Multi-objective hybrid optimization method for variable-thickness hybrid composite laminated plate

Abstract

The invention relates to the field of composite material structure design and optimization, in particular to a variable-thickness hybrid composite material laminated plate-oriented multi-objective hybrid optimization method, which comprises the following steps of: dividing a structure region and defining parameters; generating an initial sequence of a regional layering structure; layer-by-layer construction and sequence optimization of a regional layering structure are carried out; constructing an improved and optimized stacking sequence table; and multi-objective optimization and performance agent integration are carried out. According to the method, region thickness initial evaluation, constraint-driven structure generation and an intelligent agent model prediction mechanism are fused, so that efficient optimization design and multi-target performance collaborative improvement of a multi-region composite material structure are realized; the method can effectively overcome the defects of an existing method in the aspects of multi-area thickness irregular change control, hybrid material collaborative design and complex load adaptability, and high-performance, low-cost and high-reliability comprehensive optimization of the variable-thickness hybrid composite laminated plate is achieved.

Description

Technical Field

[0001] This invention relates to the field of composite material structure design and optimization, and in particular to a multi-objective hybrid optimization method for variable thickness hybrid composite laminates. Background Technology

[0002] Composite material structures, due to their high specific strength and high specific stiffness, and the ability to balance performance and cost to some extent through hybrid layup methods, have been widely used in the design of low-cost and high-performance structures in recent years. Compared with traditional laminated structures composed of single fibers and single matrix materials, variable-thickness hybrid composite material structures introduce multiple material types into the layup sequence, rationally mixing high-performance and low-cost materials. This allows for lower overall material costs and improved material utilization efficiency while meeting structural stiffness, strength, and stability requirements. However, the coupling relationships between design variables such as layup thickness, material type, and layup sequence in this type of structure are complex, resulting in a large design space and numerous combinations. Existing design methods struggle to achieve synergistic optimization of cost and performance while simultaneously considering structural performance, and the optimization process often involves high computational complexity and engineering implementation difficulties. Therefore, how to achieve low-cost and high-performance design of variable-thickness hybrid composite material structures under complex constraints remains a problem that requires further research and improvement in current technologies.

[0003] Chinese invention patent CN113011014A, entitled "A Composite Material Layup Optimization Method and System," discloses a composite material layup optimization method based on layup angle parameters. This method generates different layup angle arrangements by using the number of layup layers and angle sets. It then performs curing deformation simulation and failure strength simulation to determine the global maximum value of the absolute deformation and the global maximum load. These values ​​are input into a linear function to obtain the function value. Using the layup angle arrangement corresponding to the minimum function value as input, an optimization algorithm is employed to obtain the optimized layup scheme with the maximum load and minimum curing deformation. This method, to some extent, considers both the mechanical properties and curing deformation performance of composite material components. However, the optimization process uses only the layup angle as a single design variable, limiting the optimization scope to a single region. It does not perform multi-region division and zoned collaborative optimization of the structure, resulting in the failure to fully utilize the differences in material properties and thickness distribution. Furthermore, this method does not incorporate material type and thickness parameters into the optimization design space, limiting its ability to model and coordinate the performance of hybrid material structures. In addition, the linear function performance coupling method it uses cannot accurately reflect the nonlinear relationships between multiple performance indicators, making it unsuitable for optimization needs under complex loads and multi-objective coupling conditions. Therefore, this method is difficult to achieve comprehensive optimization design for multi-region variable thickness hybrid composite material structures.

