Static Aeroelastic Analysis Research Articles

Static aeroelastic analysis including geometric nonlinearities based on reduced order model

This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM). The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM) especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE) method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM). Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

Aeroelastic Optimization Design for High-Aspect-Ratio Wings with Large Deformation

This paper presents a framework of aeroelastic optimization design for high-aspect-ratio wing with large deformation. A highly flexible wing model for wind tunnel test is optimized subjected to multiple aeroelastic constraints. Static aeroelastic analysis is carried out for the beamlike wing model, using a geometrically nonlinear beam formulation coupled with the nonplanar vortex lattice method. The flutter solutions are obtained using the P-K method based on the static equilibrium configuration. The corresponding unsteady aerodynamic forces are calculated by nonplanar doublet-lattice method. This paper obtains linear and nonlinear aeroelastic optimum results, respectively, by the ISIGHT optimization platform. In this optimization problem, parameters of beam cross section are chosen as the design variables to satisfy the displacement, flutter, and strength requirements, while minimizing wing weight. The results indicate that it is necessary to consider geometrical nonlinearity in aeroelastic optimization design. In addition, optimization strategies are explored to simplify the complex optimization process and reduce the computing time. Different criterion values are selected and studied for judging the effects of the simplified method on the computing time and the accuracy of results. In this way, the computing time is reduced by more than 30% on the premise of ensuring the accuracy.

Static aeroelastic characteristics analysis of high-aspect-ratio wing for hydrogen-powered UAV

Static aeroelastic characteristics analysis of high-aspect-ratio wing for hydrogen-powered UAV

Nonlinear Static Aeroelasticity of High-Aspect-Ratio-Wing Aircraft by Finite Element and Multibody Methods

Two procedures for the nonlinear static aeroelastic analysis of flexible high-aspect-ratio wing aircraft subject to geometric nonlinearities are developed. The two approaches are based on the nonlinear finite element method and on multibody dynamics, and they employ aerodynamic formulations based on the doublet lattice method and strip theory, respectively. Static aeroelastic results in terms of wing integrated loads at various trim conditions for a very flexible aircraft test case are presented and compared to the linear ones. Significant differences are found between linear and nonlinear approaches, and attention is drawn to the importance of the follower force effects of the aerodynamics and of considering large displacements and rotations, which are identified as the main sources of the discrepancies, for the static flight loads computation and subsequent structural sizing of the wing.

Static Aeroelastic Analysis of an Aircraft Wind-Tunnel Model by Means of Modal RBF Mesh Updating

AbstractA numerical static aeroelastic analysis procedure, applying a modal approach in coupling the fluid dynamic and structural solutions, is presented. The method is based on a preliminary structural modal analysis from which a number of natural modes is selected to be used in the creation of a fluid dynamic domain morphing criterion. The mesh is made parametric on modal coordinates and updated using a mesh morphing tool based on radial basis functions (RBF) within the progress of the fluid dynamic computation. An intrinsically elastic numerical model is then created, and no further iteration with the structural solver is required. The modal forces are extracted by integrating the pressure on the wall boundaries and used to define the weights of the morphing action of each modal shape. This is a simplifying alternative to the traditional fluid dynamic-structural analysis coupling approach that makes it possible to bypass several complexities related to the implementation of 2-way fluid-structure intera...

Flight Loads Prediction of High Aspect Ratio Wing Aircraft Using Multibody Dynamics

A framework based on multibody dynamics has been developed for the static and dynamic aeroelastic analyses of flexible high aspect ratio wing aircraft subject to structural geometric nonlinearities. Multibody dynamics allows kinematic nonlinearities and nonlinear relationships in the forces definition and is an efficient and promising methodology to model high aspect ratio wings, which are known to be prone to structural nonlinear effects because of the high deflections in flight. The multibody dynamics framework developed employs quasi-steady aerodynamics strip theory and discretizes the wing as a series of rigid bodies interconnected by beam elements, representative of the stiffness distribution, which can undergo arbitrarily large displacements and rotations. The method is applied to a flexible high aspect ratio wing commercial aircraft and both trim and gust response analyses are performed in order to calculate flight loads. These results are then compared to those obtained with the standard linear aeroelastic approach provided by the Finite Element Solver Nastran. Nonlinear effects come into play mainly because of the need of taking into account the large deflections of the wing for flight loads computation and of considering the aerodynamic forces as follower forces.

