CN118194447B - A method and system for optimizing the structural design of a tilt-ducted aircraft wing - Google Patents

Abstract

Aiming at the structural design of the wing of a tilt-ducted fan aircraft, the present invention proposes a wing with a double main beam structure, couples the aerodynamic model and the structural model, adopts the accompanying gradient optimization method to perform preliminary optimization of the wing structure, and adopts the feasible direction method (MFD) to sequentially optimize the ply shape, ply shape tailoring, and ply thickness of the composite material on the basis of fully considering the manufacturability in actual production, and actively optimizes the ply sequence. The various technical features of the present invention support each other in function and interact with each other. On the whole, the weight of the tilt-ducted fan aircraft wing of the present invention is reduced by 45.6% after ply combination optimization, under the premise that the original load-bearing level remains unchanged, and the displacement, strain and stress of the wing in the level flight mode and the vertical take-off and landing mode meet the design requirements.

Description

A method and system for optimizing the structural design of a tilt-ducted aircraft wing

Technical Field

The present invention relates to the technical field of wing structure design, and in particular to a structure design optimization method and system applied to a wing of a tilt-ducted aircraft.

Background technique

Tilt-Duct fan aircraft, also known as tilt-ducted aircraft, is an important branch of vertical take-off and landing aircraft. The characteristic of this aircraft is that the ducted fan in its propulsion system can be tilted to achieve the conversion between the two flight modes of the fixed-wing stage level flight mode and the multi-rotor stage vertical take-off and landing mode. It has both the vertical take-off and landing capabilities of rotorcraft and the high-speed cruising capabilities of fixed-wing aircraft. The tilt-ducted fan device can be installed in different positions of the aircraft, such as the fuselage, wings, tail, etc. The tilt-ducted fan device is installed on the wing, which can minimize the impact of the ducted fan device wake on the wing, tail and other lifting surfaces. At the same time, this brings more challenges to the design of the wing of the tilt-ducted fan aircraft. More technical and functional requirements need to be considered during the design. Its wing mainly bears aerodynamic loads in the fixed-wing stage level flight mode, and mainly bears the upward thrust load provided by the wingtip duct in the multi-rotor stage vertical take-off and landing mode. In addition, internal equipment (such as servos and tilt devices) need to be installed in the limited internal space of the wing. This requires a highly integrated structural design to rationally arrange the installation of the internal equipment of the wing while meeting the specified strength and stiffness requirements with the minimum wing structure weight.

For tilt-tufted fan aircraft, the weight of the aircraft has a great impact on its performance. The lightweight structure means that under the same engine power, the aircraft can achieve a higher climb rate, longer range and better maneuverability. At the same time, the lightweight structure also helps to reduce the fuel consumption of the aircraft, reduce operating costs and improve economy. As a key component of the tilt-tufted fan aircraft, it is also crucial to reduce its weight during design. The wing needs to bear various loads from the ducted fan, engine and during flight. If the wing is too heavy, it will also affect the flight quality and safety of the aircraft. Therefore, during the design and manufacturing process, it is necessary to pursue the lightweight design of the wing as much as possible on the basis of satisfying the constraints such as the structural strength, stiffness and stability of the wing to ensure that it can maintain good performance under various flight conditions.

In the vertical take-off and landing stage, the tilt-ducted fan installed on the wing is the main component of the aircraft to generate lift; in the horizontal flight stage, the wing is the main component of the aircraft to generate lift, and the aerodynamic performance of the wing directly determines the flight performance of the aircraft. In different flight modes such as vertical take-off and landing and horizontal flight, the wing of the tilt-ducted fan aircraft needs to bear various complex loads. In the wing design, it is necessary to adopt a reasonable structural layout and material selection to improve the strength and stiffness of the wing. In addition, the wing of the tilt-ducted fan aircraft needs to tilt between vertical take-off and landing and horizontal flight. The design of the wing needs to consider how to realize this tilting mechanism and ensure the structural stability and safety of the wing during the tilting process. Through reasonable aerodynamic layout and structural design of the wing, the performance of the aircraft in terms of flight performance, structural strength and stiffness, maneuverability, maintenance and manufacturing costs can be improved, thereby ensuring that the aircraft can operate safely, reliably and efficiently.

As a high-performance aircraft, the tilt-ducted fan aircraft has far more design variables and constraints in its analysis and optimization process than traditional fixed-wing aircraft or multi-rotor aircraft. Its aviation structure is made of high-performance materials (composite materials), so it is necessary to consider many design variables such as the geometry and size of its structure and the manufacturing details of the composite materials during design. The widely used non-gradient optimization method has been successfully applied to the structural design problems of aircraft. The application difficulty of this method is low and the principle is simple, but the design variables involved in its application are limited. With the expansion of the dimension of the design space, the number of design variables has increased sharply, and the non-gradient optimization method cannot efficiently and accurately solve the optimization problem of large-scale design variables. In order to deal with the structural design problems with large-scale design variables and constraints, it is necessary to find an efficient gradient optimization method.

In summary, the existing wing design of tilt-ducted fan aircraft has the following problems:

(1) The existing wing design of tilt-ducted fan aircraft is mainly based on the fixed-wing wing structure. However, the existing fixed-wing aircraft wing configuration and related structural design are only aimed at aerodynamic loads. The design of the tilt-ducted fan aircraft wing needs to consider a series of technical functional requirements such as structural layout to accommodate more internal equipment, complex loading conditions under various flight modes (not only considering aerodynamic loads), lightweight, and manufacturing feasibility. Therefore, the existing fixed-wing aircraft wing configuration and related structural design methods are not suitable for the design of tilt-ducted fan aircraft wings.

(2) The existing wing structure optimization method of tilt-ducted fan aircraft is only optimized in the context of structural disciplines, without considering the impact of actual aerodynamic loads. It only uses empirical formulas to simulate actual aerodynamic loads. This aerodynamic loading method based on empirical formulas cannot accurately predict the aerodynamic performance of the wing, such as lift, drag, and lift-to-drag ratio, under different flight modes, which in turn reduces the fidelity of the optimization.

(3) Existing aircraft wing structure optimization methods use gradient-based optimization methods, but have problems with long calculation time and low accuracy when evaluating the gradient required for optimization. Existing aircraft wing structure gradient optimization methods require the derivation of the entire objective function in each iteration, which results in a very large amount of calculation and requires a lot of calculation time. Long gradient calculation time will limit the number of optimization iterations; existing aircraft wing structure gradient optimization methods only focus on the gradient information of the current point, without considering the global structure of the entire design space, resulting in lower accuracy. Lower accuracy will reduce the convergence tolerance of the optimization problem. For large-scale aircraft wing structure design problems with a large number of design variables and constraints, the calculation time required for the existing gradient optimization method to calculate the gradient exceeds the calculation time required for analysis, becoming a bottleneck affecting the optimization of aircraft wing structures.

(4) The existing wing design of tilt-rotor ducted fan aircraft mainly adopts alloys, while composite materials have excellent mechanical properties and low density. The use of composite materials can effectively reduce the weight of the wing. By optimizing the composite components, the weight can be further reduced. However, the existing wing design of tilt-rotor ducted fan aircraft rarely uses composite materials, and the application threshold of composite materials is higher than that of metal materials. More design constraints and manufacturing constraints need to be fully considered, which hinders the application of composite materials in the wings of tilt-rotor ducted fan aircraft.

