CN118194447A

CN118194447A - Structural design optimization method and system for tilting duct aircraft wing

Info

Publication number: CN118194447A
Application number: CN202410621455.9A
Authority: CN
Inventors: 刘尧龙; 徐尚儒; 章杰超; 张继发; 郑耀
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2024-05-20
Filing date: 2024-05-20
Publication date: 2024-06-14
Anticipated expiration: 2044-05-20
Also published as: CN118194447B

Abstract

The invention provides a wing with a double-girder structure, a pneumatic model and a structural model are coupled aiming at the structural design of a tilting duct fan aircraft wing, a wing structure is initially optimized by adopting a concomitant gradient optimization method, a MFD (MFD) is adopted to sequentially perform layer shape optimization, layer shape cutting and layer thickness optimization on composite material layers on the basis of fully considering manufacturability in actual production, and the positive layer sequence optimization is performed.

Description

Structural design optimization method and system for tilting duct aircraft wing

Technical Field

The invention relates to the technical field of wing structural design, in particular to a structural design optimization method and system applied to a tilting duct aircraft wing.

Background

A tilting ducted fan aircraft (tin-Duct FAN AIRCRAFT), also known as a tilting ducted aircraft, is an important branch of a vertical take-off and landing aircraft, and is characterized in that the ducted fan in the propulsion system of the aircraft can Tilt to realize the conversion between two flight modes, namely a fixed-wing stage flat flight mode and a multi-rotor stage vertical take-off and landing mode, and has the vertical take-off and landing capability of the rotor aircraft and the high-speed cruising capability of the fixed-wing aircraft. The tilting ducted fan device can be installed at different positions of the aircraft, such as a fuselage, wings, tail wings and the like. The tilting duct fan device is arranged on the wing, so that the influence of the wake flow of the duct fan device on lifting surfaces such as the wing and the tail wing can be reduced to the greatest extent, and meanwhile, more challenges are brought to the design of the wing of the tilting duct fan aircraft, more technical and functional requirements are required to be considered in the design, the wing mainly bears aerodynamic load in a fixed wing stage plane flying mode, and the vertical take-off and landing mode mainly bears upward thrust load provided by the wing tip duct in a multi-rotor stage plane flying mode. In addition, there is a need for internal equipment (e.g., steering engines, tilting devices) to be installed in the limited interior space of the wing, which requires a highly integrated structural design, rationally arranged installation of the wing internal equipment, while meeting specified strength and stiffness requirements with minimal wing structural weight.

For a tilting ducted fan aircraft, the weight of the aircraft has a great influence on the performance of the aircraft, and the lightweight structure means that the aircraft can obtain higher climbing rate, longer range and better maneuvering performance under the same engine power. Meanwhile, the light structure is also beneficial to reducing the fuel consumption of the aircraft, reducing the operation cost and improving the economy. The wing is also of vital importance as a key component of a tilting ducted fan aircraft in design, and the wing needs to bear various loads from ducted fans, engines and in the flight process, and if the wing is too heavy, the flight quality and safety of the aircraft are also affected, so in design and manufacturing processes, the lightweight design of the wing needs to be pursued as much as possible on the basis of meeting the constraints such as structural strength, rigidity and stability of the wing, and good performance of the wing can be ensured under various flight conditions.

In the vertical take-off and landing stage, tilting ducted fans mounted on the wing are the main components of the aircraft that generate lift; in the horizontal flight phase, the wing is a main component for generating lift force of the aircraft, and the aerodynamic performance of the wing directly determines the flight performance of the aircraft. In different flight modes such as vertical take-off, landing and flat flight, the wing needs to bear various complex loads, and reasonable structural layout and material selection are needed in the design of the wing so as to improve the strength and rigidity of the wing. Moreover, the wing of the tilting ducted fan aircraft needs to tilt between vertical take-off and landing and horizontal flight, and the design of the wing needs to consider how to realize the tilting mechanism and ensure the structural stability and safety of the wing in the tilting process. Through carrying out reasonable pneumatic layout and structural design to the wing, can improve the performance in aspects such as flight performance, structural strength and rigidity, handling property and maintenance and manufacturing cost of aircraft to ensure that the aircraft can operate safely, reliably, high-efficiently.

The tilting ducted fan aircraft is used as a high-performance aircraft, and design variables and constraint conditions in the analysis and optimization process of the tilting ducted fan aircraft are far more than those of the conventional fixed-wing aircraft or the multi-rotor aircraft. The aviation structure is made of high-performance materials (composite materials), so that a plurality of design variables such as the geometric shape and the size of the structure, the manufacturing details of the composite materials and the like are required to be considered in design. The gradient-free optimization method which is widely applied at present is successfully applied to the structural design problem of the aircraft, and the method has low application difficulty and simple principle, but the design variables involved in application are limited. Along with the expansion of the dimension of the design space, the number of design variables is increased sharply, and the gradient-free optimization method cannot efficiently and accurately solve the problem of optimizing large-scale design variables. In order to address the structural design issues of large-scale design variables and constraints, an efficient gradient optimization method needs to be sought.

In summary, the wing design of the conventional tilting ducted fan aircraft has the following problems:

(1) The existing wing design of the tilting duct fan aircraft mainly expands on the basis of a fixed wing aircraft structure, but the existing fixed wing aircraft wing configuration and related structural design are only aimed at aerodynamic loads, and the design of the tilting duct fan aircraft wing needs to consider structural layout to accommodate more internal devices, complex loading conditions under various flight modes (not only aerodynamic loads), light weight, manufacturing feasibility and other series of technical function requirements, so that the existing fixed wing aircraft wing configuration and related structural design method are not suitable for the design of the tilting duct fan aircraft wing.

(2) The existing wing structure optimization method of the tilting duct fan aircraft only optimizes under the structural discipline background, does not consider the influence of actual aerodynamic load, and only simulates the actual aerodynamic load by using an empirical formula, so that the aerodynamic loading method based on the empirical formula cannot accurately predict aerodynamic performances such as lift force, resistance, lift-drag ratio and the like of the wing under different flight modes, and further reduces the optimized fidelity.

(3) The existing aircraft wing structure optimization method has the problems of overlong calculation time and low precision when evaluating the gradient required by optimization by using a gradient-based optimization method. The existing aircraft wing structure gradient optimization method needs to derive the whole objective function in each iteration, so that the calculated amount is very large, more calculation time is needed, and the optimization iteration times can be limited by the longer gradient calculation time; the existing aircraft wing structure gradient optimization method only focuses on gradient information of the current point, and does not consider the global structure of the whole design space, so that lower precision is caused, and convergence tolerance of the optimization problem is reduced due to the lower precision. For the large-scale aircraft wing structural design problem with a large number of design variables and constraints, the calculation time required by the existing gradient optimization method for calculating the gradient exceeds the calculation time required by analysis, and the calculation time becomes a bottleneck affecting the aircraft wing structural optimization.

(4) The existing design of the wing of the tilting duct fan aircraft mainly adopts alloy, the composite material has excellent mechanical property and lower density, the weight of the wing can be effectively reduced by using the composite material, the weight of the wing can be further reduced by optimizing the composite material part, but the application of the composite material is less in the existing design of the wing of the tilting duct fan aircraft, the application threshold of the composite material is higher than that of the metal material, more design constraint and manufacturing constraint need to be fully considered, and the application of the composite material on the wing of the tilting duct fan aircraft is hindered.

Disclosure of Invention

The method aims at solving the problems that the design optimization method of the tilting duct fan aircraft wing in the prior art does not comprehensively consider the influence of the structure and the aerodynamic load, the gradient optimization method is not suitable for structural optimization, the design difficulty of the composite material is high, and the manufacturing is not feasible. The invention provides a tilting duct fan aircraft wing with a double-girder structure, which is characterized in that a pneumatic model and a structural model are coupled, an optimal primary structure of the wing is obtained by utilizing an accompanying gradient optimization method, and a practical direction method MFD is adopted to perform layering combination optimization on the tilting duct fan aircraft wing. The wing with the double-girder structure provided by the invention not only can provide enough strength and rigidity to meet the requirements of different flight modes of the tilting duct fan aircraft, but also is convenient for installing the tilting duct related mechanism. The interaction between the structure and the air-actuated of the wing is fully considered in the design optimization, the optimization problem of large-scale design variables and constraints of preliminary optimization of the double-girder wing is effectively and accurately solved by adopting a concomitant gradient optimization method, and finally, the composite material is enabled to have the manufacturing feasibility by performing the layering combination optimization of the composite material by adopting a feasible direction method MFD.

