CN108446445A - A kind of Optimization for composite wing method based on aerodynamic reduced order model - Google Patents

A kind of Optimization for composite wing method based on aerodynamic reduced order model Download PDF

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CN108446445A
CN108446445A CN201810145057.9A CN201810145057A CN108446445A CN 108446445 A CN108446445 A CN 108446445A CN 201810145057 A CN201810145057 A CN 201810145057A CN 108446445 A CN108446445 A CN 108446445A
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order
reduced
aerodynamic
state
mode
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向锦武
李道春
赵仕伟
程云
张雪娇
张志飞
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Beihang University
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/15Vehicle, aircraft or watercraft design
    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The present invention proposes a kind of Optimization for composite wing method based on aerodynamic reduced order model, belongs to technical field of aircraft design.The structural model and aerodynamic model for initially setting up reference model obtain corresponding aerodynamic reduced order model using the mode of the finite element model of reference model;Mode based on reference model obtains the reduced-order model of parameter finite element model as mode is assumed;Then the aeroelastic analysis of parameterized model is carried out;Using composite plys thickness, angle as design variable, experimental design is carried out, the design variable that experimental design is obtained obtains the agent model of parameterized model as input, aeroelastic analysis as output;Based on agent model, the optimization design of composite wing is carried out.The present invention improves the accuracy of wing aerodynamic flexibility analysis, improves the efficiency of analysis, is suitable for calculating the optimization that composite structure designs, so as to obtain the better composite wing structures of performance.

