A rigid-flexible integrated optimization design method for a compliant variant wing

Abstract

A rigid-flexible integrated optimization design method for compliant morphing wing is provided, which simultaneously considers the overall carrying stiffness, local stiffness and local morphing design requirements of the structure. Four objective functions are proposed to represent the overall stiffness, local stiffness, flexibility of the leading and trailing edge morphing parts and strain uniformity of the wing rib structure. A multi-objective optimization method is used to integrate the four objectives to construct an optimization equation, and the optimal structure layout is obtained. The deformation of the local rigid component during carrying affects the design of the flexible component, resulting in the displacement boundary of the flexible component design no longer fixed, but changing with the deformation of the rigid component. The multi-objective optimization model considering the rigid-flexible design of the structure is established, which overcomes the problem of over-rigid or over-flexible structure caused by separate design of rigid component or flexible component. The strain uniformity requirement is introduced in the design of flexible morphing, and a strain uniformity function based on strain variance is proposed to achieve the goals of flexible deformation and consistent strain distribution of the morphing part.

Description

Technical Field

[0001] This invention relates to a rigid-flexible collaborative topology optimization design method, which simultaneously considers the overall structural load-bearing stiffness, local deformation stiffness design requirements, local compliant deformation design requirements, and strain consistency requirements of compliant variant structures. It can be applied to the configuration design of compliant load-bearing wing rib structures with variant leading edges and variable camber trailing edges. Background Technology

[0002] Flexible mechanisms, as a replacement for traditional rigid mechanisms, possess superior characteristics such as no need for assembly or lubrication, reduced components, and the ability to be designed and manufactured as a whole, leading to their application in the design of variator aircraft wing structures. However, wing design involves more than just compliant deformation requirements; it often demands distributed compliant deformation characteristics, and the overall load-bearing capacity of the wing and the local deformation stiffness under variator driving forces must also be carefully guaranteed. Therefore, the design of variator wing rib structures should encompass four aspects: firstly, the wing ribs must have sufficient stiffness under aerodynamic loads to ensure the overall load-bearing capacity of the wing; secondly, the wing drive assembly needs sufficient stiffness to support and transmit large local loads; thirdly, the leading and trailing edges of the wing need sufficient flexibility to meet the active deformation requirements of the wing shape during flight; and fourthly, the deformation of the leading and trailing edges should be as uniform as possible to reduce strain and stress concentration.

[0003] In recent years, many scholars have conducted extensive research on the optimization design of wing structures. Ge Wenjie et al. published "Topology Optimization of Flexible Mechanism for Trailing Edge of Shape-Deformable Wing Based on Multi-Objective Load Path Method" in "Mechanical Science and Technology", 2010(10):150-155, taking the trailing edge of a variable-camber wing as the research object, and proposed a load path optimization method with the rigidity and flexibility of the flexible part as the objective function. Zhou Chunhua et al. published "A Study on a Topology Optimization Method in the Variable Trailing Edge of a Wing" in "Mechanical Science and Technology", 2011,30(10):1660-1663, based on the aerodynamic shape requirements of the wing trailing edge under different flight states, and with the goal of minimizing the difference between the target shape and the actual shape, they performed topology optimization on the flexible mechanism, only considering the flexible part of the wing. Xia Shenglin et al.'s patent "A Design Method for a High Aspect Ratio Airfoil Structure", 201510763377.7, used a genetic algorithm to optimize the rigid and flexible parts of the wing separately, without considering the influence of the rigid part on the flexible part. Podugu et al. presented "Topology Optimization-Based Design of a Compliant Aircraft Wing for Morphing Leading and Trailing Edges" at the ASME International Mechanical Engineering conference (IMECE2010-38159), proposing a method for designing compliant aircraft wings that can deform from a given wing shape to another given shape under the action of internal forces and provide sufficient stiffness under aerodynamic loads.

