Bionic butterfly structure optimization design method based on finite element method

Abstract

The invention relates to the field of bionics, and particularly discloses a bionic butterfly structure optimization design method based on a finite element method.The method comprises the following steps that S1, the flight attitude of a butterfly is observed, and flight data are recorded; s2, establishing a simplified three-dimensional model of the butterfly wings; s3, establishing a simplified three-dimensional model of the butterfly wing connecting piece; s4, carrying out topological optimization on the model by taking the minimum volume as a target; s5, performing model arrangement on an optimization result; and S6, performing finite element analysis on the wing connecting piece and the whole wing to obtain a final finite element result. According to the bionic butterfly structure optimization design method based on the finite element method, the flight key data of the butterfly can be accurately captured, and accordingly, a wing and connecting piece model fitting the reality is built. Through topological optimization, model arrangement and finite element analysis, the flight efficiency and the structural reliability of the bionic aircraft are effectively improved, the energy consumption is reduced, the mass is reduced, and efficient and stable flight is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of bionics, and in particular to a bionic butterfly structure optimization design method based on a finite element method. Background Art

[0002] Existing butterfly-inspired aircraft wing designs often use fixed structures or empirically parameterized models for wing connections. The high rigidity of these joints significantly limits movement coordination, resulting in low aerodynamic efficiency and high energy consumption. Furthermore, topology optimization methods are not used for structural optimization and lightweighting, leading to structural redundancy and insufficient adaptability. Furthermore, traditional methods rarely incorporate biological observation data to design butterfly wing shapes, making it impossible to accurately simulate the dynamic phase difference between the front and rear sections of a single butterfly wing, resulting in low aerodynamic efficiency.

[0003] Therefore, the aerodynamic optimization design method based on the gap between the single-sided flange of the butterfly obtains the phase difference law through biological observation, and obtains the front and rear gap between the single-sided flange of the butterfly wing with the best aerodynamic efficiency through enumeration method and finite element analysis. The butterfly wing connector is topologically optimized through finite element analysis to obtain the optimal connector shape, and the two are combined for finite element analysis verification, thereby improving the flight efficiency and structural reliability of the bionic aircraft. Summary of the Invention

[0004] The purpose of the present invention is to provide a bionic butterfly structure optimization design method based on the finite element method, which solves the problems of poor connector structure, insufficient topology optimization and lack of integration of biological observation data in the existing butterfly bionic aircraft wing design, improves the flight efficiency and structural reliability of the bionic aircraft, reduces the mass of the connectors, and optimizes the wing shape.

[0005] To achieve the above object, the present invention provides a bionic butterfly structure optimization design method based on the finite element method, comprising the following steps:

[0006] S1. Observe the flying posture of butterflies and record flight data;

[0007] S2, build a simplified three-dimensional model of the butterfly wings using the flight data recorded in S1;

[0008] S3, establishing a simplified three-dimensional model of the butterfly wing connector;

[0009] S4. Topology optimization of the model is performed with the minimum volume as the goal;

[0010] S5. Modeling the optimization results;

[0011] S6. Perform finite element analysis on the wing connector and the wing as a whole to obtain the final finite element results.

[0012] Preferably, S1 is specifically:

[0013] Use a high-speed camera to film the flying posture of the butterfly, capture the high-frequency movement details of the butterfly wings and record the flight data, including the shape of the butterfly wings, the length-to-width ratio of one side of the wings, and the front and back phase difference of the butterfly's one side of the wings when flying, as a basis for design.

[0014] Preferably, S2 is specifically:

[0015] The shape of the butterfly's wings was obtained from the flight data recorded by the S1. A simplified 3D model of the butterfly's wings was created using SolidWorks after scaling up. The length, width, thickness, and ratio of the front and back wings were designed. Multiple depths and sizes of the opening in the middle of the wing were enumerated based on the observed and recorded flight data. Multiple models were created and exported in step. format.

[0016] After S2, the following steps are also included:

[0017] Sa1, import the 3D model created in S2 into the Abaqus / CAE component function module;

[0018] Sa2. Set cross-section properties and material properties for butterfly wings;

[0019] Sa3, component assembly and analysis step setting;

[0020] Sa4. Select hexahedron and free mesh properties to mesh the butterfly wings.

