Multi-material topological optimization method for aircraft structure design

Abstract

The invention discloses a multi-material topological optimization method for aircraft structure design, and belongs to the technical field of aerospace. The method comprises the following steps: establishing an expanded design area; carrying out grid division; establishing a material interpolation model; finite element analysis is carried out, and the sensitivity of objective function quality constraint conditions is obtained; sequentially updating the design field variable, the filtering field variable and the physical field variable, and applying implicit floating projection constraint; judging whether a convergence condition is met; performing smooth design; re-dividing the structure subjected to smooth design by using an original grid, and performing sensitivity analysis; and calculating an error value, judging whether an accurate smooth design condition is met or not, and if so, ending optimization and outputting an optimal structure. According to the method, under the condition that good convergence performance is guaranteed, material selection can be carried out in the topological optimization process, meanwhile, the iteration step number needed by topology is reduced through the three-field technology, optimization efficiency is improved, and the final structure has a clear and smooth boundary and can be directly used for manufacturing.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular relates to a multi-material topology optimization method for aircraft structure design. Background Art

[0002] Topology optimization can obtain the optimal material distribution according to the boundary conditions of the structure, the optimization objectives and the optimization constraints, and is widely used in structural design in fields such as aerospace. In many engineering applications, a single material often cannot meet complex performance requirements. For example, fields such as aerospace and machinery have high requirements on the weight, strength, stiffness, durability, and functionality of the structure. Compared with single-material topology optimization, multi-material topology optimization methods can consider the distribution of multiple materials at the same time and give full play to the advantages of different properties of each material.

[0003] Compared with multi-material topology optimization under volume constraints of multiple materials, there are fewer studies on multi-material topology optimization under mass constraints for lightweight design. Multi-material topology optimization under mass constraints involves more candidate materials and competition. An outstanding issue in multi-material topology optimization under mass constraints is how to select candidate materials so that they can coexist in the final design to maximize the advantages of different materials. Since there are many candidate materials in the material library, it is very difficult to test all the combinations of materials.

[0004] Therefore, it is necessary to provide a multi-material topology optimization method for aircraft structure design, which can automatically select materials during the topology optimization process. At the same time, the computational efficiency of multi-material topology optimization needs to be further improved. Summary of the invention

[0005] The purpose of an embodiment of the present invention is to provide a multi-material topology optimization method for aircraft structure design, which takes into account the material selection problem of multi-material topology optimization, uses three-field density representation technology to accelerate the topology process, reduces the number of iterations required for topology, and improves optimization efficiency, thereby solving at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] An embodiment of the present invention provides a multi-material topology optimization method for aircraft structure design, comprising the following steps:

[0008] Step S1, establishing an expanded design area according to the optimized aircraft structure;

[0009] Step S2, meshing the enlarged design area, applying displacement and load conditions, and inputting parameters required for optimization;

[0010] Step S3, establishing a multi-material topology optimization material interpolation model according to design variables and candidate materials;

[0011] Step S4, calculating the sensitivity of the objective function and the sensitivity of the mass constraint condition according to the result of the finite element analysis;

[0012] Step S5, updating the design field variables, the filter field variables and the physical field variables in sequence, and applying implicit floating projection constraints;

[0013] Step S6, determine whether the convergence condition is met, if so, proceed to step S7, if not, return to step S3;

[0014] Step S7, performing smooth design;

[0015] Step S8, re-dividing the smooth designed aircraft structure using the original grid and performing sensitivity analysis;

[0016] Step S9, calculate the error value generated by the objective function before and after smoothing, and judge whether the conditions for accurate smooth design are met. If not, increase the floating projection control parameter and return to step S3; if satisfied, execute step S10;

[0017] Step S10, ending the optimization and outputting the optimal structure.

[0018] Preferably, in step S3, the multi-material topology optimization material interpolation model is expressed by the following formula:

[0019]

[0020] In the formula, i represents the unit number, i = 1, 2, 3, ..., N; p represents the number related to the material, p = 1, 2, 3, ..., m; E is the Young's modulus of the material, x i,p is the physical field variable with material number p in the i-th unit, and its minimum value is the set minimum value x min , whose maximum value is 1.