[0004] Currently, existing wing structure optimization methods do not consider the impact of rigid component deformation during load-bearing on flexible component deformation and topology design. Flexible and rigid design are still performed step-by-step, and flexible component design lacks consideration for deformation consistency, resulting in stress / strain concentration in the design results. In this invention, firstly, the wing structure is divided into multiple regions, including rigid and flexible components for optimization, as well as undesignable regions. Furthermore, the design boundary of the flexible component is no longer fixed but considers the overall structural and rigid component deformation under local driving loads and external aerodynamic loads, giving the flexible component an elastic boundary and achieving a flexible mechanism design considering elastic support. Secondly, in designing the flexible variant, this invention introduces a strain distribution uniformity requirement and proposes a strain uniformity function based on strain variance, achieving a distributed flexible mechanism design with flexible variant and strain consistency characteristics in the variant component. Third, considering the design requirements of overall structural load-bearing stiffness, local stiffness, local variants, and strain uniformity of variant parts, four objective functions characterizing the overall stiffness, local stiffness, leading / trailing edge flexibility, and strain uniformity of the wing rib structure are proposed. An optimization formula is constructed using a multi-objective optimization method, and the optimal compliant variant structure layout is obtained. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a rigid-flexible collaborative topology optimization design method that simultaneously considers local flexible deformation, strain consistency in deformation regions, overall load-bearing stiffness, and local deformation stiffness. This method considers the impact of deformation of rigid components under load on the design results of flexible mechanisms, making the displacement boundary of the flexible mechanism no longer fixed but changing with the deformation of the rigid components under stress. Furthermore, it requires uniform strain in the design of flexible mechanisms to improve strain concentration and achieve distributed flexible mechanism design. Based on the design requirements of overall load-bearing stiffness, local deformation stiffness, local flexible deformation, and strain distribution consistency, this invention proposes four objective functions characterizing the overall stiffness and local stiffness of the wing structure, leading and trailing edge flexibility, and strain uniformity. A multi-objective optimization method is used to construct a multi-objective optimization formula, optimizing to obtain the optimal material layout and distributed flexible mechanism design.

[0006] The technical solution of this invention:

[0007] A rigid-flexible integrated optimization design method for compliant variator wings, comprising the following steps:

[0008] First, the design domain, boundary conditions, and design conditions of the wing ribs are determined. The wing rib design domain is divided into two parts: a flexible design domain, represented by the leading and trailing edges of the wing ribs, with the design objective of maximizing the displacement of the leading or trailing edge output positions (multiple output points) and minimizing the strain distribution function; and a rigid design domain, represented by the other parts of the wing ribs, with the design objective of ensuring the ability to maintain the local configuration under the driving force of the flexible parts. The boundary conditions of the design domain are divided into three types: displacement boundary conditions, force boundary conditions, and free boundary conditions, corresponding to the fixed displacement end at the wing rib spar, the aerodynamic loads on the outer surface of the wing and the leading and trailing edge actuator parts, and the other parts of the wing, respectively. The wing operating conditions are divided into two types: one is the aerodynamic loads on the wing; the other is the actuator loads caused by deformation of the leading and trailing edges.

[0009] Secondly, a finite element model for the rigid-flexible co-design of the wing ribs was established, with the rib edges designated as undesignable domains. A geometric model of the ribs was created, a finite element mesh was generated, and information such as the element node positions was exported. The element information was read using programming to form an element stiffness matrix, which was then combined into a global stiffness matrix, and boundary conditions were applied. Finite element analysis under different load conditions was performed to obtain the displacement field.