Summary of the invention

The design optimization method of the tilt-ducted fan aircraft wing in the prior art does not comprehensively consider the influence of the structure and aerodynamic loads, the gradient optimization method is not suitable for structural optimization, and the design difficulty of composite materials is high and the manufacturing is not feasible. The present invention provides a tilt-ducted fan aircraft wing with a double-main-beam structure, couples the aerodynamic model and the structural model, and uses the accompanying gradient optimization method to obtain the optimal preliminary structure of the wing, and uses the feasible direction method MFD to optimize the ply combination of the tilt-ducted fan aircraft wing. The double-main-beam structure wing proposed by the present invention can not only provide sufficient strength and stiffness to meet the needs of different flight modes of the tilt-ducted fan aircraft, but also facilitates the installation of tilt-duct related mechanisms. In the design optimization, the interaction between the structure and aerodynamics of the wing is fully considered, and the accompanying gradient optimization method is used to efficiently and accurately solve the optimization problem of large-scale design variables and constraints for the preliminary optimization of the double-main-beam wing, and finally the feasible direction method MFD is used to optimize the ply combination of composite materials so that the composite materials have the feasibility of manufacturing.

In order to further understand the technical solution of the present invention, the terms involved in the present invention are defined as follows:

Lamination: Ply is the basic unit in composite material structure. Each layer is composed of specific materials (such as carbon fiber, glass fiber, etc.) and resin, and is stacked together through specific processes (such as lamination, hot pressing, etc.). The design and optimization of the ply is crucial to the overall performance of the composite structure and will affect the strength, stiffness, temperature resistance, corrosion resistance, etc. of the composite material.

Laminate: Laminate is a composite material board made of multiple layers of plies in different directions. The materials of the plies can be different or the same. Each layer has a specific fiber direction and material properties, and the plies are bonded together through a specific process.

The technical solution of the present invention is as follows: A structural design optimization method for a tilt-ducted aircraft wing, comprising:

S1: Obtaining the first optimal structure of the tilt-ducted fan aircraft wing

The invention discloses a method for obtaining a first design variable, a first optimization target and a first design constraint that affect a wing of a tilt-ducted fan aircraft; constructing a structural model and an aerodynamic model of the wing; coupling the aerodynamic model and the structural model through displacement data and load data; constructing a Lagrangian function of the coupling model and solving the coupling model through an adjoint gradient optimization method to obtain an optimization result; evaluating the optimization result to obtain a first optimal structure of the wing of the tilt-ducted fan aircraft;

S2: Generate a finite element model of the wing box structure of a tilt-ducted fan aircraft wing

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

S3: Obtaining the second best structure of the tilt-ducted fan aircraft wing

According to the finite element model, the second optimization goal is set to minimize the weight of the wing box structure, the second constraint includes the design constraint and the manufacturing constraint, and the composite layer combination optimization of the skin and the spar of the wing box structure is performed by using the feasible direction method to obtain the second optimal structure of the tilt-ducted fan aircraft wing;

The first design variable includes the positions of the first main beam and the second main beam on the chord, and the shapes and geometric dimensions of the spar, ribs and skin; the composite material layup optimization includes layup shape optimization, layup shape tailoring, layup thickness optimization and layup sequence optimization in sequence.

Further, obtaining a first optimal structure of a tilt-ducted fan aircraft wing includes:

S11: Determining a first design variable, a first optimization objective, and a first design constraint that affect a tilt-ducted fan aircraft wing

The first design variable refers to a parameter that affects the wing structure, including the optimal position of the first main beam and the second main beam, and the shape and geometric dimensions of the skin, ribs, and spar; the first optimization goal is the minimum wing structure weight; the first design constraint includes the strength, stiffness, and flutter requirements of the wing structure of the tilt-ducted fan aircraft under different flight modes;

S12: Using the NS equations and SA turbulence equations to establish an aerodynamic model of the tilting ducted fan aircraft wing

The NS equations and the SA turbulence equations are linked together through turbulent viscosity, and the NS equations and the SA turbulence equations constitute the aerodynamic model of the tilting ducted fan aircraft wing.

S13: Establishing a structural model of the tilt-ducted fan aircraft wing

Using three-dimensional modeling software to establish a three-dimensional structural model of a tilting ducted fan aircraft wing based on shell elements; meshing the three-dimensional structural model to form a finite element model of the wing structure, wherein the mesh is a quadrilateral mesh tending to a square;

S14: Establish a coupling model between aerodynamic model and structural model

The input variables of the aerodynamic model are set to include displacement data, and the output variables are set to include load data; the input variables of the structural model are set to include load data, and the output variables are set to include displacement data; and the aerodynamic model and the structural model are coupled through the displacement data and the load data;

S15: Constructing Lagrangian functions for coupled models

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

S16: Obtain the optimal solution of the Lagrangian function through the adjoint equation;

The first optimization objective is converted into minimizing the Lagrangian function; the gradient of the Lagrangian function is calculated through the adjoint equation; the gradient of each constraint condition with respect to the first design variable is obtained by solving, and then the gradient of the Lagrangian function with respect to the first design variable is minimized; the value of the first design variable is updated using the calculated gradient of the first design variable, so as to continue the next round of optimization iterations, and finally the optimal solution of the Lagrangian function is obtained, wherein the optimal solution of the Lagrangian function includes the optimal solution of the first design variable, and the optimal solution of the first design variable and the first design constraint constitute the first optimal structure of the wing of the tilt-ducted fan aircraft;

S17: Evaluating the first optimal configuration for a tilt-ducted fan aircraft wing

The first optimal structure is evaluated, and the evaluation includes evaluating the displacement, strain, stress, and vibration of the first optimal structure under different flight modes: if the first optimal structure meets the expected performance target, the first optimal structure is accepted as the optimal preliminary structural layout of the tilt-ducted fan aircraft wing; if it does not meet the target, return to step S12 to continue iterative optimization until the first optimal structure meets the design requirements and performance indicators;

Among them, S12 and S13 are performed simultaneously.

The present invention also provides a tilt-ducted aircraft wing structural design optimization system, which can implement the above-mentioned tilt-ducted aircraft wing structural design optimization method, and comprises:

The structural preliminary design module is used to obtain the first optimal structure of the wing of the tilt-ducted fan aircraft, set the first design variable, the first optimization target and the first design constraint that affect the wing of the tilt-ducted fan aircraft; construct the structural model and the aerodynamic model of the wing; couple the aerodynamic model and the structural model; construct the Lagrangian function of the coupling model and solve the coupling model by the adjoint gradient optimization method to obtain the optimization result; evaluate the optimization result to obtain the first optimal structure of the wing of the tilt-ducted fan aircraft;

A wing box structure generation model is used to generate a finite element model of a wing box structure of a tilting ducted fan aircraft wing according to the optimal preliminary structure;

A composite material layup optimization module is used to optimize the layup of the skin and spar of the wing box structure. According to the finite element model, the second optimization goal is set to minimize the weight of the wing box structure, and the second constraint includes a design constraint and a manufacturing constraint. The composite material layup combination optimization of the skin and spar of the wing box structure is performed using a feasible direction method to obtain a second optimal structure of the tilt-ducted fan aircraft wing.

The first design variable includes the positions of the first main beam and the second main beam on the chord, and the shapes and geometric dimensions of the spar, ribs and skin; the composite material layup optimization includes layup shape optimization, layup shape tailoring, layup thickness optimization and layup sequence optimization in sequence.

The present invention also discloses a server, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the above method when executing the computer program.

Compared with the prior art, the structural design optimization method and system for tilt-ducted aircraft wings provided by the present invention have the following beneficial effects:

(1) The present invention proposes a wing with a double main beam structure for a tilt-ducted fan aircraft. The structure uses two main beams to share the load, thereby increasing the bending and torsional stiffness of the wing. For a tilt-ducted fan aircraft that needs to switch between different flight modes, the wing with a double main beam structure can provide sufficient strength and stiffness to adapt to the requirements of these different flight modes, which is crucial to the stability and reliability of the wing and the aircraft. Moreover, the wing with a double main beam structure of the present invention allows designers to have more choices in the internal layout of the wing, and the equipment can be installed between the two main beams without affecting the overall mechanical properties of the wing structure. In addition, the wing will experience multiple load cycles during flight. The wing with a double main beam structure of the present invention can better disperse stress, thereby improving fatigue resistance. In extreme cases, if one main beam is damaged, the other main beam can still provide the necessary support, thereby increasing the safety of the aircraft.

