A Flapping Wing Structure Optimization Method Based on Stiffness Similarity

Abstract

The present invention discloses a flapping wing structure optimization method based on stiffness similarity, which belongs to the field of aircraft structure optimization. The present invention uses a variable density method to perform structural topology optimization on a finite element model, achieving the optimal minimum compliance of the flapping wing structure, thereby improving the structural stiffness of the flapping wing. Furthermore, based on insect wing stiffness experiments, the relationship between the flapping wing's spanwise bending stiffness and span length is established, and a stiffness similarity criterion is established using principal component analysis. A linear linear function of the flapping wing model's spanwise bending stiffness as a function of span length is solved, and the spanwise bending stiffness at different span lengths of the flapping wing is determined. With minimum structural mass as the optimization goal, the parameters of each vein line width function are used as variables, and the spanwise bending stiffness at different span lengths and the upper and lower boundaries of the line width that meet the structural strength, processing size, and engineering precision requirements of the insect wing are used as constraints, the flapping wing is optimized, thereby determining the flapping wing's veined structural layout and improving the flapping wing's lift and aerodynamic performance.

Description

Technical Field

[0001] The invention relates to a flapping wing structure optimization method for a micro flapping wing and flapping rotor aircraft, and belongs to the field of aircraft structure optimization. Background Art

[0002] Since the 1990s, biomimetic flapping-wing micro-aircraft have attracted increasing attention from scholars. Compared to fixed-wing and rotary-wing micro-aircraft, flapping-wing micro-aircraft have high aerodynamic efficiency and good maneuverability, and can achieve vertical take-off and landing and hovering functions, but they have the disadvantage of complex mechanical structure. To overcome the technical bottleneck of flapping-wing aircraft, some scholars have proposed the concept of flapping-rotor aircraft. The flapping-rotor combines the kinematic characteristics of flapping wings and rotary wings. By installing a pair of centrally symmetrical wings, the flapping wings generate a pair of force couples on the two wing surfaces as they flap up and down, causing the flapping wings to produce a self-spinning motion. No external torque is required for balancing, so there is no need for balancing devices such as tail rotors, which reduces energy consumption while simplifying the structure of the aircraft.

[0003] Currently, research on micro-flapping wing and flapping rotor aircraft focuses primarily on the design of drive mechanisms that achieve biomimetic flapping motion and the numerical simulation and experimental verification of the aircraft's aerodynamic characteristics. Flapping wings typically utilize a simple beam-membrane structure, which cannot meet the requirements of micro-aircraft for wing structural quality, lift, and flight efficiency. However, biomimetic flapping wing designs can effectively improve flapping wing aerodynamic efficiency. Summary of the Invention

[0004] The purpose of the present invention is to provide a flapping wing structure optimization method based on stiffness similarity. For flapping wing structures used in micro flapping wing and flapping rotor aircraft, combined with the wing structure characteristics of flying organisms in nature, a variable density method is used to perform structural topology optimization on a finite element model to achieve the optimal minimum flexibility of the flapping wing structure, thereby improving the structural stiffness of the flapping wing; in addition, based on the insect wing stiffness experiment, a relationship between the spanwise bending stiffness of the flapping wing and the span length is established, and a principal component analysis method is used to establish a stiffness similarity criterion based on the relationship between the bending stiffness of insect wings at different scales in nature and the geometric morphological parameters of the insects. The spanwise bending stiffness of the flapping wing model is solved according to the stiffness similarity criterion. A linear linear function that changes with the span length is used to determine the spanwise bending stiffness of the flapping wing at different span lengths based on the linear linear function. The section moment of inertia at different span lengths is determined based on the material properties of the flapping wing and the spanwise bending stiffness at different span lengths, and then the section size at different span lengths is determined. The flapping wing is optimized with the minimum structural mass as the optimization goal, the parameters of each vein line width function as the design variables, and the spanwise bending stiffness at different span lengths and the upper and lower boundaries of the line width that meet the structural strength, processing size and engineering precision requirements of the insect wing as constraints, thereby determining the bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift aerodynamic performance of the flapping wing.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention discloses a flapping wing structure optimization method based on stiffness similarity, comprising the following steps:

[0007] Step 1: Establish a finite element model of the insect wing-like flat plate structure, and perform structural topology optimization of the finite element model using the variable density method to achieve the optimal minimum flexibility of the flapping wing structure; based on the topological optimization results with optimal minimum flexibility and insect wing biological samples, establish a simplified insect wing-like model.