[0004] Chinese invention patent CN115946372A, entitled "A Method for Laying Up Variable Thickness Composite Materials," proposes a layup design method for composite materials where the thickness gradually changes along the length of the component. This method sets a difference in the number of layup layers between the front and rear ends and divides the transition layup area into several fabric block regions according to a block numbering rule. The blocks are numbered sequentially from largest to smallest, and the rearrangement of the block distribution reduces step effects and delamination risks, thereby achieving a smooth transition in the thickness direction and improving the molding quality and service life of the structure. However, this method assumes that the thickness increases continuously in a single direction and is only applicable to components with a clear thickness variation pattern. It is difficult to handle complex situations such as local nonlinear thickness changes or multi-directional gradient transitions. Furthermore, this scheme is only designed for single-material systems and cannot be applied to hybrid composite structures composed of multiple materials. It also cannot reflect the performance coordination issues between different material layers, thus making it difficult to play a role in multi-region thickness collaborative optimization and hybrid material collaborative design. This method is not applicable to composite structures with irregular thickness distributions or multiple material combinations and is difficult to achieve overall performance coordination and stable optimization under complex load conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization method for variable-thickness hybrid composite laminates. This method integrates initial assessment of regional thickness, constraint-driven structure generation, and intelligent surrogate model prediction mechanism to achieve efficient optimization design and synergistic improvement of multi-objective performance of multi-region composite structures. Structural quality indicators are introduced, but not simply for lightweighting as the optimization goal. Instead, they are used as important reference quantities reflecting the overall physical properties of the structure and the level of material usage. These indicators participate in multi-objective trade-offs along with cost objectives and multiple performance indicators to avoid a decline in the overall engineering rationality of the structure due to local performance or cost optimization. This effectively overcomes the shortcomings of existing methods in controlling irregular variations in multi-region thickness, collaborative design of hybrid materials, and adaptability to complex loads, achieving comprehensive optimization of high performance, low cost, and high reliability for variable-thickness hybrid composite laminates.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The present invention provides a multi-objective hybrid optimization method for variable thickness hybrid composite laminates, comprising the following steps:

[0008] Step 1: Structural region division and parameter definition;

[0009] The structure is divided according to the different forces it is subjected to. Sub-regions;

[0010] remember This indicates the number of ply layers in different regions, where Let r be the layer number of the r-th region;

[0011] remember Indicates the ply sequence of each region, where The ply angle sequence for the r-th region;

[0012] remember This indicates the ply material for each area, where Let be the layup material sequence for the r-th region.

[0013] Step 2: Generate the initial sequence of the regional ply structure;

[0014] After determining the division of each region in Step 1, the initial ply structure of each sub-region is generated sequentially, and the overall initial generation sequence of regions is determined according to the order of region thickness from thinnest to thickest. Under the premise of satisfying regional geometric constraints and stress constraints, a basic symmetrical ply structure that balances engineering manufacturability and structural stability is constructed as the initial base for subsequent intercalation optimization. Based on this, to obtain candidate ply schemes that meet buckling performance requirements, this invention proposes an intercalation generation mechanism based on layer-by-layer insertion and buckling determination, the specific process of which is as follows:

[0015] Phase 1: Insert a single-layer ply in the middle of the initial symmetrical ply (top-bottom symmetrical) sequence and calculate the current buckling factor. ;like If the sequence is successful, it is recorded as a candidate solution; if it fails to meet the requirements, the layup is withdrawn and the process proceeds to the second stage.

[0016] Second stage: Insert two identical layers at symmetrical positions above and below the sequence and recalculate. If the buckling factor is still less than 1 at this point, the layup is preserved and the intercalation and evaluation operations are continued, i.e., returning to the first stage until... It is important to note that single-layer and double-layer layups are alternated during the plying process. The difference lies in that a single-layer layup is withdrawn if it fails to meet the constraints, while a double-layer layup is retained even if it does not meet the requirements. This design makes single-layer insertion more advantageous in terms of improving material utilization, reducing structural weight and manufacturing costs, while the introduction of double-layer layups helps to improve local thickness and overall stability, and maintain the symmetry and ply balance of the laminate. Because single-layer insertions are withdrawn if they fail to meet the requirements, only one single-layer layup inserted in the middle of the final structure can be retained, thus avoiding ply discontinuities and mechanical inconsistencies caused by frequent insertions.

[0017] The buckling factor is calculated based on the classical buckling theory of composite laminates, and its expression is: in, and They are respectively regions Length and width, and Applying along the region and Compression load in the direction; , , and It is based on the ply sequence The calculated bending stiffness term, and is the half-wave number of the buckling mode.