(2) The present invention couples the aerodynamic model and the structural model through displacement data and load data when obtaining the first optimal structure of the wing of the tilt-ducted fan aircraft, fully considering the interaction between the structural deformation of the wing and the aerodynamic load in actual flight, and improving the flight performance, structural strength and stiffness of the tilt-ducted fan aircraft through reasonable aerodynamic layout and structural design of the wing.

(3) The present invention adopts the adjoint gradient optimization method to perform preliminary optimization on the wing structure of a dual-girder tilt-ducted fan aircraft, and obtains the lightest wing structure while ensuring the requirements of geometric constraints and mechanical constraints. Compared with traditional optimization methods, the wing structure optimization method of the present invention can efficiently and accurately solve the optimization problems of large-scale design variables and constraints. The introduction of aerodynamic and structural coupling technology greatly improves the fidelity of optimization.

(4) The present invention adopts the feasible direction method MFD when optimizing the ply combination of the tilt-ducted fan aircraft wing. On the basis of fully considering the manufacturability in actual production, the composite material ply combination optimization (ply shape, thickness, and sequence optimization) is carried out, thereby better exerting the load-bearing capacity of the composite material, reducing the structural weight of the wing, and overcoming the problem that the composite material design in the existing tilt-ducted fan aircraft wing cannot meet the manufacturing requirements.

(5) The present invention proposes a double-main-beam wing structure for the structural design of the wing of a tilt-ducted fan aircraft, couples the aerodynamic model and the structural model, adopts the accompanying gradient optimization method to perform preliminary optimization of the wing structure, and uses the feasible direction method (MFD) to perform ply combination optimization on the wing. The various technical features of the present invention support each other in function and interact with each other. On the whole, the weight of the wing of the tilt-ducted fan aircraft of the present invention is reduced by 45.6% through ply combination optimization, provided that the original load-bearing level remains unchanged and the displacement, strain and stress of the wing in the level flight mode and the vertical take-off and landing mode meet the design requirements.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG1 is a schematic structural diagram of a double-main-beam wing proposed in the present invention.

FIG. 2 is a schematic flow chart of the wing structure design optimization method proposed in the present invention.

FIG3 is a schematic diagram of the process flow of composite material ply combination optimization proposed by the present invention.

FIG. 4 is a schematic diagram of the skin of the finite element model of the wing box structure according to a specific embodiment of the present invention.

FIG5 is a schematic diagram of the internal structure of a finite element model of a wing box structure according to a specific embodiment of the present invention.

FIG6 is a schematic diagram of the loading condition of the wing box in the multi-rotor stage according to a specific embodiment of the present invention.

FIG. 7 is a schematic diagram of the loading condition of the wing box in the fixed-wing stage according to a specific embodiment of the present invention.

FIG8 is a diagram showing iterative changes in wing box weight during ply shape optimization in a specific embodiment of the present invention.

FIG. 9 is a diagram showing iterative changes in wing box weight during ply thickness optimization in a specific embodiment of the present invention.

FIG. 10 is a cloud diagram showing the distribution of composite material plies thickness of the skin of a specific embodiment of the present invention.

FIG. 11 is a cloud diagram showing the distribution of composite material plies thickness of a wing spar according to a specific embodiment of the present invention.

FIG. 12 is an analysis diagram of the wing box displacement in level flight mode according to the optimization result of a specific embodiment of the present invention.

FIG. 13 is an analysis diagram of wing box strain in level flight mode according to an optimization result of a specific embodiment of the present invention.

FIG. 14 is an analysis diagram of wing box stress in level flight mode according to the optimization result of a specific embodiment of the present invention.

FIG. 15 is an analysis diagram of the wing box displacement in the vertical take-off and landing mode according to the optimization result of a specific embodiment of the present invention.

FIG. 16 is an analysis diagram of the wing box strain in the vertical take-off and landing mode according to the optimization result of a specific embodiment of the present invention.

FIG. 17 is an analysis diagram of the wing box stress in the vertical take-off and landing mode according to the optimization result of a specific embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with examples and accompanying drawings. It should be understood that the examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit and scope of the present invention, variations and advantages that those skilled in the art can expect are all included in the present invention, and are protected by the appended claims and equivalents.

It is understood that the term "one" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "one" cannot be understood as a limitation on the number. In the present invention, except for the names and terms that have been clearly defined by the inventor, other names and terms are common names in the art.

In one embodiment of the present invention, a structural design optimization method and system for a tilt-ducted aircraft wing is provided. As shown in FIG1 , the present invention proposes a double-main-beam wing structure. Composite materials are mainly selected as materials. The main components include a first main beam, a second main beam, a leading edge, a rear wall, a wing rib, a skin (hidden in the diagram to show the internal structure), ailerons, aileron servos, a tilt device, and a duct. The main load-bearing components of the wing structure of the present invention are the first main beam and the second main beam. In the wingtip area, internal wing equipment such as aileron servos and a tilt device are installed between the first main beam and the second main beam. The wing structure can not only evenly and effectively bear the different complex loads in the level flight mode and the vertical take-off and landing mode, but also can place internal equipment in the limited and narrow internal space of the wing.

The advantages of the tilt-ducted fan aircraft wing with a double main beam structure proposed in the present invention are: (1) Compared with the traditional fixed-wing aircraft wing, the present invention carries a duct device and a matching tilt device at the wingtip of the wing, which occupies the limited internal space of the wing to a great extent. The advantage of using double main beams is that it allows designers to have more choices in the internal layout of the wing. The internal equipment can be installed between the two main beams without affecting the overall mechanical properties of the wing structure; (2) The double main beam structure of the wing of the present invention improves the structural rigidity of the wing and enhances the load-bearing capacity of the wing. The double main beam structure shares the load through two main beams, increases the bending and torsional rigidity of the wing, and is effective for the wing. For a tilt-ducted fan aircraft that needs to switch between different flight modes, the dual-main-beam structure can provide the wing with sufficient strength and rigidity to adapt to the requirements of these modes, which is crucial to the stability and reliability of the wing and the tilt-ducted fan aircraft. In addition, the wing of a tilt-ducted fan aircraft will experience multiple load cycles during flight. The dual-main-beam structure can better disperse stress concentration, thereby improving fatigue resistance and extending the service life of the wing. (3) The dual-main-beam structure of the wing structure of the present invention increases redundancy. In extreme cases, if one main beam is damaged, the other main beam can still provide the necessary support, thereby increasing the safety of the aircraft.

The present invention proposes a structural design optimization method and system for tilt-ducted aircraft wings, which is developed around a double-main-beam wing structure. As shown in FIG2 , the present invention is mainly divided into a conceptual design stage S1 and a detailed design stage S3.

The conceptual design stage S1 aims to obtain the optimal preliminary structure of the tilt-ducted fan aircraft wing, that is, the first optimal structure, set the first design variable, the first optimization target and the first design constraint that affect the tilt-ducted fan aircraft wing; construct the structural model and the aerodynamic model of the wing; couple the aerodynamic model and the structural model through displacement data and load data; construct the Lagrangian function of the coupling model and solve the coupling model through the adjoint gradient optimization method to obtain the optimization result; evaluate the optimization result, and obtain the first optimal structure of the tilt-ducted fan aircraft wing. The specific method includes:

S11: Determining a first design variable, a first optimization objective, and a first design constraint that affect a tilt-ducted fan aircraft wing

The first design variable and the first optimization target that affect the structural performance of the wing of the tilt-ducted fan aircraft are determined. The first design variable refers to the parameters that affect the wing structure, including the positions of the first main beam and the second main beam on the chord, and the shapes and geometric dimensions of the wing beam, wing ribs and skin. The first optimization target is the minimum structural weight of the wing in the level flight mode and the vertical take-off and landing mode. The first design constraint is the strength, stiffness, flutter, etc. of the wing structure of the tilt-ducted fan aircraft in different flight modes (vertical take-off and landing, transition flight, horizontal flight, hovering, etc.).