[0008] Step 1.1: Based on the shape and dimensions of natural insect wings, establish an optimized design model for the flat plate structure of an insect wing. Define the leading edge vein as the non-design domain and the rest of the model as the design domain. Build a finite element model of the insect wing planar structure, meshing it with shell elements and defining the element material properties. Apply a uniformly distributed load to the wing surface, and set six degrees of freedom constraints at the wing root.

[0009] Step 1.2: Use the variable density method to perform structural topology optimization on the finite element model, and select the solid isotropic material with penalization (SIMP) model as the interpolation model.

[0010] The SIMP model interpolation formula is:

[0011]

[0012] Where, E i is the elastic modulus after interpolation, E0 is the real elastic modulus of the material, x i is the pseudo density of the i-th unit, and p is the penalty factor.

[0013] A flapping wing structure topology optimization model is established as shown in formula (2), where the design variable is the pseudo-density of each unit, the optimization target is the minimum compliance of the structure, and the constraint condition is the material retention ratio.

[0014]

[0015] Where x i is the pseudo-density of the i-th unit, C is the overall flexibility of the structure, F is the structural node force vector, U is the structural node displacement vector, M is the structural mass, M0 is the original mass of the structure, f is the material retention ratio, which means the proportion of the material retained in the optimized structure to the original structural material, K is the overall structural stiffness matrix, x min The minimum value of pseudo density of the element is introduced to prevent the singularity of the stiffness matrix. The smaller the C value, the greater the structural stiffness.

[0016] Step 1.3: For the topology optimization mathematical model of step 1.2, determine the interpolation model penalty coefficient and material retention ratio, and perform topology optimization to achieve the optimal minimum compliance of the flapping wing structure. Combine the topology optimization results of the finite element model of the insect wing plane structure with the geometric shape, size, and wing vein structure layout of real insect wings in nature to establish a simplified insect-like wing model.

[0017] Step 2: Based on the insect wing stiffness experiment, a relationship between the spanwise bending stiffness of the flapping wing and the span length is established. The principal component analysis method is used to establish a stiffness similarity criterion based on the relationship between the bending stiffness of insect wings at different scales in nature and the geometric morphological parameters of insects. According to the stiffness similarity criterion, a linear linear function of the spanwise bending stiffness of the simplified insect wing model described in step 1 and the spanwise bending stiffness of the flapping wing at different span lengths is solved. According to the linear linear function, the spanwise bending stiffness of the flapping wing at different span lengths is determined. According to the material properties of the flapping wing and the spanwise bending stiffness at different span lengths, the section moment of inertia at different span lengths is determined, and then the cross-sectional dimensions at different span lengths are determined. With the minimum structural mass as the optimization goal, the parameters of each vein line width function are used as design variables, and the spanwise bending stiffness at different span lengths and the upper and lower boundaries of the line width that meet the structural strength, processing size and engineering precision requirements of the insect wing are used as constraints, the flapping wing is optimized and designed, thereby determining a bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift aerodynamic performance of the flapping wing.

[0018] Step 2.1: Use the cantilever beam bending test method to measure the bending stiffness of insect wings at different span lengths and establish the relationship between the spanwise bending stiffness of the flapping wings and the span length.

[0019]

[0020] Where E is the elastic modulus of the material used for the flapping wing, I i is the section moment of inertia at i×10% of the flapping wing span, m and n are unknown quantities, where m is the slope of the linear linear function of spanwise bending stiffness varying with span, and n is the intercept of the linear linear function; α is the proportionality coefficient, whose value is measured experimentally.