[0021] Sa5, boundary conditions and loading conditions setting;

[0022] Sa6, solution model settings;

[0023] Sa7. Analyze and evaluate the simulation results;

[0024] Sa8. Repeat Sa1 to Sa7 to determine the butterfly wing shape with the best phase angle.

[0025] Preferably, Sa1 is specifically:

[0026] Import a simplified 3D model of a butterfly wing created by S2 into the Abaqus / CAE component function module. After importing, check the integrity of the model. The basic principles of finite element analysis are as follows:

[0027] Divide a complex continuum structure into multiple small discrete units, and use shape functions to approximate the unknown field variables in each unit:

[0028]

[0029] Among them, u e(x) is the field variable at a point in the unit, N i (x) is the shape function, is the field variable value at the node, i is the index of the unit node, representing the node number currently being calculated, n is the total number of unit nodes, and x is the spatial coordinate of a point in the unit;

[0030] Convert the strong form partial differential equation to a weak form in integral form using the weak form and variational principle, using the principle of virtual work:

[0031]

[0032] Among them, σ is the stress tensor, ∈ is the strain tensor, b is the volume force, and t is the surface force;

[0033] The stiffness matrix and load vector of each element are assembled into a global system of equations according to the nodal degrees of freedom:

[0034] KU=F;

[0035] Where K is the global stiffness matrix, U is the node displacement vector, and F is the equivalent node load vector. By introducing constraints and boundary conditions, modifying the global equations, and solving the equations to obtain the node variables, the stress and strain are then calculated.

[0036] Preferably, Sa2 is specifically:

[0037] Open the Material Manager, click Create, and set the density, Young's modulus, Poisson's ratio, and failure criterion of the material.

[0038] Open the Section Manager, click Create, and set the wings to solid, homogeneous sections;

[0039] Open the Section Assignment Manager, click Create, and assign the previously set material to the section.

[0040] Preferably, Sa3 is specifically:

[0041] Click Create Instance and select the wing component to import;

[0042] Open the analysis step manager, click Create, select Statics as the type, General, turn on Geometric Nonlinearity, set the minimum time increment step, maximum time increment step and total time length;

[0043] Open the Field Output Request Manager and Process Output Request Manager, check the data you want to simulate, and uncheck the data you don't want.

[0044] Preferably, Sa5 is specifically:

[0045] Open the Boundary Condition Manager, create a boundary condition, select Symmetric / Antisymmetric / Fully Fixed type, set the inner connector of the wing to be fully fixed, and restrict all translational and rotational degrees of freedom;

[0046] The loading conditions are that the front and rear wings are subjected to upward and downward loads respectively during flight. The front wing edge exerts an upward force to simulate lift, and the rear wing edge exerts a downward force to simulate drag, and the direction is perpendicular to the wing surface.

[0047] Preferably, S3 is specifically:

[0048] Use SolidWorks to create a simplified 3D model of the butterfly wing connector, set the bottom as a cuboid, and convert it into step. format for export;

[0049] S3 also includes the following steps:

[0050] Sb1. Import the 3D model of the butterfly wing connector created in S3 into the software and assign material parameters to the model, including material, density, Young's modulus, and Poisson's ratio;

[0051] Sb2. Assign the lower half of the model as the design space, fix the upper half at the connection hole, and apply the load on the connecting rod to the model in the lower design space to simulate the force exerted by the flapping wings of a butterfly during flight.

[0052] Sb3. Divide the butterfly wing connector into tetrahedral meshes.