[0010] Finally, a multi-objective topology optimization model for the wing ribs was constructed and solved. Four objective functions for topology optimization were determined: First, to ensure the overall load-bearing capacity of the wing ribs under aerodynamic loads, the first objective function is to minimize the overall compliance of the wing ribs under aerodynamic load conditions, i.e., maximize overall stiffness; second, to ensure that the rigid parts of the wing can still withstand loads and maintain local configuration under actuator action, the second objective function is to minimize the structural compliance of the rigid parts of the wing under driving force, i.e., maximize local stiffness; third, to ensure that the leading and trailing edges of the wing can undergo sufficient deformation under actuator action, the third objective function is to maximize the output displacement at specified positions on the leading and trailing edges of the wing under actuator action; and fourth, to ensure uniform deformation of the leading and trailing edges of the wing, the fourth objective function is to minimize the strain distribution function at the leading and trailing edges, i.e., achieve strain uniformity during the compliant deformation process. The topology optimization constraints were to set upper limits on the volume fraction of material used in the flexible and rigid parts of the wing ribs, i.e., to set overall weight constraints. The optimal design variable is the relative density of the elements. A material interpolation model is constructed using the Solid Isotropic Material with Penalization (SIMP) method. Mathematical programming is used to solve the multi-objective optimization problem to obtain the optimal material layout and compliant variant structure design.

[0011] The specific steps are as follows:

[0012] S1, Determine the wing rib design domain; the design region Ω is divided into design domains Ω dAnd the non-design domain Ω0, where the design domain Ω d Divided into flexible design domain Ω f and rigid design domain Ω s Consider two operating conditions for the wing ribs: one is the aerodynamic load experienced during wing flight; the other is the actuator load experienced due to deformation of the leading and trailing edges. Based on this, the boundary condition for operating condition one is to constrain the displacement at the fixed end of the design domain, with the outer surface of the wing subjected to an aerodynamic load F. e The boundary condition for condition two is to constrain the displacement at the fixed end of the design domain, and the airfoil is subjected to a rightward driving force F at the junction of the rigid and flexible design domains. d ;

[0013] S2: Construct a finite element model and mesh the design region in S1, and export the element node location information and element connectivity information; read the node location information and element connectivity information through programming, calculate the element stiffness matrix of each element in the design region, and apply the two boundary conditions set in S1.

[0014] S3, select the relative density ρ of each unit divided in S2. i As a design variable, an isotropic material penalty model, i.e., SIMP, is applied to each element to obtain the elastic modulus penalty relationship of the element under different relative densities:

[0015]

[0016] Where E0 is the elastic modulus of the solid material; E min Let E be the elastic modulus corresponding to the hole. min =10 -9 ;k p This is the penalty coefficient, with a value of 3;

[0017] S4, Assemble the element stiffness matrix calculated in S2 into a global stiffness matrix K, including the stiffness matrix K of the rigid part. s , flexible part stiffness matrix K f Given the undesignable domain K0, the finite element method is used to solve the overall displacement domain U of the structure under load condition 1. e Displacement domain U under working condition two d Displacement domain U d Displacement domain U including rigid parts ds and flexible displacement domain U df :

[0018]

[0019] S5, considering the overall structural load-bearing stiffness and local stiffness design requirements, the structural local flexibility variant design requirements, and the strain uniformity requirements of the flexible part, proposes four objective functions to characterize the overall stiffness, local stiffness, leading and trailing edge flexibility, and strain uniformity of the wing rib structure:

[0020]

[0021]

[0022] f3 = L T U df (3)

[0023]

[0024] The sensitivities of the four objective functions are as follows:

[0025]

[0026]

[0027]

[0028]

[0029] Among them, the sensitivities f1 and f2 are obtained by the direct method, the sensitivity f3 is obtained by the adjoint method, and the sensitivity f4 is obtained by the chain rule. The adjoint vector is L, which is the extracted position identifier vector, and has a non-zero element at the position of the output degree of freedom; u e u ds and u df For U e U ds and U df The unit component, ρ i For the relative density of the unit cell, For unit equivalent strain, For the average equivalent strain in the flexible region. The equivalent variable vector of the unit;

[0030] S6 integrates the optimization problems of maximizing overall load-bearing stiffness, maximizing local stiffness, maximizing local variants and strain uniformity of variant parts into a minimization objective function f through a weighted approach;

[0031]

[0032] Where w1, w2, w3, and w4 are weights;

[0033] S7, In order to restrict the volume of both the rigid and flexible parts, the volume fractions of the flexible and rigid parts are determined as ξ. f and ξ s :

[0034]

[0035] S8, the multi-objective optimization formula is constructed as follows:

[0036]

[0037] Where n is the total number of elements in the design domain, which is also the number of design variables. These are the upper volume limits for the flexible and rigid regions, respectively.