[0018] This layer-by-layer insertion and buckling determination mechanism adaptively generates multiple sets of region layup schemes that satisfy buckling and manufacturing constraints without exhaustively listing all combinations. Based on this, statistical analysis of the layer number characteristics of each candidate scheme further determines the initial distribution pattern of region thickness, and generates an initial region sequence according to a gradual trend from thin to thick.

[0019] To ensure the generated scheme meets engineering manufacturability requirements, the candidate ply must satisfy the following manufacturing constraints during the generation process to guarantee the rationality and feasibility of the ply sequence. These constraints mainly include:

[0020] (1) Structural symmetry constraint: The ply of each region should be symmetrical about the center plane, that is, the first ply... Layer and First The layer layup angles satisfy ;

[0021] (2) Direction angle ratio constraint: the direction of each typical ply (e.g. The proportion should meet the following requirements. To ensure the uniformity of the angle distribution, among which For the first Regional perspective The quantity.

[0022] (3) Constraint on angle variation between adjacent layers: The angle variation between adjacent layers shall not exceed ,Right now ;

[0023] (4) Angle Discrete Constraint: The allowed ply angles come from a finite discrete set. .

[0024] (5) Limitation on the number of layers with the same angle: The number of consecutive layers with the same angle shall not exceed 4, that is, it is prohibited to have more than 4 consecutive layers with the same angle, in order to avoid local stiffness abnormalities.

[0025] (6) Outermost layer consistency constraint: The outermost layer angle of each region should be consistent to ensure interlayer continuity and integrity;

[0026] In addition to satisfying the above manufacturing constraints, buckling stability constraints are further introduced, requiring that the buckling factor of each sub-region under the design load meets the following requirements. This is to ensure that the structure does not experience local buckling instability.

[0027] Step 3: Layer-by-layer construction and sequential optimization of the regional ply structure;

[0028] Based on the initial order of regions from thinnest to thickest obtained in step two, the ply information of the thinnest region is first retained as the basis for subsequent construction, while the initial ply data of the remaining regions are not retained. Subsequently, the ply structures of each region are generated sequentially from thinnest to thickest. During this process, manufacturing constraints and buckling factor constraints are simultaneously satisfied, and intercalation mechanisms and region sequence optimization mechanisms are introduced to generate the regional ply structures. Furthermore, traditional methods require strict symmetry among the regions, i.e. However, the actual ply generation of this invention allows for a slight asymmetric structure, that is, it allows for a slight asymmetric structure when the number of plies is odd. This results in a layered structure that is "locally asymmetrical but globally symmetrical," thus maintaining overall symmetry while effectively avoiding continuous discontinuities in intermediate layers and improving the structural feasibility for manufacture.

[0029] The intercalation mechanism is a cyclic intercalation generation method used in the process of building structures from thin to thick.

[0030] Specifically, interlayer continuity and overall symmetry are achieved through symmetrical or locally asymmetrical intercalation; this intercalation mechanism utilizes buckling factors. To determine the evaluation criteria, the system calculates the results promptly after each interpolation. And based on this, decide whether to accept intercalation or continue iteration; when When, save the current sequence as a candidate; if If the buckling constraint is satisfied or the iteration limit is reached, then continue to execute the next round of intercalation and judgment until the buckling constraint is satisfied or the iteration limit is reached;

[0031] The intercalation process is divided into two cases based on the parity of the number of layers in the previous region:

[0032] A: Even-numbered layers

[0033] A1: Divide the previous region sequence into symmetrical front and rear halves. Select an intercalation position in the front half to insert a new layer and merge them to generate a complete sequence. Calculate... ;like If so, then save the sequence; if Cancel the intercalation and proceed to the next step;

[0034] A2: Interpolate again in the first half, replace the second half with the updated mirror image of the first half, merge to generate the complete sequence, and recalculate. ;like If the result is satisfactory, save and end; otherwise, continue iterating until... Or it may reach its limit;

[0035] B: Odd-numbered layer cases

[0036] B1: Divide the sequence into two parts, making the first part one layer longer than the second part; directly mirror the first part to generate a new second part and merge them into a complete sequence, then calculate... ;like If, then save; if Proceed to the next step;

[0037] B2: While maintaining the first half with one more layer, first mirror the first half to generate a temporary second half, then insert a layer into the first half to form a new complete sequence, and recalculate. ;like If the condition is met, save the result; otherwise, continue the loop iteration until the condition is met. Or it may reach the iteration limit.