Description

A kind of Optimization for composite wing method based on aerodynamic reduced order model
Technical field
The invention belongs to technical field of aircraft design, are related to a kind of composite wing based on aerodynamic reduced order model Optimum design method can be used for high-aspect-ratio composite wing aeroelasticity optimization design.
Background technology
Aircaft configuration loss of weight is the important content of Flight Vehicle Design.Composite material is two or more materials of different nature The new material made of physics or chemical method.It has specific strength, specific stiffness are high, coefficient of thermal expansion is small, endurance, Anticorrosive, the advantages that manufacturing cycle is short and easy to maintenance.It can be by different directions, difference portion during machine-shaping The reasonable laying of position improves strength of aircraft, rigidity, to reduce Aircraft Quality.
Optimal Structure Designing is to realize the important way of structural weight reduction.Composite material can cut out the characteristics of design, make compound Design on material structure has more selection spaces, but increases the complexity of design simultaneously.It was designed in composite structure Cheng Zhong needs overlay thickness and each layer of laying angle that composite material is designed according to the design objective of structure.These designs Variable influences each other, it is necessary to could carry out reasonable disposition by optimum design method.The optimum structure design method of mature and reliable It is successful to be the key that composite structure designs.
In the design of modern aircraft aerofoil, aeroelastic stability is important constraint.Composite material cuts out characteristic not It can only improve the quality of airfoil structure, mitigate airfoil structure weight, and allow that there are material couplings.It is coupled by these, Quiet, the dynamic aeroelastic stability of airfoil structure can be improved.Accordingly, it is considered to which the optimization of the composite wing of aeroelasticity is set The it is proposed of meter method has important practical usage.Traditional flutter of aerofoil analysis aerodynamic force uses vortex lattice method or dipole technique meter It calculates, does not account for the influence of the factors such as camber and thickness, aerodynamic force order of accuarcy is relatively low.
Invention content
For the Aerodynamic Analysis methods such as above-mentioned traditional vortex lattice method, panel method there are the problem of, the present invention proposes a kind of Composite wing structures optimum design method based on aerodynamic reduced order model, is substituted traditional using aerodynamic reduced order model The Aerodynamic Analysis method such as vortex lattice method, panel method, greatly improves the accuracy to Aerodynamic Analysis, to obtain better composite wood Expect wing structure.
Optimization for composite wing method provided by the invention based on aerodynamic reduced order model, including following step Suddenly:
Step 1, the structural model of reference model is established, model analysis obtains the modal frequency and the vibration shape of the structural model;
Step 2, the aerodynamic model for establishing reference model, using the mode of the finite element model of reference model, by each rank mould The state vibration shape obtains the pneumatic force-responsive under corresponding mode, and then obtain corresponding aerodynamic reduced order model as input;
Step 3, it is based on 3 d modeling software, parametrization wing structure model is established, establishes structural finite element model, and right The model analysis obtains the mass matrix, stiffness matrix, damping matrix of the model;
Step 4, the mode based on reference model obtains the reduced-order model of parameter finite element model as mode is assumed;
Step 5, the structure reduced-order model based on pneumatic depression of order power model and parametrical finite element, carries out parameterized model Aeroelastic analysis;
Step 6, using composite plys thickness, angle as design variable, experimental design is carried out, experimental design is obtained Design variable as input, aeroelastic analysis as output, obtain the agent model of parameterized model;
Step 7, the agent model obtained based on step 6 carries out the optimization design of composite wing.
Method provided by the invention the advantage is that compared with existing Optimization for composite wing method:
(1) it uses the aerodynamic force that CFD is calculated to carry out aeroelastic analysis, compares traditional vortex lattice method or dipole side Method, improves the accuracy of wing aerodynamic flexibility analysis, so as to obtain the better composite wing structures of performance;
(2) it using the mode of reference model as mode is assumed, is introduced into the depression of order of structural model, so without for every One parameterized model carries out aerodynamic response analysis, improves the efficiency of analysis, is suitable for designing composite structure excellent Change and calculates.
Description of the drawings
Fig. 1 is the flow chart of the Optimization for composite wing method of the present invention;
Fig. 2 is that CFD unsteady aerodynamic forces calculate unstrctured grid
Fig. 3 is broad sense aerodynamic coefficient and reduced-order model comparison under step response
Mode generalized displacement response when Fig. 4 Mach 2 ships 0.2
Specific implementation mode
Below in conjunction with drawings and examples, the present invention is described in further detail.
Fig. 1 be the present invention is based on the overall step of the Optimization for composite wing method of aerodynamic reduced order model, under It is specifically described in face of each realization step.
Step 1, the structural finite element model of initial reference wing (i.e. initial reference model) is established, model analysis is somebody's turn to do The mode Φ of structural model includes the frequency and the vibration shape of mode.
Step 2, aerodynamic force is calculated using CFD, establishes the aerodynamic model of initial reference model.Using the limited of reference model The mode Φ of meta-model obtains the pneumatic force-responsive under corresponding mode using each rank Mode Shape step signal as input.
According to the processing mode in step response, single order Volterra cores are the difference of the adjacency of step response:
Wherein, k is discrete time kth step number, and y is step response, and h is Volterra cores.Y (k) is in kth time step Step response.
Assuming that being h (k), k=1,2 ..., K by the single order core that Volterra series picks out, then Hankel matrixes can To be written as:
Wherein, r is the line number of Hankel matrixes, and s is Hankel matrix column numbers, and n is initial time step number.
By finally obtaining aerodynamic reduced order model to Hankel Singular Value Decompositions:
Wherein, subscript a is expressed as Aerodynamic Model, xaIt is the state variable of the state space of the aerodynamic reduced order model, ua For the input of the state space.xa(k) be state space kth time step state variable.In the research of Aeroelastic Problems, Primary concern is that the coupling effect of the elastic force of aerodynamic force and structure, so, input here is the deformation quantity of structure, i.e., extensively Adopted position is moved, Aa、Ba、Ca、DaFor aerodynamic reduced order model state space parameter, yaThe output of the aerodynamic reduced order model state space Amount, as broad sense aerodynamic force.
Step 3, using 3 d modeling softwares such as CATIA, parametrization wing structure model is established, is had using Nastran etc. Finite element analysis software establishes structural finite element model, and analyzes the structural finite element model, and the mould is obtained using DMAP language Mass matrix, stiffness matrix and the damping matrix of type, the kinetics equation of the model are as follows:
Wherein M, K, C are respectively mass matrix, stiffness matrix, damping matrix, and the point above character indicates derivation, two points Indicate that secondary derivation, a point indicate a derivation.U (t) indicates that the displacement of t moment, f (t) indicate the external force of t moment.
Step 4, the mode Φ based on reference model introduces coordinate transform u (t)=Φ x (t) as mode is assumed, to ginseng Numberization structural finite element model carries out depression of order, obtains the mass matrix M of corresponding reduced-order models, stiffness matrix KsAnd damping matrix Cs
MsTM Φ, KsTK Φ, CsT
To which the reduced-order model for obtaining parameter finite element model is as follows:
The form that above formula is write as to state space, obtains:
Wherein, each coefficient matrix is respectively:
Cs=[I];Ds=[0];
Wherein, I indicates unit matrix.State variable xs(t) it is:
By above-mentioned continuous time configuration state spatial model sliding-model control, structural separation time system state space is obtained Model:
Wherein, As'、Bs'、Cs'、Ds' it is corresponding structural separation time system state-space model parameter.K represents kth Time step;xs(k) it is the state variable of kth time step, u (k) is the displacement of kth time step, and f (k) is the outer of kth time step Power.
Step 5, the structure reduced-order model based on aerodynamic reduced order model and parametrical finite element, carries out parameterized model Aeroelastic analysis.
Depression of order, Φ are carried out since broad sense aerodynamic force still is based on initial modeTF (t) is without computing repeatedly, pneumatically Elastic model is as follows:
Wherein, q indicates dynamic pressure.
Step 6, using composite plys thickness, angle as design variable, based on experimental designs sides such as Latin hypercubes Method carries out experimental design, and the design variable that experimental design is obtained responds (such as flutter speed, fitful wind as input, aeroelasticity Response) as output, obtain the agent model of the parameterized model.
Step 7, the agent model obtained based on step 6 carries out the optimization design of composite wing.Such as can be used with Maximum flutter speed, minimum gust response, minimal structure weight are design object, to meet the rigidity of structure, intensity for constraint item Part carries out multi-objective optimization design of power using optimization methods such as genetic algorithms.
It is that verification refers to AGARD446.5 wings, calculates its flutter speed in 0.9Ma.Utilize the aerodynamic force of depression of order Model is coupled with structural model, is acquired under the Mach number, the flutter situation corresponding to different dynamic pressures, and Fig. 2 is the unsteady gas of CFD Cable Power Computation unstrctured grid.Fig. 3 is broad sense aerodynamic coefficient and reduced-order model comparison under step response, reduced-order model calculating As a result it coincide with CFD results preferable, can be used for subsequent aeroelasticity modeling.Mode broad sense when with Fig. 4 being Mach 2 ship 0.2 Dynamic respond, it can be seen that quadravalence response of mode displacement is restrained at this time, final to determine that the flutter speed at 0.9Ma is 0.25Ma.The result of order reducing method and the result of experiment are almost consistent, and pneumatic bomb can be carried out to the wing based on the above results Property response optimization.