[0038] S9, update the design variable ρ using gradient-based mathematical programming. new ;

[0039] S10, Determine the convergence condition:

[0040] ||ρ new -ρ||≤η

[0041] Where η is the set convergence criterion value. If the condition is met, the iteration ends. If the condition is not met, return to step S3 and continue iterating until the convergence condition is met.

[0042] The beneficial effects of this invention are as follows: This invention establishes a design that simultaneously considers the requirements for local flexible variant design, strain uniformity requirements for flexible parts, overall load-bearing stiffness, and local stiffness design requirements. It proposes indices characterizing the flexibility and strain uniformity of the wing's leading and trailing edges, as well as the overall and local stiffness of the structure. It considers four objectives: maximizing the output point displacement of the flexible part, minimizing the strain distribution variance, minimizing the overall structural compliance, and minimizing the compliance of the rigid part. A multi-objective optimization formula is constructed. In particular, it considers the impact of deformation of the rigid part during load-bearing on the design of the flexible part, enabling topology optimization of a rigid-flexible collaborative structure. This overcomes the problem of excessive rigidity or flexibility caused by designing rigid or flexible components alone. Furthermore, by introducing a strain uniformity objective, it achieves the design of a distributed flexible mechanism, avoiding local strain concentration that could affect the service life of the flexible variant structure. Attached Figure Description

[0043] Figure 1 This is a flowchart of a rigid-flexible integrated optimization design method for wing ribs used in load-bearing and flexible variants.

[0044] Figure 2 This is a schematic diagram of the wing airfoil of the NACA4421.

[0045] Figure 3 This is a schematic diagram of the wing rib structure design domain.

[0046] Figure 4 This is a schematic diagram of aerodynamic loads on the outer surface of the wing, (a) upper surface, (b) lower surface.

[0047] Figure 5 This is a schematic diagram of the finite element model and mesh generation of the wing ribs.

[0048] Figure 6 (a) is the topology design diagram; (b) is the initial design schematic diagram; and (c) is the final topology optimization design result.

[0049] Figure 7 A modified schematic diagram of the final topology optimization design result.

[0050] Figure 8 This is a schematic diagram of topology reconstruction. Detailed Implementation

[0051] To better illustrate the technical solution of the present invention, the following describes in detail the implementation examples provided by the present invention with reference to the accompanying drawings, but the implementation of the present invention is not limited thereto.

[0052] Example 1

[0053] like Figure 1 As shown, this embodiment is a rigid-flexible integrated optimization design method for wing ribs of load-bearing and flexible variants, including the following steps:

[0054] S1. In this example, the NACA4421 airfoil is selected as the design domain. Figure 2 As shown. For simplicity, this example only uses the left half of the wing rib as the design domain, and the airfoil curve is obtained from the NACA parametric airfoil expression.

[0055] Airfoil thickness distribution formula:

[0056]

[0057] In the formula: c is the airfoil chord length; x is the distance from the leading edge point along the chord length direction; τ is the ratio of the maximum airfoil thickness to the chord length. In this example, c = 1000 mm, τ = 0.21, and the optimization area is taken as the length of the leading half of the wing rib, c / 2 = 500 mm.

[0058] Formula for airfoil mid-curve:

[0059]

[0060] In the formula, β is the maximum camber of the airfoil; p is the chordal distance from the point of maximum camber to the leading edge.

[0061] By combining equations (8) and (9), the coordinate expressions for the upper and lower surfaces of the airfoil can be obtained:

[0062]

[0063] In this example, β = 0.04, p = 0.4, (x, y u Let (x, y) be the coordinates of the upper surface of the airfoil. d ) represents the coordinates of the lower surface of the airfoil.

