A topology optimization method for multi-material structures of aircraft under inertial loads

Abstract

The present invention belongs to the field of aerospace technology, and discloses a method for topological optimization of a multi-material structure of an aircraft under inertial load, comprising the following steps: S1, establishing a finite element model, defining a design domain, dividing the structure, and applying boundary conditions; S2, assigning material parameters and determining optimization parameters, and then defining design variables; S3, using an alternating active phase algorithm to decompose the multi-material optimization problem into multiple sub-problems and solve them; S4, updating the structure and making a convergence judgment, if the conditions are met, proceed to step S5, if the conditions are not met, return to step S3; S5, performing a smooth design, and analyzing the change in the objective function before and after the smooth design, if the conditions are met, the optimization ends, if the conditions are not met, return to step S2. The present invention realizes the lightweight design of the structure under inertial load, and the obtained multi-material structure has better structural performance.

Description

Technical Field

[0001] The invention relates to the field of aerospace technology, and in particular to a method for topological optimization of a multi-material structure of an aircraft under inertial load. Background Art

[0002] Topology optimization is a structural optimization method that optimizes material distribution under given areas, constraints, and load conditions. It is widely used in various engineering practices. Inertial loads, as a design-related load, are commonly found in aerospace structures. Its characteristic is that it is coupled with the structure. As the structure changes, the load will also change, such as deadweight, centrifugal loads, and loads generated by acceleration. There are three unique challenges in solving this problem using density-based topology optimization methods, namely, the non-monotonic behavior of the objective function, possible constraint failure of the optimal structure, and parasitic effects in low-density areas.

[0003] Most of the current topology optimization is single-material topology optimization, and it is difficult to achieve specific performance with a single material. Compared with traditional single-material topology optimization, multi-material topology optimization has greater design freedom and better structural performance. With the development of multi-material additive manufacturing technology, multi-material topology optimization methods have received more and more attention. Considering multi-material topology optimization in topology optimization technology can better improve the comprehensive performance of the structure and achieve specific functions.

[0004] Therefore, it is necessary to provide a topology optimization method for multi-material structures of aircraft under inertial loads, which has high versatility and iteration efficiency and can obtain structures with better performance. Summary of the invention

[0005] The present invention discloses a method for topological optimization of a multi-material structure of an aircraft under inertial load, which improves the guided-weight method, realizes the effectiveness of volume constraints, and improves convergence performance. The method solves three unique problems existing in topological optimization under inertial load, and has high versatility and iteration efficiency. The method is extended to multi-material topological optimization design to obtain a structure with superior performance, which can effectively solve the technical problems involved in the background technology.

[0006] To achieve the above object, the technical solution of the present invention is:

[0007] A method for topological optimization of a multi-material structure of an aircraft under inertial load comprises the following steps:

[0008] S1. Establish a finite element model, define the design domain, divide the structure, and apply boundary conditions;

[0009] S2, assign material parameters and determine optimization parameters, and then define design variables;

[0010] S3, using the alternating active phase algorithm to decompose the multi-material optimization problem into multiple sub-problems and solve them;

[0011] S31, select alternative materials, the total number of materials is P, and sort the materials, the sequence numbers from large to small are 1, 2, 3...P;

[0012] S32, select the material number according to the order, and assign it to a, b;

[0013] S33, apply inertial load to the structure and perform finite element analysis;

[0014] S34, calculating unit sensitivity according to the results of finite element analysis;

[0015] S35, performing sensitivity filtering;

[0016] S36, updating the design variables;

[0017] S37, judging whether all materials are involved in the optimization, if so, proceeding to step S4; if not, returning to step S32;

[0018] S4, update the structure and make a convergence judgment. If the conditions are met, proceed to step S5; if the conditions are not met, return to step S3;

[0019] S5, perform smooth design, and analyze the change of the objective function before and after the smooth design. If the conditions are met, the optimization ends; if the conditions are not met, return to step S2.