[0021] Step 2.2: Use principal component analysis to determine the relationship between insect wing stiffness and geometric parameters at different scales. Establish a stiffness similarity criterion to determine the relationship between flapping wing spanwise bending stiffness and flapping wing half-span, chord length, flapping wing area, and vehicle mass. The calculation method is:

[0022] Step 2.2.1: Standardize the data on insect wing length, chord length, wing area, and insect mass to calculate the correlation coefficient matrix

[0023]

[0024] Where r ij is the correlation coefficient between index j and index k, and its calculation formula is:

[0025]

[0026] Step 2.2.2: Calculate the eigenvalue λ of the correlation coefficient matrix R i (i=1,2,…,p) and the corresponding eigenvector e i (i=1,2,…,p), and arranged in order of size as λ1≥λ2≥…≥λ p ≥0.

[0027] Step 2.2.3: Calculate the variance contribution rate of each principal component and determine the number of principal components based on the cumulative contribution rate, where principal component z i The contribution rate of

[0028]

[0029] The cumulative contribution rate is

[0030]

[0031] Usually choose the cumulative contribution rate The eigenvalues λ1,λ2,…,λ m The corresponding 1st, 2nd, ..., mth (m≤p) principal components.

[0032] Step 2.2.4: Calculate principal component loadings

[0033]

[0034] Thus, the principal component expression is obtained

[0035] z i =w i1 logl+w i2 logb+w i3 logS+w i4 logm(i=1,2,…,p) (9)

[0036] where z i is the i-th principal component.

[0037] Step 2.2.5: Based on the principal component expression, a logarithmic function is used to fit the first principal component consisting of wing length, chord length, wing area and mass to the data of insect spanwise bending stiffness. The relationship between the comprehensive index consisting of wing length, chord length, wing area and mass and the insect spanwise bending stiffness is obtained.

[0038]

[0039] Where m is the number of principal components, a0, a i are the coefficients in the relationship, and the insect wing stiffness similarity criterion using wing length, chord length, wing area and mass as comprehensive indicators is obtained.

[0040] Step 2.3: Based on the relationship between the spanwise bending stiffness of insect wings and span length determined by stiffness experiments (Equation (3)) and the insect wing stiffness similarity criterion (Equation (10)) using wing length, chord length, wing area, and mass as comprehensive indicators, solve the linear linear function of the spanwise bending stiffness of the flapping wing model in Equation (3) according to the stiffness similarity criterion described in Equation (10) for the variation of spanwise bending stiffness with span length.

[0041] EI i =mi+n(N·m 2 ) (11)

[0042] The values of the unknown quantities m and n.

[0043] The spanwise bending stiffness of the simplified insect wing model at different spans described in step 1 is determined according to the linear linear function shown in formula (11). The section moments of inertia at different spans can be determined according to the material properties of the wing model and the spanwise bending stiffness at different spans, and then the section dimensions at different spans can be determined.

[0044] Step 2.4: Based on the relationship between the cross-sectional size change of insect wings and the spanwise bending stiffness change of flapping wings along the span (11), the width of each vein line changes according to a linear function. When the cross-sectional shape is rectangular and the thickness of the flapping wing vein is constant, the minimum structural mass is taken as the optimization goal, the parameters of each vein line width function are used as design variables, and the spanwise bending stiffness at different spans and the upper and lower boundaries of the line width that meet the requirements of the insect wing structural strength, processing size and engineering accuracy are used as constraints to optimize the flapping wing design:

[0045]

[0046] Where, l j =a j x+b j is the line width function of each vein, where l j is the line width at x on the vein, a j is the slope of the linear function, b j is the intercept of the linear function, x is the position of a point on the vein, j is the jth vein, and W is the mass of the flapping wing model.