[0064] S2, construct the finite element model and mesh it, derive the element node location information and element connectivity information; read the node location information and element connectivity information through programming, and calculate the element stiffness matrix of each element in the design area. Define boundary conditions as follows. Figure 3 As shown: The boundary condition for operating condition one is to constrain the displacement at the right end of the design domain, and the outer surface of the wing is subjected to an aerodynamic load F. e The boundary condition for condition two is to constrain the displacement at the right end of the design domain, and the airfoil experiences a rightward driving force F at the junction of its rigid and flexible design domains. d Working condition one corresponds to the solution conditions for the overall structural bearing stiffness; working condition two corresponds to the solution conditions for local deformation stiffness, local compliant deformation, and strain uniformity. Based on this, the four objective functions under the two working conditions are superimposed.

[0065] The forces acting on the aerodynamic load are:

[0066]

[0067]

[0068] Among them, y U For the load on the upper surface of the wing, y L For the load on the lower surface of the wing, x U Apply length x to the load on the upper surface of the wing L Apply a length A(x) to the load on the lower surface of the wing. U1 ,y U1 ),B(x U2 ,y U2 ),C(x L1 ,y L1 ),D(x L2 ,y L2 Define the point for the aerodynamic load function, where x U1 x U2 x L1 x L2 This represents the chordal positions of these four key points on the upper and lower surfaces, y U1 y U2 y L1 y L2 The load diagram corresponds to the magnitude of the load at that location, as shown below. Figure 4 As shown.

[0069] S3, determine the design variable as the relative density ρ of each element. i The material modulus penalty formula is obtained by applying the solid isotropic material penalty model SIMP to each element:

[0070]

[0071] Where, k p The value is 3.

[0072] S4 assembles the element stiffness matrix calculated in S2 into a global stiffness matrix K (including the stiffness matrix K of the rigid part). s , flexible part stiffness matrix K f And the undesignable domain K0), and use the finite element method to solve the overall displacement domain U of the structure under load condition one. e Displacement domain U under working condition two d (including the displacement domain U of the rigid part) ds and flexible displacement domain U df ):

[0073]

[0074] S5, calculate the four objective functions respectively:

[0075]

[0076] The sensitivities of the four objective functions are as follows:

[0077]

[0078] Among them, the sensitivities f1 and f2 are obtained by the direct method, the sensitivity f3 is obtained by the adjoint method, and the sensitivity f4 is obtained by the chain rule. Let L be the adjoint vector, and let u be the extracted position identifier vector, which has a non-zero element at the position of the output degree of freedom. e u ds and u df For U e U ds and U df The unit component, ρ i For the relative density of the unit cell, For unit equivalent strain, For the average equivalent strain in the flexible region. It is an equivalent variable vector.

[0079] S6 integrates the optimization problems of maximizing overall load-bearing stiffness, maximizing local stiffness, maximizing local variants, and maximizing strain uniformity in variant parts into a weighted approach, which is then minimized as the objective function f:

[0080]

[0081] Among them, w1, w2, w3, and w4 are weights, which can be assigned values ​​based on the relative importance of f1, f2, f3, and f4.

[0082] S7, calculate the volume fractions of the flexible and rigid parts respectively as ξ f and ξ s The upper limits for the volume fraction of the flexible and rigid parts are 0.3 and 0.5, respectively.

[0083]

[0084] S8, the optimized column is constructed as follows:

[0085]

[0086] Where n is the total number of elements in the design domain, which is also the total number of design variables. These are the upper limits of the volume for the flexible region and the rigid region, respectively, and in this example, they are set to 0.3 and 0.5.

[0087] S9, update the design variable ρ using gradient-based mathematical programming. new ;

[0088] S10, Determine the convergence condition:

[0089] ||ρ new -ρ||≤η (20)

[0090] Where η is the set convergence criterion value. If the condition is met, the iteration ends. If the condition is not met, return to step S3 and continue iterating until the convergence condition is met.