[0038] The region optimization mechanism is a method for dynamically adjusting the generation order of regions during the construction of multiple regions. The steps of the region optimization mechanism are as follows:

[0039] (1) For the current region to be generated Calculate the previous region Buckling factor under the current boundary conditions ;

[0040] (2) If Continue tracing back to the region Until the first one is found area ;

[0041] (3) Move the current area Insert into region Then, it serves as a new starting point for generation;

[0042] (4) For the inserted region and its subsequent regions, the layup is regenerated based on the layup sequence of the previous region to ensure interlayer continuity and overall stability;

[0043] (5) Update the generation order of all subsequent regions according to the new regional order, and calculate the buckling factor of each region. To verify stability;

[0044] (6) Repeat the above steps until all regions are generated in order of increasing thickness, forming a final stable and continuous multi-region layered structure.

[0045] During the generation process, the system simultaneously performs the determination of manufacturing constraints and buckling factor constraints, wherein the manufacturing constraints include the following:

[0046] (1) Structural symmetry constraint: The ply of each region should be symmetrical about the center plane, that is, the first ply... Layer and First The layer layup angles satisfy ;

[0047] (2) Direction angle ratio constraint: the direction of each typical ply (e.g. The proportion should meet the following requirements. To ensure the uniformity of the angle distribution, among which For the first Regional perspective Quantity;

[0048] (3) Regional inter-layer consistency constraints: If the region The number of layers is less than the area ,but Its ply angle set should be a subset of the latter to maintain consistency between regions;

[0049] (4) Constraint on angle variation between adjacent layers: the angle variation between adjacent layers shall not exceed ,Right now ;

[0050] (5) Angle Discrete Constraint: The allowed ply angles come from a finite discrete set. ;

[0051] (6) Limitation on the number of layers with the same angle: The number of consecutive layers with the same angle shall not exceed 4, that is, it is prohibited to have more than 4 consecutive layers with the same angle, in order to avoid local stiffness abnormalities.

[0052] (7) Outermost layer consistency constraint: The outermost layer angle of each region should be consistent to ensure interlayer continuity and integrity;

[0053] (8) Continuity constraint of interrupted layer: In the interrupted area, there should be at least one continuous ply angle in every three adjacent areas, that is, there should be at least one continuous ply every three layers to maintain the continuity of the local structure.

[0054] Step 4: Improve and optimize the construction of stacked sequence lists;

[0055] Based on the multi-region feasible layup generated in step three, this invention further constructs an Improved Optimization Stacking Sequence Table (ioSST). This table is used to achieve a unified expression and optimization solution of layup information in different regions, providing a standardized structural coding foundation for subsequent multi-objective evolutionary algorithms. Through the construction of ioSST, layup relationships, thickness distributions, and material configuration information between regions can be effectively integrated, thereby supporting optimization algorithms to perform co-evolution and performance prediction of stacking sequences at the global level.

