBIL). The Pareto optimum results of both strategies lead to different unconventional wing structures which are superior to their conventional counterparts. From the results, the design strategy that uses simultaneous partial topology, sizing, and shape optimization is superior to the others based on a hypervolume indicator. The aeroelastic parameters of the obtained morphing wing subject to external actuating torques are analyzed and it is shown that it is practicable to apply the unconventional wing structures for an aircraft.     

Application of genetic algorithms to conceptual design of a micro-air vehicle

This paper investigates the feasibility of automating the conceptual design of a micro-air vehicle on a personal computer system. The proposed design methodology adopts the use of genetic algorithms as the search engine in the design process. The multidisciplinary optimization problem here is to maximize the lift-to-drag ratio subjected to static longitudinal stability, performance and physical constraints. The six design parameters chosen are angle of attack, main wing twist angle, winglet span, main wing chord length, main wing taper ratio and winglet taper ratio. A case study has been carried out to compare the performance of using genetic algorithms with well-established non-linear optimization method based on sequential quadratic programming.     

Multiobjective evolutionary computation for supersonic wing-shapeoptimization

This paper discusses the design optimization of a wing for supersonic transport (SST) using a multiple-objective genetic algorithm (MOGA). Three objective functions are used to minimize the drag for supersonic cruise, the drag for transonic cruise, and the bending moment at the wing root for supersonic cruise. The wing shape is defined by 66 design variables. A Euler flow code is used to evaluate supersonic performance, and a potential flow code is used to evaluate transonic performance. To reduce the total computational time, flow calculations are parallelized on an NEC SX-4 computer using 32 processing elements. The detailed analysis of the resulting Pareto front suggests a renewed interest in the arrow wing planform for the supersonic wing     

Optimization of airplane wing structures under taxiing loads

A methodology is presented for the optimum design of aircraft wing structures subjected to taxiing loads. The dynamic stresses induced in the wing as the airplane accelerates or decelerates on the runway during take-off or landing are computed by considering the interaction between the landing gear and the flexible airplane structure. The procedure is capable of taking into account both the effects of discrete runway bumps and the effects of runway unevenness. A numerical step-by-step method is developed for solving the nonlinear differential equations of motion. The optimization methodology is illustrated with two examples. The first example deals with the design of the typical section (symmetric double wedge airfoil). This example is studied by using a graphical procedure mainly to understand qualitatively the behavior of wing structures under taxiing loads and also to obtain a physical insight into the nature of the optimum solution. The second example is concerned with the design of a more realistic wing structure. In this case, the problem is formulated and solved as a constrained nonlinear programming problem based on finite element modeling.     

Optimization of airplane wing structures under gust loads

A methodology is presented for the optimum design of aircraft wing structures subjected to gust loads. The equations of motion, in the form of coupled integro-differential equations, are solved numerically and the stresses in the aircraft wing structure are found for a discrete gust encounter. The gust is assumed to be one minus cosine type and uniform along the span of the wing. In order to find the behavior of the wing structure under gust loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling and the optimum solution is found by using the interior penalty function method. A sensitivity analysis is conducted to find the effects of changes in design variables about the optimum point on the response quantities of the wing structure.     

Aircraft wing box rapid modeling based on skeleton model

In the process of traditional aircraft structure design, repetitive manual modeling of aircraft wing box parts is time consuming. Meanwhile, it's difficult to update associated models when product design changes. Aiming at solving these problems, a method for rapid modeling and updating associated models was put forward. Based on skeleton model, combining with the technology of template re-use, it makes aircraft wing box rapid modeling and correct updating possible. The detailed implementation process of the method was given, and a certain aircraft wing box was taken as an instance to verify the feasibility and effectiveness of this method.     

Interval-based optimization of aircraft wings under landing loads

An interval-based automated optimization of aircraft wing structures subjected to landing loads is discussed in this paper. The interaction between landing gear and flexible airplane structure is considered as a coupled system. The uncertain system parameters are described as interval numbers. The computational aspects of the optimization procedure are illustrated with two examples – symmetric double-wedge airfoil, and supersonic airplane wing. Since, in most cases only the ranges of uncertain parameters are known with their probability distribution functions unknown, the present methodology is expected to be more realistic for the optimum design of aircraft structures under landing loads.     

