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.     

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.     

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.     

Optimization process for configuration of flexible joined-wing

An optimized configuration design utilizing both structural and aerodynamic analyses of a flexible joined-wing configuration is presented in this paper. The joined-wing aircraft concept fulfills a proposed long-endurance surveillance mission and incorporates a load-bearing antenna structure embedded in the wing skin. Aerodynamic, structural, and optimization analyses are completed a number of times. A range of joined-wing configurations were trimmed for critical flight conditions and then structurally optimized for trimmed flight and gust loads to achieve a minimum weight for each configuration. A response surface statistical analysis was then applied to determine optimal joined-wing aircraft configurations. The response surface showed trends in the design of lightweight joined-wing aircraft. The revised version of this paper was presented at the 10th MAO Multidisciplinary Analysis and Optimization Conference, August 30–September 1, 2004.     

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.     

Automated optimum design of wing structures: A probabilistic approach

The optimization of aircraft wing structures is presented by considering the dynamic stresses developed during landing impact and gust load conditions. The random nature of the sinking speed and the forward velocity at the instant of contact is considered in the calculation of landing stresses. The vertical velocity due to gust is treated as a stochastic process for the computation of gust-induced stresses. The optimum designs of a symmetric double wedge airfoil, based on beam type of analysis, and a supersonic airplane wing, based on finite element analysis, are considered to illustrate the procedure. A graphical procedure is used in the case of the double wedge airfoil, and nonlinear programming techniques are used in the case of the supersonic wing, for finding the optimum solutions.     

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.     

Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. A high fidelity computational fluid dynamics (CFD) algorithm modelling the Euler equations is used to calculate the aerodynamic properties of complex three-dimensional aircraft configurations. The design process is greatly accelerated through the use of both control theory and parallel computing. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented in parallel using a domain decomposition approach, an optimized communication schedule, and the Message Passing Interface (MPI) Standard for portability and efficiency. In our earlier studies, the serial implementation of this design method, was shown to be effective for the optimization of airfoils, wings, wing–bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In this work, our concern will be to extend the methodologies such that the combined capabilities of these new technologies can be used routinely and efficiently in an industrial design environment. The aerodynamic optimization of a supersonic transport configuration is presented as a demonstration test case of the capability. A particular difficulty of this test case is posed by the close coupling of the propulsion/airframe integration.     

Improved optimum structural design by passive control

The problem of optimum structural design by passive control is stated in a nonlinear programming form. A solution procedure, based on a successive selection of design and control variables, is presented. Neglecting the implicit analysis equations, the solution becomes independent of the control variables and a lower bound (LB) on the optimum can easily be obtained. The control variables are then selected to satisfy all constraints. If this cannot be achieved, the LB constraints are modified and the control variables are chosen for the revised optimal design. These two steps are repeated until the final optimum is reached.Employing the proposed procedure on various structural systems subjected to static loads showed that the final optimum has been achieved after a very small number of iteration cycles. The numerical examples illustrate a solution with two types of control devices: a linear spring device and a limited displacement device. It has been found that the final optimum is often identical or close to the initial LB solution. Savings of 14 to 63 percent in weight, compared with conventional optima without control, have been demonstrated for some common structures.     

Integrated aerodynamic-structural-control wing design

The aerodynamic-structural-control design of a forward-swept composite wing for a high subsonic transport aircraft is considered. The structural analysis is based on a finite-element method. The aerodynamic calculations are based on a vortex-lattice method, and the control calculations are based on an output feed-back control law. The wing is designed for minimum weight subject to structural, performance/aerodynamic and control constraints. Efficient techniques are developed to calculate the control-deflection and control-effectiveness sensitivities which appear as second-order derivatives in the control constraint equations. To suppress the aeroelastic divergence of the forward-swept wing, and to minimize the take-off gross weight of the design aircraft, two separate cases are studied: (1) combined application of aeroelastic tailoring and active controls; and (2) aeroelastic tailoring alone. For the particular example problem considered in this study, the aeroelastic tailoring was found to have a substantially greater influence than active controls on weight minimization and divergence suppression.     

Disturbance rejection for an aircraft flying in atmospheric disturbances

For an aircraft flying in atmospheric disturbances a static state feedback controller is designed. The design goal is that of rejecting the influence of a rotary gust disturbance to the vertical and forward velocity of the aircraft. The necessary and sufficient condition for this problem to have a solution is derived in terms of simple forms involving only the flight stability derivatives of the aircraft. The general analytical expression of the disturbance rejection controller matrix and the resulting closed, loop system, are derived in forms involving the aircraft parameters as well as arbitrary design parameters. The necessary and sufficient conditions for disturbance rejection with simultaneous stabilizability of the closed loop flight system are also established.     

Component allocation and supporting frame topology optimization using global search algorithm and morphing mesh

This paper proposes a stepwise structural design methodology where the component layout and the supporting frame structure is sequentially found using global search algorithm and topology optimization. In the component layout design step, the genetic algorithm is used to handle system level multiobjective problem where the optimal locations of multiple components are searched. Based on the layout design searched, a new Topology Optimization method based on Morphing Mesh technique (TOMM) is applied to obtain the frame structure topology while adjusting the component locations simultaneously. TOMM is based on the SIMP method with morphable FE mesh, and component relocation and frame design is simultaneously done using two kinds of design variables: topology design variables and morphing design variables. Two examples are studied in this paper. First, TOMM method is applied to a simple cantilever beam problem to validate the proposed design methodology and justify inclusion of morphing design variables. Then the stepwise design methodology is applied to the commercial Boeing 757 aircraft wing design problem for the optimal placement of multiple components (subsystems) and the optimal supporting frame structure around them. Additional constraint on the weight balance is included and the corresponding design sensitivity is formulated. The benefit of using the global search algorithm (genetic algorithm) is discussed in terms of finding the global optimum and independency of initial design guess. It has been proved that the proposed stepwise method can provide innovative design insight for complex modern engineering systems with multi-component structures.     