Aeroelastic predictions for steady and unsteady flow characteristics of the HIRENASD wing

In this study, we focus on static and dynamic aeroelastic analyses of the HIRENASD wing based on reference experimental data for two different flight conditions for Aeroelastic Prediction Workshop-1. The major anticipations from the HIRENASD project are to improve the knowledge about aero-structural dynamics, and to get experimental and computational data in a wide range of flight conditions. The experiments have been formerly conducted in cryogenic medium to investigate steady and unsteady aeroelastic responses in transonic regime for low and high Reynolds numbers. For current aeroelastic computations, first, a free vibration analysis is performed in Nastran using the latest structural model provided by NASA. Sequentially, the modal solution is imported from the finite element solver to Zeus software which is an Euler equations based aeroelastic solver coupled with integral boundary layer method. The aerodynamic model and fluid structure interaction parameters are constructed in Zeus. Steady and unsteady aeroelastic results are examined for the specified stations along the wing span, and interpolated for chordwise direction so as to match them with the wind tunnel test points. The designated output parameters such as steady aerodynamic lift, moment and drag coefficients, and steady and unsteady pressure distributions along the chordwise direction are compared to the experimental data and NASA's FUN3D code results which are provided in literature.

Static Aeroelastic Analysis on Two Stage Rocket Body

Static Aeroelastic Analysis on Two Stage Rocket Body

Support Vector Regression 기반 공력-비선형 구조해석 연계시스템을 이용한 유연날개 다목적 최적화

유연날개의 공력 및 구조 설계값을 설계 변수로 하여 정적 상태에서의 정적 공탄성해석 및 최적화를 수행하였다. 정적 공탄성해석과 최적화를 위해 상용 해석소프트웨어들이 연계된 강건한 다분야 최적설계 시스템을 개발하였다. 최적화 설계변수로는 가로세로비, 테이퍼비, 후퇴각과 날개 위아래 스킨 두께를 설정하였다. 전역적 다목적 최적화를 위해 실수기반 적응영역 다목적 유전자 알고리즘을 적용하였으며 계산시간을 줄이기 위해 메타모델로 서포트벡터회귀 기법을 적용하였다. 유연날개에 대한 파레토 결과 분석을 통해 최대 항속시간과 최소 중량에 대한 최적 결과를 확인하였다. The static aeroelastic analysis and optimization of flexible wings are conducted for steady state conditions while both aerodynamic and structural parameters can be used as optimization variables. The system of multidisciplinary design optimization as a robust methodology to couple commercial codes for a static aeroelastic optimization purpose to yield a convenient adaptation to engineering applications is developed. Aspect ratio, taper ratio, sweepback angle are chosen as optimization variables and the skin thickness of the wing. The real-coded adaptive range multi-objective genetic algorithm code, which represents the global multi-objective optimization algorithm, was used to control the optimization process. The support vector regression(SVR) is applied for optimization, in order to reduce the time of computation. For this multi-objective design optimization problem, numerical results show that several useful Pareto optimal designs exist for the flexible wing.

Semi-analytical static aeroelastic analysis and response of flexible subsonic wings

A semi-analytical model for the combined static aeroelastic analysis and response of flexible subsonic wings is presented. Based on a general variational formulation, the proposed aeroelastic models allow any arbitrary distribution of the flexible wing’s physical properties and provide with a continuous solution of the wing’s displacement along the span, as suitable for parametric optimisation studies within preliminary wing design. Numerical results which provide sound insights on the behaviour of a flexible wing in subsonic flow are obtained and critically discussed for all aeroelastic models, with respect to the most relevant aerodynamic and structural parameters as well as the computational efficiency. Different degrees of fidelity are considered for the aerodynamic modelling and the formulated modified strip theory is shown to be an excellent compromise between the lower complexity of standard strip theory and the higher accuracy of lifting line theory. The modified strip theory is hence suggested as a general and effective steady aerodynamic tool for the multidisciplinary design and optimisation of flexible wings in the subsonic regime.