[0021] It should be noted that the use of the above-mentioned multi-material topology optimization material interpolation model allows the exclusion of inefficient materials during optimization and enables automatic material selection.

[0022] Preferably, in step S4, the sensitivity of the objective function and the sensitivity of the quality constraint are calculated by the following formulae respectively:

[0023]

[0024] In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p) represents the constraint function, i.e., mass constraint; u is the displacement of the unit; k is the stiffness matrix of the unit; V is the volume of the unit; and ρ is the density of the unit.

[0025] Preferably, in step S5, sequentially updating the design field variables, the filter field variables and the physical field variables specifically includes:

[0026] The design field variables are updated according to the OC and MMA methods, and then the design field variables are converted into filter field variables through filters. Finally, the filter field variables are converted into physical field variables according to the Heaviside projection; where:

[0027] First establish the Lagrangian function:

[0028] L=C(x i,p )+λ(M(x i,p )-M * )

[0029] In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the mass constraint; M* represents the mass fraction of the target structure; λ represents the Lagrange multiplier;

[0030] According to the Kuhn-Tucker condition, the optimal solution that meets the conditions is:

[0031]

[0032] The OC update criterion of the unit is obtained, and the design field variables are updated according to it, which is expressed as follows:

[0033]

[0034] Where k represents the kth iteration; represents the design field variable; λ represents the Lagrange multiplier, which is obtained by the bisection method according to the constraints;

[0035] Update the filter field variables according to the design field variables, which is expressed as follows:

[0036]

[0037] In the formula, represents the filter field variable; ω e,i Represents the weight factor in filtering, which is calculated by the filter radius, the distance between the center of unit e and the center of unit i;

[0038] Update the physical field variables according to the filtered field variables, which is expressed as follows:

[0039]

[0040] Where β1 represents the projection control factor.

[0041] Preferably, in step S5, after updating the variable, the 0 / 1 constraint on the variable is implemented by an implicit floating projection constraint, which is expressed as follows:

[0042]

[0043] Where α is the control parameter of the constraint generated by the floating projection; th is the threshold of the projection, which is determined by the dichotomy method to ensure that the sum of the design variables before and after the projection does not change.

[0044] Preferably, in step S7, performing smooth design specifically includes:

[0045] First, linear interpolation is performed on the given variable distribution to obtain the variable value on a finer grid, and then a suitable threshold is found by the dichotomy method so that the smoothed variable distribution has the same total amount as the original variable distribution. Finally, the aircraft structure is smoothly designed by introducing the level set function, which is expressed as follows:

[0046]

[0047] It should be noted that this method can effectively eliminate irregular and discontinuous shapes in the topology optimization results, thus facilitating manufacturing or further optimization.

[0048] Preferably, in step S8, after the structure after smooth design is re-divided using the original grid, a finite element analysis needs to be performed to obtain the displacement matrix and stiffness matrix of the unit, and then a sensitivity analysis is performed.

[0049] Preferably, in step S9, the error value generated by the objective function before and after smoothing is calculated, and the error before and after smoothing is used as the termination condition of the optimization, which is expressed by the following formula:

[0050]

[0051] In the formula, C * (x i,p ) represents the objective function of the smoothed aircraft structure; C(x i,p ) represents the objective function of the vehicle structure before smoothing; τ is the calculated error. When τ<0.01, the optimization is terminated. If it is not satisfied, the control parameters in the floating projection are increased and the process returns to step S3.

[0052] The beneficial effects of the embodiments of the present invention are:

[0053] 1. The present invention fully considers the convergence performance of the multi-material topology optimization algorithm and the 0 / 1 distribution constraints of the final design variables, and can realize the topology optimization design of the aircraft structure containing multiple materials and achieve lightweight design.

[0054] 2. The present invention uses implicit floating projection constraints instead of material penalties to implement 0 / 1 constraints on design variables, avoiding the impact of traditional material penalties on the convergence of multi-material topology optimization. At the same time, under certain quality constraints, the algorithm can automatically select materials during the topology optimization process, achieving a better performance design and avoiding local optimal solutions caused by the inability to exclude inefficient materials.