For further understanding of the technical solution of the present invention, the terms related to the present invention are defined as follows:

Layering: ply is a basic unit in a composite material structure, each layer is composed of specific materials (such as carbon fibers, glass fibers and the like) and resin and the like, and the specific materials (such as lamination, hot pressing and the like) are overlapped, and the design and optimization of the Ply are critical to the overall performance of the composite material structure and can influence the strength, the rigidity, the temperature resistance, the corrosion resistance and the like of the composite material.

Laminated plate: and the Laminate is a composite material plate formed by superposing a plurality of layers in different directions, the materials of the layers can be different or the same, each layer of the Laminate has specific fiber directions and material properties, and the layers are bonded together through a specific process.

The technical scheme of the invention is as follows: a structural design optimization method of a tilting ducted aircraft wing comprises the following steps:

s1: obtaining a first optimal configuration of a tilting ducted fan aircraft wing

Setting a first design variable, a first optimization objective and a first design constraint that affect a tilting ducted fan aircraft wing; constructing a structural model and a pneumatic model of the wing; coupling the pneumatic model and the structural model by displacement data and load data; constructing a Lagrangian function of the coupling model, and solving the coupling model by a concomitant gradient optimization method to obtain an optimization result; evaluating the optimization result to obtain a first optimal structure of the wing of the tilting ducted fan aircraft;

s2: generating a finite element model of a wing box structure of a tilting ducted fan aircraft wing

Generating a finite element model of a wing box structure of the tilting ducted fan aircraft wing according to the first optimal structure;

s3: obtaining a second optimal configuration of a tilting ducted fan aircraft wing

According to the finite element model, setting a second optimization target to minimize the weight of the wing box structure, wherein the second constraint comprises design constraint and manufacturing constraint, and performing composite material layering combination optimization on the skin and the spar of the wing box structure by adopting a feasible direction method to obtain a second optimal structure of the wing of the tilting ducted fan aircraft;

The first design variables include the locations of the first and second main beams on the chord, the shape and geometry of the spar, rib, and skin; the composite material layering optimization sequentially comprises layering shape optimization, layering shape cutting, layering thickness optimization and layering sequence optimization.

Further, obtaining a first optimal configuration of a tilting ducted fan aircraft wing comprises:

S11: determining a first design variable, a first optimization objective, and a first design constraint affecting a tilting ducted fan aircraft wing

The first design variable refers to parameters affecting the wing structure, including the optimal positions of the first main beam and the second main beam, and the shape and geometric dimensions of the skin, the ribs and the spar; the first optimization objective is minimum wing structural weight; the first design constraint comprises the strength, rigidity and flutter requirements of wing structures of the tilting ducted fan aircraft in different flight modes;

s12: establishing a pneumatic model of a tilting ducted fan aircraft wing by adopting an NS equation and an SA turbulence equation

The NS equation and the SA turbulence equation are connected through the turbulence viscosity, and the NS equation and the SA turbulence equation form a pneumatic model of the tilting ducted fan aircraft wing;

S13: building structural model of tilting duct fan aircraft wing

Using three-dimensional modeling software to establish a three-dimensional structural model of the tilting ducted fan aircraft wing based on the shell unit; dividing the three-dimensional structure model into grids to form a finite element model of the wing structure, wherein the grids are quadrilateral grids which tend to be square;

s14: establishing a coupling model of a pneumatic model and a structural model

Setting the input variable of the pneumatic model to comprise displacement data, the output variable of the pneumatic model to comprise load data, setting the input variable of the structural model to comprise load data, and coupling the pneumatic model and the structural model through the displacement data and the load data;

S15: lagrangian function for constructing coupling model

Substituting the first design constraint into a corresponding Lagrangian multiplier, and converting the original optimization problem with the design constraint into an unconstrained optimization problem through a Lagrangian function;

S16: obtaining an optimal solution of the Lagrangian function through an accompanying equation;

Converting the first optimization objective to a minimized lagrangian function; solving a gradient of the Lagrangian function through an accompanying equation; solving to obtain the gradient of each constraint condition with respect to the first design variable, and further obtaining the gradient of the minimized Lagrangian function with respect to the first design variable; updating the numerical value of the first design variable by using the gradient of the first design variable obtained through calculation, so as to continue the optimization iteration of the next round, and finally obtaining the optimal solution of the Lagrangian function, wherein the optimal solution of the Lagrangian function comprises the optimal solution of the first design variable, and the optimal solution of the first variable and the first design constraint form a first optimal structure of the tilting duct fan aircraft wing;

s17: evaluating a first optimal configuration of a tilting ducted fan aircraft wing

Evaluating the first optimal structure, the evaluating comprising evaluating displacement, strain, stress, vibration of the first optimal structure in different flight modes: accepting the first optimal structure as an optimal preliminary structural layout for a tilting ducted fan aircraft wing if the first optimal structure meets an expected performance goal; if the first structure does not reach the standard, returning to the step S12 to continue iterative optimization until the first optimal structure meets the design requirement and the performance index;

wherein S12 and S13 are performed synchronously.

The invention also provides a structural design optimization system of the tilting duct aircraft wing, which can realize the structural design optimization method of the tilting duct aircraft wing, and comprises the following steps:

The structure preliminary design module is used for obtaining a first optimal structure of the tilting ducted fan aircraft wing, and setting a first design variable, a first optimization target and a first design constraint which influence the tilting ducted fan aircraft wing; constructing a structural model and a pneumatic model of the wing; coupling the pneumatic model and the structural model; constructing a Lagrangian function of the coupling model, and solving the coupling model by a concomitant gradient optimization method to obtain an optimization result; evaluating the optimization result to obtain a first optimal structure of the wing of the tilting ducted fan aircraft; ;

the wing box structure generating model is used for generating a finite element model of the wing box structure of the tilting ducted fan aircraft wing according to the optimal primary structure;

The composite material layering optimization module is used for optimizing layering of the skin and the spar of the wing box structure, setting a second optimization target to minimize the weight of the wing box structure according to the finite element model, wherein the second constraint comprises design constraint and manufacturing constraint, and performing composite material layering combination optimization on the skin and the spar of the wing box structure by adopting a feasible direction method to obtain a second optimal structure of the wing of the tilting ducted fan aircraft;

The invention also discloses a server, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and is characterized in that: the steps of the method as described above are implemented when the processor executes the computer program.

Compared with the prior art, the structural design optimization method and system for the tilting duct aircraft wing provided by the invention have the beneficial effects that:

(1) The invention provides a wing with a double-girder structure aiming at a tilting duct fan aircraft, wherein the structure shares load through two girders, and the bending and torsional rigidity of the wing are increased. For tilting ducted fan aircraft that need to switch between different flight modes, the wings of the dual girder structure can provide sufficient strength and stiffness to accommodate the requirements of these different flight modes, which is critical to the stability and reliability of the wings and the aircraft. Moreover, the dual girder wing of the present invention allows a designer more options in the internal layout of the wing, and the device can be installed between two girders without affecting the overall mechanical properties of the wing structure. In addition, the wing can experience various load cycles in the flight process, and the wing with the double-girder structure can better disperse stress so as to improve the fatigue resistance, and in extreme cases, if one girder is damaged, the other girder can still provide necessary support, so that the safety of an aircraft is improved.

(2) According to the invention, when the first optimal structure of the wing of the tilting duct fan aircraft is obtained, the pneumatic model and the structural model are coupled through the displacement data and the load data, the interaction between the structural deformation and the pneumatic load of the wing in actual flight is fully considered, and the performance in the aspects of flight performance, structural strength, rigidity and the like of the tilting duct aircraft is improved through reasonable pneumatic layout and structural design of the wing.

(3) According to the invention, the wing structure of the double-main beam tilting duct fan aircraft is initially optimized by adopting the accompanying gradient optimization method, so that the wing structure with the lightest weight is obtained under the requirements of geometric constraint and mechanical constraint.

(4) The invention adopts a feasible direction method MFD when the layering combination optimization is carried out on the tilting duct fan aircraft wing, optimizes the layering unfolding combination (layering shape, thickness and sequence optimization) of the composite material on the basis of fully considering manufacturability in actual production, better plays the bearing capacity of the composite material, reduces the structural weight of the wing, and solves the problem that the composite material design in the existing tilting duct fan aircraft wing cannot meet the manufacturing requirement.

(5) The invention provides a wing with a double-girder structure, a pneumatic model and a structural model which are coupled, a wing structure is initially optimized by adopting a concomitant gradient optimization method, the wing is subjected to layering combination optimization by adopting a feasible direction method MFD, and the like aiming at the structural design of the tilting duct fan aircraft wing.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive faculty for a person skilled in the art.

Fig. 1 is a schematic structural view of a double girder type wing according to the present invention.