[0020] The optimization process can be divided into an outer loop and an inner loop. The steps of the outer loop are: (1) define the design domain, mesh and apply boundary conditions; (2) input optimization parameters and define design variables; (3) enter the inner loop to solve sub-problems; (4) after the inner loop is completed, perform convergence judgment. If the conditions are met, proceed to the next step. If not, return to step (3); (5) perform smooth design and analyze the smooth design variation. If the conditions are met, end the optimization. If not, return to step (2). The steps of the inner loop are: 1) select alternative materials according to the alternating active phase algorithm; 2) perform finite element analysis on the structure; 3) perform sensitivity calculation; 4) perform sensitivity filtering; 5) update the design variables according to the improved weight-conducting method; 6) determine whether all materials are involved in the optimization. If so, exit the inner loop. If not, return to step 1). There are many aircraft structures dominated by inertial loads, such as the centrifugal load of high-speed rotation of engine turbine disks and blades, the deadweight load of aircraft hanger structures, the load generated by acceleration, the loads generated by acceleration and deceleration of aircraft fuselages and wings, etc. The present invention improves the weight-guiding method and utilizes an alternating active phase algorithm to solve the problems of volume constraint failure, non-monotonic objective function and parasitic effects in low-density areas, and realizes lightweight design through multi-material topological optimization design under inertial loads, while further improving the structural performance.

[0021] As a preferred improvement of the present invention: in the step S1, a planar four-node rectangular grid is used to divide the structure.

[0022] As a preferred improvement of the present invention: in step S2, the material parameters include Young's modulus, density and Poisson's ratio, the optimization parameters include filtering radius, penalty factor, step size and volume constraint, and the design variables are defined according to the volume constraint.

[0023] As a preferred improvement of the present invention: in step S2, a multi-material RAMP interpolation model is used as the material interpolation model.

[0024]

[0025] Among them, E ab Young's modulus, E, used for the subproblems dealing with materials a and b a is the Young's modulus of material a, E b is the Young's modulus of material b, the subscript i represents the unit number, and x i is the design variable of the current sub-problem, and q is the penalty factor.

[0026] As a preferred improvement of the present invention: in the step S31, the materials are sorted according to the size of Young's modulus, and the P materials include a void phase material.

[0027] As a preferred improvement of the present invention: in the step S33, an inertial load is applied to the material according to the material properties, and the inertial load is calculated by the following formula:

[0028]

[0029] Among them, i is the unit volume, ρ i is the unit density, A is the acceleration of the structure, is the direction matrix of the inertial load.

[0030] As a preferred improvement of the present invention: in step S34, the sensitivity expression is:

[0031]

[0032] Where C(x) is the total flexibility of the structure, x i is the design variable, ρ0 is the initial density, the subscript i represents the unit number, and v i is the volume of the i-th unit, A is the acceleration, u i is the displacement matrix of the ith unit, is the transpose of the unit displacement matrix, is the stiffness matrix of the initial unit, E a is the Young's modulus of material a, E b is the Young's modulus of material b, q is the penalty factor, is the direction matrix of the inertial load.

[0033] As a preferred improvement of the present invention: in the step S36, the design variables are updated by using the improved weight transfer method, the Lagrange coefficient λ in the improved weight transfer method is solved by using the dichotomy method, a lower limit and an upper limit are set for λ, and λ is continuously adjusted by the dichotomy method within this interval so that the total volume of the updated structure is consistent with the set volume retention amount. When the difference between the upper limit and the lower limit of the final interval is less than 10 -3 When the conditions are met;

[0034] At the same time, the step size is introduced to increase convergence, and its expression is:

[0035]

[0036]

[0037] Among them, move is the introduced step size, α is the step factor, the subscript i represents the unit number, G i is the conductivity of the i-th unit, Hi is the bulk density of the i-th unit, is the current design variable, Updated design variables, x minis the minimum value of the set design variable, k represents the kth iteration, is the sensitivity obtained after sensitivity filtering.