S12: Using the NS equations and SA turbulence equations to establish an aerodynamic model of the tilting ducted fan aircraft wing

The purpose of establishing the wing aerodynamic model of the tilt-ducted fan aircraft is to simulate the aerodynamic performance of the wing of the tilt-ducted fan aircraft in different flight modes. This includes the prediction and calculation of aerodynamic characteristics such as lift, drag, and pitch moment of the wing. The accurate prediction of these aerodynamic characteristics is crucial to the stability, maneuverability, and performance of the aircraft. The flow field control equations are the basic equations that describe fluid motion, including the continuity equation, momentum conservation equation, and energy conservation equation. These equations are used to describe the distribution and changes of physical quantities such as velocity, pressure, and density when the fluid flows around the wing. In the design of the tilt-ducted fan aircraft, the aerodynamic model of the wing needs to be combined with the flow field control equations. By solving the flow field control equations, detailed information about the flow field around the wing can be obtained, such as streamline distribution, pressure distribution, vortex structure, etc. This information is crucial to understanding and optimizing the aerodynamic performance of the wing. Moreover, in special flight modes such as vertical takeoff and landing and transition flight of tilt-ducted fan aircraft, the interaction between the wing and the ducted fan will be more complicated. At this time, the aerodynamic model of the wing needs to more carefully consider the impact of the airflow generated by the ducted fan on the wing flow field. By solving the flow field control equations, this complex interaction can be simulated, thereby more accurately predicting the aerodynamic performance of the wing.

The aerodynamic model is a mathematical and physical model used to simulate and analyze the flow characteristics of air or other gases around solid objects and how these flows affect the objects themselves. The present invention uses the NS equation and the SA turbulence equation to construct the aerodynamic model. The NS equation (Navier-Stokes equation) is also called the flow field control equation. It is a three-dimensional steady-state turbulence equation. The continuity equation, momentum conservation equation, and energy conservation equation of the NS equation are expressed as follows:

(1)

Where, ρ is the flow density, U = [ u,k,w ] is the flow velocity vector, u,k,w are the velocities in the x, y, z directions respectively, p is the flow pressure, E is the total energy of the flow, q is the heat flux of the flow, τ is the viscous stress tensor of the flow, τ is U , the turbulent molecular viscosity and turbulent viscosity The function.

The SA equation (Spalart-Allmaras equation), also known as the SA turbulence equation, can be used to convert the turbulent viscosity into In conjunction with other variables in the NS equation, the SA turbulence equation is expressed as follows:

(2)

In formula (2), , , , They represent the convection, diffusion, production and near-wall destruction of turbulence respectively. σ is the Prandtl number, which is used to represent the diffusion of turbulent viscosity. C _b2 , C _b1 and C _w1 are all model constants obtained by fitting experimental data. is a function of strain rate, a composite quantity that takes into account local shear and rotation effects, fw _is a function calculated based on the wall distance d , used to correct the turbulent viscosity near the wall, v is the kinematic viscosity, is the corrected kinematic viscosity, Related to the turbulent kinematic viscosity vt _, .

The NS equations and SA turbulence equations involve complex flow phenomena and boundary conditions and are difficult to solve directly. Therefore, in order to perform numerical solutions 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 discretization of the 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 so that the aerodynamic global residual satisfies:

A(b,e(b))=0 (3)

Where b is the design variable vector, e is the state variable vector, and formula (3) contains nonlinear equations involving millions of state variables.

S13: Establishing a structural model of the tilt-ducted fan aircraft wing

(1) Use 3D modeling software to establish a 3D structural model of the tilt-ducted fan aircraft wing based on shell elements;

(2) Establish a finite element model of the wing structure based on the 3D structural model of the wing

The three-dimensional structural model is given material properties, structural constraints, etc. The three-dimensional structural model can provide the structural response of the wing under different load conditions, such as displacement, stress, vibration, etc. Then, the three-dimensional structural model of the wing is meshed to form a finite element model of the wing structure, and the mesh is mainly a quadrilateral mesh tending to a square.

(3) Static analysis of the finite element model of the wing

The static analysis finite element method is used to perform static analysis on the finite element model of the wing. The structural residual of the nonlinear analysis is: S ( u ) = 0. The control equation in the nonlinear analysis is: S ( u ) = Ku - f = 0, where K , u , and f represent the overall stiffness matrix, global displacement vector, and load vector of the entire unit, respectively.

In the finite element analysis of the tilting ducted fan aircraft structure of the present invention, shell elements are used for attribute definition, and a p -order double Lagrangian shape function is used to interpolate the mid-surface displacement U ₀ and the small rotation angle θ of each element in the domain. The double Lagrangian shape function is expressed as follows:

(4)

in, is the shape function, ne _is the number of nodes in the element, are isoparametric coordinates, is the element state variable of the jth element under the ith load case, and p is the order.

In the static analysis finite element method, the structural global residual is the overall measure of all structural unit residuals within the entire wing structure finite element model, reflecting the accuracy of the overall solution of the model. The structural global residual is obtained through all structural unit residuals. The structural unit residual is based on the virtual work method. It is expressed as follows:

(5)

in, is the structural element residual of the jth element under the ith load case, is the unit state variable , unit node position and a function of the material design variable X _M , represents the increment, T represents the transpose of the matrix, Represents unit state variables The transposed differential, X _G is the geometric design variable, the unit node position Obtained by the unit operator P _j .

Structural unit residuals The relationship with the structural global residual R _i is as follows:

(6)

in, represents the Kronecker product, I ₆ is the 6*6 identity matrix, u _i is the global state variable, and the unit state variable and unit node locations The calculation formula is as follows:

(7)

Where I ₃ is the 3*3 identity matrix, represents the transpose of the unit operator Pj _, is the global node position vector, which represents the node position in the global coordinate system.

S12 and S13 are performed synchronously.

S14: Establish a coupling model between aerodynamic model and structural model

After the load is applied to the wing, the wing structure will deform, and the aerodynamic performance of the wing will also change after deformation, so the deformed wing needs to be analyzed again. Displacement data is the displacement of the wing structure after being loaded, and this data is provided by the structural model. The displacement data includes: the displacement vector of each point of the wing structure, including the displacement in three spatial directions (x, y, z); the new shape or structural contour of each component after the wing structure is deformed; and the displacement of the key points of the structure or the whole. The displacement data is very critical for evaluating the stiffness and overall deformation of the wing structure.

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

The aerodynamic model and the structural model provide a method for aerodynamic analysis and structural analysis of the wing of a tilting ducted fan aircraft. In the coupling analysis, there is an effective data exchange mechanism between the aerodynamic model and the structural model. The present invention sets the displacement as one of the input variables of the aerodynamic model and one of the output variables of the structural model, and sets the load as one of the output variables of the aerodynamic model and one of the input variables of the structural model. The aerodynamic model and the structural model are coupled through displacement and load so that the load and displacement data can be shared in real time between the two models: (1) load transfer, the aerodynamic load data generated by the aerodynamic model analysis is transferred to the structural model, and the structural model uses the load data to calculate the structural response, and the structural response includes the displacement data; (2) displacement feedback, the displacement data generated by the structural model analysis is fed back to the aerodynamic model, and the aerodynamic model uses the displacement data to update the flow field information and recalculate the aerodynamic load.