[0053] Preferably, in S4, the basic principle of topology optimization is as follows:

[0054] The design space is discretized into finite elements, each of which is assigned a material density variable ρ e , indicating whether the unit has material, ρ e =1 for entity, ρ e =0 is a gap;

[0055] Map density variables to material properties through interpolation functions, using the SIMP model:

[0056]

[0057] Among them, E e (ρ e ) is the Young's modulus of the butterfly wing connector unit, E0 is the Young's modulus of the solid material, E min is the minimum value, p is the penalty factor, It is a power penalty used to suppress intermediate density;

[0058] For a single-objective optimization problem, the objective function and constraints are as follows:

[0059] Objective function: min C(ρ) = F T U;

[0060] Constraint: stV(ρ)≤V target ;

[0061] 0≤ρ e ≤1;

[0062] KU=F;

[0063] Where C(ρ) is the flexibility, K is the global stiffness matrix, U is the node displacement vector, F is the equivalent node load vector, V(ρ) is the volume at the corresponding density, V target is the target volume;

[0064] The objective function is the minimum flexibility, the first constraint is the volume constraint of the butterfly wing connector, the second constraint is the material density variable constraint, and the third constraint is the global equation.

[0065] Preferably, S5 is specifically:

[0066] Import the optimization results into SolidWorks and use the fill surface tool to repair non-closed surfaces or holes in the optimized model to ensure geometric integrity;

[0067] Add fillets to sharp corners to avoid stress concentration; use the thicken command to strengthen the stress concentration areas in a targeted manner, then assemble the optimized model with the final wing model and export it in step. format.

[0068] Therefore, the present invention adopts the above-mentioned bionic butterfly structure optimization design method based on the finite element method, and the beneficial effects are as follows:

[0069] (1) The present invention uses a high-speed camera to accurately observe real butterfly wings, record the real front-to-back phase difference of a single wing, and use the real data as the design basis.

[0070] (2) The present invention uses enumeration method and finite element analysis based on real data to obtain wing shape data and front and rear wing edge gap data with optimal flight efficiency.

[0071] (3) The present invention uses finite element analysis to analyze the wing connector and performs topological optimization on it, which reduces the mass of the connector and makes the connector structure more suitable for the bionic butterfly to achieve optimal flight efficiency.

[0072] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1This is an overall design flow chart of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0074] Figure 2 This is a model assembly diagram of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0075] Figure 3 This is a schematic diagram of setting material properties in an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0076] Figure 4 This is a schematic diagram of assigning cross-sectional properties to an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0077] Figure 5 1. It is a schematic diagram of the setting and analysis steps of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0078] Figure 6 This is a schematic diagram of setting a grid for an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0079] Figure 7 This is a schematic diagram of setting boundary conditions and applying loads in an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0080] Figure 8 Result cloud diagrams of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention, wherein (a) is a displacement cloud diagram, (b) is an axonometric force cloud diagram, and (c) is a near y-axis force cloud diagram;

[0081] Figure 9 This is a schematic diagram before topology optimization of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0082] Figure 10 This is a schematic diagram of topology optimization in an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention;

[0083] Figure 11 This is a schematic diagram of the topology optimization results of an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention after being sorted by SolidWoks;

[0084] Figure 12 This is a schematic diagram of butterfly shooting in an embodiment of a bionic butterfly structure optimization design method based on the finite element method of the present invention. DETAILED DESCRIPTION

[0085] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0086] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0087] like Figure 1 As shown, a bionic butterfly structure optimization design method based on the finite element method includes the following steps:

[0088] S1. Observe the butterfly's flight posture and record flight data, specifically:

[0089] like Figure 12 As shown, a high-speed camera is used to capture the flying posture of the butterfly, ensuring that the high-frequency movement details of the butterfly wings are captured and the flight data is recorded, including the shape of the butterfly wings, the length-to-width ratio of one side of the wings, and the front-to-back phase difference of the butterfly's one side of the wings when flying, which is used as a basis for design.

[0090] S2. Build a simplified 3D model of butterfly wings, specifically:

[0091] Using data recorded by the S1 and relevant literature, the butterfly wing shape was determined. After scaling up, a simplified 3D model of the butterfly wing was created using SolidWorks. The design was for a single wing length of 500mm, a width of 260mm, a thickness of 0.1mm, and a front-to-back wing length ratio of approximately 2.1:2.9. Based on observed and recorded flight data, multiple opening depths and sizes were enumerated for the central opening on each wing at 30mm from the wing root in 5mm increments. Multiple models were created and exported in step.format.