[0047] Step 2.5: Based on the optimization results, the parameters in the line width function of each vein are obtained, and the flapping wing structure is optimized based on stiffness similarity, thereby determining the bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift aerodynamic performance of the flapping wing.

[0048] Step 3: Based on the bionic flapping wing vein structure layout obtained in Step 2.5, select appropriate materials to manufacture the wing veins and wing membrane. The wing veins are machined and cut. The flapping wing veins and wing membrane are bonded together to form a flapping wing.

[0049] Beneficial effects:

[0050] 1. The present invention discloses a flapping wing structure optimization method based on stiffness similarity. Based on the insect wing stiffness experiment, the relationship between the span-wise bending stiffness of the flapping wing and the span length is established. The principal component analysis method is used to establish a stiffness similarity criterion based on the relationship between the bending stiffness of the insect wing at different scales in nature and the geometric parameters of the insect. According to the stiffness similarity criterion, a linear function of the span-wise bending stiffness of the flapping wing model and the span length is solved. The span-wise bending stiffness at different span lengths of the flapping wing is determined based on the linear function. According to the flapping wing material properties, the span-wise bending stiffness of the flapping wing model is determined based on the stiffness similarity criterion. The flapping wing is optimized based on the spanwise bending stiffness and the spanwise bending stiffness at different spans, thereby determining the cross-sectional moments of inertia at different spans, and then the cross-sectional dimensions at different spans. With minimizing structural mass as the optimization goal, the parameters of each vein linewidth function are used as design variables, and the spanwise bending stiffness at different spans and the upper and lower width boundaries that meet the structural strength, processing size, and engineering precision requirements of insect wings are used as constraints. This results in a biomimetic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift and aerodynamic performance of the flapping wing. The flapping wing designed by this method has similar stiffness and geometry to biological insect wings, and has better biomimetic properties.

[0051] 2. The present invention discloses a flapping wing structure optimization method based on stiffness similarity. For flapping wing structures used in micro flapping wing and flapping rotor aircraft, combined with the wing structure characteristics of flying organisms in nature, the variable density method is used to perform structural topology optimization on the finite element model to achieve the optimal minimum flexibility of the flapping wing structure, thereby improving the structural stiffness of the flapping wing.

[0052] 3. The present invention discloses a flapping wing structure optimization method based on stiffness similarity. On the basis of achieving beneficial effects 1 and 2, the flapping wing structure optimized by the present invention has better aerodynamic performance than the traditional rectangular flat wing and the flapping wing designed based on geometric similarity, and can achieve a significant increase in lift. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is an overall flow chart of a flapping wing structure optimization method based on structural similarity of the present invention;

[0054] Figure 2 The dragonfly wing sample and vein distribution diagram in Example 1 of the flapping wing structure optimization method based on structural similarity of the present invention;

[0055] Figure 3 This is a flowchart of wing structure topology optimization in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0056] Figure 4 This is a finite element model diagram of the dragonfly wing plane structure in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0057] Figure 5 This is a diagram showing the topology optimization results of the wing structure in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0058] Figure 6 This is a diagram of a simplified dragonfly-like wing design model in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0059] Figure 7 Schematic diagram of a method for measuring the bending stiffness of dragonfly wings in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0060] Figure 8 FIG1 is a diagram of a flapping wing design model based on stiffness similarity in Example 1 of a flapping wing structure optimization method based on structural similarity of the present invention;

[0061] Figure 9 This is a real picture of the flapping wing in Example 1 of the flapping wing structure optimization method based on structural similarity of the present invention. DETAILED DESCRIPTION

[0062] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0063] Example 1:

[0064] like Figure 1 As shown, this embodiment discloses a flapping wing structure optimization method based on stiffness similarity, and the specific implementation method is as follows:

[0065] Step 1: Establish a finite element model of the insect wing plate structure, and perform structural topology optimization on the finite element model using the variable density method to achieve the optimal minimum compliance of the flapping wing structure; based on the topological optimization results of the optimal minimum compliance and the insect wing biological sample, establish a simplified insect wing model. The specific implementation steps are as follows: Figure 2 As shown, including:

[0066] Step 1.1: Based on the shape and size of the dragonfly wings, establish an optimized design model of the dragonfly wing plate structure. In this embodiment, the dragonfly wing structure is as follows: Figure 3 As shown in the figure, the finite element model is Figure 4 As shown in the figure, the purple part is the design domain. A finite element model of the dragonfly wing plane structure is established, and the unit material is specified as Teflon, with an elastic modulus of 6.1 GPa, a Poisson's ratio of 0.25, and a density of 1200 kg / m 3 A uniform load is applied to the wing surface, and a six-degree-of-freedom constraint is set at the wing root.

[0067] Step 1.2-1.3: Establish a mathematical model for topology optimization as shown in formula (2), set the interpolation model penalty coefficient and material retention ratio, and perform topology optimization. In this implementation, the interpolation model penalty coefficient is p = 4, and the material retention ratio is f = 0.189-0.191. The optimization results are as follows: Figure 5 Based on the topological optimization results of the minimum compliance and the biological sample of dragonfly wings, a simplified dragonfly wing model is established, as shown in Figure 6 shown.

[0068] Step 2: Based on the dragonfly wing stiffness experiment, the relationship between the spanwise bending stiffness of the flapping wing and the span length is established. The principal component analysis method is used to establish a stiffness similarity criterion based on the relationship between the bending stiffness of the dragonfly wing at different scales in nature and the geometric parameters of the dragonfly. According to the stiffness similarity criterion, the linear function of the spanwise bending stiffness of the simplified dragonfly wing model described in step 1 and the spanwise bending stiffness at different span lengths of the flapping wing is solved. According to the linear function, the spanwise bending stiffness at different span lengths of the flapping wing is determined. According to the material properties of the flapping wing and the different span lengths, the spanwise bending stiffness of the dragonfly wing is determined. The spanwise bending stiffness at different spans is used to determine the section moment of inertia at different spans, and then the section size at different spans is determined. Taking the minimum structural mass as the optimization goal, the parameters of each vein linewidth function are used as design variables, and the spanwise bending stiffness at different spans and the upper and lower boundaries of the linewidth that meet the structural strength, processing size and engineering accuracy requirements of the wing model as constraints, the flapping wing is optimized to determine the bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft, so as to improve the lift aerodynamic performance of the flapping wing.

[0069] Step 2.1: Use the cantilever beam bending test method to measure the bending stiffness of the dragonfly forewing at different spans. The specific steps are as follows: Use scissors to cut the complete forewing from the wing root of the dragonfly, and use glue to glue the dragonfly wing to the base to fix it. Attach a thin wire to the load application point, and hang a mass block on the other end of the thin wire. The principle diagram of the dragonfly stiffness test is as follows Figure 7 The displacement at the load-applied point is measured and the bending stiffness of the dragonfly wing is calculated.

[0070] Applying loads of varying magnitudes at different locations yields the displacement at the applied loads. The bending stiffness (EI) of the dragonfly's forewing is calculated using the following formula:

[0071]

[0072] Where F is the concentrated force on the wing bending, L is the effective bending length, and δ is the displacement at the force application point.

[0073] According to the experimental measurement results, the relationship between span-wise bending stiffness and span length is obtained:

[0074]

[0075] Step 2.2: Use principal component analysis to determine the relationship between dragonfly wing stiffness and geometric parameters at different scales. Establish a stiffness similarity criterion and determine the relationship between flapping wing spanwise bending stiffness and flapping wing half-span, chord length, flapping wing area, and aircraft mass.

[0076] Step 2.2.1: Standardize the data on wing length, chord length, wing area, and mass, and calculate the correlation coefficient matrix:

[0077]

[0078] Steps 2.2.2-2.2.3: The eigenvalues and variance contributions of each principal component are calculated and shown in Table 1.