To transfer loads and displacements between the aerodynamic and structural models, the present invention uses a matching-based load and displacement extrapolation method to transfer displacements from the structural grid to the aerodynamic grid by linking each aerodynamic surface node to a fixed number of the nearest structural nodes; the displacement of each aerodynamic surface node is calculated by finding the best rigid rotation and translation, which are calculated based on the displacements of a set of linked structural nodes. The use of a rigid rotation matrix makes the calculated displacement transfer geometrically accurate.

The interaction between the aerodynamic model and the structural model introduces additional complexity, and the two models need to be solved iteratively until the interaction between the two reaches a balance. This requires not only considering the aerodynamic global residual and the structural global residual separately, but also considering the coupling effect between the two residuals. For example, structural deformation will affect aerodynamic performance, and changes in aerodynamic performance will generate new aerodynamic loads on the structure. Therefore, in the coupled analysis, the aerodynamic global residual and the structural global residual need to be considered simultaneously, and a coupled iterative solver is required to ensure that the residuals of all physical quantities are reduced to an acceptable level. This coupled solution process requires powerful computing power and accurate models to ensure reliable and accurate results. Combining the aerodynamic global residual and the structural global residual above, the coupled residual R of the model after the aerodynamic model and the structural model are coupled is written as:

(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: Constructing Lagrangian functions for coupled models

According to the first design constraint of the wing structure (such as displacement, strain, stress, vibration, etc. under different flight modes), the corresponding Lagrangian multiplier is introduced. If there are m constraints, m Lagrangian multipliers are introduced, denoted as λ1,λ2,..., λm . In this process, the Lagrangian function transforms 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)

Where x is the optimization variable vector, i.e., the first design variable, including the optimal positions of the first and second main beams, as well as the shapes and geometric dimensions of the skin, ribs, and spar; λ=[ λ1,λ2,...,λm ] is the Lagrange multiplier vector; f (x) is the objective function of the wing structure, i.e., the objective function of the first optimization objective, specifically, minimizing the structural weight of the wing in level flight mode and vertical take-off and landing mode; gi (x) is the constraint function of the i -th constraint condition.

S16: Obtain the optimal solution of the Lagrangian function by solving the adjoint equation

The first optimization objective is converted into minimizing the 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 adjoint equation is a set of equations obtained by calculating the gradient of the Lagrangian function. The adjoint equation can provide gradient information about the first design variable, thereby guiding the optimization algorithm to update the first design variable. The adjoint equation is:

(10)

Gradient-based design optimization methods can solve large-scale design problems within a reasonable computing time only if analysis and gradient evaluation are performed effectively. Because the number of functions and variables involved in the present invention is large, the present invention adopts an adjoint method to ensure that the number of functions in each load case can be reduced to a manageable number by using constraint aggregation technology.

By solving, we can get the gradient of each constraint gi (x) with respect to the design variable x , and then we can get the gradient of the objective function f ( x ) with respect to the first design variable x Finally, the calculated gradient of the first design variable is used to update the value of the first design variable, so as to continue the next round of optimization iteration, and finally the optimal solutions x * and λ * of the Lagrangian function are obtained, that is, the optimal first design variable x * . The optimal design variable x * and the first design constraint constitute the optimal preliminary structure of the tilt-ducted fan aircraft wing.

S17: Evaluating the first optimal configuration for a tilt-ducted fan aircraft wing

The optimized wing structure design scheme, i.e., the first optimal structure, is evaluated to verify whether it meets the design requirements and performance indicators, which mainly includes analyzing the performance of the first optimal wing structure design scheme, including the evaluation of the displacement, strain, stress, vibration and other aspects of the first optimal wing structure design scheme under different flight modes, and judging the pros and cons of the current design and whether the expected performance target has been achieved through the evaluation results. If it meets the standard, the first optimal structure design scheme of the wing is the optimal preliminary structural layout of the wing of the tilt-ducted fan aircraft; if it does not meet the standard, it returns to step S12 to continue iterative optimization, and adjusts the value of the first design variable to further improve the performance of the wing structure. The present invention uses an optimization algorithm to update the value of the first design variable according to the gradient information of the first design variable, and re-solves the adjoint equation, and then evaluates the result again. This process will continue until the design requirements and performance indicators are met.

Since the main load-bearing structure of the wing is the wing box, the optimal preliminary structure/first optimal structural layout of the highly integrated tilt-ducted fan aircraft wing obtained in the conceptual design stage is converted into a wing box three-dimensional model using the 3D modeling method. The structural performance of the wing box is taken as the primary goal in the structural analysis. The wing box three-dimensional model obtained in the conceptual design stage will be used as the input in the detailed design stage, so the detailed design stage mainly optimizes the wing box.

In the detailed design stage, the wing box three-dimensional model is used to generate a finite element model for subsequent composite material ply combination optimization. The composite material ply combination optimization of the wing box structure is carried out, and the ply combination optimization is in turn ply shape optimization, ply shape cutting, ply thickness optimization and ply sequence optimization. Finally, a lightweight wing box structure solution that meets the design requirements is obtained, which is the second best structure of the tilt-ducted fan aircraft wing.

The present invention optimizes the ply combination of the wing box. The design optimization of the wing box is a comprehensive design process for the second optimization target (minimum wing box weight) under the premise of satisfying the design constraints and manufacturing constraints, that is, finding the best design under the premise of satisfying the second constraint. The second constraint includes the ply design constraint and the ply manufacturing constraint. As for the ply design constraint, it can be known from the mechanical properties of composite laminates that the material properties, ply thickness, ply angle and ply sequence of the composite material can change its mechanical properties. However, due to the limitations of existing composite material processes, the ply angles of the composite material are generally 0°, 45°, -45°, and 90°, and there are requirements for the thickness of a single manufacturable ply material. The composite ply combination optimization design is to optimize the ply shape, thickness and sequence of these four ply angles to reduce the structural mass under the conditions of satisfying the structural stiffness and strength requirements.

In the present invention, in addition to considering the design constraints such as strength, stiffness, stability and weight of the structure, the manufacturing constraints of the ply must also be considered when optimizing the ply combination of the composite wing box, so that the optimization result has processability. The importance and necessity of considering manufacturing constraints in composite layup combination optimization are reflected in the following aspects: (1) Actual production connection: If the actual feasibility of the manufacturing process of composite materials is not considered during the design stage, the optimized overall design scheme will be difficult to manufacture. Manufacturing constraints ensure that the design scheme is both efficient and manufacturable. In addition, there are many industry standards and specifications for composite material manufacturing. Considering these manufacturing constraints during design helps to ensure that the overall design scheme meets industry specifications, making it easier to pass safety and quality inspections. (2) Cost control: Taking the limiting factors in the manufacturing process as optimization constraints can control manufacturing costs and avoid designing solutions that exceed the budget or are uneconomical. For example, complex-shaped layups can theoretically be manufactured, but they will bring about a significant increase in processing costs. (3) Quality assurance: Manufacturing constraints can ensure the quality and reliability of the product. For example, the order of composite material layups will affect the porosity and residual stress of the final product. The use of a large proportion of single-layer directional layups is an important guarantee of product quality. Reasonable manufacturing constraints can avoid structural defects such as wrinkles or delamination, thereby improving the performance and strength of the final product.

Common ply manufacturing constraints and the ply manufacturing constraints of composite materials used in this paper are: (1) In composite laminates, the ply thickness in each direction must have a constraint, that is, the total ply thickness in each direction is a percentage of the total thickness of the laminate. Generally, 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 constraints apply to all points on the laminate; (2) The thickness of a single ply that can be manufactured is generally 0.1mm-2mm. The specific value depends on the manufacturing process and material type. The outermost ply should be a ply at an angle of ±45°, and no more than 4 layers can be laid in the same direction.