[0056] ioSST employs a five-chromosome genotype coding strategy. Indicates the area code. Indicates the number of plies in the region. Indicates the ply angle of the thickest region. This indicates the ply material in the thickest area. Indicates the area where the ply first appears;

[0057] The construction steps are as follows:

[0058] (1) Chromosome : Used to represent the number of each sub-region, and sorted in order from thinnest to thickest, with a length of . an integer vector;

[0059] (2) Chromosomes : Used to describe the number of ply layers in each sub-region, corresponding one-to-one with the region number;

[0060] (3) Chromosomes : Used to describe the complete ply angle sequence of the thickest region, with a length of an integer vector;

[0061] (4) Chromosomes : Used to describe the complete ply material sequence of the thickest region, with the same length as the angle sequence, indicating the material type corresponding to each ply;

[0062] (5) Chromosomes : A region number used to identify the first occurrence of each ply, with a length of . an integer vector; where the first... The digit indicates the first position. The earliest area numbering system introduced for layer-by-layer plying was the one that was first introduced.

[0063] Step 5: Multi-objective optimization and performance proxy integration.

[0064] The ioSST stacked sequence list constructed in step four is combined with the NSGA-II multi-objective evolutionary algorithm and the BP neural network intelligent agent model to form a multi-objective optimization module for composite laminates.

[0065] The BP neural network was trained using finite element simulation samples and was used to establish structural design variables. The nonlinear mapping relationship between performance response and the training of the BP intelligent agent model allows for rapid prediction of structural response, including the first-order natural frequency, during optimization iterations. Maximum stress With maximum deformation This significantly reduces the cost of finite element analysis.

[0066] The optimization process is driven by the NSGA-II algorithm, which realizes global search and multi-objective balance. NSGA-II evaluates and screens candidate structural schemes based on BP prediction results, and completes the iterative optimization of multi-region variable thickness hybrid composite laminate.

[0067] The optimization objectives include five categories of performance metrics:

[0068] (1) First-order frequency objective function:

[0069] (2) Objective function for maximum stress:

[0070] (3) Objective function for maximum deformation:

[0071]

[0072] (4) Structural quality objective function:

[0073] in It is the first Region 1 Density of the layered materials It is the first Region 1 The thickness of a single layer of plywood, It is the first The ply area of ​​each region;

[0074] (5) Structural cost objective function:

[0075]

[0076] in It is the first Region 1 Unit volume cost of layered materials.

[0077] Through the synergistic optimization of the above five objective functions, NSGA-II completes the parallel search and optimization of candidate solutions based on the non-dominated sorting and crowding determination mechanism, and achieves a comprehensive balance between quality, cost, stiffness, stress and stability of composite laminates.

[0078] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0079] 1. This invention divides the composite material structure into multiple functional regions and introduces interlayer consistency constraints and buckling stability constraints during the optimization process, thereby achieving coordinated optimization of thickness and material distribution in multiple regions. This overcomes the shortcomings of existing methods that can only perform local optimization in a single region, and improves the coordination and reliability of the overall structural design.

[0080] 2. This invention proposes an adaptive intercalation generation mechanism based on buckling factor, which can dynamically adjust the number of ply layers and angles through layer-by-layer insertion and buckling determination without exhaustive calculation, thereby effectively improving the buckling stability of the structure while ensuring manufacturing feasibility.

[0081] 3. This invention constructs an improved optimized stacked sequence list ( This method unifies the encoding and expression of information such as ply angle, material type, and regional thickness, thereby achieving standardized data transfer between the optimization algorithm and the performance proxy model and improving the versatility and integration efficiency of the optimization process.

[0082] 4. This invention utilizes a non-dominated sorting genetic algorithm ( )and By combining neural network performance proxy models, a nonlinear mapping relationship between design variables and multiple performance responses of composite laminates was established, realizing parallel optimization of multiple objective performances such as frequency, stress, deformation, mass and cost, which significantly reduced the cost of finite element calculation and improved the optimization convergence efficiency.

[0083] The ply constraint system established in this invention comprehensively considers factors such as symmetry, angular proportions, interlayer continuity, and manufacturing feasibility. The resulting ply sequence not only meets engineering processing constraints but also takes into account the stiffness, strength, and stability of the structure. Attached Figure Description

[0084] Figure 1 Flowchart of a multi-objective hybrid optimization method for layup of variable thickness hybrid composite laminates

[0085] Figure 2 This is a schematic diagram of the horseshoe-shaped structure and stress distribution of the 18 panels in an embodiment of the present invention.