[0055] 3. Compared with the method of multi-material topology optimization under volume constraints which requires multiple solutions to determine the optimal material ratio, the algorithm of the present invention can obtain the optimal material ratio and material distribution using only one topology optimization.

[0056] 4. The present invention uses three-field technology to reduce the number of iteration steps required for topology and improve optimization efficiency. By continuously adjusting the threshold in the floating projection, the error between the smooth design and the unit-based design is continuously reduced, and finally the smooth design can completely replace the unit-based design.

[0057] 5. The final structure of the present invention has a clear and smooth boundary and can be directly used for manufacturing, avoiding errors caused by model reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0059] Figure 1 A flow chart of a multi-material topology optimization method for aircraft structure design provided by the present invention;

[0060] Figure 2 An initial design drawing of the aircraft engine hanger structure provided by the present invention;

[0061] Figure 3 A topology optimization process diagram for an aircraft engine hanger provided by the present invention;

[0062] Figure 4 This is a structural diagram of the aircraft engine bracket after multi-material optimization provided by the present invention. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] The terms "first", "second", etc. in the specification and claims of the present invention are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0065] See also Figure 1 As shown, an embodiment of the present invention provides a multi-material topology optimization method for aircraft structure design, comprising the following steps:

[0066] Step S1, establishing an expanded design area according to the optimized aircraft structure;

[0067] Step S2, meshing the enlarged design area, applying displacement and load conditions, and inputting parameters required for optimization;

[0068] Step S3, establishing a multi-material topology optimization material interpolation model according to design variables and candidate materials;

[0069] Step S4, calculating the sensitivity of the objective function and the sensitivity of the mass constraint condition according to the result of the finite element analysis;

[0070] Step S5, updating the design field variables, the filter field variables and the physical field variables in sequence, and applying implicit floating projection constraints;

[0071] Step S6, determine whether the convergence condition is met, if so, proceed to step S7, if not, return to step S3;

[0072] Step S7, performing smooth design;

[0073] Step S8, re-dividing the smooth designed aircraft structure using the original grid and performing sensitivity analysis;

[0074] Step S9, calculate the error value generated by the objective function before and after smoothing, and judge whether the conditions for accurate smooth design are met. If not, increase the floating projection control parameter and return to step S3; if satisfied, execute step S10;

[0075] Step S10, ending the optimization and outputting the optimal structure.

[0076] In step S1, the design area is reasonably expanded according to the characteristics of the structure and boundary conditions of the structure to be optimized, and a finite element model is established.

[0077] In step S2, finite element meshing is performed, wherein the 2D structure uses a planar four-node unit and the 3D structure uses a regular hexahedron unit, displacement and load conditions are applied, and parameters such as the filter radius, projection control parameters, and mass fraction required for optimization are input.

[0078] In step S3, the multi-material topology optimization material interpolation model is expressed as follows:

[0079]

[0080] In the formula, i represents the unit number, i = 1, 2, 3, ..., N, N is a positive integer; p represents the number related to the material, p = 1, 2, 3, ..., m, m is a positive integer; E is the Young's modulus of the material, x i,p is the physical field variable with material number p in the i-th unit, and its minimum value is the set minimum value x min , its maximum value is 1;.

[0081] It should be noted that the use of the above-mentioned multi-material topology optimization material interpolation model allows the exclusion of inefficient materials during optimization and enables automatic material selection.

[0082] In step S4, finite element analysis is performed to calculate the displacement matrix of the unit, and the stiffness matrix of the unit is calculated according to the established material interpolation model. Then, the sensitivity of the objective function and the sensitivity of the mass constraint condition are calculated by the following formulas:

[0083]

[0084] In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the constraint function, i.e., mass constraint; u is the displacement of the unit; k is the stiffness matrix of the unit; V is the volume of the unit; and ρ is the density of the unit.