The present invention imposes non-mandatory manufacturing constraints in the ply shape optimization stage and more detailed manufacturing constraints in the ply sequence optimization stage. Non-mandatory manufacturing constraints refer to manufacturing-related constraints that can be considered but not enforced during the design and optimization of composite structures. These constraints are not intended to ensure the basic function or safety of the structure, but to optimize the manufacturing process, reduce costs, simplify assembly or improve manufacturing efficiency. The non-mandatory manufacturing constraints of the present invention include: (1) Although a specific ply sequence may help improve the performance of a component, in some cases, adjusting the ply sequence can simplify the manufacturing process or reduce the risk of manufacturing errors, and the impact on performance may be acceptable; (2) ply symmetry: ply symmetry for composite structures can reduce warping and internal stress, but in some designs, symmetry requirements are relaxed in order to optimize performance or reduce weight; (3) minimum ply thickness: a minimum ply thickness constraint is set to simplify manufacturing, but this is not for structural performance considerations, but to avoid problems in the manufacturing process, such as the laying and curing of prepregs. In the design and optimization process, non-mandatory manufacturing constraints provide a certain flexibility, allowing engineers to consider the convenience and economy of actual manufacturing while meeting performance requirements. By properly balancing these non-mandatory constraints and design goals, more efficient and cost-effective product designs can be achieved.

The optimization algorithms that can be used in ply combination optimization include the method of feasible directions (MFD), sequential quadratic programming, dual optimizer based on separable convex approximation, and large-scale optimization algorithm. The present invention adopts the feasible direction method MFD in the optimization of composite ply combination. The use of the feasible direction method MFD for composite ply combination optimization has the following advantages: (1) quickly find improved solutions while satisfying various composite material specific constraints; (2) composite plies involve many design constraints due to their own complexity. MFD can handle these linear or nonlinear constraints well and find reasonable feasible directions; (3) composite ply optimization involves nonlinear material and structural responses. MFD can better solve nonlinear optimization problems; (4) MFD can be calculated in parallel, which can greatly improve the calculation efficiency, which is particularly important for high-dimensional problems in composite ply optimization.

In order to improve the optimization efficiency, the present invention improves the existing MFD and modifies some constraints according to the characteristics of composite materials, making MFD more suitable for composite material optimization. The following is a mathematical description of the feasible direction method MFD of the present invention in the composite wing structure ply combination optimization:

Let f (x) be the objective function, which in the present invention is to minimize the wing structure mass, is a vector of design variables. The constraints are divided into equality constraints hj (x)=0, j =1,..., m , that is, there are m equality constraints, and inequality constraints gi (x)≤0, i =1,..., p , that is, there are p inequality constraints.

In the feasible direction method MFD, the solution is updated iteratively, and each iteration includes the following steps:

(1) Determine a feasible direction: Let d be a feasible direction at the current point x( k ), the gradient direction that satisfies all inequality constraints: , for all i such that ; and the gradient direction that satisfies all equality constraints: for all j such that , where x( k ) refers to the kth design variable in the design variable vector x.

(2) Reduce the objective function: Select d so that the gradient of the objective function in this direction is negative, that is, .

(3) Selecting step size: Choose a step size λ>0 such that x( k +1)=x( k) +λd is feasible under all constraints and f (x( k +1))< f (x( k) ).

(4) Update the solution: set the newly obtained x( k +1) as the current solution;

(5) Convergence judgment: If x( k +1) has satisfied the specified convergence criteria, such as the improvement of the solution is lower than a certain threshold or the maximum number of iterations has been reached, then the iteration is stopped and x( k +1) is taken as the optimal solution; otherwise, set k = k +1 and return to step (1) to repeat the iteration.

The improved feasible direction method MFD adopted by the present invention continuously reduces the value of the objective function while ensuring the feasibility of the solution in each iteration. This method is achieved by finding a suitable direction on the limit of the constraint and moving forward.

As shown in FIG3 , the composite material ply combination optimization of the present invention includes ply shape optimization, ply shape tailoring, ply thickness optimization and ply sequence optimization in sequence.

The purpose of ply shape optimization is to determine the shape of the plies in all directions, including:

(1) The ply angles of each unit of the wing box structure are set, and the initial thickness of the plies at different angles is equal; the ply angles include 45°, 90°, -45°, and 0°, and the initial thickness of these four plies is equal. This can greatly reduce the number of plies and reduce the influence of factors such as ply angle, sequence, and thickness on the ply shape optimization results;

(2) In addition to considering the design constraints such as the strength, stiffness, stability and weight of the wing box structure, the manufacturing constraints of the production process must also be considered to make the optimization results processable. Non-mandatory manufacturing constraints are imposed in the conceptual design stage of the ply shape optimization. In order to improve the optimization efficiency, the influence of the ply sequence is ignored at this stage.

(3) In the optimization process, the thickness of each unit of the composite laminate is used as the design variable, and the weight of the wing box structure is used as the optimization target to find the optimal thickness distribution of the laminate that meets the design constraints and non-mandatory manufacturing constraints;

(4) Using the MFD optimization algorithm to optimize the composite material layup shape of the wing box structure skin and spar;

(5) In order to better present the optimization results, the present invention sets a threshold value. If the thickness of a unit of the laminate is less than the threshold value, the unit is directly discarded; if the thickness of a unit of the laminate is greater than or equal to the threshold value, the unit is completely retained; the threshold value is 0.05 to 0.2 times the thickness of a single manufacturable ply, generally 0.1 times the thickness of a single manufacturable ply.

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

Design variables: thickness of each element of the laminate

Optimization goal: Minimize the weight of the wing box structure

Restrictions:

in, is the thickness of the kth element of the ith laminate, is the minimum value of the thickness of the kth element of the ith laminate, is the maximum value of the thickness of the kth element of the ith laminate, is the number of laminates, is the total number of laminate elements in the design area, where , These are all pre-set values.

Laminate shape cutting. The laminate shape obtained after laminate shape optimization is irregular, with many discontinuous areas and independent areas, which will bring additional costs to the manufacturing process. Therefore, each laminate needs to be analyzed and cut to make the final shape of each laminate as consistent as possible with the optimization result and meet the process requirements of actual manufacturing, so as to obtain a laminate shape that can be actually processed and prepare for the next step of laminate thickness optimization.

Optimize ply thickness. Since the ply shape obtained after ply shape optimization and ply shape tailoring is the shape and thickness of the overall ply (i.e., laminate) that can be actually processed, and the thickness of each ply has not been specifically designed, the purpose of ply thickness optimization is to determine the specific thickness of each angle and each shape of ply, and discretize the plies of different thicknesses at each angle obtained after ply shape tailoring into plies that meet the manufacturing constraint thickness based on the design constraints and manufacturing constraints of the load response. The specific process of ply thickness optimization is described as follows:

(1) A general stacking model of composite materials is established. The tensile stiffness matrix A, coupling stiffness matrix B and bending stiffness matrix D can be calculated as:

(11)

zk is the distance between the middle plate of the laminate and the side of the kth layer away from the middle plate, i and j represent the row and column of the 6*6 stiffness matrix Q respectively, is the transformed 6*6 simplified stiffness matrix.

In composite material 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), and represents the stiffness matrix of a single-layer laminate after the ply angle transformation. The difference between the two matrices is that the stiffness they each represent is relative to a different reference system. Q is expressed as follows:

(12)

Where, E and G are engineering constants of the material, E 11 is the elastic modulus along the fiber direction, E 22 is the elastic modulus along the transverse direction; v represents the principal Poisson's ratio of the material, v 12 is the principal Poisson's ratio of a specific material type; G 12 represents the shear modulus of the ply.