[0038] As a preferred improvement of the present invention: in the step S5, a smooth design function is introduced, which uses a grid interpolation method to expand the unit density to a finer grid to improve the smoothing effect, and a threshold is searched by a binary search method so that the sum of the smoothed design variables is equal to the sum of the original design variables. For each unit, the average value of the design variables on the fine grid around it is calculated, and the threshold is used to truncate it to obtain the smoothed design variables;

[0039] After the smooth design is performed, the smooth designed structure is projected back to the original finite element mesh, an additional finite element analysis is performed, and its structural flexibility is calculated. The rate of change τ is then calculated using the following formula,

[0040]

[0041] Among them, C(x) is the structural flexibility obtained by the last optimization before smoothing, and C(x′) is the structural flexibility obtained by projecting back to the original mesh after smoothing and performing finite element analysis;

[0042] When τ<0.01, the smooth design is reasonable.

[0043] The beneficial effects of the present invention are as follows:

[0044] The present invention fully considers the design relevance of the load, making the topology optimization results under design-related loads more accurate and reliable. By improving the weight-conducting method, three unique problems under inertial loads based on the density method are successfully solved, namely, the non-monotonic behavior of flexibility, possible constraint failure of the optimal solution, and parasitic phenomena in low-density areas. The optimized structure under inertial load is obtained, and the multi-material topology optimization method is used to further improve the performance of the structure and achieve lightweight design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] 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:

[0046] Figure 1 A flowchart of a method for topological optimization of a multi-material structure of an aircraft under inertial load according to the present invention;

[0047] Figure 2 It is a finite element model diagram corresponding to the structure under deadweight load of the present invention;

[0048] Figure 3 Material property diagram selected for the present invention;

[0049] Figure 4 The structure of the present invention is a structure after topological optimization of the structure under deadweight load;

[0050] Figure 5 This is a topology optimization process diagram of the present invention. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0052] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0053] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0054] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0055] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0056] See also Figure 1As shown, the present invention provides a method for topological optimization of a multi-material structure of an aircraft under inertial load, including an outer loop and an inner loop.

[0057] The external circulation is realized by the following technical solutions:

[0058] In the first step, the design area is selected, the structure is meshed using a planar four-node rectangular mesh, and boundary conditions are applied to the finite element model;

[0059] In the second step, assign material parameters such as Young's modulus, density, Poisson's ratio, etc., input optimization parameters such as filter radius, penalty factor, step length, etc., and define design variables according to volume constraints. The material properties are calculated using the multi-material RAMP interpolation model:

[0060]

[0061] Among them, E ab Young's modulus, E, used for the subproblems dealing with materials a and b a is the Young's modulus of material a, E b is the Young's modulus of material b, the subscript i represents the unit number (i = 1, 2, 3...N, there are N units in total), that is, the i-th unit, x i is the design variable of the current sub-problem, and q is the penalty factor.

[0062] The third step is to decompose the multi-material topology optimization problem into a series of sub-problems using the alternating active phase algorithm, enter the inner loop, and solve the sub-problems using the improved weight-conduction method; a multi-phase material topology optimization problem can be decomposed into P(P-1) / 2 two-phase material sub-problems using the alternating active phase algorithm, where P is the total number of materials and includes empty materials; for each sub-problem, only two phases are active, the topology design variables will change, and the topology of the remaining (P-2) phases will be fixed to the last known value, and "a" and "b" are used to represent the active phases in each sub-problem;

[0063] The fourth step is to update the structure after the inner loop ends, and then make a convergence judgment. If the conditions are met, proceed to the next step. If the conditions are not met, return to the third step. The convergence judgment is: for any i, if |x i (k+1) -x i (k) |<0.01, it is considered convergent;