[0085] In step S5, updating the design field variables, the filter field variables and the physical field variables in sequence specifically includes:

[0086] The design field variables are updated according to the OC and MMA methods, and then the design field variables are converted into filter field variables through filters. Finally, the filter field variables are converted into physical field variables according to the Heaviside projection; where:

[0087] First establish the Lagrangian function:

[0088] L=C(x i,p )+λ(M(x i,p )-M * )

[0089] In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the mass constraint; M* represents the mass fraction of the target structure; λ represents the Lagrange multiplier;

[0090] According to the Kuhn-Tucker condition, the optimal solution that meets the conditions is:

[0091]

[0092] The OC update criterion of the unit is obtained, and the design field variables are updated according to it, which is expressed as follows:

[0093]

[0094] Where k represents the kth iteration; represents the design field variable; λ represents the Lagrange multiplier, which is obtained by the bisection method according to the constraints;

[0095] Update the filter field variables according to the design field variables, which is expressed as follows:

[0096]

[0097] In the formula, represents the filter field variable; ω e,i Represents the weight factor in filtering, which is calculated by the filter radius, the distance between the center of unit e and the center of unit i;

[0098] Update the physical field variables according to the filtered field variables, which is expressed as follows:

[0099]

[0100] Where β1 represents the projection control factor.

[0101] In step S5, after updating the variable, the 0 / 1 constraint on the variable is implemented by an implicit floating projection constraint, which is expressed as follows:

[0102]

[0103] Where α is the control parameter of the constraint generated by the floating projection; th is the threshold of the projection, which is determined by the dichotomy method to ensure that the sum of the design variables before and after the projection does not change.

[0104] In step S7, performing smooth design specifically includes:

[0105] First, linear interpolation is performed on the given variable distribution to obtain the variable value on a finer grid, and then a suitable threshold is found by the dichotomy method so that the smoothed variable distribution has the same total amount as the original variable distribution. Finally, the aircraft structure is smoothly designed by introducing the level set function, which is expressed as follows:

[0106]

[0107] It should be noted that this method can effectively eliminate irregular and discontinuous shapes in the topology optimization results, thus facilitating manufacturing or further optimization.

[0108] In step S8, after the smooth designed structure is re-divided using the original mesh, a finite element analysis is required to obtain the displacement matrix and stiffness matrix of the unit, and then a sensitivity analysis is performed.

[0109] In step S9, the error value generated by the objective function before and after smoothing is calculated, and the error before and after smoothing is used as the termination condition of optimization, which is expressed by the following formula:

[0110]

[0111] In the formula, C * (x i,p ) represents the objective function of the smoothed aircraft structure; C(x i,p ) represents the objective function of the vehicle structure before smoothing; τ is the calculated error. When τ<0.01, the optimization is terminated. If it is not satisfied, the control parameters in the floating projection are increased and the process returns to step S3.

[0112] The multi-material topology optimization method for aircraft structure design provided by the present invention is described in detail below with reference to specific embodiments.

[0113] Example

[0114] The method provided by the present invention is used to perform multi-material topology optimization of an aircraft engine hanger under mass constraints, specifically including:

[0115] Step S1: Select an aircraft engine hanger. To obtain the optimal design, the design area is reasonably expanded to seek a better material distribution, such as Figure 2 shown.

[0116] Step S2: Perform finite element meshing using regular hexahedron units. According to the actual structural conditions, the conditions for applying displacement and load are as follows: Figure 2 As shown, the load only considers the weight and thrust of the engine, ignoring the aerodynamic load with less influence, assembly pressure, etc., and considering the extreme working conditions. Input the filter radius 2 and projection control parameter 10 required for optimization -6 , mass fraction 10%, control parameter increment 0.5, minimum design variable 10 -6 ;

[0117] Step S3, establishing a multi-material topology optimization material interpolation model according to design variables and candidate materials;

[0118] The established material model is as follows:

[0119]

[0120] Where i represents the unit number, i = 1, 2, 3, ..., N; p represents the number related to the material, p = 1, 2, 3, ..., m; E is the Young's modulus of the material; x i,p is the physical field variable with material number p in the i-th unit, and its minimum value is the set minimum value x min , and its maximum value is 1. Among them, four commonly used materials in aircraft structure design are selected, as shown in Table 1.

