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.     

Reliability-based design optimization of aeroelastic structures

Aeroelastic phenomena are most often either ignored or roughly approximated when uncertainties are considered in the design optimization process of structures subject to aerodynamic loading, affecting the quality of the optimization results. Therefore, a design methodology is proposed that combines reliability-based design optimization and high-fidelity aeroelastic simulations for the analysis and design of aeroelastic structures. To account for uncertainties in design and operating conditions, a first-order reliability method (FORM) is employed to approximate the system reliability. To limit model uncertainties while accounting for the effects of given uncertainties, a high-fidelity nonlinear aeroelastic simulation method is used. The structure is modelled by a finite element method, and the aerodynamic loads are predicted by a finite volume discretization of a nonlinear Euler flow. The usefulness of the employed reliability analysis in both describing the effects of uncertainties on a particular design and as a design tool in the optimization process is illustrated. Though computationally more expensive than a deterministic optimum, due to the necessity of solving additional optimization problems for reliability analysis within each step of the broader design optimization procedure, a reliability-based optimum is shown to be an improved design. Conventional deterministic aeroelastic tailoring, which exploits the aeroelastic nature of the structure to enhance performance, is shown to often produce designs that are sensitive to variations in system or operational parameters.     

Aeroelastic topology optimization of membrane structures for micro air vehicles

This work considers the aeroelastic optimization of a membrane micro air vehicle wing through topology optimization. The low aspect ratio wing is discretized into panels: a two material formulation on the wetted surface is used, where each panel can be membrane (wing skin) or carbon fiber (laminate reinforcement). An analytical sensitivity analysis of the aeroelastic system is used for the gradient-based optimization of aerodynamic objective functions. An explicit penalty is added, as needed, to force the structure to a 0–1 distribution. The dependence of the solution upon initial design, angle of attack, mesh density, and objective function are presented. Deformation and pressure distributions along the wing are studied for various load-augmenting and load-alleviating designs (both baseline and optimized), in order to establish a link between stiffness distribution and aerodynamic performance of membrane micro air vehicle wings. The work concludes with an experimental validation of the superiority of select optimal designs.     

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.     

Reliability-based shape optimization of structures undergoing fluid–structure interaction phenomena

Fluid–structure interaction phenomena are often roughly approximated when the stochastic nature of a system is considered in the design optimization process, leading to potentially significant epistemic uncertainty. In this paper, after reviewing the state-of-the-art methods in robust and reliability-based design optimization of problems undergoing fluid–structure interaction phenomena, a computational framework is presented that integrates a high-fidelity aeroelastic model into reliability-based design optimization. The design optimization problem is formulated pursuant to the reliability index and performance measure approaches. The system reliability is evaluated by a first-order reliability analysis method. The steady-state aeroelastic problem is described by a three-field formulation and solved by a staggered procedure, coupling a potentially detailed structural finite element model and a finite volume discretization of the Euler flow. The design and imperfection sensitivities are computed by evaluating the analytically derived direct and adjoint coupled aeroelastic sensitivity equations. The computational framework is verified by the optimization of three-dimensional wing structures. The lift-to-drag ratio is maximized, subject to stress constraints, by varying shape, thickness, and material properties. Uncertainties in structural parameters, including design parameters, operating conditions, and modeling uncertainties are considered. The results demonstrate the need for reliability-based optimization methods, for the design of structures undergoing fluid–structure interaction phenomena, and the applicability of the proposed framework to realistic design problems. Comparing the optimization results for different levels of uncertainty shows the importance of accounting for uncertainties in a quantitative manner.     

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 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.     

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.     

Aeroelastic tailoring considering uncertainties in material properties

The robustness of aeroelastic design optimization with respect to uncertainties in material and structural properties is studied both numerically and experimentally. The model consists of thin orthotropic composite wings virtually without fuselage. Three different configurations with consistent geometry but varying orientation of the main stiffness axis of the material are investigated. The onset of aeroelastic instability, flutter, is predicted using finite element analysis and the doublet-lattice method for the unsteady aerodynamic forces. The numerical results are experimentally verified in a low-speed wind tunnel. The optimization problem is stated as to increase the critical air speed, above that of the bare wing by massbalancing. It is seen that the design goals are not met in the experiments due to uncertainties in the structural performance of the wings. The uncertainty in structural performance is quantified through numerous dynamic material tests. Once accounting for the uncertainties through a suggested reformulation of the optimization problem, the design goals are met also in practice. The investigation indicates that robust and reliable aeroelastic design optimization is achievable, but careful formulation of the optimization problem is essential.     

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.     

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.     