[0092] After S2, the following steps are also included:

[0093] Sa1, such as Figure 2 As shown, a simplified 3D model of a butterfly wing created by S2 is imported into the Abaqus / CAE component function module. After importing, the integrity of the model is checked. The basic principles of finite element analysis are as follows:

[0094] A complex continuum structure is divided into multiple small discrete units, and the shape and size of each unit can be arbitrarily selected. Within each unit, the unknown field variables (such as displacement and temperature) are approximated using shape functions:

[0095]

[0096] Among them, u e (x) is the field variable at a point in the unit, N i (x) is the shape function, is the field variable value at the node, i is the index of the unit node, representing the node number currently calculated, n is the total number of unit nodes, and x is the spatial coordinate of a point in the unit.

[0097] Afterwards, the strong form partial differential equation is converted to a weak form of integral form through the weak form and variational principle to reduce the smoothness requirement of the solution, using the principle of virtual work:

[0098]

[0099] Among them, σ is the stress tensor, ∈ is the strain tensor, b is the volume force, and t is the surface force.

[0100] The stiffness matrix and load vector of each element are assembled into a global system of equations according to the nodal degrees of freedom:

[0101] KU=F;

[0102] Where K is the global stiffness matrix, U is the nodal displacement vector, and F is the equivalent nodal load vector. By introducing constraints and boundary conditions, the global equations are modified. The equations are then solved to obtain nodal variables, allowing the calculation of derived quantities such as stress and strain.

[0103] Sa2. Set the cross-section properties and material properties for the butterfly wings, specifically:

[0104] like Figure 3 As shown, open the material manager, click Create, and set parameters such as density, Young's modulus, Poisson's ratio, and material failure criterion.

[0105] The actual material of butterfly wings is a biocomposite film, such as a chitin-protein complex. In engineering simulations, it is often simplified to parameters similar to polymer films. Therefore, its material parameters are set to a density of 1.20 g / cm 3 , Young's modulus 2.8GPa, Poisson's ratio 0.35.

[0106] like Figure 4 As shown, open the Section Manager, click Create, and set the wings to solid, homogeneous sections.

[0107] Open the Section Assignment Manager, click Create, and assign the previously set material to the section.

[0108] Sa3, component assembly and analysis step settings, specifically:

[0109] like Figure 5 As shown, click Create Instance and select the wing component to import.

[0110] Open the Step Manager, click Create, select "Statics, General" for the type, turn on "Geometric Nonlinearity", set the minimum time increment to 0.1, the maximum time increment to 0.15, and the total time to 1.

[0111] Open the Field Output Request Manager and the Process Output Request Manager, check the data that needs to be simulated, such as stress, displacement, and strain, and uncheck unnecessary data to improve the efficiency of numerical simulation calculations.

[0112] Sa4, such as Figure 6 As shown in the figure, considering computational efficiency in numerical simulation, the "hexahedral, free" mesh properties were selected for meshing the butterfly wing. Due to the small wing thickness, the seed density was slightly reduced in the global seed to ensure that some elements were appropriately sized for mesh generation. Hexahedral meshes offer high computational accuracy and efficiency in static analysis. Their structured nature results in regular element shapes, enabling more accurate simulation of stress distribution in complex geometries, particularly in areas of stress concentration.

[0113] Hexahedral shape functions offer strong numerical stability during integration, requiring fewer integration points and significantly reducing computational resource consumption. Furthermore, hexahedral meshes offer clear node connectivity and more intuitive boundary condition application, so they were chosen.

[0114] Sa5, boundary conditions and loading conditions settings, specifically:

[0115] like Figure 7 As shown, open the boundary condition manager, create a boundary condition, select the "Symmetric / Antisymmetric / Fully Fixed" type, set the inner connection of the wing to be completely fixed, and restrict all translational and rotational degrees of freedom.

[0116] The loading conditions are that the front and rear wings are subjected to upward and downward loads respectively during flight. An upward force of 20N is applied to the front wing edge to simulate lift, and a downward force of 10N is applied to the rear wing edge to simulate drag. The direction is perpendicular to the wing surface. The load increases linearly with time through the "amplitude curve".