[0079] Table 1 Eigenvalue and principal component contribution table

[0080]

[0081] Step 2.2.4: As can be seen from the table above, the cumulative contribution of the first principal component is greater than 85%, so only the first principal component needs to be calculated. For the eigenvalue λ1 = 3.8846, its eigenvector is calculated as e1 = (0.5002, 0.5026, 0.5064, 0.4906). Then, the loading of each variable on the principal component is calculated. The principal component expression is:

[0082] z1=0.9858logl+0.9906logb+0.9982logS+0.9671logm (15)

[0083] Step 2.2.5: Based on the principal component expression shown in Equation (15), a logarithmic function is used to fit the first principal component consisting of wing length, chord length, wing area, and mass to the data of insect spanwise bending stiffness. The relationship between the comprehensive index consisting of wing length, chord length, wing area, and mass and the insect spanwise bending stiffness is obtained as follows:

[0084] logy=-0.1781+0.41106z1 (16)

[0085] The stiffness similarity criterion is applied to flapping wings, with the wing length corresponding to the half span of the flapping wing, the wing chord length and wing area corresponding to the chord length and flapping area of the flapping wing, respectively, and the insect mass corresponding to the aircraft mass.

[0086] According to the size of the bionic flapping wing, set l = 0.16m, b = 0.04m, S = 0.005m 2 , m = 0.03 kg, then according to the stiffness similarity criterion, the spanwise bending stiffness of the flapping wing at 70% of its span is 0.002417 N·m 2 .

[0087] Step 2.3: Based on the relationship between the span-wise bending stiffness of the dragonfly wing and the span length and the stiffness similarity criterion, the relationship shown in equation (17) can be determined:

[0088]

[0089] Where, E is the elastic modulus of carbon fiber, E = 26GPa, I i is the section moment of inertia at i×10% of the flapping wing span, m is the slope of the linear function of spanwise bending stiffness varying with span, and n is the intercept of the linear function.

[0090] By solving the above equation, we can obtain the linear function of spanwise bending stiffness changing with span length:

[0091] EI i =(-0.5876i+6.526)×10 -3 N·m 2 (18)

[0092] The section moment of inertia can be determined as

[0093] I i =(-0.0226i+0.251)mm 4 (19)

[0094] Step 2.4: Based on the cross-sectional size variation of dragonfly wings and the relationship between the spanwise bending stiffness of the flapping wing along the span shown in formula (18), the width of each vein line changes according to a linear function. When the cross-sectional shape is rectangular and the thickness of the flapping wing vein is constant, the minimum structural mass is taken as the optimization goal, the parameters of each vein line width function are used as design variables, and the spanwise bending stiffness at different spans and the upper and lower boundaries of the line width are used as constraints. The flapping wing is optimized and the optimization mathematical model shown in formula (20) is established for optimization design:

[0095]

[0096] Step 2.5: Based on the optimization results, obtain the parameter a in the line width function of each vein j and b j In this embodiment, the parameters of the main vein line width function are shown in Table 2.

[0097] Table 2 Parameters of the main vein linewidth functions of the flapping wing model

[0098]

[0099] Based on the parameter a in the line width function of each vein j and b j The line width of each vein can be determined, and based on the flapping wing structure model with similar stiffness, the bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft can be determined, such as Figure 8 shown.

[0100] Step 3: Based on the obtained bionic flapping wing vein structure layout, 0.6mm thick carbon fiber is used to process the wing veins, and 0.015mm thick polyimide film is used to process the wing membrane. The wing veins are processed and made using a machining process. Glue is used to bond the flapping wing veins and wing membrane to obtain a flapping wing. Figure 9 shown.

[0101] The present embodiment discloses a flapping wing structure optimization method based on stiffness similarity, which is not only applicable to the optimization of dragonfly-like flapping wing structures, but can also be extended to the optimization of stiffness similarity structures of other insect wings.