Topology optimization of three-dimensional structures using optimum microstructures

In this paper, optimum three-dimensional microstructures derived in explicit analytical form by Gibianski and Cherkaev (1987) are used for topology optimization of linearly elastic three-dimensional continuum structures subjected to a single case of static loading. For prescribed loading and boundary conditions, and subject to a specified amount of structural material within a given three-dimensional design domain, the optimum structural topology is determined from the condition of maximum integral stiffness, which is equivalent to minimum elastic complicance or minimum total elastic energy at equilibrium.The use of optimum microstructures in the present work renders the local topology optimization problem convex, and the fact that local optima are avoided implies that we can develop and present a simple sensitivity based numerical method of mathematical programming for solution of the complete optimization problem.Several examples of optimum topology designs of three-dimensional structures are presented at the end of the paper. These examples include some illustrative full three-dimensional layout and topology optimization problems for plate-like structures. The solutions to these problems are compared to results obtained earlier in the literature by application of usual two-dimensional plate theories, and clearly illustrate the advantage of the full three-dimensional approach.     

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.     

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.     

Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme

This paper describes a versatile methodology for solving topology design optimization problems using a genetic algorithm (GA). The key to its effectiveness is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving ‘target matching’ problems—simulated topology optimization problems in each of which a ‘target’ geometry is first created and predefined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this target shape. The methodology is then applied to design two path-generating compliant mechanisms—large-displacement flexural structures that undergo some desired displacement paths at some point when given a straight line input displacement at some other point—by an actual process of topology/shape optimization.     

Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Topology optimization methods using discrete elements such as frame elements can provide useful insights into the underlying mechanics principles of products; however, the majority of such optimizations are performed under deterministic conditions. To avoid performance reductions due to later-stage environmental changes, variations of several design parameters are considered during the topology optimization. This paper concerns a reliability-based topology optimization method for frame structures that considers uncertainties in applied loads and nonstructural mass at the early conceptual design stage. The effects that multiple criteria, namely, stiffness and eigenfrequency, have upon system reliability are evaluated by regarding them as a series system, where mode reliabilities can be evaluated using first-order reliability methods. Through numerical calculations, reliability-based topology designs of typical two- or three-dimensional frames are obtained. The importance of considering uncertainties is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs.     

Recent advances in maneuver loads analysis

The conceptual design of an aircraft system requires a number of analysis cycles involving the study of various configurations for which aerodynamic and structural properties are not well defined. The aeroelastic stability and structural strength considerations are very important factors in the determination of the aerodynamic and the structural configurations. Therefore, this paper briefly reviews the specifications leading to the design loads criteria and the current analysis methods. Suggestions for research activities required in the development of a computational fluid dynamics (CFD) code and its application to predict the design loads are also included.     

Stress-based design of thermal structures via topology optimization

The design of thermal structures in the aerospace industry, including exhaust structures on embedded engine aircraft and hypersonic thermal protection systems, poses a number of complex design challenges. These challenges are particularly well addressed by the material layout capabilities of structural topology optimization; however, no topology optimization methods are readily available with the necessary thermoelastic considerations for these problems. This is due in large part to the emphasis on cases of maximum stiffness design for structures subjected to externally applied mechanical loads in the majority of topology optimization applications. In addition, while limited work in the literature has investigated thermoelastic topology optimization, a direct treatment of thermal stresses is not well documented. Such a treatment is critical in the design of thermal structures where excessive thermal stresses are a primary failure mode. In this paper, we present a method for the topology optimization of structures with combined mechanical and thermoelastic (temperature) loads that are subject to stress constraints. We present the necessary steps needed to address both the design-dependent thermal loads and accommodate the challenges of stress-based design criteria. A relaxation technique is utilized to remove the singularity phenomenon in stresses and the large number of stress constraints is handled using a scaled aggregation technique that has been shown previously to satisfy prescribed stress limits in mechanical problems. Finally, the stress-based thermoelastic formulation is applied to two numerical example problems to demonstrate its effectiveness.     

Adaptive topology optimization

Topology optimization of continuum structures is often reduced to a material distribution problem. Up to now this optimization problem has been solved following a rigid scheme. A design space is parametrized by design patches, which are fixed during the optimization process and are identical to the finite element discretization. The structural layout is determined, whether or not there is material in the design patches. Since many design patches are necessary to describe approximately the structural layout, this procedure leads to a large number of optimization variables. Furthermore, due to a lack of clearness and smoothness, the results obtained can often only be used as a conceptual design idea.To overcome these shortcomings adaptive techniques, which decrease the number of optimization variables and generate smooth results, are introduced. First, the use of pure mesh refinement in topology optimization is discussed. Since this technique still leads to unsatisfactory results, a new method is proposed that adapts the effective design space of each design cycle to the present material distribution. Since the effective design space is approximated by cubic or Bézier splines, this procedure does not only decrease the number of design variables and lead to smooth results, but can be directly joined to conventional shape optimization. With examples for maximum stiffness problems of elastic structures the quality of the proposed techniques is demonstrated.