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.     

基于风扰动预测的阵风减缓最优控制研究

目前大多数阵风减缓控制方法都是等到飞机到达风场之后才起作用,由此带来了时滞与舵面速率饱和等问题。为了解决这一问题,提出了一种基于风扰动预测的阵风减缓控制系统方案。首先,对风扰动预测技术进行了研究,利用二阶互补滤波器实现了一种基于激光测风雷达获取的阵风信息与其它渠道获取的阵风信息的数据融合算法。其次,以某型民用飞机模型为对象,采用LQR方法设计最优状态调节器使得性能指标最小。接着,引入基于风扰动预测的前馈补偿,使得在未来阵风到达时飞机状态要尽可能保持不变。仿真结果表明,基于风扰动预测的阵风减缓最优控制系统能大幅度地减少阵风干扰对飞机法向过载和俯仰角速度的影响,证明了所设计的控制系统方案的正确性和有效性。     

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。     

Topology Optimization for Manufacturable Configuration Design of Aircraft Tail Rib

A methodology is implemented to find the optimum reduced weight configuration design of an operating structure of a civil aircraft vertical tail fin. FE (finite element) based topology optimization is executed to find the optimum material distribution of initial design space of rib by maximizing the stiffness. Loads pertinent to the operating and ground conditions are estimated and applied, considering the orientation of structural assembly members and built-in supports offered in the main structure. Manufa...     

机翼气动结构耦合数值分析方法

针对机翼的静气动弹性问题,为准确预测其气动特性,研究一种实用有效的气动结构耦合仿真方法.以客机机翼设计为例,通过机翼的静气动弹性问题分析和机翼的气动结构耦合分析流程的分解,建立参数化、自动化、模块化的气动结构耦合仿真分析平台.该平台的流程包括基于全速势方程的气动分析、基于MSC Nastran的结构仿真、应用MATLAB的载荷到结构模型的传递、结构变形向气动外形的映射等环节.算例表明该方法能较好地解决机翼的静气动弹性分析问题.     

Blended wing body structures in multidisciplinary pre-design

The structural analysis of blended wing body (BWB) aircraft configurations is presented in the context of a preliminary, multidisciplinary aircraft design process by means of the aircraft design and optimization program (PrADO) of the Institut of Aircraft Design and Lightweight Structures of the TU Braunschweig. A multidisciplinary process is described that enables parametric creation of detailed finite element models and its loads. Iteratively different flight conditions are trimmed and corresponding pressure distributions calculated by the higher-order subsonic and supersonic panel code HISSS. Each defined loading condition is used for the iterative structural sizing of the primary structure. Based on finite element idealization, a mass estimation of all structural masses is performed. The primary and secondary masses are fed back into the closed overall aircraft optimization loop of PrADO until this iterative procedure shows convergence on calculated aircraft variables (e.g., aircraft masses and static engine thrust). This automated process enables further configuration improvements using manual parametric variations or optimization features of PrADO with an objective function being defined by fuel consumption, aircraft mass, or direct operating costs. Different structural solutions and their integration in the global model are presented for passenger versions of a 700 passenger BWB with special consideration of a pressurized cabin. As an example, structural masses and parametric studies on the influence of the center body rib spacing are presented and compared by weight breakdowns.     

Constraint aggregation for large number of constraints in wing surrogate-based optimization

The method of aggregating a large number of constraints into one or few constraints has been successfully applied to wing structural design using gradient-based local optimization. However, numerical difficulties may occur in the case that the local curvatures of the aggregated constraint become extremely large and then ill-conditioned Hessian matrix may be yielded. This paper aims to test different methods of constraint aggregation within the framework of a gradient-free optimization, which makes use of cheap-to-evaluate surrogate models to find the global optimum. Three constraint aggregation approaches are investigated: the maximum constraint approach, the constant parameter Kreisselmeier-Steinhauser (KS) function, and the adaptive KS function. We also explore methods of aggregating constraints over the entire structure and within sub-domains. Examples of structural optimization and aero-structural optimization for a transport aircraft wing are employed and the results show that (1) the KS function with a larger constant parameter ρ can lead to better optimization results than the adaptive method, as the active constraints are approximated more accurately; (2) lumping the constraints within sub-domains instead of all together can improve the accuracy of the aggregated constraint and therefore helps find a better design. Finally, it is concluded from current test cases that the most efficient way of handling large-scale constraints for wing surrogate-based optimization is to aggregate constraints within sub-domains and with a relatively large constant parameter.

     

Stacking sequence design of a composite wing under a random gust using a genetic algorithm

The layup optimization by genetic algorithm (GA) for the composite wing subject to random gust is presented. The aim of optimization is to maximize the strength of wing and the failure index of Tsai-Hill criterion is used as the objective function. The failure index is calculated by Monte Carlo simulation because the external loading and the material properties have random characteristics. The optimization results are validated by comparing the failure probability of the initial and optimal designs. In addition, the optimum by maximum stiffness criterion is also obtained to show that current objective function is appropriate for the design of composite wing.