Advanced Aerostructural Optimization Techniques for Aircraft Design

Traditional coupled aerostructural design optimization (ASDO) of aircraft based on high-fidelity models is computationally expensive and inefficient. To improve the efficiency, the key is to predict aerostructural performance of the aircraft efficiently. The cruise shape of the aircraft is parameterized and optimized in this paper, and a methodology named reverse iteration of structural model (RISM) is adopted to get the aerostructural performance of cruise shape efficiently. A new mathematical explanation of RISM is presented in this paper. The efficiency of RISM can be improved by four times compared with traditional static aeroelastic analysis. General purpose computing on graphical processing units (GPGPU) is adopted to accelerate the RISM further, and GPU-accelerated RISM is constructed. The efficiency of GPU-accelerated RISM can be raised by about 239 times compared with that of the loosely coupled aeroelastic analysis. Test shows that the fidelity of GPU-accelerated RISM is high enough for optimization. Optimization framework based on Kriging model is constructed. The efficiency of the proposed optimization system can be improved greatly with the aid of GPU-accelerated RISM. An unmanned aerial vehicle (UAV) is optimized using this framework and the range is improved by 4.67% after optimization, which shows effectiveness and efficiency of this framework.

Investigation of Computational Non-Linear Aeroelastic Response of High Aspect Ratio Wing

Aircrafts with high aspect ratio wings are most eligible candidates for high altitude and long endurance flights. Such wings show a non-linear deformation behavior because of structural geometric non-linearity. In the present study both linear and non-linear static aeroelastic behaviors of a high aspect ratio rectangular flat plate wing are analyzed using a simplified approach. The main emphasis lies in the tremendous change of lift distribution on the flexible high aspect ratio wing when large deflections are incorporated in the static aeroelastic analysis. The computational static aeroelastic simulations are performed in the finite element method based commercial software ANSYS-14. The aerodynamic load is calculated using the strip theory. Since the aero-load changes with the twisting deformation hence a user defined script is written using ANSYS parametric design language (APDL). The computationally achieved divergence velocity results are compared with the analytical results. The results of parametric study at different flight load conditions and angles of attack have highlighted the role of geometric nonlinearities in both bending and twisting deformations. The impact of follower pressure forces on the aeroelastic response is also investigated.

An Analysis Method of Static Aeroelastic Response with Nonlinear Aerodynamic Data on 3D Bodysurface Panel Element

A static aeroelastic responses analysis method based on mapping external nonlinear aerodynamic forces onto 3D body surface panel elements is proposed. The external nonlinear aerodynamic force data can be obtained by Euler solver, Navier-Stokes solver and wind tunnel tests. In this paper, the method is applied to obtain static aeroelastic responses of a flexible aircraft, and the emphasis is placed on the change of aerodynamic coefficient, aerodynamic pressure distribution and flight load. The results are compared with static aeroelastic responses calculated by high-order panel method. It is concluded that the method presented in this study is feasible, credible and efficient, and can provide an assessment of static aeroelastic response characteristics for the detailed stage of aircraft design.

An Analysis Method of Static Aeroelastic Response with Nonlinear Aerodynamic Data on 3D Bodysurface Panel Element

A static aeroelastic responses analysis method based on mapping external nonlinear aerodynamic forces onto 3D body surface panel elements is proposed. The external nonlinear aerodynamic force data can be obtained by Euler solver, Navier-Stokes solver and wind tunnel tests. In this paper, the method is applied to obtain static aeroelastic responses of a flexible aircraft, and the emphasis is placed on the change of aerodynamic coefficient, aerodynamic pressure distribution and flight load. The results are compared with static aeroelastic responses calculated by high-order panel method. It is concluded that the method presented in this study is feasible, credible and efficient, and can provide an assessment of static aeroelastic response characteristics for the detailed stage of aircraft design.

Stiffness Optimization of Composite Wings with Aeroelastic Constraints

The drive for ever more efficient aircraft structures stimulates the research to use the full potential of anisotropy of composite materials. The stiffness optimization of the upper and lower skins of a composite wing is demonstrated in this paper. The wing was optimized taking into consideration the mass, strength, buckling, aerodynamic twist, and aileron effectiveness. The elements of the in-plane and bending stiffness matrices and laminate thicknesses were used as design variables. Static aeroelastic analysis was performed using Nastran to find the responses of the structure and their sensitivities to the design variables. The results of aeroelastic finite element analysis were processed to create efficient structural approximations of the responses. The approximations were used by a gradient-based optimizer to update the design variables. The separable and continuous approximations in terms of the design variables allowed for the use of efficient parallel computing strategies, in which single or multimodal objective functions were minimized. The first numerical results for a generic wing confirmed a functional setup for multiload case stiffness optimizations with aeroelastic design responses. Stiffness-optimized unbalanced laminates demonstrated a clear advantage over balanced laminates for mass or aileron effectiveness optimizations, with constraints on strength and buckling.