[0064] The fifth step is to perform smooth design and introduce a smooth design function, which uses grid interpolation to expand the unit density to a finer grid to improve the smoothing effect. Use the binary search method to search for a threshold so that the smoothed design variables are equal to the sum of the original design variables. For each unit, calculate the average value of the design variables on the fine grid around it, and truncate it with the threshold to obtain the smoothed design variables. This method can effectively eliminate irregular and discontinuous shapes in the topology optimization results, making it easier to manufacture or further optimize. Project the structure after smooth design back to the original grid, perform an additional finite element analysis, and calculate its structural flexibility. Then, calculate the rate of change τ using the following formula, and make a smooth design judgment. If the conditions are met, the optimization ends. If not, return to the second step.

[0065] The smooth design conditions are:

[0066]

[0067] Among them, C(x) is the structural flexibility obtained by the last optimization before smoothing, and C(x′) is the structural flexibility obtained by projecting back to the original mesh after smoothing and performing finite element analysis. When τ < 0.01 is satisfied, the smooth design is reasonable.

[0068] The inner loop is realized by the following technical solutions:

[0069] Step 1: Select candidate materials according to the alternating active phase algorithm. The total number of materials is P, including empty phase materials. The materials are sorted according to the size of Young's modulus. The numbers from large to small are 1, 2, 3...P. The material numbers are selected according to the material order and assigned to a and b.

[0070] In the second step, an inertial load is applied to the material according to the material properties, and a finite element analysis is performed. The inertial load distributes the force applied to the geometric center of the unit to the four nodes of the unit according to the finite element method. The inertial load is calculated by the following formula:

[0071]

[0072] Among them, v i is the unit volume, ρ i is the unit density, A is the acceleration of the structure (gravitational acceleration, centrifugal acceleration, etc.), is the direction matrix of the inertial load.

[0073] Step 3: Calculate the cell sensitivity based on the calculation results obtained from the finite element analysis:

[0074]

[0075] Where C(x) is the objective function, i.e., the total flexibility of the structure. The subscript i represents the sequence number of the unit (i = 1, 2, 3, ... N, with a total of N units), i.e., the i-th unit, x i is the design variable, F v is the inertia load, U is the displacement matrix, U T is the transpose of the displacement matrix, K is the stiffness matrix, and combined with the multi-material RAMP interpolation model, the final sensitivity expression is obtained:

[0076]

[0077] Where C(x) is the total flexibility of the structure, x i is the design variable, ρ0 is the initial density, the subscript i represents the unit number, and v i is the volume of the i-th unit, A is the acceleration, u i is the displacement matrix of the ith unit, is the transpose of the unit displacement matrix, is the stiffness matrix of the initial unit, E a is the Young's modulus of material a, E b is the Young's modulus of material b, q is the penalty factor, is the direction matrix of the inertial load.

[0078] Step 4: Use the sensitivity filter to filter the sensitivity. The sensitivity filtering is as follows:

[0079]

[0080] R ei =max(0, r min -r ei ),

[0081] The subscript i represents the unit number (i = 1, 2, 3 ... N, there are N units in total), that is, the i-th unit, e is the currently determined central unit, R ei is the weight coefficient, r ei is the distance from the center of the filter unit e to the centers of other units, r min is the filter radius, N e is a set containing elements whose distance from the center of element i to the center of element e is less than the filter radius, is the sensitivity obtained after sensitivity filtering, This is the minimum design variable to prevent the denominator from being 0. It is usually set to 10. -3 .

[0082] Step 5: Update the design variables using the improved weight-guiding method

[0083] The process of the weight-guiding method is:

[0084] Construct the Lagrangian function L with minimum flexibility as the goal:

[0085] L=C(x)+λ(M(x)-fM0),

[0086] Among them, C(x) is the objective function, that is, the structural flexibility, λ is the Lagrangian coefficient, M(x) is the volume of the structure, M0 is the initial volume, and f is the set volume constraint.