[0121] Table 1 Commonly used materials in the design of four types of aircraft structures

[0122] Material Young's modulus density Mg AM60 43GPa <![CDATA[1790kg / m 3 ]]> Al 2024 73GPa <![CDATA[2770kg / m 3 ]]> TC4 109GPa <![CDATA[4440kg / m 3 ]]> Mild steel 210GPa <![CDATA[7850kg / m 3 ]]>

[0123] Step S4, perform finite element analysis, calculate the displacement matrix of the unit, calculate the stiffness matrix of the unit according to the established material interpolation model, calculate the sensitivity of the objective function flexibility and mass constraint to the design variables, and the sensitivity of the objective function and the sensitivity of the mass constraint condition are calculated by the following formulas respectively:

[0124]

[0125] In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the constraint function, i.e., mass constraint; u is the displacement of the unit; k is the stiffness matrix of the unit; V is the volume of the unit; ρ is the density of the unit;

[0126] Step S5, updating the design field variables, the filter field variables and the physical field variables in sequence, and applying implicit floating projection constraints;

[0127] Create the Lagrangian function:

[0128] L=C(x i,p)+λ(M(x i,p )-M * )

[0129] Among them, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the mass constraint; M* represents the mass fraction of the target structure; λ represents the Lagrange multiplier;

[0130] According to the Kuhn-Tucker condition, the optimal solution that meets the conditions is:

[0131]

[0132] Get the OC update criterion of the unit and update the design field variables according to it:

[0133]

[0134] Where k represents the kth iteration; represents the design field variable; λ represents the Lagrange multiplier, which is obtained by the bisection method according to the constraints;

[0135] Update the filter field variables based on the design field variables:

[0136]

[0137] in, represents the filter field variable; ω e,i Represents the weight factor in filtering, which is calculated by the filter radius, the distance between the center of unit e and the center of unit i;

[0138] Update the physics variables based on the filtered field variables:

[0139]

[0140] In the formula, β1 represents the projection control factor;

[0141] After updating the variable, the 0 / 1 constraint on the variable is implemented via an implicit floating projection constraint:

[0142]

[0143] Among them, α is the control parameter of the constraint generated by the floating projection; th is the threshold of the projection, which is determined by the dichotomy method to ensure that the sum of the design variables before and after the projection does not change.

[0144] Step S6, determine whether the convergence condition is met, if so, proceed to step S7; if not, return to step S3; wherein the convergence condition is that the maximum value of the change value of the design field variable before and after the iteration is less than 0.001, that is:

[0145]

[0146] Step S7: Perform smooth design, perform linear interpolation on the given variable distribution, and obtain the variable value on a finer grid. Next, use the dichotomy method to find a suitable threshold so that the smoothed variable distribution has the same total amount as the original variable distribution. Smooth the structure by introducing the level set function:

[0147]

[0148] Step S8, re-dividing the structure after smooth design using the original grid, performing a finite element analysis, obtaining the displacement matrix and stiffness matrix of the unit, and performing sensitivity analysis;

[0149] Step S9, calculate the error value generated by the objective function before and after smoothing, and judge whether the conditions for accurate smooth design are met. If not, increase the floating projection control parameter and return to step S3; if satisfied, execute step S10;

[0150] Calculate the error value of the objective function before and after smoothing, and use the error before and after smoothing as the termination condition of optimization, which is expressed by the following formula:

[0151]

[0152] In the formula, C * (x i,p ) represents the objective function of the smoothed aircraft structure; C(x i,p ) represents the objective function of the vehicle structure before smoothing; τ is the calculated error. When τ<0.01, the optimization is terminated. If it is not satisfied, the control parameters in the floating projection are increased and the process returns to step S3.

[0153] Step S10: End the optimization and output the optimal structure.

[0154] See also Figure 3 As shown in the figure, it is the optimization iteration history obtained by the multi-material topology optimization method for aircraft structure design. It can be seen that the flexibility of the structure is gradually reduced, and the structural performance is improved. At the same time, the material Mg AM60 and the material TC4 are gradually excluded in the optimization. In the end, there are only two materials in the structure, and their volumes are V Al =0.236,V Mild = 0.017, combined with the material density, it can be judged that the quality constraint of the final structure mass fraction of 10% is met. The algorithm realizes the automatic selection of materials in the topology optimization process, excludes inefficient materials with little contribution to performance under certain quality constraints, and obtains higher structural performance.