[0117] Sa6, solve the model settings, specifically:

[0118] Open the Job Manager, click Create, enter a name, and select Continue. Click "Parallel," check "Use multiple processors," and enter the number of processors appropriate for your computer to achieve the maximum solution speed.

[0119] Sa7, post-processing to analyze and evaluate the simulation results, specifically:

[0120] Open the job manager, select the simulation job you want to view, click Results, and observe the force and displacement cloud maps of the wings, such as Figure 8As shown, the maximum stress area is the root of the notch.

[0121] Sa8. Repeat Sa1 to Sa7 to determine the butterfly wing shape with the best phase angle, where the opening depth is 36 mm from the leftmost side.

[0122] S3. Build a simplified 3D model of the butterfly wing connector, specifically:

[0123] By consulting relevant materials, SolidWorks was used to create a simplified three-dimensional model of the butterfly wing connector. The bottom was set as a cuboid with a length of 65mm, a width of 18mm, and a height of 3.3mm, and was converted into step. format for export.

[0124] S3 also includes the following steps:

[0125] Sb1. Import the 3D model of the butterfly wing connector created in S3 into Altair Inspire software and assign material parameters to the model, including specifying the material as nylon and the density as 1.15g / cm 3 , Young's modulus 3GPa and Poisson's ratio 0.35. Nylon was selected due to its excellent specific strength (2.61GPa·cm 3 / g), better than ABS (2.21GPa·cm 3 / g), and its elongation at break is as high as 50%, and it can withstand high-frequency deformation without failure.

[0126] Table 1 Material selection comparison table

[0127]

[0128] Sb2. Assign space and apply load: Assign the lower half of the model as the design space, and fix the upper half at the connection holes. Apply a vertical upward load of 10N to the connecting rods of the model in the lower design space, simulating the force exerted on a butterfly due to flapping wings during flight.

[0129] Sb3. Divide the butterfly wing connector into tetrahedral meshes.

[0130] Due to its unstructured nature, tetrahedral meshes exhibit strong geometric adaptability in topology optimization. They can quickly generate initial meshes for complex or irregular design domains and are particularly suitable for dynamically changing optimization processes. Tetrahedral elements perform well in automatic meshing tools and can handle sharp edges or curved surfaces without manual adjustments, significantly improving optimization efficiency. In addition, when the topology optimization algorithm SIMP adjusts material distribution through density variables, the flexible node layout of the tetrahedral mesh helps to clearly express the optimized topology, while supporting efficient sensitivity analysis and gradient updates to ensure the feasibility and convergence of the optimization results.

[0131] S4, such as Figure 9-10 As shown, the model is topologically optimized with the minimum volume as the goal. The basic principles of topology optimization are as follows:

[0132] The design space is discretized into finite elements, each of which is assigned a material density variable ρ e (continuous variable), indicating whether the material exists in the unit, ρ e =1 for entity, ρ e =0 is a gap.

[0133] The density variable is mapped to the material properties through the interpolation function, using the SIMP (Solid Isotropic Material with Penalization) model:

[0134]

[0135] Among them, E e (ρ e ) is the Young's modulus of the butterfly wing connector unit, E0 is the Young's modulus of the solid material, E min is the minimum value to avoid numerical singularity, p is the penalty factor, usually taking o≥3. The larger the value, the more "uneconomical" the material with intermediate density, and the closer the optimization result is to the 0-1 distribution. It is a power penalty that suppresses the intermediate density and forces the design variables to tend to 0 or 1, thus obtaining a clear topological structure.

[0136] Next is a single-objective optimization problem, the objective function and constraints are as follows:

[0137] Objective function: min C(ρ) = F T U;

[0138] Constraint: stV(ρ)≤V target ;

[0139] 0≤ρ e ≤1;

[0140] KU=F;

[0141] Where C(ρ) is the flexibility, K is the global stiffness matrix, U is the node displacement vector, F is the equivalent node load vector, V(ρ) is the volume at the corresponding density, V target is the target volume.

[0142] The objective function is the minimum flexibility, the first constraint is the volume constraint of the butterfly wing connector, the second constraint is the material density variable constraint, and the third constraint is the global equation.