[0087] Based on the Kuh-Tucker optimality condition, to obtain the optimal solution, the following requirements must be met:

[0088]

[0089] Where L is the Lagrangian function, C(x) is the objective function, i.e., the structural flexibility, λ is the Lagrangian coefficient, M(x) is the volume of the structure, M0 is the initial volume, f is the set volume constraint, the subscript i represents the unit number (i = 1, 2, 3...N, there are N units in total), x i is the design variable, x min is the minimum design variable set.

[0090] According to the above formula, we can get:

[0091]

[0092] According to the weight-guided method, the definitions of four important variables are given:

[0093] W i =x i H i ,

[0094] Among them, H i is the bulk density of the i-th unit, M(x) is the volume of the structure, x i is the design variable, W i is the generalized weight of the i-th unit, C(x) is the structural flexibility, G i is the guided weight of the ith unit, and G is the total guided weight of the structure.

[0095] The following formula can be obtained:

[0096]

[0097] Introducing the step factor gives the iterative formula:

[0098]

[0099] Among them, α is the step factor, G iis the conductivity of the i-th unit, Hi is the bulk density of the i-th unit, is the current design variable, The updated design variables, χ min is the minimum value of the set design variable, and k represents the kth iteration.

[0100] The Lagrange coefficient is obtained by the following formula:

[0101]

[0102] Among them, H i is the bulk density of the i-th unit, x i is the design variable, W i is the generalized weight of the ith unit, G i is the guided weight of the ith unit, and G is the total guided weight of the structure.

[0103] The improvement of the weight-derived method includes using the bisection method to solve the Lagrange coefficient λ and setting a lower limit for λ (usually 10 -9 ) and an upper limit (usually 10 9 ), and within this interval, λ is continuously adjusted by the binary method to make the updated total volume of the structure (the volume of the structure after each iteration) consistent with the set volume retention. When the difference between the upper and lower limits of the final λ interval is less than 10 -3 , it is considered to meet the conditions.

[0104] At the same time, the step size is introduced to increase convergence, and its expression is:

[0105]

[0106]

[0107] Among them, move is the introduced step size, usually with a value of 0.2, α is the step factor, which is used to consider the iteration history to enhance the convergence performance, the subscript i represents the unit number, Gi is the guide weight of the i-th unit, Hi is the bulk density of the i-th unit, is the current design variable, Updated design variables, x min is the minimum value of the set design variable, k represents the kth iteration, For the sensitivity obtained after sensitivity filtering, a structural step is introduced and the iteration type is changed. The advantage is that the convergence performance of the algorithm is further improved.

[0108] Step 6: Determine whether all materials are involved in the sub-problem, that is, whether a and b are equal to the coefficient of the second-to-last material phase and the coefficient of the first-to-last material phase respectively. If so, exit the inner loop and enter the fourth step of the outer loop. Otherwise, assign values ​​to a and b and return to the second step.

[0109] A method for topological optimization of a multi-material structure of an aircraft under inertial load is applied to the multi-material topological optimization of a structure subjected to self-weight load, wherein the topologically optimized basic structure in the first step refers to the basic structure of a beam that needs to be topologically optimized, and after executing an outer loop and an inner loop, a multi-material optimized structure under gravity load is obtained.

[0110] Example 1: Topology optimization process of beam structure subjected to self-weight load

[0111] In step 1, meshing is performed on the basic structure to be topologically optimized. In this embodiment, the aspect ratio of the beam is 2:1. Figure 2 shown.

[0112] In step 2, the properties of the materials are determined and three materials are selected to optimize the structure, where the values ​​of Young's modulus and density are as follows: Figure 3 As shown, the Poisson's ratio is 0.3. In this example, the topology optimization parameters filter radius, penalty factor, step size, and volume constraint are 2, 10, 0.2, and 0.3, respectively, and the initial design variable definition is the same as the volume constraint.

[0113] In step three, the alternating active phase algorithm is used to transform the multi-material topology optimization problem under inertial load into a series of single-material sub-problems and enter the inner loop.