Fig. 2 is a schematic flow chart of an optimization method for wing structural design according to the present invention.

FIG. 3 is a schematic flow chart of the composite lay-up combination optimization proposed by the present invention.

Fig. 4 is a schematic illustration of the skin of a finite element model of a wing box structure in accordance with an embodiment of the present invention.

Fig. 5 is a schematic view showing the internal structure of a finite element model of a wing box structure according to an embodiment of the present invention.

Figure 6 is a schematic view of a multi-rotor stage wing box loaded condition according to an embodiment of the present invention.

Fig. 7 is a schematic view of a loading situation of a fixed wing stage wing box according to an embodiment of the present invention.

FIG. 8 is a graph of the iterative change in weight of a wing box during ply shape optimization in accordance with an embodiment of the present invention.

FIG. 9 is a graph of the iterative change in weight of a wing box during ply thickness optimization in accordance with an embodiment of the present invention.

Figure 10 is a cloud of composite layup thickness distribution for a skin according to an embodiment of the present invention.

FIG. 11 is a cloud of composite layup thickness distribution of a spar of an embodiment of the present invention.

FIG. 12 is a graph of an analysis of wing box displacement in a fly-by-fly mode for optimization results in accordance with an embodiment of the present invention.

FIG. 13 is a graph of an analysis of wing box strain in a fly-by-fly mode for optimization results for an embodiment of the invention.

FIG. 14 is a graph of an analysis of wing box stress in a fly-by-fly mode for optimization results for an embodiment of the present invention.

FIG. 15 is an analysis of wing box displacement in vertical takeoff and landing mode for an optimization result of an embodiment of the present invention.

FIG. 16 is an analysis of wing box strain in vertical takeoff and landing mode for an optimized result of an embodiment of the present invention.

FIG. 17 is an analysis chart of wing box stress in vertical takeoff and landing mode for the optimized results of an embodiment of the present invention.

Detailed Description

The invention will be further elucidated with reference to the examples and the accompanying drawing. It is understood that the examples are given solely for the purpose of illustration and are not intended to limit the scope of the invention. Variations and advantages that would occur to those skilled in the art are included within the invention without departing from the spirit and scope of the inventive concept, and the appended claims and their equivalents are intended to be covered thereby.

It will be understood that the terms "a" and "an" should be interpreted as referring to "at least one" or "one or more," i.e., in one embodiment, the number of elements may be one, while in another embodiment, the number of elements may be plural, and the term "a" should not be interpreted as limiting the number. In the present invention, other names and terms are common names in the art, except for the names and terms that the inventors have explicitly defined.

In an embodiment of the present invention, a structural design optimization method and system for a tilting duct aircraft wing are provided, as shown in fig. 1, the present invention provides a dual main beam type wing structure, wherein materials are mainly selected from composite materials, and main components include a first main beam, a second main beam, a front edge, a rear wall, a wing rib, a skin (hidden in order to show an internal structure diagram), an aileron steering engine, a tilting device, and a duct. The main bearing parts of the wing structure are a first main girder and a second main girder, and wing internal equipment such as an aileron steering engine, a tilting device and the like in the wing tip area are arranged between the first main girder and the second main girder. The wing structure not only can uniformly and effectively bear different complex loads applied to a horizontal flight mode and a vertical take-off and landing mode, but also can be used for arranging internal equipment in a limited and narrow wing internal space.

The tilting duct fan aircraft wing with the double-girder structure has the advantages that: (1) Compared with the traditional fixed wing aircraft wing, the wing tip of the wing is provided with the duct device and the matched tilting device, so that the limited internal space of the wing is occupied to a great extent, and the double main beams have the advantages of allowing a designer to have more choices on the internal layout of the wing, and the internal equipment can be arranged between the two main beams without affecting the integral mechanical property of the wing structure; (2) The wing with the double-girder structure improves the structural rigidity of the wing, enhances the bearing capacity of the wing, shares the load through the two girders, increases the bending and torsional rigidity of the wing, and can provide enough strength and rigidity for the wing to adapt to the requirements of different flight modes for the aircraft needing to be switched between by the tilting duct fan aircraft, and is critical to the stability and reliability of the wing and the tilting duct fan aircraft, and the wing of the tilting duct fan aircraft can undergo various load cycles in the flight process, so that the double-girder structure can better disperse stress concentration, thereby improving the fatigue resistance and prolonging the service life of the wing; (3) The wing structure of the double girder structure of the present invention increases redundancy, and in extreme cases, if one girder is damaged, the other girder can still provide necessary support, thereby increasing the safety of the aircraft.

The structural design optimization method and system for the tilting duct aircraft wing provided by the invention are developed around a double main beam type wing structure, as shown in fig. 2, and mainly comprise a conceptual design stage S1 and a detailed design stage S3.

The conceptual design stage S1 aims at obtaining an optimal preliminary structure, i.e. a first optimal structure, of the tilting ducted fan aircraft wing, setting a first design variable, a first optimization objective and a first design constraint affecting the tilting ducted fan aircraft wing; constructing a structural model and a pneumatic model of the wing; coupling the pneumatic model and the structural model by displacement data and load data; constructing a Lagrangian function of the coupling model, and solving the coupling model by a concomitant gradient optimization method to obtain an optimization result; and (3) evaluating an optimization result to obtain a first optimal structure of the tilting ducted fan aircraft wing, wherein the method comprises the following steps of:

Determining a first design variable and a first optimization target which influence the performance of the wing structure of the tilting ducted fan aircraft, wherein the first design variable refers to parameters influencing the wing structure, and comprises the positions of a first main beam and a second main beam on a wing chord, the shapes and the geometric dimensions of a wing beam, a wing rib and a skin, the first optimization target is the structural weight of the minimum wing in a flat flight mode and a vertical take-off and landing mode, and the first design constraint is the strength, the rigidity, the flutter and the like of the wing structure of the tilting ducted fan aircraft under different flight modes (vertical take-off and landing, transitional flight, horizontal flight, hovering and the like).

The wing aerodynamic model of the tilting ducted fan aircraft is built to simulate the aerodynamic performance of the wing of the tilting ducted fan aircraft in different flight modes. This includes predictions and calculations of aerodynamic properties of the wing, such as lift, drag, pitch moment, etc., which are critical to the stability, maneuverability, and performance of the aircraft. The flow field control equation is a basic equation describing the motion of fluid, and comprises a continuity equation, a momentum conservation equation, an energy conservation equation and the like, wherein the equations are used for describing the distribution and change of physical quantities such as speed, pressure, density and the like when the fluid flows around the wing. In the design of a tilting ducted fan aircraft, the aerodynamic model of the wing needs to be combined with a flow field control equation. By solving the flow field control equation, detailed information of the flow field around the wing, such as streamline distribution, pressure distribution, vortex structure and the like, can be obtained. This information is critical to understanding and optimizing the aerodynamic performance of the wing. In addition, in special flight modes such as vertical take-off and landing and transitional flight of the tilting ducted fan aircraft, the interaction between the wing and the ducted fan can be more complex, and at this time, the aerodynamic model of the wing needs to more finely consider the influence of the airflow generated by the ducted fan on the wing flow field. By solving the flow field control equation, the complex interaction can be simulated, thereby more accurately predicting the aerodynamic performance of the wing.

Pneumatic models are mathematical and physical models for modeling and analyzing the flow characteristics of air or other gases around a solid object, and how these flows affect the object itself. The invention adopts an NS equation and an SA turbulence equation to construct a pneumatic model, wherein the NS equation (Navier-Stokes equation) is also called a flow field control equation, and is a three-dimensional steady-state turbulence equation, and a continuity equation, a momentum conservation equation and an energy conservation equation of the NS equation are respectively expressed as follows:

（1）

Where ρ is the flow field density, U= [ U, v, w ] is the flow field velocity vector, U, k, w are the velocities in the x, y, z directions, respectively, p is the flow field pressure, E is the total energy of the flow field, q is the flow field heat flux, τ is the flow field viscous stress tensor, τ is U, the turbulent flow molecular viscosity And turbulent viscosityIs a function of (2).