[0143] S5. Model the optimization results, specifically:

[0144] Because topology optimization aims for lightweighting, it may generate structures with extremely thin walls or thin rods in certain areas. While these structures may meet strength requirements in static simulations, they are susceptible to fatigue fracture under actual dynamic loads. Furthermore, 3D printing has limitations on minimum printable dimensions. Ultra-thin areas in the optimized results cannot be reliably molded using existing processes, requiring adjustments to wall thickness to avoid printing failures or structural defects.

[0145] Therefore, the optimization results are imported into SolidWorks, such as Figure 11 As shown in the figure, use the Fill Surface tool to repair non-closed surfaces or holes in the optimized model to ensure geometric integrity.

[0146] Add fillets to sharp corners to avoid stress concentration; use the "Thicken" command to strengthen the stress concentration areas in a targeted manner. Then assemble the optimized model with the final wing model and export it in step. format.

[0147] S6. Repeat Sa1 to Sa6, apply the same boundary conditions and loads, perform finite element analysis on the wing connector and the wing as a whole, and obtain the final finite element results.

[0148] Therefore, the present invention adopts the above-mentioned bionic butterfly structure optimization design method based on the finite element method, obtains real data by accurately observing the butterfly's flight posture, and uses enumeration method, finite element analysis and topology optimization to obtain the optimal wing shape and connector structure, effectively improving the flight efficiency and structural reliability of the bionic aircraft.

[0149] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A bionic butterfly structure optimization design method based on finite element method, characterized in that: The following steps are involved: S1. Observe the flying posture of butterflies and record flight data; S2, build a simplified three-dimensional model of the butterfly wings using the flight data recorded in S1; S3, establishing a simplified three-dimensional model of the butterfly wing connector; S4. Topology optimization of the model is performed with the minimum volume as the goal; S5. Modeling the optimization results; S6. Perform finite element analysis on the wing connector and the wing as a whole to obtain the final finite element results.

2. The bionic butterfly structure optimization design method based on finite element method according to claim 1 is characterized in that: S1 is specifically: Use a high-speed camera to film the flying posture of the butterfly, capture the high-frequency movement details of the butterfly wings and record the flight data, including the shape of the butterfly wings, the length-to-width ratio of one side of the wings, and the front and back phase difference of the butterfly's one side of the wings when flying, as a basis for design.

3. The bionic butterfly structure optimization design method based on finite element method according to claim 2 is characterized in that: S2 is specifically: The shape of the butterfly's wings was obtained from the flight data recorded by the S1. A simplified 3D model of the butterfly's wings was created using SolidWorks after scaling up. The length, width, thickness, and ratio of the front and back wings were designed. Multiple depths and sizes of the opening in the middle of the wing were enumerated based on the observed and recorded flight data. Multiple models were created and exported in step. format. After S2, the following steps are also included: Sa1, import the 3D model created in S2 into the Abaqus / CAE component function module; Sa2. Set cross-section properties and material properties for butterfly wings; Sa3, component assembly and analysis step setting; Sa4. Select hexahedron and free mesh properties to mesh the butterfly wings. Sa5, boundary conditions and loading conditions setting; Sa6, solution model settings; Sa7. Analyze and evaluate the simulation results; Sa8. Repeat Sa1 to Sa7 to determine the butterfly wing shape with the best phase angle.

4. The method for optimizing the bionic butterfly structure based on the finite element method according to claim 3, characterized in that: Sa1 is specifically: Import a simplified 3D model of a butterfly wing created by S2 into the Abaqus / CAE component function module. After importing, check the integrity of the model. The basic principles of finite element analysis are as follows: Divide a complex continuum structure into multiple small discrete units, and use shape functions to approximate the unknown field variables in each unit: Among them, u e (x) is the field variable at a point in the unit, N i (x) is the shape function, is the field variable value at the node, i is the index of the unit node, representing the node number currently being calculated, n is the total number of unit nodes, and x is the spatial coordinate of a point in the unit; Convert the strong form partial differential equation to a weak form in integral form using the weak form and variational principle, using the principle of virtual work: Among them, σ is the stress tensor, ∈ is the strain tensor, b is the volume force, and t is the surface force; The stiffness matrix and load vector of each element are assembled into a global system of equations according to the nodal degrees of freedom: KU=F; Where K is the global stiffness matrix, U is the node displacement vector, and F is the equivalent node load vector. By introducing constraints and boundary conditions, modifying the global equations, and solving the equations to obtain the node variables, the stress and strain are then calculated.