Parallelized structural topology optimization and CFD coupling for design of aircraft wing structures

A set of structural optimization tools are presented for topology optimization of aircraft wing structures coupled with Computational Fluid Dynamics (CFD) analyses. The topology optimization tool used for design is the material distribution technique. Because reducing the weight requires numerous calculations, the CFD and structural optimization codes are parallelized and coupled via a code/mesh coupling scheme. In this study, the algorithms used and the results obtained are presented for topology design of a wing cross-section under a given critical aerodynamic loading and two different spar positions to determine the optimum rib topology.     

The stiffness spreading method for layout optimization of truss structures

A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures. In this method, stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffness matrices which are embedded in a weak background mesh. When the proposed method is used, it is unnecessary for the bar elements in a truss structure to be connected to each other during the optimization process, and each of the bar elements can move independently in the design domain to form an optimized design. Another feature of the method is that the sensitivity analysis can be done analytically, making gradient based optimization algorithms applicable in the solution. This method realizes the size, shape and topology design optimization of truss structures simultaneously and allows for more flexibility in topology change. Numerical examples illustrate the feasibility and effectiveness of the proposed method.

     

Design of aircraft wings subjected to gust loads: A system reliability approach

A method for system reliability-based design of aircraft wing structures is presented. A wing of a light commuter aircraft designed for gust loads according to the FAA regulations is compared with one designed by system reliability optimization. It is shown that system reliability optimization has the potential of improving dramatically the safety and efficiency of new designs. The reasons for the differences between the deterministic and reliability-based designs are explained.     

A hybrid multilevel approach for aeroelastic optimization of composite wing-box

The quest for finding optimum solutions to engineering problems has been existing for a long time. In the last decade several optimization techniques have been applied to the structural design of composite wing structures. Generally many of these proposed procedures have dealt with different disciplines such as aerodynamics, structures, or dynamics separately. However an aeronautical design process is multidisciplinary since it involves strong couplings and interactions among, for instance, aerodynamics, dynamics, flight mechanics and structures. The main problem in a multidisciplinary aircraft design is usually the development of an efficient method to integrate structures or structural properties, which can be considered both as “global” and “local” design variables. This paper describes an integrated aerodynamic / dynamic / structural optimization procedure for a composite wing-box design. The procedure combines an aeroelastic optimization of a composite wing based on a general purpose optimizer such as the Sequential Quadratic Programming (SQP) and a composite optimization using Genetic Algorithm (GA). Both the optimizations are implemented through a hybrid multilevel decomposition technique.     

Optimization of airplane wing structures under landing loads

A methodology is presented for the optimum design of aircraft wing structures subjected to landing loads. The stresses developed in the wing during landing are computed by considering the interaction between the landing gear and the flexible airplane structure. The landing gear is assumed to have nonlinear characteristics typical of conventional gears, namely, velocity squared damping, polytropic air-compression springing and exponential tire force-deflection characteristics. The coupled nonlinear differential equations of motion that arise in the landing analysis are solved by using a step-by-step numerical integration technique. In order to find the behavior of the wing structure under landing loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double-wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling. The optimum solutions are found by using the interior penalty function method. A sensitivity analysis is conducted to find the effect of changes in design variables about the optimum point on the various response parameters on the wing structure.     

Structural optimization of lifting surfaces with divergence and control reversal constraints

In this paper, the static aeroplastic characteristics, divergence velocity, control effectiveness and lift effectiveness are considered in obtaining an optimum weight structure. Swept wing structures are used with upper and lower skins, spar and rib thicknesses, and spar cap and vertical post cross-sectional areas as the design parameters. The aerodynamic strip theory is used to derive the constraint formulations and aerodynamic load matrices. A Sequential Unconstrained Minimization Technique (SUMT) algorithm is used to optimize the wing structure to meet the desired aeroelastic constraints.     