SA equation (Spalart-Allmaras equation), also known as SA turbulence equation, by which turbulence viscosity can be determinedIn connection with other variables in the NS equation, the SA turbulence equation is expressed as follows:

（2）

In formula (2) 、、、Representing convection, diffusion, production and near wall disruption of turbulence, respectively, σ is Prandtl number, representing diffusion of turbulence viscosity, C _b2、C_b1、C_w1 is model constant, which are obtained by fitting experimental data,As a function of strain rate, a complex quantity, taking into account the effects of local shear and rotation, f _w is a function calculated from the wall distance d for correcting the turbulence viscosity in the vicinity of the wall, v is the kinematic viscosity,For the corrected kinematic viscosity,Related to the turbulent kinematic viscosity v _t,。

The NS equation and the SA turbulence equation involve complex flow phenomena and boundary conditions, and are difficult to directly solve, so in order to perform numerical solution on a computer, these continuous partial differential equations need to be converted into discrete algebraic equations, and the discretization process can improve the stability and convergence of the numerical solution. The dispersion of NS equations and SA turbulence equations in the present invention is obtained by a fluid solver. For a given design variable vector, the discrete equation solves the state variable vector such that the pneumatic global residual satisfies:

A(b,e(b))=0 （3）

where b is a design variable vector and e is a state variable vector, equation (3) contains nonlinear equations involving millions of state variables.

S13: building structural model of tilting duct fan aircraft wing

(1) Using three-dimensional modeling software to establish a three-dimensional structural model of the tilting ducted fan aircraft wing based on the shell unit;

(2) Building a finite element model of a wing structure according to a three-dimensional structure model of the wing

Endowing the three-dimensional structure model with material properties, structural constraints and the like, wherein the three-dimensional structure model can provide structural responses of the wing under different loading conditions, such as displacement, stress, vibration and the like; then, carrying out grid division on the three-dimensional structure model of the wing to form a finite element model of the wing structure, wherein the grid is mainly a quadrangle grid which tends to be square;

(3) Static analysis of finite element models of airfoils

Carrying out static analysis on a finite element model of the wing by adopting a static analysis finite element method, wherein the structural residual error of nonlinear analysis is as follows: s (u) =0, the control equation in the nonlinear analysis is: s (u) =ku-f=0, where K, u, f represent the overall stiffness matrix, global displacement vector, and load vector, respectively, of the overall unit.

In the finite element analysis of the tilting ducted fan aircraft structure, the shell unit is used for attribute definition, the p-order double Lagrange shape function is used for interpolating the surface displacement U ₀ and the small rotation angle theta of each unit in the domain, and the double Lagrange shape function is expressed as follows:

（4）

Wherein, Is a shape function, n _e is the number of nodes of the cell,Is an isoparametric coordinate,Is the cell state variable for the jth cell under the ith load, and p is the order.

In the static analysis finite element method, the structural global residual is the overall measurement of all structural unit residual in the range of the whole wing structural finite element model, reflects the accuracy of model overall solution, is obtained through all structural unit residual, is obtained based on the virtual work method, and is obtained based on the virtual work methodThe expression is as follows:

（5）

Wherein, Is the structural unit residual error of the jth unit under the ith load condition,Is the cell state variableUnit node locationAnd a material design variable X _M,Represents the increment, T represents the transpose of the matrix,Representing cell state variablesTransposed derivative, X _G is a geometric design variable, cell node positionObtained by the unit operator P _j.

Residual of structural unitThe relationship with the structural global residual R _i is as follows:

（6）

Wherein, Representing the Kronecker product, I ₆ is the identity matrix of 6*6, u _i is the global state variable, the cell state variableAnd cell node positionThe calculation formula of (2) is as follows:

（7）

Where I ₃ is the identity matrix of 3*3, Representing the transpose of the unit operator P _j,Is a global node position vector representing the node position in the global coordinate system.

S12 and S13 are performed synchronously.

S14: establishing a coupling model of a pneumatic model and a structural model

After the load is applied to the wing, the wing structure is deformed, and the aerodynamic performance of the deformed wing is also changed, so that aerodynamic analysis is needed to be carried out on the deformed wing again. Displacement data is the amount of displacement that occurs in the wing structure after loading, and is provided by the structural model. The displacement data includes: the displacement vector of each point of the wing structure comprises displacement amounts in three spatial directions (x, y and z); new shapes or structural contours of the components after deformation of the wing structure; and structural key points or overall displacement, displacement data are critical to assessing the stiffness and overall deformation of the wing structure.

The surface pressure of the wing obtained through pneumatic analysis is required to be converted into corresponding load to be loaded on the surface of the wing during structural analysis. The loads are forces and moments acting on the wing structure, these data are provided by the aerodynamic model, the load data include: pressure distribution: positive and negative pressure profiles applied by the fluid to the solid surface; shear force distribution: tangential force distribution of the fluid on the solid surface; aerodynamic forces and moments: the total lift, drag and pitching moment are obtained by integrating the pressure and shear force distribution.

The aerodynamic and structural models provide a method for aerodynamic and structural analysis of a tilting ducted fan aircraft wing. In the coupling analysis, an effective data exchange mechanism is arranged between the pneumatic model and the structural model, the displacement is set as one of the input variables of the pneumatic model and one of the output variables of the structural model, the load is set as one of the output variables of the pneumatic model and one of the input variables of the structural model, and the pneumatic model and the structural model are coupled through the displacement and the load, so that load and displacement data are shared between the two models in real time: (1) The load transmission, the pneumatic load data generated by the pneumatic model analysis are transmitted to the structural model, the structural response is calculated by the structural model through the load data, and the structural response comprises displacement data; (2) And feeding back displacement data generated by the structural model analysis to the pneumatic model, and updating flow field information and recalculating pneumatic load by using the displacement data by the pneumatic model.

In order to transfer load and displacement between aerodynamic and structural models, the present invention employs a matching-based load and displacement extrapolation to transfer displacement from structural grid to aerodynamic grid by linking each aerodynamic surface node to a fixed number of nearest structural nodes; the displacement of each aerodynamic surface node is calculated by finding the optimal rigid rotations and translations calculated from the displacements of a set of linked structural nodes. The use of a rigid rotation matrix allows the calculated displacement transfer to be geometrically accurate.

The interaction between the aerodynamic model and the structural model introduces additional complexity, requiring iterative solutions of the two models until the interaction between the two is balanced, which takes into account not only the aerodynamic global residual and the structural global residual alone, but also the coupling effect between the two residuals, for example, structural deformations may affect aerodynamic performance, and changes in aerodynamic performance may in turn create new aerodynamic loads on the structure. Thus, in coupling analysis, the pneumatic global residual and the structural global residual need to be considered simultaneously, and a coupling iterative solver is required to ensure that the residuals of all physical quantities are reduced to acceptable levels, which requires powerful computational power and accurate models to ensure reliable and accurate results. Combining the pneumatic global residual error and the structural global residual error, and writing a coupling residual error R of the model after coupling the pneumatic model and the structural model into:

（8）

The coupling analysis of the aerodynamic model and the structural model is to find a solution (w, u) that satisfies the coupling residual equation.

S15: lagrangian function for constructing coupling model

According to a first design constraint (such as displacement, strain, stress, vibration, etc. in different flight modes) of the wing structure, the corresponding lagrangian multipliers are brought, and if m constraint conditions exist, m lagrangian multipliers are introduced and are denoted as λ1, λ2. In this process, the Lagrangian function converts the original constrained optimization problem into an unconstrained optimization problem and provides a unified framework to guide the optimization process of the wing structure. The expression of the Lagrangian function is as follows:

（9）

Wherein x is an optimized variable vector, namely a first design variable, specifically comprising the optimal positions of the first main beam and the second main beam, as well as the shape and geometry of the skin, the ribs and the spar, λ= [ λ ₁,λ₂,...,λ_m ] is a lagrange multiplier vector, and f (x) is an objective function of the wing structure, namely an objective function of the first optimization objective, specifically minimizing the structural weight of the wing in the plane-flight mode and the vertical-lift mode; g _i (x) is a constraint function of the ith constraint.

S16: obtaining an optimal solution of the Lagrangian function through the solution of the accompanying equation

The first optimization objective is converted into a minimized lagrangian function minimize L (x, λ) and the optimal optimization variable vector/first design variable x and lagrangian multiplier vector λ are obtained by solving.

The accompanying equation is a set of equations obtained by gradient the lagrangian function, and the accompanying equation can provide gradient information about the first design variable, so as to guide the optimization algorithm to update the first design variable, and is:

（10）

The gradient-based design optimization method can solve the problem of large-scale design within reasonable calculation time only under the condition of effectively analyzing and evaluating the gradient, and the function quantity under each load can be reduced to a manageable quantity by adopting a constraint aggregation technology due to the fact that the function quantity and the variable quantity are large in the method.

The gradient of each constraint g _i (x) with respect to the design variable x can be obtained by solvingFurthermore, the gradient/>, with respect to the first design variable x, of the objective function f (x) can be obtainedAnd finally, updating the numerical value of the first design variable by using the gradient of the first design variable obtained through calculation, so as to continue the optimization iteration of the next round, and finally obtaining the optimal solutions x and lambda of the Lagrangian function, namely the optimal first design variable x, wherein the optimal design variable x and the first design constraint and the like form the optimal primary structure of the tilting ducted fan aircraft wing.