The stiffness matrix Q of a single-layer plate is a 3*3 matrix, and The stiffness matrix of a single-layer laminate after the ply angle transformation is a 6*6 matrix. Q is originally a 6*6 matrix. The main direction of the fiber ply of Q is the same as the direction of the coordinate axis x, so many items in it are 0 and simplified to 3*3. However, the main direction of the fiber ply of the ply after the ply angle transformation has an angle of θ with the direction of the coordinate axis x (θ is the angle of the ply), so It cannot be simplified, it is still 6*6 as before.

The elements of are calculated as follows:

(13)

Where θ is the angle of the ply.

(2) The general stacking model can be used to accurately formulate design constraints and manufacturing constraints in its design space. The design constraints in the ply thickness optimization stage include ply strain, stress, and wing tip displacement. The manufacturing constraints include the upper and lower limits of the total thickness of the laminate, the upper and lower limits of the percentage of the total thickness of the laminate at the same angle, and the ply thickness at the angles of ±45° must be equal.

(3) Continuous thickness optimization is performed. In this process, the design variable is the thickness of each ply in the laminate, while the stacking order and direction remain unchanged (the same as the initial design). The optimization goal is to minimize the weight of the wing box. The objective function of the optimization goal can be expressed as , where ρi is the density of the i -th layer of material, Ai is the area of the i- th layer of ply, and x=[ x1 , x2 ,..., xi ] is the thickness of the i- th layer of ply. The present invention uses the above-mentioned feasible direction method MFD method for optimization, and obtains the ply thickness optimization result as shown in "Ply Thickness Optimization" in Figure 3, and the optimization result is an idealized optimal continuous thickness distribution;

(4) The optimization result is an idealized optimal continuous thickness distribution and cannot be used directly. This is because in actual manufacturing, composite materials do not have only four layers of this thickness, and these thicknesses are all idealized. They need to be divided into many manufacturable single layers of the same thickness. This process is called discretization. Moreover, these thicknesses are generally not an integer multiple of the thickness of the manufacturable single layer, which involves a process similar to rounding. Therefore, they must be discretized into layers that meet the manufacturing constraint thickness.

The ply thickness needs to be discretized into continuous thickness. The minimum manufacturable single-layer thickness is a known value, so the total thickness of the plies in four different directions can be "rounded off" to a close integer number of layers. In order to ensure that the discretized design meets the strength constraints, it is necessary to focus on the buckling and strength constraints. The discretization method in the present invention is as follows:

Assuming that the total number of continuous layers laid in a single direction is represented by vθ (the value obtained by dividing the thickness of the layer by the thickness of the single layer that can be manufactured, which is generally not an integer), the total number of discrete layers of layers laid in a single direction in the actual structure is represented by nθ , where the index Indicates different ply directions. , then the thicknesses can be rounded according to the following conditions:

if ,but ,otherwise ,in .

l corresponds to the fractional part of vθ . When the fractional part exceeds l , the number of layers corresponding to nθ will be rounded up. The advantage of this discrete method is that it can impose mandatory constraints more directly. For example, in the present invention, the number of plies at ±45° must be equal, so it can be set as follows: , θ1 =45°, θ2 =-45°.

Since the overall performance of the composite laminate structure changes with the change of its layup sequence, based on this designable characteristic of composite materials, the stacking sequence of the plies needs to be optimized to meet the layup rules of the composite materials while keeping the laminate performance unchanged or even improving it as much as possible.

Lamination sequence optimization is the last step in the optimization of composite material ply combinations. In this stage, the thickness and direction of the plies, as well as the order of plies in the same direction remain unchanged, and only the ply sequence is changed. After the ply sequence is optimized, it can ensure that the stacking order of the plies meets the ply rules and manufacturing constraints of the composite materials, while keeping the overall performance of the laminate unchanged or even improved as much as possible. More manufacturing constraints need to be considered in the ply sequence optimization. All design responses in this stage of optimization are the same as those in the ply thickness optimization stage. When optimizing the ply sequence, keep all objective functions, design responses, and non-mandatory manufacturing constraints unchanged, and impose more detailed manufacturing constraints.

The optimization of ply order needs to solve the search problem of discrete and nonlinear space, and the improved feasible direction method MFD of the present invention can solve this problem well. The specific process of ply order optimization includes:

(1) The stacking order of all plies is used as the design variable, the minimization of wing box weight is used as the optimization goal, and the design constraints and manufacturing constraints are fully considered;

(2) The feasible direction method (MFD) optimization algorithm is used to optimize the layup sequence of composite materials for the skin and spar of the wing box structure;

Design constraints include ply strain, stress and wing tip displacement of the wing box; manufacturing constraints include the maximum number of consecutive plies at the same angle, the outermost ply angle must be a group of ±45° plies, the upper and lower limits of the total thickness of the laminate, the upper and lower limits of the percentage of the total thickness of the plies at the same angle to the total thickness of the laminate, and the ply thicknesses at the two angles of ±45° must be equal.

The present invention uses specific embodiments to illustrate the technical solution and technical effect of a shield machine fault monitoring and diagnosis method and system based on cloud-edge collaboration.

Taking the wing of a 40kg-class tilt-ducted fan aircraft as an example, we first define the thickness and material properties of each component of the wing, and the components are made of carbon fiber composite materials.

The conceptual design phase aims to obtain the best preliminary structure of the wing of a 40kg-class tilt-ducted fan aircraft, with the optimization goal of minimizing the structural weight of the wing in level flight mode and vertical take-off and landing mode. The design variables mainly include: parameter variables of the wing geometry, such as span, airfoil, root chord length, root-to-tip ratio, aspect ratio, dihedral angle, sweep angle (front cistern sweep angle and rear cistern sweep angle), installation angle, etc.; the position of the first main beam and the second main beam on the chord, the distribution of ribs along the chord, etc.; the shape and geometric dimensions of ribs, spars, ribs and skins, etc. The strength, stiffness, flutter, etc. of the tilt-ducted fan aircraft wing structure under different flight modes (vertical take-off and landing, transition flight, horizontal flight, hovering, etc.) are design constraints.

Then, an aerodynamic model is established to analyze the aerodynamic characteristics of the wing under different flight conditions; at the same time, a structural model is established to evaluate the structural response of the wing. The coupling between aerodynamic loads and structural responses is achieved to ensure that changes in aerodynamic loads can be reflected in the structural response, and vice versa. The Lagrangian function of the coupling model is constructed, and the corresponding Lagrangian multipliers are introduced according to the constraint information of the wing structure (such as displacement, strain, stress, vibration, etc. under different flight modes). The Lagrangian function transforms the original constrained optimization problem into an unconstrained optimization problem, and provides a unified framework to guide the optimization process of the wing structure. By establishing the adjoint equation and solving it to obtain the gradient of the objective function relative to the design variable, the adjoint-based gradient design optimization method is used for analysis and gradient evaluation. The gradient of each constraint condition with respect to the design variable is obtained by solving it, and the gradient of the objective function with respect to the design variable is obtained. Finally, the calculated gradient of the design variable is used to update the value of the design variable for optimization iteration. After each iteration, the coupling analysis is repeated to update the aerodynamic and structural models. Finally, the optimized wing structure is evaluated to verify whether it meets the design requirements and performance indicators until it meets the design requirements and performance indicators.

The model is obtained by three-dimensional modeling based on the preliminary wing structure scheme obtained in the conceptual design stage. The tilting ducted fan aircraft wing structure in this embodiment is mainly composed of composite laminates and belongs to a plate-shell structure. Therefore, a quadrilateral two-dimensional grid (CQUAD4) is used to model the skin, wing spar, and wing rib structure to form a finite element model of the wing box structure. As shown in Figures 4 and 5, the finite element model of the wing box structure (skin and wing spar) has a total of 5345 shell units, and then the model is given composite material properties, including material properties, ply information, and unit direction.