机翼复合材料张力蒙皮结构抗鸟撞分析

针对飞行器采用机翼前缘复合材料结构抗鸟撞的设计要求,提出一种新的设计构型,即张力蒙皮结构。使用显式碰撞动力分析软件PAMCRASH,建立了四种复合材料张力层乎板模型,并采用流固耦合方法对其进行鸟撞仿真分析和比较,从而确定张力层有限元模型形式;依据上述情况对复合材料张力蒙皮构成的机翼前缘结构抗鸟撞性能进行仿真分析。计算结果得到了张力层展开的位移、撞击最大接触力、鸟体动能下降百分比等几方面数据。结果表明：在同等条件下复合材料张力蒙皮结构与普通机翼蒙皮相比,能更好地防止鸟体穿透机翼蒙皮,证明可用于机翼结构的抗鸟撞设计中。     

Computer-augmented preliminary design of aircraft wing structures

A computer system to aid in the preliminary design of aircraft wing structures for minimum weight is described. The system was developed to utilize effectively the best attributes of both computers and the human mind in the iterative process of analyzing highly redundant trial structures and using these results to select new trial structures with the objective of minimizing weight. The computer is used for the routine data processing, and the designer performs those tasks which require judgement and intuition. Cathode ray tube graphical displays are provided for checking input data and for evaluating results. From given basic information on the wing structure, loads, and material properties, a finite element model is developed, analyzed, modified to eliminate violations of design criteria, and optimized to obtain the structural configuration of least weight. The optimization proceeds automatically, but the designer may monitor progress with the aid of tabular and graphical displays and modify the direction in which the optimization is proceeding. The impetus for this work was provided by a need for such a system in teaching structural design to aeronautical engineering students. The modular system was developed for the Control Data Corporation 6400/6500 computer installation at Purdue University using the Purdue Interactive Remote Access Terminal Environment (PIRATE).     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

Computer graphics in sizing and analysis of aircraft structures

A computerized system for preliminary sizing and analysis of aircraft wing and fuselage structures is described. The system is based upon repeated application of analytical program modules, which are interactively interfaced and sequence-controlled during the iterative design process with the aid of design-oriented graphics software modules. The entire process is initiated and controlled via low cost interactive graphics terminals driven by a remote computer in a time-sharing mode.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

Influence of the Tensor Product Model Representation of qLPV Models on the Feasibility of Linear Matrix Inequality Based Stability Analysis

The paper investigates and proves the statement, that the convex hull of the polytopic tensor product (TP) model representation influences the feasibility of linear matrix inequality (LMI) based stability analysis methods. The proof is based on a complex stability analysis example of a given quasi linear parameter varying (qLPV) state‐space model. Specifically, the three degree of freedom (3‐DoF) aeroelastic wing section model including Stribeck friction is used as the tool for the example model. The proof is achieved by utilizing TP model transformation and LMI based tools. As a first step, numerous TP model type control solutions holding different convex hulls are systematically derived of the qLPV model via LMI based control design methods. As a second step, each control solution is further equivalently transformed for different TP model representations holding different convex hulls. Finally, the stability of all solutions over all TP model representations are checked via LMI based stability analysis methods. As a result of the two steps, a two dimensional (2D) convex hull space is attained for the 3‐DoF aeroelastic wing section model. The two dimensions are denoted by the LMI based control design and the LMI based stability analysis for different convex hulls. Based on the numerical results, a detailed, comprehensive analysis is provided. The paper as a novelty proves the statement, that the polytopic TP model representation of a given control solution strongly influences the feasibility of LMI based stability analysis methods.     

Optimal segmentation of beam and disk structures

Large structures are usually composed of elements by properly designed connections. The optimal design solution in such cases should provide optimal size and number of elements together with optimal connection stiffness. The problem is formulated by assuming the element cost to be a nonlinear function of its size and the cost of connection to depend on its stiffness or transmitted forces. The number of elements and the connection stiffness now constitute the design parameters to be determined. A two-level procedure is proposed for determination of the optimal segmentation for beam and plate structures. Several illustrative examples are presented.