The optimized wing structural design scheme, namely the first optimal structure is evaluated to verify whether the design requirement and the performance index are met, wherein the method mainly comprises the steps of analyzing the performance of the first optimal structural design scheme of the wing, evaluating displacement, strain, stress, vibration and the like of the first optimal structural design scheme of the wing in different flight modes, and judging whether the current design is good or bad and whether the expected performance target is met or not according to evaluation results. If the first structural design scheme of the wing reaches the standard, the first structural design scheme of the wing is the optimal primary structural layout of the tilting ducted fan aircraft wing; if not, the process returns to step S12 to continue the iterative optimization and the values of the first design variables are adjusted to further improve the performance of the wing structure. According to the gradient information of the first design variable, the numerical value of the first design variable is updated by using an optimization algorithm, the accompanying equation is solved again, and then the result is evaluated again. This process will continue until the design requirements and performance criteria are met.

The main bearing structure of the wing is a wing box, and the optimal primary structure/first optimal structure layout of the high-integration tilting ducted fan aircraft wing obtained in the conceptual design stage is converted into a wing box three-dimensional model by utilizing a three-dimensional modeling method, and the structural performance of the wing box is taken as a primary target in structural analysis, and the wing box three-dimensional model obtained in the conceptual design stage is taken as input of the detailed design stage, so that the detailed design stage mainly optimizes the wing box.

The detailed design stage utilizes the wing box three-dimensional model to generate a finite element model for the subsequent composite material layering combination optimization. And (3) performing composite material layering combination optimization on the wing box structure, wherein the layering combination optimization sequentially comprises layering shape optimization, layering shape cutting, layering thickness optimization and layering sequence optimization. Finally, a light wing box structural scheme meeting the design requirement, namely a second optimal structure of the tilting duct fan aircraft wing, is obtained.

According to the invention, the wing box is subjected to layering combination optimization, and the design optimization of the wing box is a comprehensive design process of a second optimization target (minimum wing box weight) on the premise of meeting design constraint, manufacturing constraint and the like, namely, the best design is found on the premise of meeting the second constraint, wherein the second constraint comprises layering design constraint and layering manufacturing constraint. The mechanical properties of the composite material laminated plate can be known, the mechanical properties of the composite material can be changed, the material property, the layering thickness, the layering angle and the layering sequence of the composite material can be changed, and the layering angle of the composite material is generally 0 DEG, 45 DEG and 90 DEG due to the limitation of the existing composite material process, and the single manufacturable layering material thickness has the requirement. The optimal design of the composite material layering combination is to optimize the layering shape, thickness and sequence of the four layering angles under the condition of meeting the requirements of structural rigidity and strength, and lighten the structural quality.

In the invention, in the process of carrying out ply combination optimization on the composite wing box, not only the design constraint factors such as strength, rigidity, stability, weight and the like of a structure are considered, but also the manufacturing constraint of the ply is considered, so that the optimization result has processability. The importance and necessity of considering manufacturing constraints in composite layup optimization is manifested in several aspects: (1) actual production butt joint: if the practical feasibility of the manufacturing process of the composite material is not considered in the design stage, the optimized overall design scheme is difficult to manufacture, and the manufacturing constraint ensures that the design scheme is efficient and manufacturable; in addition, there are many industry standards and specifications for composite manufacturing, and design considerations for these manufacturing constraints help ensure that the overall design meets industry specifications, making it easier to pass safety and quality checks; (2) cost control: limiting factors in the manufacturing process are used as optimized constraint conditions, so that the manufacturing cost can be controlled, and the design of schemes exceeding budget or uneconomic, such as layering with complex shapes, can be avoided, and the manufacturing process can be theoretically manufactured, but the manufacturing cost is greatly increased; (3) quality assurance: manufacturing constraints can ensure the quality and reliability of the product, for example, the composite lay-up sequence can affect the porosity and residual stress of the final product, the application of a large proportion of single-layer directional lay-up is an important guarantee of product quality, and reasonable manufacturing constraints can avoid structural flaws such as wrinkles or layering, thereby improving the performance and strength of the final product.

Common layup manufacturing constraints and the composite materials employed herein are: (1) In composite laminates, there must be a constraint on the ply thickness in each direction, i.e., the total ply thickness in each direction is a percentage of the total ply thickness in the laminate, typically providing that the total ply thickness in each direction must be greater than 10% of the laminate thickness and less than 70% of the laminate thickness, such constraint being applied at all points on the laminate; (2) The thickness of the single ply which can be manufactured is generally 0.1mm-2mm, the specific value depends on the manufacturing process and the type of materials, the outermost ply is a ply with an angle of +/-45 degrees, and the ply in the same direction cannot continuously exceed 4 layers.

The present invention imposes optional manufacturing constraints during the ply shape optimization stage and more detailed manufacturing constraints during the ply order optimization stage. Non-constrained ply manufacturing constraints (Non-mandatory manufacturing constraints) refer to manufacturing related constraints that may be considered but not enforced during the composite structural design and optimization process, not to ensure basic functionality or safety of the structure, but to optimize the manufacturing process, reduce costs, simplify assembly, or improve manufacturing efficiency. The optional manufacturing constraints of the present invention include: (1) While a particular layup sequence may help to improve the performance of the component, in some cases, adjusting the layup sequence may simplify the manufacturing process or reduce the risk of manufacturing errors, while the impact on performance may be acceptable; (2) ply symmetry: warpage and internal stress can be reduced for composite structural ply symmetry, but in some designs, symmetry requirements are relaxed for optimum performance or weight reduction; (3) minimum ply thickness: the constraint of minimum layer thickness is set for simplicity of manufacture, but this is not a consideration for structural performance, but rather to avoid problems in the manufacturing process such as lay-up and curing of prepregs. During design and optimization, non-mandatory manufacturing constraints provide a degree of flexibility that allows engineers to consider practical manufacturing convenience and economy while meeting performance requirements. By properly weighting these non-mandatory constraints and design goals, a more efficient, cost-effective product design can be achieved.

Among the optimization algorithms that can be used in the optimization of the ply-combining are the available direction method (MFD, method of feasible directions), sequence quadratic programming, dual optimizers based on separable convex approximations, and large-scale optimization algorithms. The invention adopts a feasible direction method MFD in the optimization of the ply combination of the composite material, and the ply combination optimization of the composite material by using the feasible direction method MFD has the following advantages: (1) Under the condition of meeting specific constraint conditions of various composite materials, quickly finding an improved solution; (2) Because of its own complexity, composite lay-ups involve many design constraints that the MFD can handle well, looking for reasonable feasible directions; (3) The composite material layering optimization relates to nonlinear material and structural response, and the MFD can better solve the nonlinear optimization problem; (4) The MFD can be calculated in parallel, so that the calculation efficiency can be greatly improved, and the method is particularly important for the high-dimensional problem in the composite material layering optimization.

In order to improve the optimization efficiency, the invention improves the existing MFD, and modifies partial constraint conditions aiming at the characteristics of the composite material, so that the MFD is more suitable for optimizing the composite material. The following is a mathematical description of the MFD of the viable orientation method of the present invention in composite wing structure ply-combining optimization:

let f (x) be the objective function, in the present invention to minimize the wing structural mass, Is a vector of design variables, the constraint is divided into the equality constraint h _j (x) =0, j=1, m, i.e. there are m equality constraints, and the inequality constraint g _i (x) is less than or equal to 0, i=1, p, i.e. there are p inequality constraints.

In a viable direction method MFD, the solution is iteratively updated, each iteration comprising the steps of:

(1) Determining a feasible direction: let d be one feasible direction at the current point x (k), the gradient direction satisfying all inequality constraints: make/> for all i ; And gradient direction satisfying all the equality constraints: let/>, for all jWhere x (k) refers to the kth design variable in the design variable vector x.

(2) Reducing the objective function: d is chosen such that the gradient of the objective function in this direction is negative, i.e。

(3) Selecting step length: one step λ >0 is chosen such that x (k+1) =x (k) +λd is viable under all constraints, and f (x ^(k+1))<f(x^(k)).

(4) Updating solution: setting the newly obtained x ^(k+1) as the current solution;

(5) Convergence judgment, namely stopping iteration and taking x ^(k+1) as an optimal solution if x (k+1) meets a specified convergence criterion, such as the improvement of the solution is lower than a specific threshold value or the maximum iteration number is reached; otherwise, let k=k+1 and go back to step (1) to repeat the iteration.