Claims (5)

1. a kind of Optimization for composite wing method based on aerodynamic reduced order model, which is characterized in that including following step Suddenly:
Step 1, the structural model of reference model is established, model analysis obtains the modal frequency and the vibration shape of the structural model;
Step 2, corresponding mode is obtained using each rank Mode Shape as input using the mode of the finite element model of reference model Under pneumatic force-responsive, and then obtain corresponding aerodynamic reduced order model;
Step 3, it is based on 3 d modeling software, parametrization wing structure model is established, establishes structural finite element model, and to the mould Type analysis obtains the mass matrix, stiffness matrix and damping matrix of the model;
Step 4, the mode based on reference model obtains the reduced-order model of parametrization structural finite element model as mode is assumed;
Step 5, the reduced-order model based on aerodynamic reduced order model and parametrization structural finite element model, carries out parameterized model Aeroelastic analysis;
Step 6, using composite plys thickness, angle as design variable, experimental design is carried out, is set what experimental design obtained Variable is counted as input, aeroelastic analysis obtains the agent model of parameterized model as output;
Step 7, the agent model obtained based on step 6 carries out the optimization design of composite wing.
2. according to the method described in claim 1, it is characterized in that, in the step 2, obtained aerodynamic reduced order model table The state-space model being shown as under discrete time, it is as follows:
Wherein, xaIt is the state variable of the state space of aerodynamic reduced order model, uaFor the input of the state space, yaFor the shape The output of state space;K is discrete time kth step number;Aa、Ba、Ca、DaFor aerodynamic reduced order model state space parameter.
3. according to the method described in claim 1, it is characterized in that, in the step 4, using the finite element mould of reference model The mode Φ of type carries out depression of order as mode is assumed, to parametrization structural finite element model;
The mass matrix M of reduced-order model is obtained firsts, stiffness matrix KsWith damping matrix Cs, as follows:
MsTM Φ, KsTK Φ, CsTCΦ;
Wherein, M, K, C mass matrix that step 3 obtains respectively, stiffness matrix, damping matrix;
Coordinate transform u (t)=Φ x (t) are introduced, the reduced-order model for obtaining parameter finite element model is:
Wherein, t indicates that t moment, u indicate that displacement, f indicate external force;
The form that above formula is write as to state space, obtains:
Wherein, each coefficient matrix is respectively:
Cs=[I];Ds=[0];
I indicates unit matrix;
State variable xs(t) it is:
4. according to the method described in claim 3, it is characterized in that, the reduced-order model of the parameter finite element model indicates It is as follows for the state-space model under Offtime:
Wherein, As'、Bs'、Cs'、Ds' it is state-space model parameter of the reduced-order model under discrete time;K is discrete time Kth step number;xsFor the state variable of the state space under reduced-order model Offtime.
5. according to the method described in claim 1, it is characterized in that, in the step 5, aerodynamic reduced order model and ginseng are utilized State-space model of the reduced-order model of numberization structural finite element model under discrete time obtains state space under discrete time The aeroelastic model of form is as follows:
Wherein, k is kth time step;xaIt is the state variable of the state space of aerodynamic reduced order model, xsHave for parametrization structure Limit the state variable of the state space of the reduced-order model of meta-model;Aa、Ba、Ca、DaJoin for the state space of aerodynamic reduced order model Number;As'、Bs'、Cs' for parametrization structural finite element model reduced-order model state space parameter, q indicate dynamic pressure.
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