[0086] Figure 3This is a flowchart illustrating the statistical analysis of the initial region generation sequence of the 18 panels in the horseshoe-shaped structure example of this invention.

[0087] Figure 4 This is a schematic diagram illustrating the initial region generation of the 18-panel horseshoe-shaped structure in an embodiment of the present invention.

[0088] Figure 5 This is a schematic diagram of the optimized horseshoe-shaped structure of 18 panels in an embodiment of the present invention. Detailed Implementation

[0089] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention.

[0090] For ease of explanation, this embodiment uses an 18-panel horseshoe-shaped composite laminate structure as an example to illustrate the specific implementation steps of the multi-objective hybrid optimization method of the present invention, such as... Figure 1 As shown. This method mainly includes the following steps:

[0091] Step 1: Divide the structure into different categories according to the different forces applied. Figure 2 The 18 sub-regions are shown.

[0092] remember This indicates the number of ply layers in different regions, where Let r be the layer number of the r-th region; denoted as Indicates the ply sequence of each region, where For the ply angle sequence of the r-th region, It is the ply angle of the k-th layer in the r-th region;

[0093] remember This indicates the ply material for each area, where For the layup material sequence of region r, It is the layup material of the k-th layer in the r-th region.

[0094] Step 2: Considering geometric and force constraints, multiple candidate layering schemes are generated for each region, and the initial order of the regions from thinnest to thickest is generated by statistically analyzing the candidate schemes. The boundary conditions of each sub-region are set as simply supported on four sides to ensure the rationality of the overall stress and deformation.

[0095] To ensure that the generated solution meets engineering manufacturability requirements, the candidate layup must satisfy the following manufacturing constraints during the generation process:

[0096] (1) Structural symmetry constraint: The ply of each region should be symmetrical about the center plane. .

[0097] (2) Direction angle ratio constraint: the direction of each typical ply (e.g. The proportion should meet the following requirements. This is to ensure the uniformity of the angle distribution.

[0098] (3) Regional inter-layer consistency constraints: If the region The number of layers is less than the area ,but To maintain the nested relationship between regions.

[0099] (4) Constraint on angle variation between adjacent layers: the angle variation between adjacent layers shall not exceed ,Right now .

[0100] (5) Angle Discrete Constraint: The allowed ply angles come from a finite discrete set. .

[0101] (6) Limit on the number of layers with the same angle: The number of consecutive layers with the same angle shall not exceed 4.

[0102] (7) Outermost layer consistency constraint: The outermost layer angle of each region should be consistent to ensure the continuity of the upper and lower surfaces.

[0103] (8) Continuity constraint of interrupted layers: In the interrupted area, there should be at least one continuous layer every three layers to maintain the continuity of the local structure.

[0104] In this step, to facilitate the initial thickness estimation, each region is generated independently, so the constraints of item (3) "inter-layer consistency" and item (8) "continuity within the interrupted layer" are not considered for the time being, and only the remaining manufacturing constraints and basic buckling constraints are retained.

[0105] To ensure the structural stability of the candidate schemes, each candidate ply configuration must satisfy buckling constraints, specifically: the buckling factor corresponding to each sub-region under the design load. Must meet

[0106] That is when At that time, the candidate solution was deemed buckling unsafe in the corresponding mode and region and was not accepted.

[0107] The buckling factor is calculated using the classical plate buckling theory, and the expression is as follows: in, and They are respectively regions Length and width, and Applying along the region and Compression load in the direction; , , and It is based on the ply sequence The calculated bending stiffness term, and This represents the half-wave number of the buckling mode. This embodiment considers the first three modes. and with the smallest of all modes The value is used for judgment.

[0108] Under the premise of satisfying the above manufacturing and buckling constraints, an initial layup sequence of 8 layers is generated for each region. The initial sequence consists of typical angles. The initial sequence is randomly shuffled and arranged symmetrically to ensure a reasonable angular ratio and compliance with basic manufacturing requirements. The buckling factor of this initial sequence has been calculated. This indicates that the structure does not yet possess buckling stability at this stage.