The improved viable direction method MFD employed by the present invention continuously reduces the value of the objective function while ensuring the feasibility of the solution in each iteration by finding the appropriate direction and advancing on the limits of the constraint.

As shown in FIG. 3, the composite material ply combination optimization comprises ply shape optimization, ply shape cutting, ply thickness optimization and ply sequence optimization in sequence.

Ply shape optimization aims to determine the shape of a ply in all directions, including:

(1) Setting the layering angles of each unit of the wing box structure, wherein the initial thickness of layering at different angles is equal; the angle of the paving layer comprises 45 degrees, 90 degrees, 45 degrees and 0 degrees, and the initial thickness of the 4 paving layers is equal, so that the number of the paving layers can be greatly reduced, and the influence of factors such as the angle, the sequence and the thickness of the paving layers on the optimization result of the paving layer shape can be greatly reduced;

(2) In addition to these design constraints, such as strength, stiffness, stability and weight of the wing box structure, manufacturing constraints in terms of production process must also be considered, so that the optimization results are workable, imposing non-mandatory manufacturing constraints in the conceptual design stage of the ply shape optimization; to improve the optimization efficiency, the influence of the layering sequence is ignored at this stage;

(3) In the optimization process, the thickness of each unit of the composite material laminated plate is taken as a design variable, the weight of the wing box structure is taken as an optimization target, and the optimal thickness distribution of the laminated plate meeting design constraint and optional manufacturing constraint is searched;

(4) Adopting an optimization algorithm of an MFD (MFD) method to optimize the layering shape of the composite material for the skin and the spar of the wing box structure;

(5) In order to better present the optimization result, the invention sets a threshold value, and if the thickness of a certain unit of the laminated board is smaller than the threshold value, the unit is directly abandoned; if the thickness of a certain unit of the laminated plate is greater than or equal to the threshold value, the unit is completely reserved; the threshold is 0.05 to 0.2 times the thickness of a single manufacturable ply, typically 0.1 times the thickness of a single manufacturable ply.

The mathematical model of the ply shape optimization problem is expressed as:

Design variable: thickness of each unit of laminated plate

Optimization target: minimizing the weight of the wing box structure

Constraint conditions:

In the method, in the process of the invention, For the thickness of the kth unit of the ith laminate,Is the minimum value of the thickness of the kth unit of the ith laminated plate,Maximum value of thickness of kth unit of ith laminated plate,For the number of laminated boards,To design the total number of area laminate units, wherein、All have preset values.

The shape of the layer is cut. The shape of the layer obtained after the optimization of the layer shape is irregular, and has a plurality of discontinuous areas and independent areas, which bring additional cost to the manufacturing process, so that each layer needs to be analyzed and cut, the shape of each layer finally keeps the same as possible with the optimization result, the process requirements of actual manufacturing are met, the layer shape which can be actually processed is obtained, and preparation is made for the next layer thickness optimization.

And optimizing the thickness of the layer. Because the mat shape obtained after the mat shape optimization and the mat shape cutting are the shape and thickness of the mat overall (i.e., the laminate) which can be actually processed, no specific design is made for the thickness of each mat, the purpose of the mat thickness optimization is to determine the specific thickness of each angle and each shape mat, and the mats with different thicknesses, which are obtained by cutting the mat shape, are scattered into mats with the thickness conforming to the manufacturing constraint according to the design constraint and the manufacturing constraint of the load response. The specific process of optimizing the ply thickness is described as follows:

(1) Building a general stacking model of the composite material, wherein a tensile stiffness matrix A, a coupling stiffness matrix B and a bending stiffness matrix D can be calculated as follows:

（11）

z _k is the distance between the middle plate of the laminate and the side of the kth layer remote from the middle plate, i, j representing the rows and columns respectively of the stiffness matrix Q of 6*6, Is a simplified stiffness matrix of 6*6 after transformation.

In the composite mechanics, Q represents the stiffness matrix of a single layer laminate (in engineering, a single layer laminate refers to a laminate with only one ply laid up), whileRepresenting a matrix of stiffness of the single ply laminate after ply angle conversion, the difference between the two matrices being that the stiffness they each represent is relative to a different frame of reference. Q is represented as follows:

（12）

Wherein E and G are engineering constants of the material, E ₁₁ is the elastic modulus in the fiber direction, and E ₂₂ is the elastic modulus in the transverse direction; v represents the main poisson's ratio of the material, v ₁₂ is the main poisson's ratio of the particular material type; g ₁₂ represents the shear modulus of the ply.

The stiffness matrix Q of the single-layer plate is 3*3 matrix, andThe stiffness matrix of the single-layer laminated board subjected to ply angle transformation is a 6*6 matrix, Q is a 6*6 matrix, and the main direction of the fiber ply of Q is the same as the direction of the coordinate axis x, so that the fact that the inside is better than 0 is simplified to 3*3. But the main direction of the fiber layer of the layer subjected to layer angle transformation forms an included angle theta with the direction of the coordinate axis x (theta is the angle of the layer), soNot simplified, or 6*6 before.

The elements of (2) are calculated as follows:

（13）

Where θ is the angle of the layup.

(2) Design constraints and manufacturing constraints can be accurately formulated in the design space through the universal stacking model, and the design constraints in the layering thickness optimization stage comprise layering strain, stress and wing box wing tip displacement; manufacturing constraints include upper and lower limits on the total thickness of the laminate, upper and lower limits on the percentage of the total thickness of the laminate that are made up of the total thickness of the laminate for the same angle, and equal ply thicknesses for the two angles of 45.

(3) Continuous optimization of the thickness is performed, wherein the design variable is the thickness of each layer in the laminated plate, and the stacking sequence and the stacking direction are kept unchanged (same as the initial design), the optimization target is to minimize the weight of the wing box, and the objective function of the optimization target can be expressed asWhere ρi is the density of the i-th layer material, ai is the area of the i-th layer layup, x= [ x1, x2,., xi ] is the thickness of the i-th layer layup. The invention adopts the MFD method of the feasible direction method to optimize, and the obtained ply thickness optimization result is shown as 'ply thickness optimization' in figure 3, and the optimization result is the optimal continuous thickness distribution of idealization;

(4) The optimal continuous thickness distribution, which is idealized as a result of the optimization, cannot be used directly because in actual manufacture the composite is not just four layers of this thickness, and these thicknesses are all idealized, dividing it into a number of manufacturable monolayers of the same thickness, a process called discretization; and these thicknesses are generally not possible to be integer multiples of the manufacturable monolayer thickness, involving a process like rounding, they must be discretized into a ply that meets manufacturing constraints.

The ply thickness needs to be discretized for a continuous thickness, with a known value for the minimum manufacturable monolayer thickness, so that the total thickness of four differently oriented plies can be "rounded" to a near integer number of layers. In order to ensure that the discretized design meets the strength constraint, the buckling and strength constraints need to be considered seriously, the discretization method in the invention is as follows:

Assuming that the total number of consecutive layers of unidirectional ply is represented by v _θ (the ply thickness divided by the thickness of the manufacturable monolayer, the resulting value is generally not an integer), the total number of discrete layers of unidirectional ply in an actual structure is represented by n _θ, where the index Representing different ply directions, in the present inventionThe individual thicknesses can be rounded according to the following conditions: /(I)

If it isThenOtherwiseWherein。

L corresponds to the fractional part of v _θ, and when the fractional part exceeds l, the number of layers corresponding to n _θ is rounded up, which is advantageous in that the discretization method can apply the constraint more directly. If the number of plies of + -45 deg. in the present invention must be equal, it may be set,，θ₁=45°,θ₂=-45°。

Because the overall performance of the composite laminated board structure changes along with the change of the layering sequence of the composite laminated board structure, the layering sequence of the layering needs to be optimized according to the designable characteristic of the composite material, so that the layering sequence meets the layering rules of the composite material, and meanwhile, the performance of the laminated board is kept unchanged or even improved as much as possible.

The layering sequence is the last step of composite material layering combination optimization, the layering thickness and the layering direction at the stage and the layering sequence in the same direction are kept unchanged, and only the layering sequence is changed. After the layering sequence is optimized, the layering sequence of the layering can be ensured to meet the layering rules and manufacturing constraints of the composite material, and meanwhile, the overall performance of the laminated board is kept unchanged or even improved as much as possible. More manufacturing constraints need to be considered in ply sequence optimization, and all design responses and ply thickness optimization stages in this stage of optimization are the same. The ply sequence optimization is performed with all objective functions, design responses, and optional manufacturing constraints unchanged and with more detailed manufacturing constraints imposed.