[0114] In step 4, the convergence is judged and the change of the design variables in the current iteration step is calculated. If the change is less than 0.01, the structure is considered to have converged.

[0115] In step 5, a smooth design function is introduced, which uses the grid interpolation method to expand the cell density to a finer grid to improve the smoothing effect. After calculation, τ < 0.01, and it is considered that the smooth design is reasonable and effective.

[0116] In step 1, there are four types of candidate materials, including empty materials. The materials are sorted 1, 2, 3, and 4 according to the size of Young's modulus, where 4 is the empty material phase. Let a=1, b=2.

[0117] In step 2, the inertial load (taking deadweight load as an example) is applied by the following formula:

[0118]

[0119] Among them, the subscript i represents the unit number, υ i is the unit volume, ρ i is the unit density, g is the gravitational acceleration, is the direction matrix of the gravity load.

[0120] In step 3, the sensitivity is calculated taking into account the design relevance of the deadweight load and is calculated as follows:

[0121]

[0122] Where C(x) is the total flexibility of the structure, x i is the design variable, ρ0 is the initial density, the subscript i represents the unit number, and v i is the volume of the ith unit, g is the acceleration due to gravity (usually 9.8), u i is the displacement matrix of the ith unit, is the transpose of the unit displacement matrix, is the stiffness matrix of the initial unit, E a is the Young's modulus of material a, E b is the Young's modulus of material b, q is the penalty factor, is the direction matrix of the inertial load.

[0123] Step 4, sensitivity filtering;

[0124]

[0125] R ei =max(0, r min -r ei ),

[0126] The subscript i represents the unit number (i = 1, 2, 3 ... N, there are N units in total), that is, the i-th unit, e is the currently determined central unit, R ei is the weight coefficient, r ei is the distance from the center of the filter unit e to the centers of other units, r min is the filter radius, N e is a set containing elements whose distance from the center of element i to the center of element e is less than the filter radius, This is the minimum design variable to prevent the denominator from being 0. It is usually set to 10. -3 .

[0127] In step 5, the updating criterion of the unit is the improved weight transfer method, and the specific expression is:

[0128]

[0129]

[0130] Among them, move is the introduced step size (value is 0.2), α is the step factor (value is 0.5), the subscript i represents the unit number, Gi is the guide weight of the i-th unit, Hi is the bulk density of the i-th unit, is the current design variable, Updated design variables, x min is the minimum value of the set design variable, k represents the kth iteration, is the sensitivity obtained after sensitivity filtering.

[0131] Step 6, determine whether all materials are involved in the sub-problem, that is, determine whether a is equal to 3 and b is equal to 4. If so, exit the inner loop and enter the fourth step of the outer loop. Otherwise, select the material to traverse all materials and assign them to a and b, and return to step 2.

[0132] Figure 4 The final topology optimized structure obtained by the topology optimization method of the multi-material structure of the aircraft under inertial load, (a) is the final structure using only material 1 and empty material, (b) is the final structure using materials 1, 2 and empty material, (c) is the final structure using materials 1, 2, 3 and empty material. The final structure is smooth and has no parasitic effects in low-density areas, which can be used for manufacturing or further optimization.

[0133] Figure 5 This is an iterative process of the topology optimization method for multi-material structures of aircraft under inertial loads. Compared with the final structure obtained by using material 1 alone, the final structures using materials 1, 2 and materials 1, 2, 3 have a total structural flexibility reduced by 9.02% and 16.14%, respectively, and have a higher overall stiffness while reducing weight.