Loads are applied to the finite element model of the wing. The load application conditions in the two flight modes are as follows: (1) Wing load condition in the multi-rotor stage. The tilt-ducted fan aircraft relies on the lift provided by four ducted devices to complete vertical take-off and landing and hovering. The total lift generated by the four ducts is 100 kg. According to the overall design, the aircraft can withstand a maximum wind speed of 16 m/s. According to the "Normal Category Rotorcraft Airworthiness Regulations", the maximum overload factor of the aircraft in the multi-rotor state is 3.0, and the minimum overload factor is -1.0; as shown in Figure 6 As shown in Figure 7, the wing root of the main beam is completely fixed, and the structural gravity and the concentrated force generated by the duct are applied. This force acts on the wing tip and is vertically upward. (2) The load on the wing in the fixed-wing stage. As shown in Figure 7, the lift is generated by the wing in the fixed-wing stage, so the focus is on the aerodynamic load. According to the calculation stipulated in the relevant regulations of the "Airworthiness Regulations for Normal, Utility, Stunt and Commuter Category Aircraft", the maximum maneuvering load of the aircraft is 3.8, the minimum overload factor is -1.9, and the tilt duct at the wing tip provides a concentrated forward pull.

When optimizing the ply shape, it is first assumed that the ply forms of the wing structure components are [45°, 90°, -45°, 0°], and the initial thickness of these four plies is equal. The original thickness of the upper and lower skins is set to 1mm, the original thickness of the first and second main beams is set to 2mm, the original thickness of the rear wall is set to 1.6mm, and the original thickness of the rib is set to 1mm. The global responses such as structural weight and strain are optimized and constrained, and the minimum manufacturable single-layer thickness is set to 0.1mm. The thickness of each unit of the composite laminate is used as the design variable, and the structural quality objective function is used to find the optimal thickness distribution of the laminate that meets the constraints. In order to better present the optimization results, the threshold is set to 0.01mm (one-tenth of the thickness of a single manufacturable ply). If the thickness of a unit is less than the threshold, the unit is directly discarded; otherwise, the unit is retained intact.

After ply shape optimization, the weight of the wing box has been greatly reduced. As shown in Figure 8, the ply shape converged after 113 iterations. The weight of the wing box after ply shape optimization was 0.498 kg, and the initial design weight was 1.34 kg, a weight reduction of 62.8%. The weight of the wing box will also change after ply thickness optimization. As shown in Figure 9, the ply thickness optimization converged after 7 iterations. The weight of the wing box after ply thickness optimization was 0.729 kg, and the initial design weight was 0.498 kg (mass after ply shape optimization), and the weight increased by 0.231 kg. This is because during the thickness optimization process, the proportion of ply group shapes that can improve the strength of the laminate will increase slightly, which will lead to an increase in mass after thickness optimization. The ply shape trimming stage is to trim each ply and does not change the weight of the wing box. The ply sequence optimization stage only changes the order of the plies, and the mass of the wing box does not change. From the perspective of the entire layup combination optimization, the initial total weight of the wing box is 1.34kg. After optimizing the skin and wing spar as the research objects, the weight of the wing box is reduced to 0.729kg after the layup combination optimization of the wing box, a weight reduction of 45.6%, and the weight reduction effect is obvious.

The final composite material layup thickness distribution cloud diagrams of the wing box skin and wing spar are shown in Figures 10 and 11, where the maximum thickness is 2 mm and the minimum thickness is 0.4 mm. Compared with the wing tip area, the composite material distribution in the wing root area is the thickest, and the material distribution in the wing tip area is the thinnest, because the material in the wing root area needs to bear more loads.

In order to verify the performance of the tilt-ducted fan aircraft wing structure finally optimized in the present invention, the displacement, strain and stress of the wing structure after the ply combination optimization in the level flight mode and the vertical take-off and landing mode are analyzed respectively. The displacement, strain and stress analysis results of the tilt-ducted fan aircraft wing in the level flight mode are shown in Figures 12-14 respectively. In the fixed-wing stage level flight mode, the maximum displacement of the wing box is at the wing tip, which is 12.24mm; the maximum strain of the wing box is at the wing root, which is 2587με; the maximum stress is at the wing root, which is 405.3MPa. In the multi-rotor stage vertical take-off and landing mode, the displacement, strain and stress analysis results of the tilt-ducted fan aircraft wing are shown in Figures 15-17 respectively. The maximum displacement of the wing box is at the wing tip, which is 18.12mm; the maximum strain is also at the wing root, which is 2478με; the maximum stress is also at the wing root, which is 388.2MPa.

The ultimate performance of the carbon fiber composite material used in the embodiment of the present invention is as follows: longitudinal tensile strength 1548MPa, longitudinal compressive strength 1226MPa, transverse tensile strength 55.5MPa, transverse compressive strength 218MPa, in-plane shear strength 89.9MPa. According to the design experience of composite wing box structure, it is stipulated that the strain of the wing box structure is not allowed to exceed 3000με, the maximum stress of the wing box structure is not allowed to exceed 450MPa, and the maximum displacement of the wing tip is not allowed to exceed 5% of the wing span (i.e. 25mm). Therefore, the performance of the tilt-ducted fan aircraft wing of the present invention meets the design requirements.

It can be seen that, under the premise that the original load-bearing level of the tilt-ducted fan aircraft wing of the present invention remains unchanged, and the displacement, strain and stress of the wing in level flight mode and vertical take-off and landing mode meet the design requirements, the weight of the tilt-ducted fan aircraft wing of the present invention is reduced by 45.6% after ply combination optimization.

In summary, the present invention provides a tilt-ducted fan aircraft wing with a double-main-beam structure that can provide sufficient strength and rigidity to adapt to the requirements of different flight modes of the tilt-ducted fan aircraft; the present invention couples the aerodynamic model and the structural model and uses the accompanying gradient optimization method to obtain the optimal preliminary structure of the wing, thereby greatly improving the fidelity of the optimization; the feasible direction method MFD is used to perform ply combination optimization on the tilt-ducted fan aircraft wing, making the composite material feasible for manufacturing.

Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

The above-mentioned specific implementation methods are used to explain the present invention and are only preferred embodiments of the present invention, rather than limiting the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims (9)

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

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

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 positions of the first main beam and the second main beam on the wing chord, and the shapes and geometric dimensions of the wing spar, the wing rib and the skin; 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;

Wherein S12 and S13 are performed synchronously;

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 the optimal solution of the Lagrangian function through the 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 design variable and the first design constraint form a first optimal structure of the tilting ducted 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;

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 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;

The composite material layering optimization sequentially comprises layering shape optimization, layering shape cutting, layering thickness optimization and layering sequence optimization.

2. The method of claim 1, wherein the NS equation is expressed as follows:

where ρ is the flow field density, U= [ U, k, 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 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 the turbulent viscosity near the wall, v is the kinematic viscosity, is the corrected kinematic viscosity,In relation 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.

3. 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.

4. 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:

Where λ1, λ2, &..λm is the lagrange multiplier, m refers to the number of first design constraints, x is the optimization variable vector, i.e., the first design variable, λ= [ λ1, λ2, &..λm ] is the lagrange multiplier vector, and f (x) is the objective function of the wing structure, i.e., the objective function of the first optimization objective; gi (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 of each constraint gi (x) with respect to the first design variable x by solving ; Thereby obtaining the gradient of the objective function f (x) relative 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.

5. 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;

(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) 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.

6. 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.

7. The method of claim 6, 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 Indicating the different ply direction,；

(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 nθ is rounded up.

8. 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 1-7, the system comprising:

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 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.

9. 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 1-7.