Ply sequence optimization aims to solve the problem of searching discrete and nonlinear spaces, and the MFD can well solve the problem by using the improved feasible direction method. The specific layering sequence optimization process comprises the following steps:

(1) Taking the stacking sequence of all the layers as a design variable, taking the weight minimization of the wing box as an optimization target, and fully considering design constraint and manufacturing constraint;

(2) Performing layering sequence optimization of composite materials on the skin and the spar of the wing box structure by adopting a feasible-direction MFD optimization algorithm;

design constraints include ply strain, stress, and wing box tip displacement; manufacturing constraints include the maximum number of consecutive ply at the same angle, the ply angle of the outermost ply must be a set of + -45 deg. plies, the upper and lower limits of the total thickness of the laminate, the upper and lower limits of the total thickness of the ply at the same angle as a percentage of the total thickness of the laminate, and the ply thicknesses at the two angles + -45 deg. must be equal.

The technical scheme and the technical effect of the shield machine fault monitoring and diagnosing method and the system based on cloud edge cooperation are described in a specific embodiment.

Taking a wing of a 40 kg-class tilting ducted fan aircraft as an example, firstly defining the thickness and material properties of each part of the wing, and using carbon fiber composite materials as the parts.

The conceptual design stage aims to obtain the optimal primary structure of the wing of the 40 kg-class tilting ducted fan aircraft, and aims to optimize the structure weight of the minimized wing in a flat flight mode and a vertical take-off and landing mode. The design variables mainly include: parameters variables of wing geometry such as span, airfoil, root chord length, root tip ratio, presentation ratio, dihedral angle, backswept angle (toe backswept angle and toe backswept angle), stagger angle, etc.; the positions of the first main beam and the second main beam on the chord, the distribution of the ribs along the chord, and the like; rib, spar, rib and skin shapes and geometries, etc. The strength, rigidity, flutter and the like of the wing structure of the downtilt ducted fan aircraft in different flight modes (vertical take-off and landing, transitional flight, horizontal flight, hovering and the like) are design constraint conditions.

Then, establishing a pneumatic model, and analyzing the pneumatic characteristics of the wing under different flight conditions; and simultaneously, building a structural model and evaluating the structural response of the wing. The coupling between the pneumatic load and the structural response is achieved, ensuring that the change in the pneumatic load can be reflected in the structural response and vice versa. And constructing a Lagrangian function of the coupling model, bringing corresponding Lagrangian multipliers according to constraint information (such as displacement, strain, stress, vibration and the like in different flight modes) of the wing structure, converting an original constraint optimization problem into an unconstrained optimization problem by the Lagrangian function, and providing a unified framework to guide the optimization process of the wing structure. The method comprises the steps of establishing an accompanying equation, solving to obtain the gradient of an objective function relative to a design variable, analyzing and evaluating the gradient by adopting an accompanying gradient-based design optimization method, obtaining the gradient of each constraint condition relative to the design variable by solving to obtain the gradient of the objective function relative to the design variable, and finally updating the numerical value of the design variable by using the calculated gradient of the design variable to perform optimization iteration. After each iteration, the coupling analysis is performed again, updating the aerodynamic and structural models. And finally, evaluating the optimized wing structure, and verifying whether the design requirement and the performance index are met or not until the design requirement and the performance index are met.

According to the wing preliminary structure scheme obtained in the conceptual design stage, a model is obtained by three-dimensional modeling, and the tilting duct fan aircraft wing structure in the embodiment mainly comprises composite material laminated plates and belongs to a plate-shell structure, so that a quadrilateral two-dimensional grid (CQUAD) is used for modeling a skin, a wing spar and a wing rib structure, and a finite element model of a wing box structure is formed. As shown in fig. 4 and 5, the finite element model of the wing box structure (skin and spar) has 5345 shell elements in total, and then the model is given composite material properties including material properties, layup information, element orientation, etc.

The load is applied to the finite element model of the wing, and the load application conditions in two flight modes are as follows: (1) Under the loading condition of the wings at the multi-rotor stage, the tilting ducted fan aircraft completes vertical take-off and landing and hovering actions by virtue of lifting force provided by four ducted devices, the total lifting force generated by 4 ducts is 100kg, and according to the overall design, the maximum bearable wind speed of the aircraft is 16m/s; taking the maximum usage overload coefficient of 3.0 and the minimum usage overload coefficient of-1.0 of the multi-rotor state of the aircraft according to the airworthiness regulation of a normal-class rotor aircraft; as shown in fig. 6, the root of the main girder is completely fixed, and structural gravity and concentrated force generated by the duct are applied, wherein the force acts on the wing tip and is vertically upwards; (2) The fixed wing stage is under load, as shown in fig. 7, and the fixed wing stage generates lift force by the wing, so that the focus is on aerodynamic load, and according to the calculation specified by relevant regulations in airworthiness regulations of normal, practical, special effect and commute airworthiness regulations, the maximum using maneuvering load of the aircraft is 3.8, the minimum using overload coefficient is-1.9, and the forward concentrated pulling force provided by tilting the duct at the wing tip is carried out.

When the shape of the layer is optimized, the layer forms of all components of the wing structure are [45 DEG, 90 DEG, -45 DEG and 0 DEG ] firstly, the initial thicknesses of the 4 layers are equal, the initial thickness of the upper skin and the lower skin is set to be 1mm, the initial thickness of the first main girder and the second main girder is set to be 2mm, the initial thickness of the rear wall is set to be 1.6mm, and the initial thickness of the wing rib is set to be 1mm. Global response to structure weight, strain, etc. is optimized and constrained while the minimum manufacturable monolayer thickness is set to 0.1mm. And (3) taking the thickness of each unit of the composite material laminated plate as a design variable, and searching the optimal thickness distribution of the laminated plate meeting the constraint condition by using a structural quality objective function. In order to better present the optimization result, a threshold value of 0.01mm (one tenth of the thickness of a single manufacturable ply) is set, and if a cell thickness is less than the threshold value, the cell is directly discarded; otherwise, the unit is completely reserved.

The weight of the wing box after the optimization of the shape of the layer is greatly reduced, as shown in fig. 8, the shape of the layer converges after 113 iterations, the weight of the wing box after the optimization of the shape of the layer is 0.498kg, the initial design weight is 1.34kg, and the weight is reduced by 62.8%. The weight of the wing box after the optimization of the thickness of the layer is also changed, as shown in fig. 9, the wing box after the optimization of the thickness of the layer converges after 7 iterations, the weight of the wing box after the optimization of the thickness of the layer is 0.729kg, the initial design weight is 0.498kg (mass after the optimization of the shape of the layer), and the weight is increased by 0.231kg, because the proportion of the shape of the layer group which can improve the strength of the laminated plate in the process of the optimization of the thickness is slightly improved, and the mass after the optimization of the thickness is further increased. The layer shape cutting stage is to cut each layer without changing the weight of the wing box, and the layer sequence optimizing stage only changes the sequence of the layers without changing the quality of the wing box. From the perspective of the whole layering combination optimization, the initial total weight of the wing box is 1.34kg, the weight of the wing box is reduced to 0.729kg after the layering combination optimization is carried out on the wing box by taking the skin and the spar as research objects, the weight is reduced by 45.6%, and the weight reduction effect is obvious.

The resulting composite lay-up thickness profile cloud of the skin and spar of the wing box is shown in figures 10, 11, where the maximum thickness is 2mm and the minimum thickness is 0.4mm, compared to the wing tip region, which is the thickest because the material of the wing root region needs to withstand more load, and the thinnest.

In order to verify the performance of the wing structure of the tilting ducted fan aircraft finally optimized in the invention, the displacement, strain, stress and other analysis results of the wing structure of the tilting ducted fan aircraft under the flat flight mode and the vertical take-off and landing mode after the layering combination optimization are respectively analyzed, wherein the displacement, strain, stress and other analysis results of the wing of the tilting ducted fan aircraft under the flat flight mode are respectively shown in fig. 12-14, and the maximum displacement of a wing box is 12.24mm at the wing tip under the flat flight mode of the fixed wing stage; the maximum strain of the wing box is 2587 mu epsilon at the wing root; the maximum stress is 405.3MPa at the wing root. In the multi-rotor stage vertical take-off and landing mode, the analysis results of displacement, strain, stress and the like of the wing of the tilting ducted fan aircraft are respectively shown in fig. 15-17, and the maximum displacement of the wing box is 18.12mm at the wing tip; the maximum strain is 2478 mu epsilon at the wing root; the maximum stress is also at the wing root and is 388.2MPa.