[0102] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A flapping wing structure optimization method based on stiffness similarity, characterized by: The steps include: Step 1: Establish a finite element model of the insect wing plate structure and perform structural topology optimization of the finite element model using the variable density method to achieve the optimal minimum compliance of the flapping wing structure; Based on the topology optimization results of the minimum compliance and the biological sample of insect wings, a simplified insect wing model was established; Step 2: Based on the insect wing stiffness experiment, a relationship between the spanwise bending stiffness of the flapping wing and the span length is established. A principal component analysis method is used to establish a stiffness similarity criterion based on the relationship between the bending stiffness of insect wings at different scales in nature and the geometric morphological parameters of insects. According to the stiffness similarity criterion, a linear linear function of the spanwise bending stiffness of the simplified insect wing model described in step 1 and the spanwise bending stiffness of the flapping wing at different span lengths is solved. According to the linear linear function, the spanwise bending stiffness of the flapping wing at different span lengths is determined. According to the material properties of the flapping wing and the spanwise bending stiffness at different span lengths, the section moment of inertia at different span lengths is determined, and then the cross-sectional dimensions at different span lengths are determined. With the minimum structural mass as the optimization goal, the parameters of each vein line width function are used as design variables, and the spanwise bending stiffness at different span lengths and the upper and lower boundaries of the line width that meet the requirements of the insect wing structural strength, processing size and engineering precision are used as constraints, the flapping wing is optimized, thereby determining a bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift aerodynamic performance of the flapping wing. Step 3: According to the bionic flapping wing vein structure layout obtained in step 2, materials are selected to process the wing veins and wing membrane; wherein, the wing veins are processed and manufactured using a machining cutting process; the flapping wing veins and wing membrane are bonded together to obtain a flapping wing with optimized lift aerodynamic performance.

2. The flapping wing structure optimization method based on stiffness similarity according to claim 1, wherein: Step 1 is implemented as follows: Step 1.1: Based on the shape and size of insect wings in nature, an optimization design model for the flat plate structure of an insect wing is established. The leading edge vein of the model is defined as the non-design domain, and the rest of the model is defined as the design domain. A finite element model of the insect wing plane structure is established, using shell elements for meshing, defining the element material properties, applying a uniformly distributed load to the wing surface, and setting a six-degree-of-freedom constraint at the wing root. Step 1.2: Use the variable density method to perform structural topology optimization on the finite element model, and select the solid isotropic material with penalization (SIMP) model as the interpolation model; The SIMP model interpolation formula is: Where, E i is the elastic modulus after interpolation, E0 is the real elastic modulus of the material, x i is the pseudo density of the i-th unit, and p is the penalty factor; A flapping wing structure topology optimization model is established as shown in formula (2), where the design variable is the pseudo-density of each unit, the optimization target is the minimum compliance of the structure, and the constraint condition is the material retention ratio. Where x i is the pseudo-density of the i-th unit, C is the overall flexibility of the structure, F is the structural node force vector, U is the structural node displacement vector, M is the structural mass, M0 is the original mass of the structure, f is the material retention ratio, which means the proportion of the material retained in the optimized structure to the original structural material, K is the overall structural stiffness matrix, x min The minimum value of pseudo density of the element is introduced to prevent the singularity of the stiffness matrix; the smaller the C value, the greater the structural stiffness; Step 1.3: For the topology optimization mathematical model of step 1.2, determine the interpolation model penalty coefficient and material retention ratio, and perform topology optimization to achieve the optimal minimum compliance of the flapping wing structure. Combine the topology optimization results of the finite element model of the insect wing plane structure with the geometric shape, size, and wing vein structure layout of real insect wings in nature to establish a simplified insect-like wing model.