Static aeroelastic analysis of very flexible wings based on non-planar vortex lattice method

A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.

A refined structural model for static aeroelastic response and divergence of metallic and composite wings

A refined beam model with hierarchical features is in this work extended to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. The refined structural one-dimensional (1D) theory is based on the Carrera Unified Formulation and it permits to take into account any cross-section deformation, including warping effects. The vortex lattice method is employed to provide aerodynamic loadings along the two in-plane wing directions (wing span and wing cross-section). Applications are obtained by developing a coupled aeroelastic computational model which is based on the finite element method. The accuracy of the proposed 1D model is shown by a number of applications related to various wings made of metallic and composite materials. The effect of the cross-section deformation is evaluated on the aeroelastic static response and divergence of the considered wings. The need of higher-order expansions is underlined as well as the limitations of beam results which are based on classical theories. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by the present analysis.

Effects of static aeroelasticity on composite wing characteristics under different flight attitudes

Composite wing static aeroelasticity was analyzed through a loosely coupled method and the effects on composite wing characteristics under different flight attitudes were presented. Structural analysis and aerodynamic analysis were carried out through finite element method (FEM) software NASTRAN and computational fluid dynamics (CFD) software FLUENT, respectively. Correlative data transfer and mesh regenerate procedure were applied to couple the results of computational structure dynamics (CSD) and CFD. After static aeroelasticity analysis under different flight attitudes, it can be seen that lift increases with the increase of flight speed and the incremental value enlarges gradually in both rigid and elastic wings. Lift presents a linear increment relationship with the increase of attack angle when the flight speed is 0.4Ma or 0.6Ma, but nonlinear increment in elastic wing when flight speed is 0.8Ma. On the effect of aeroelasticity, the maximum of deformation increases with the increase of flight speed and attack angle, and the incremental value decreases with the increase of flight speed while uniform with different attack angles. The results provide a reference for engineering applications.

Static Aeroelasticity Analysis of High Aspect Ratio Wing and the Jig-Shape Design Based on Multi-Block Structural Grid

The influence of structural elastic deformation on the aerodynamic characterisitcs of large transport aircraft has been researched. A method of static aeroelasticity based on multi-block structural grid of high aspect ratio wing has been established, and then a design method of jig-shape is developed. The technology of RBF interpolation is used to exchange the data of CFD/CSD. Based on RBF&Delaunay technology, a mesh motion method is developed to make the design process less time-consuming, which can be applied to large deformation of multi-block structural grid. The static aeroelastic deformation of a wing-body of large transport aircraft is analyzed. Then the wing-body's jig-shape is designed. Compared the aerodynamic characteristics between design cruise shape and target cruise shape, it shows that the aerodynamic characteristics of design cruise shape is almost equal to target cruise shape and the design process of jig-shape is feasible.

대형 풍력로터시스템의 정적 공탄성해석을 위한 등가강성모델링 기법 적용에 관한 연구

A equivalent stiffness modeling has been performed for extracting the equivalent stiffness properties which are orthotropic elastic model from a large scale wind turbine rotor blade so that structure model can be constructed more simply for the three dimensional static aeroelastic analysis. In order to present the procedure of equivalent stiffness modeling, NREL 5MW class wind turbine rotor having the three stiffness information which are flapewise, edgewise and torsional stiffness was chosen. This method is based on applying unit moment at the tip of the blade as well as fixing all degree of freedom at the blade root and calculating the displacement from the load analysis to obtain the elastic modulus corresponding to equivalent stiffness referred to the NREL reports on blade divided into 5 sections respectively. In addition, one section was divided into 3 parts and the trend functions were used to make the equivalent stiffness model more correctly and quickly. Through the comparison of stiffness between the reference values and calculated values from equivalent stiffness model, the investigation of the accuracy on the stiffness values and the efficiency for constructing the model was conducted.