[0134] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the embodiments. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for topological optimization of multi-material structures of aircraft under inertial loads, characterized in that: The following steps are involved: S1. Establish a finite element model, define the design domain, divide the structure, and apply boundary conditions; S2, assign material parameters and determine optimization parameters, and then define design variables; S3, using the alternating active phase algorithm to decompose the multi-material optimization problem into multiple sub-problems and solve them; S31, select alternative materials, the total number of materials is P, and sort the materials, the sequence numbers from large to small are 1, 2, 3...P; S32, select the material number according to the order, and assign it to a, b; S33, apply inertial load to the structure and perform finite element analysis; S34, calculating unit sensitivity according to the results of finite element analysis; S35, performing sensitivity filtering; S36. Update the design variables. Use the improved weight transfer method to update the design variables. In the improved weight transfer method, the Lagrange coefficient λ is solved by the binary method. A lower limit and an upper limit are set for λ. Within this interval, the binary method is used to continuously adjust λ so that the total volume of the updated structure is consistent with the set volume retention. When the difference between the upper limit and the lower limit of the final interval is less than 10 -3 When the conditions are met; At the same time, the step size is introduced to increase convergence, and its expression is: ， ， Among them, move is the introduced step size, α is the step factor, the subscript i represents the unit number, G i is the guide weight of the ith unit, H i is the bulk density of the ith unit, is the current design variable, The updated design variables, is the minimum value of the set design variable, k represents the kth iteration, is the sensitivity obtained after sensitivity filtering; S37, judging whether all materials are involved in the optimization, if so, proceeding to step S4; if not, returning to step S32; S4, update the structure and make a convergence judgment. If the conditions are met, proceed to step S5; if the conditions are not met, return to step S3; S5, perform smooth design, and analyze the change of the objective function before and after the smooth design. If the conditions are met, the optimization ends; if the conditions are not met, return to step S2.

2. The method for topological optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In the step S1, a planar four-node rectangular grid is used to divide the structure.

3. The method for topological optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In step S2, the material parameters include Young's modulus, density and Poisson's ratio, the optimization parameters include filtering radius, penalty factor, step length and volume constraint, and the design variables are defined according to the volume constraint.

4. The method for topology optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In step S2, a multi-material RAMP interpolation model is used as a material interpolation model. ， in, Young's modulus used for the subproblem dealing with materials a, b, is the Young's modulus of material a, is the Young's modulus of material b, the subscript i represents the unit number, is the design variable of the current sub-problem, and q is the penalty factor.

5. The method for topology optimization of multi-material structures of aircraft under inertial load according to claim 1, characterized in that: In the step S31, the materials are sorted according to the size of Young's modulus, and the P materials include a void phase material.

6. The method for topological optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In step S33, an inertial load is applied to the material according to the material properties, and the inertial load is calculated by the following formula: ， in, is the unit volume, is the cell density, is the acceleration of the structure, is the direction matrix of the inertial load.

7. The method for topology optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In step S34, the sensitivity expression is: ， in, is the total flexibility of the structure, is the design variable, is the initial density, the subscript i represents the unit number, is the volume of the ith unit, A is the acceleration, is the displacement matrix of the ith unit, is the transpose of the unit displacement matrix, is the stiffness matrix of the initial unit, E a is the Young's modulus of material a, E b is the Young's modulus of material b, q is the penalty factor, is the direction matrix of the inertial load.

8. The method for topology optimization of a multi-material structure of an aircraft under inertial load according to claim 1, characterized in that: In step S5, a smooth design function is introduced, which uses a grid interpolation method to expand the cell density to a finer grid to improve the smoothing effect, and a threshold is searched by a binary search method so that the sum of the smoothed design variables is equal to the sum of the original design variables. For each cell, the average value of the design variables on the fine grid around it is calculated, and the value is truncated by the threshold to obtain the smoothed design variables; After the smooth design is performed, the smooth designed structure is projected back to the original finite element mesh, an additional finite element analysis is performed, and its structural flexibility is calculated. The rate of change τ is then calculated using the following formula, ， in, It is the structural flexibility obtained by the last optimization before smoothing. The structural flexibility is obtained by projecting the original mesh back to the original mesh after smoothing and performing finite element analysis. When τ<0.01, the smooth design is reasonable.

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