The ultimate properties of the carbon fiber composite material adopted in the embodiment of the invention are as follows: longitudinal tensile strength 1548MPa, longitudinal compressive strength 1226MPa, transverse tensile strength 55.5MPa, transverse compressive strength 218MPa and in-plane shear strength 89.9MPa. According to the design experience of the composite wing box structure, the strain of the wing box structure is not allowed to exceed 3000 mu epsilon, the maximum stress of the wing box structure is not exceeded 450MPa, and the maximum displacement of the wing tip is not exceeded 5% of the wing span (namely 25 mm), so that the performance of the wing of the tilting duct fan aircraft meets the design requirement.

Therefore, the weight of the tilting duct fan aircraft wing is reduced by 45.6% through layering combination optimization on the premise that the original bearing level of the tilting duct fan aircraft wing is unchanged and the displacement, strain and stress of the wing in a flat flight mode and a vertical take-off and landing mode meet design requirements.

In summary, the present invention provides a wing of a tilting ducted fan aircraft with a dual-girder structure, which can provide sufficient strength and rigidity to adapt to the requirements of different flight modes of the tilting ducted fan aircraft; according to the invention, the aerodynamic model and the structural model are coupled, and the optimal preliminary structure of the wing is obtained by utilizing the accompanying gradient optimization method, so that the optimized fidelity is greatly improved; the MFD is adopted to perform layering combination optimization on the tilting duct fan aircraft wing, so that the composite material has manufacturing feasibility.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.

The above detailed description is intended to illustrate the present invention by way of example only and not to limit the invention to the particular embodiments disclosed, but to limit the invention to the precise embodiments disclosed, and any modifications, equivalents, improvements, etc. that fall within the spirit and scope of the invention as defined by the appended claims.

Claims

1. A structural design optimization method for a tilting ducted aircraft wing, the method comprising:

According to the finite element model, setting a second optimization target to minimize the weight of the wing box structure, wherein the second constraint comprises a layering design constraint and a layering manufacturing constraint, and performing composite material layering combination optimization on the skin and the spar of the wing box structure by adopting a feasible direction method to obtain a second optimal structure of the wing of the tilting duct fan aircraft;

2. The method according to claim 1, wherein S1 comprises:

S13: building structural model of tilting duct fan aircraft wing

s14: establishing a coupling model of a pneumatic model and a structural model

S15: lagrangian function for constructing coupling model

s16: obtaining the optimal solution of the Lagrangian function through the accompanying equation

wherein S12 and S13 are performed synchronously.

3. The method of claim 2, wherein the NS equation is expressed as follows:

Where ρ is the flow field density, U= [ U, v, w ] is the flow field velocity vector, U, k, w are the velocities in the x, y, z directions, respectively, p is the flow field pressure, E is the total energy of the flow field, q is the flow field heat flux, τ is the flow field viscous stress tensor, τ is U, the turbulent flow molecular viscosity And turbulent viscosityIs a function of (a) and (b),

The SA turbulence equation is expressed as follows:

Where σ is the Prandtl number, which is used to represent the diffusion of turbulent viscosity, C _b2、C_b1、C_w1 is the model constant, which is obtained by fitting experimental data, As a function of strain rate, is a composite, taking into account local shear and rotation effects, f _w is a function calculated from wall distance d for correcting turbulence viscosity near the wall, v is kinematic viscosity, is corrected kinematic viscosity,Related to the turbulent kinematic viscosity v _t,；

Viscosity by turbulent flowAnd (3) connecting an NS equation and an SA turbulence equation, wherein the NS equation and the SA turbulence equation form an aerodynamic model of the wing of the tilting ducted fan aircraft.

4. The method according to claim 1, wherein the displacement data is a displacement amount of the wing structure after being loaded, the displacement data is provided by the structural model, and the displacement data includes a displacement vector of each point of the wing structure, a new shape of each part of the wing structure after being deformed, and a displacement amount of key points and the whole of the wing structure;

the load data are forces and moments acting on the wing structure, the load data are provided by the aerodynamic model, the load data comprise positive pressure and negative pressure distribution of fluid applied to the solid surface, tangential force distribution of the fluid generated on the solid surface and total lift force, resistance and pitching moment obtained by integrating the pressure and shear force distribution;

Transmitting the load data generated by the pneumatic model analysis to the structural model, wherein the structural model calculates a structural response by using the load data, and the structural response comprises displacement data; and feeding back the displacement data generated by the structural model analysis to the pneumatic model, wherein the pneumatic model updates flow field information and recalculates load data by using the displacement data.

5. The method of claim 1, wherein the S15 and the S16 comprise:

S15: and (3) banding the first design constraint of the wing structure into a corresponding Lagrange multiplier, and converting an original band design constraint optimization problem into an unconstrained optimization problem by using a Lagrange function, wherein the Lagrange function is expressed as follows:

Wherein λ ₁,λ₂,...,λ_m is a lagrange multiplier, m refers to the number of first design constraints, x is an optimization variable vector, i.e., a first design variable, λ= [ λ ₁,λ₂,...,λ_m ] is a lagrange multiplier vector, and f (x) is an objective function of the wing structure, i.e., an objective function of a first optimization objective; g _i (x) is a constraint function of the ith first design constraint;

S16: the first optimization objective is converted to a minimized lagrangian function minimize L (x, λ), which is graded by a concomitant equation, expressed as follows:

Obtaining the gradient/>, with respect to the first design variable x, of each constraint g _i (x) by solving ; Thereby obtaining the gradient/>, of the objective function f (x) with respect to the first design variable x; Updating the value of the first design variable by using the gradient of the first design variable obtained through calculation, so that the iteration of the next round is continued, and finally, the optimal solution of the Lagrangian function is obtained: the optimal first design variables x and λ, and hence the first optimal configuration of the tilting ducted fan aircraft wing, are obtained.

6. The method of claim 1, wherein the ply shape optimization comprises:

(1) Setting the layering angles of each unit of the wing box structure, wherein the initial thickness of layering at different angles is equal; the ply angle comprises 45 degrees, 90 degrees, 45 degrees and 0 degrees, and the initial thicknesses of the 4 plies are equal;

(2) Setting design constraints and optional manufacturing constraints; the design constraints include strength, stiffness, stability, and weight of the wing box structure, the optional manufacturing constraints include ply sequence adjustability, ply asymmetry, and minimum ply thickness;

(3) Taking the thickness of each unit of the composite material laminated plate as a design variable and taking the weight of the wing box structure as an optimization target, searching the optimal thickness distribution of the laminated plate meeting the design constraint and the optional manufacturing constraint;

(5) Setting a threshold value, and directly discarding a certain unit of the laminated board if the thickness of the unit is smaller than the threshold value; if the thickness of a certain unit of the laminated plate is larger than or equal to the threshold value, the unit is completely reserved; the threshold is 0.05-0.2 times the thickness of a single manufacturable ply.

7. The method of claim 1, wherein the ply thickness optimization comprises:

(1) Building a general stacking model of the composite material;

(2) Design constraints and manufacturing constraints for setting ply thickness optimization stage

The design constraints include ply strain, stress, and wing box tip displacement; the manufacturing constraint comprises the upper limit and the lower limit of the total thickness of the laminated plate, the upper limit and the lower limit of the total thickness of the laminated plate in percentage of the total thickness of the laminated plate in the same angle, and the thickness of the laminated plate in the two angles of +/-45 degrees are required to be equal;

(3) Continuous optimization of thickness

Setting design variables as the thickness of each layer in the laminated board, keeping the stacking sequence and direction of the layers unchanged, and optimizing the aim to minimize the weight of the wing box;

(4) Optimizing by a feasible direction method to obtain an idealized optimal continuous thickness distribution of the ply thickness optimization;

(5) The idealized optimal continuous thickness profile is discretized into a layup conforming to a manufacturing constraint thickness.

8. The method of claim 7, wherein the discretizing the idealized optimal continuous thickness profile into a layup that conforms to a manufacturing constraint thickness comprises:

(1) Assuming that the total number of consecutive plies in a single direction is denoted by v _θ, v _θ denotes the number of plies divided by the thickness of the manufacturable monolayer, the number is not always an integer;

(2) The total number of discrete layers of the unidirectional ply in the actual structure is represented by n _θ, where the index Representing different ply directions, in the present invention；

(3) The individual thicknesses were rounded according to the following conditions:

If it is Then; Otherwise；

Wherein the method comprises the steps ofL corresponds to the fractional part of vθ and when the fractional part exceeds l, the number of layers corresponding to n _θ is rounded up.

9. A structural design optimization system for a tilting ducted aircraft wing, wherein the system is capable of implementing the method of any one of claims 1-8, the system comprising:

10. A server comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized by: the processor, when executing the computer program, implements the steps of the method according to any one of claims 1-8.