[0109] To obtain a feasible ply structure that satisfies buckling stability, this paper adopts a two-step intercalation mechanism that combines layer-by-layer intercalation with buckling constraint determination:

[0110] Step 1: Insert a layer in the middle of the sequence and recalculate the buckling factor. If the buckling factor If the buckling factor is..., then remove that layer and proceed to the second step; If the sequence is not found, then the generation process is stopped.

[0111] Step 2: Insert two identical layers at the symmetrical position of the sequence and evaluate the buckling factor again; when the buckling factor... Save the sequence; if the requirements are still not met, save the sequence and repeat step one until the condition is met.

[0112] This intercalation mechanism can gradually improve the buckling stability of the structure while ensuring manufacturing feasibility, thereby obtaining a regional ply structure that meets buckling constraints. After the intercalation iteration is completed, the system automatically generates multiple candidate ply schemes and performs statistical analysis on the distribution of the number of ply layers in different regions.

[0113] In this embodiment, a total of 21 candidate layup schemes were generated (e.g. Figure 3 (As shown). By statistically analyzing the number of ply layers in each region under different schemes, the median is taken as the estimated initial ply thickness for that region. Subsequently, based on the relationship between the median thicknesses of each region, the regions are arranged in order from thinnest to thickest, thereby determining the initial order for generating subsequent regions.

[0114] Step 3: Based on the initial region generation order obtained in Step 2, the ply information of the thinnest region is retained as the basis for subsequent construction, while the initial ply data of the remaining regions are not retained. Subsequently, the system generates the ply structure of each region in order from thinnest to thickest (e.g., ...). Figure 4 (As shown).

[0115] During the generation process, the system simultaneously performs the determination of manufacturing constraints and buckling factor constraints, and combines intercalation mechanism and regional sequence optimization mechanism to achieve the continuity and overall stability of the structure in terms of thickness distribution and stress performance.

[0116] The intercalation mechanism is a cyclic intercalation generation strategy used to ensure interlayer continuity and overall symmetry as the structural thickness gradually increases.

[0117] When performing intercalation generation, the system uses the buckling factor This serves as the determining factor. After each interpolation, the system calculates in real time and determines whether to accept the interpolation based on the calculation results. When the current sequence is determined to satisfy the buckling constraint, it is saved; when the current sequence is not satisfied, the interpolation is canceled and the next round of interpolation operation continues iteratively until the current sequence is satisfied. Or it may reach the preset iteration limit.

[0118] The specific interpolation operation rules are as follows:

[0119] When the number of layers in the previous area is even (even number)

[0120] The system first divides the previous region sequence into two symmetrical parts, and then inserts a new layer at an intercalation position in the first half to form a new symmetrical sequence; the buckling factor is then calculated. If... If the interpolation fails, the interpolation is canceled and a new position is selected for the next round of interpolation, until the maximum number of iterations is reached.

[0121] (2) When the number of layers in the previous area is odd ( (Odd number)

[0122] The system divides the sequence into a first half and a second half, making the first half one layer longer than the second half. The first half is mirrored to generate the second half, and then merged to form the complete sequence. If the sequence fails, a layer is inserted into the first half, and the sequence is mirrored and merged again, continuing the iterative calculation. This continues until the iteration limit is reached.

[0123] The aforementioned regional sequence optimization mechanism is used to dynamically adjust the generation order of each region based on buckling performance feedback during the multi-regional layered construction process, so as to achieve stress balance and maximize stability of the overall structure.