3. The flapping wing structure optimization method based on stiffness similarity according to claim 2, characterized in that: Step 2 is implemented as follows: Step 2.1: Use the cantilever beam bending test method to measure the bending stiffness of insect wings at different span lengths and establish the relationship between the spanwise bending stiffness of the flapping wings and the span length. Where E is the elastic modulus of the material used for the flapping wing, I i is the section moment of inertia at i×10% of the flapping wing span, m and n are unknown quantities, where m is the slope of the linear function of spanwise bending stiffness varying with span, and n is the intercept of the linear function; α is the proportionality coefficient, whose value is measured experimentally; Step 2.2: Use principal component analysis to determine the relationship between insect wing stiffness and geometric parameters at different scales. Establish a stiffness similarity criterion to determine the relationship between flapping wing spanwise bending stiffness and flapping wing half-span, chord length, flapping wing area, and vehicle mass. The calculation method is: Step 2.2.1: Standardize the data on insect wing length, chord length, wing area, and insect mass to calculate the correlation coefficient matrix Where r ij is the correlation coefficient between index j and index k, and its calculation formula is: Step 2.2.2: Calculate the eigenvalue λ of the correlation coefficient matrix R i and the corresponding eigenvector e i , i=1,2,…,p, and arranged in order of size as λ1≥λ2≥…≥λ p ≥0; Step 2.2.3: Calculate the variance contribution rate of each principal component and determine the number of principal components based on the cumulative contribution rate, where principal component z i The contribution rate of The cumulative contribution rate is Usually choose the cumulative contribution rate The eigenvalues λ1,λ2,…,λ m The corresponding 1st, 2nd, ..., mth principal components, m≤p; Step 2.2.4: Calculate principal component loadings Thus, the principal component expression is obtained z i =w i1 logl+w i2 logb+w i3 logS+w i4 logm(i=1,2,…,p) (9) where z i is the i-th principal component; Step 2.2.5: Based on the principal component expression, a logarithmic function is used to fit the first principal component consisting of wing length, chord length, wing area and mass to the data of insect spanwise bending stiffness. The relationship between the comprehensive index consisting of wing length, chord length, wing area and mass and the insect spanwise bending stiffness is obtained. Where m is the number of principal components, a0, a i are the coefficients in the relationship, and the similarity criterion of insect wing stiffness using wing length, chord length, wing area and mass as comprehensive indicators is obtained; Step 2.3: Based on the relationship between the spanwise bending stiffness of insect wings and span length (Equation (3)) determined from the stiffness experiment and the insect wing stiffness similarity criterion (Equation (10)) using wing length, chord length, wing area, and mass as comprehensive indicators, solve the linear linear function of the spanwise bending stiffness of the flapping wing model in Equation (3) according to the stiffness similarity criterion described in Equation (10) for the variation of spanwise bending stiffness with span length. THEY i =mi+n (N m 2 ) (11) The values of the unknown quantities m and n; The spanwise bending stiffness of the simplified insect wing model at different spans described in step 1 is determined according to the linear linear function shown in formula (11). The section moments of inertia at different spans can be determined according to the material properties of the wing model and the spanwise bending stiffness at different spans, and thus the section dimensions at different spans can be determined. Step 2.4: Based on the relationship between the cross-sectional size change of insect wings and the spanwise bending stiffness change of flapping wings along the span (11), the width of each vein line changes according to a linear function. When the cross-sectional shape is rectangular and the thickness of the flapping wing vein is constant, the minimum structural mass is taken as the optimization goal, the parameters of each vein line width function are used as design variables, and the spanwise bending stiffness at different spans and the upper and lower boundaries of the line width that meet the requirements of the insect wing structural strength, processing size and engineering accuracy are used as constraints to optimize the flapping wing design: Where, l j =a j x+b j is the line width function of each vein, where l j is the line width at x on the vein, a j is the slope of the linear function, b j is the intercept of the linear function, x is the position of a point on the vein, j is the jth vein, and W is the mass of the flapping wing model; Step 2.5: Based on the optimization results, the parameters in the line width function of each vein are obtained, and the flapping wing structure is optimized based on stiffness similarity, thereby determining the bionic flapping wing vein structure layout suitable for micro flapping wing and flapping rotor aircraft to improve the lift aerodynamic performance of the flapping wing.

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