[0091] Compared to the initial structure, the optimized design results in this example show a 35.95% increase in the overall stiffness of the wing ribs; a 99.17% increase in the stiffness of the rigid portion of the wing under the actuator action; a 2751.52% increase in the sum of the output displacements at the defined point on the wing leading edge; and an 84.00% reduction in the non-uniformity of the wing leading edge strain. This example employs a multi-objective optimization model that considers both rigid and flexible structural design, overcoming the problem of excessive stiffness or flexibility resulting from designing rigid or flexible components in isolation. The resulting structure has clear boundaries and possesses certain practical engineering value.

Claims

1. A rigid-flexible integrated optimization design method for compliant variator wings, characterized in that, The steps are as follows: S1, Determine the wing rib design domain, design area Divided into design domains Non-design domain Design domain Divided into flexible design domains and rigid design domain Considering two operating conditions for the wing ribs: one is the aerodynamic load experienced during wing flight; the other is the actuator load experienced due to deformation of the leading and trailing edges. Based on this, the boundary condition for operating condition one is to constrain the displacement at the fixed end of the design domain, with the outer surface of the wing subjected to aerodynamic loads. ; The boundary conditions for condition two are to constrain the displacement at the fixed end of the design domain, and the junction of the rigid and flexible design domains of the wing is subjected to a driving force to the right. ; S2: Construct a finite element model and mesh the design region in S1, and export the element node location information and element connectivity information. By reading node location information and element connectivity information through programming, the element stiffness matrix of each element in the design area is calculated, and the two boundary conditions set in S1 are applied. S3, select the relative density of each unit divided in S2. As a design variable, an isotropic material penalty model, i.e., SIMP, is applied to each element to obtain the elastic modulus penalty relationship of the element under different relative densities: (1) in, The elastic modulus of a solid material; Let the elastic modulus corresponding to the hole be taken as... ; This is the penalty coefficient, with a value of 3; S4 assembles the element stiffness matrix calculated in S2 into a global stiffness matrix. Including the stiffness matrix of the rigid part Flexible part stiffness matrix and undesignable domains The displacement domain of the entire structure under load condition 1 is solved using the finite element method. Displacement domain under working condition two Displacement domain Displacement domain including rigid parts and flexible displacement domain : (2) S5, considering the overall structural load-bearing stiffness and local stiffness design requirements, the structural local flexibility variant design requirements, and the strain uniformity requirements of the flexible part, proposes four objective functions to characterize the overall stiffness, local stiffness, leading and trailing edge flexibility, and strain uniformity of the wing rib structure: (3) The sensitivities of the four objective functions are as follows: (4) in, and Sensitivity was obtained using the direct method. Sensitivity was obtained using the adjoint method. Sensitivity is obtained using the chain rule; , For the adjoint vector, To extract the position identifier vector, there is a non-zero element at the position of the output degree of freedom; , and for , and unit components, For the relative density of the unit cell, For unit equivalent strain, For the average equivalent strain in the flexible region. The equivalent variable vector of the unit; S6 integrates the optimization problems of maximizing overall load-bearing stiffness, maximizing local stiffness, maximizing local variants, and maximizing strain uniformity in variant parts into a minimization objective function through a weighted approach. ; (5) in, , , , As weight; S7, In order to limit the volume of both the rigid and flexible parts, the volume fractions of the flexible and rigid parts are determined as follows: and : (6) S8, the multi-objective optimization formula is constructed as follows: (7) in, This refers to the total number of elements within the design domain, which is also the number of design variables. , These are the upper volume limits for the flexible and rigid regions, respectively. S9, using gradient-based mathematical programming to update design variables. ; S10, Determine the convergence condition: in, η The set convergence criterion value is used. If the condition is met, the iteration ends. If the condition is not met, return to step S3 and continue iterating until the convergence condition is met.

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