5. The method for optimizing the bionic butterfly structure based on the finite element method according to claim 4, characterized in that: Sa2 is specifically: Open the Material Manager, click Create, and set the density, Young's modulus, Poisson's ratio, and failure criterion of the material. Open the Section Manager, click Create, and set the wings to solid, homogeneous sections; Open the Section Assignment Manager, click Create, and assign the previously set material to the section.

6. The method for optimizing the bionic butterfly structure based on the finite element method according to claim 5, characterized in that: Sa3 is specifically: Click Create Instance and select the wing component to import; Open the analysis step manager, click Create, select Statics as the type, General, turn on Geometric Nonlinearity, set the minimum time increment step, maximum time increment step and total time length; Open the Field Output Request Manager and Process Output Request Manager, check the data you want to simulate, and uncheck the data you don't want.

7. The bionic butterfly structure optimization design method based on finite element method according to claim 6 is characterized in that: Sa5 is specifically: Open the Boundary Condition Manager, create a boundary condition, select Symmetric / Antisymmetric / Fully Fixed type, set the inner connector of the wing to be fully fixed, and restrict all translational and rotational degrees of freedom; The loading conditions are that the front and rear wings are subjected to upward and downward loads respectively during flight. The front wing edge exerts an upward force to simulate lift, and the rear wing edge exerts a downward force to simulate drag, and the direction is perpendicular to the wing surface.

8. The method for optimizing the bionic butterfly structure based on the finite element method according to claim 7, characterized in that: S3 specifically: Use SolidWorks to create a simplified 3D model of the butterfly wing connector, set the bottom as a cuboid, and convert it into step. format for export; S3 also includes the following steps: Sb1. Import the 3D model of the butterfly wing connector created in S3 into the software and assign material parameters to the model, including material, density, Young's modulus, and Poisson's ratio; Sb2. Assign the lower half of the model as the design space, fix the upper half at the connection hole, and apply the load on the connecting rod to the model in the lower design space to simulate the force exerted by the flapping wings of a butterfly during flight. Sb3. Divide the butterfly wing connector into tetrahedral meshes.

9. The method for optimizing the bionic butterfly structure based on the finite element method according to claim 8, characterized in that: In S4, the basic principles of topology optimization are as follows: The design space is discretized into finite elements, each of which is assigned a material density variable ρ e , indicating whether the unit has material, ρ e =1 for entity, ρ e =0 is a gap; Map density variables to material properties through interpolation functions, using the SIMP model: Among them, E e (ρ e ) is the Young's modulus of the butterfly wing connector unit, E0 is the Young's modulus of the solid material, E min is the minimum value, p is the penalty factor, It is a power penalty used to suppress intermediate density; For a single-objective optimization problem, the objective function and constraints are as follows: Objective function: min C(ρ) = F T U; Constraint: stV(ρ)≤V target ; 0≤ρ e ≤1; KU=F; Where C(ρ) is the flexibility, K is the global stiffness matrix, U is the node displacement vector, F is the equivalent node load vector, V(ρ) is the volume at the corresponding density, V target is the target volume; The objective function is the minimum flexibility, the first constraint is the volume constraint of the butterfly wing connector, the second constraint is the material density variable constraint, and the third constraint is the global equation.

10. The bionic butterfly structure optimization design method based on finite element method according to claim 9, characterized in that: S5 is specifically: Import the optimization results into SolidWorks and use the fill surface tool to repair non-closed surfaces or holes in the optimized model to ensure geometric integrity; Add rounded corners to sharp edges to avoid stress concentration; The stress concentration areas are targeted for strengthening using the thickening command. The optimized model is then assembled with the final wing model and exported in step. format.

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