[0155] See also Figure 4The figure shows the final topology optimization structure obtained by the multi-material topology optimization method for aircraft structure design. By automatically adjusting the distribution of materials, a better design is obtained. Compared with the design using only Mild steel material, there are two comparisons: 1. At the same mass, the structural stiffness is increased by 20.2%. 2. At the same stiffness level, the mass of the structure is reduced by 21.8%. This method can achieve a better lightweight design.

[0156] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0157] In addition, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0158] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A multi-material topology optimization method for aircraft structure design, characterized in that: The following steps are involved: Step S1, establishing an expanded design area according to the optimized aircraft structure; Step S2, meshing the enlarged design area, applying displacement and load conditions, and inputting parameters required for optimization; Step S3, establishing a multi-material topology optimization material interpolation model according to design variables and candidate materials; Step S4, calculating the sensitivity of the objective function and the sensitivity of the mass constraint condition according to the result of the finite element analysis; Step S5, updating the design field variables, the filter field variables and the physical field variables in sequence, and applying implicit floating projection constraints; Step S6, determine whether the convergence condition is met, if so, proceed to step S7, if not, return to step S3; Step S7, performing smooth design; Step S8, re-dividing the smooth designed aircraft structure using the original grid and performing sensitivity analysis; Step S9, calculating the error value generated by the objective function before and after smoothing, judging whether the conditions for accurate smooth design are met, if not, increasing the floating projection control parameter, and returning to step S3; If satisfied, execute step S10; Step S10, ending the optimization and outputting the optimal structure.

2. The method according to claim 1, characterized in that In step S3, the multi-material topology optimization material interpolation model is expressed as follows: In the formula, i represents the unit number, i = 1, 2, 3, ..., N; p represents the number related to the material, p = 1, 2, 3, ..., m; E is the Young's modulus of the material, x i,p is the physical field variable with material number p in the i-th unit, and its minimum value is the set minimum value x min , whose maximum value is 1.

3. The method according to claim 2, characterized in that In step S4, the sensitivity of the objective function and the sensitivity of the quality constraint are calculated by the following formulas: In the formula, C(x i,p ) represents the objective function, i.e., the flexibility of the structure; M(x i,p ) represents the constraint function, i.e., mass constraint; u is the displacement of the unit; k is the stiffness matrix of the unit; V is the volume of the unit; and ρ is the density of the unit.

4. The method according to claim 3, characterized in that In step S5, updating the design field variables, the filter field variables and the physical field variables in sequence specifically includes: The design field variables are updated according to the OC and MMA methods, and then the design field variables are converted into filter field variables through filters. Finally, the filter field variables are converted into physical field variables according to the Heaviside projection; where: Update the design field variables, expressed as follows: Where k represents the kth iteration; represents the design field variable; λ represents the Lagrange multiplier, which is obtained by the bisection method according to the constraints; Update the filter field variables according to the design field variables, which is expressed as follows: In the formula, represents the filter field variable; ω e,i Represents the weight factor in filtering, which is calculated by the filter radius, the distance between the center of unit e and the center of unit i; Update the physical field variables according to the filtered field variables, which is expressed as follows: Where β1 represents the projection control factor.

5. The method according to claim 5, characterized in that: In step S5, the implicit floating projection constraint is applied as follows: Where α is the control parameter of the constraint generated by the floating projection; th is the threshold of the projection, which is determined by the dichotomy method to ensure that the sum of the design variables before and after the projection does not change.

6. The method according to claim 5, characterized in that In step S7, performing smooth design specifically includes: The level set function is introduced to perform smooth design on the aircraft structure, which is expressed as follows:

7. The method according to claim 6, characterized in that In step S9, the error value generated by the objective function before and after smoothing is calculated, which is expressed as follows: In the formula, C * (x i,p ) represents the objective function of the smoothed aircraft structure; C(x i,p ) represents the objective function of the vehicle structure before smoothing; τ is the calculated error. When τ<0.01, the optimization is terminated. If it is not satisfied, the control parameters in the floating projection are increased and the process returns to step S3.

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