[0124] Its execution process includes the following steps:

[0125] (1) Before generating the current region r to be constructed, the previous region is... The buckling factor of the ply sequence is calculated under the boundary conditions and load conditions of the current region;

[0126] (2) At that time, it was determined that the stability of the ply structure in the current region was insufficient and needed to be reinforced by intercalation; when Then, continue backtracking to the previous region until a certain region is found. The plying in this region is the first occurrence under the current regional conditions. The situation;

[0127] (3) Determine the current area It should be inserted after the area;

[0128] (4) If the region Since several regions have already been generated, the buckling factor is calculated by placing the ply structure of region a under the boundary conditions of these regions. And based on stability relations Define area The optimal insertion position;

[0129] (5) The area Insert after the region, and with the region The layered structure was used as a reference for reconstruction;

[0130] (6) Once the insertion position of the region is determined, the original region is extended to become the new region. The region is based on the new region. The layer information is reconstructed; then, the generation order of each region is updated, and the regions are regenerated according to the new region sequence. The subsequent layering structure (i.e., the new area) is used to ensure the continuity and stability of the overall configuration.

[0131] Step 4: Based on the feasible layup generated above, construct the Improved Optimization Stacking Sequence Table (hereinafter referred to as...) This is used to uniformly express the ply sequence, ply angle, material type, and thickness information of each region. As shown in Table 1, a schematic diagram of a four-region structure, namely, an improved and optimized stacking sequence list (ioSST) diagram of a four-region structure, is presented. It serves as a unified interface for optimization algorithms and performance prediction models, enabling standardized input and integrated management of multivariate structural information.

[0132]

[0133] Table 1

[0134] To break with tradition The (Improved Stacking Sequence Table) method has limitations in terms of fixed regional order and unique intercalation paths. The construction method described here employs an improved structural representation based on a five-chromosome genotype coding strategy. This method comprehensively characterizes the configurational information of variable-thickness hybrid composite structures through multidimensional gene expression, enhancing the flexibility and controllability of the structural evolution process. The specific construction steps are as follows:

[0135] i. Chromosome: Used to represent the number of each subregion, ordered from thinnest to thickest, with a length of [missing information]. An integer vector.

[0136] ii. Chromosome: Used to describe the number of layers in each subregion, corresponding one-to-one with the region number.

[0137] iii. Chromosomes : Used to describe the complete ply angle sequence of the thickest region, and is an integer vector of length .

[0138] iv. Chromosomes : Used to describe the complete sequence of ply materials in the thickest region, with the same length as the angle sequence, indicating the material type corresponding to each ply.

[0139] v. Chromosome: A region number used to identify the first occurrence of a layer in each ply; it is a sequence of lengths... An integer vector. The i-th bit represents the region number where the i-th layer was first introduced.

[0140] Through the coordinated coding of the above five chromosomes, the It can achieve a unified description of the thickness, material and angle distribution between regions while maintaining the continuity and symmetry of the overall structure, providing standardized data support for subsequent multi-objective optimization and surrogate model prediction.

[0141] Step 5: Combine the stacked sequence list constructed in Step 4 with the multi-objective evolutionary algorithm. This, combined with a neural network intelligent agent model, forms a multi-objective optimization module for composite material structures. In this step, The neural network is trained using prior finite element simulation samples to establish a nonlinear mapping relationship between structural feature parameters and performance response. The trained neural network... Neural network surrogate models can rapidly estimate structural responses, including first-order natural frequencies, maximum stress, and maximum deformation, during optimization iterations, thus significantly reducing the computational cost of finite element simulations. The optimization process is algorithm-driven. It is used to achieve global search and multi-objective balance, evaluate and screen candidate structural schemes based on the prediction results output by the neural network, and complete the multi-objective iterative optimization of variable thickness hybrid composite laminate.

[0142] In this step, the optimization objectives include five categories of performance metrics, as follows:

[0143] (1) First-order frequency objective function:

[0144] Used to maximize the structure frequency.

[0145] (2) Objective function for maximum stress:

[0146] Used to minimize structural stress.

[0147] (3) Objective function for maximum deformation:

[0148] Used to minimize structural deformation.

[0149] (4) Structural quality objective function:

[0150] in, Let be the density of the k-th layer of the ply material in the k-th region, and be the thickness of a single layer. This represents the area of ​​the region used to calculate the total mass of the structure.

[0151] (5) Structural cost objective function:

[0152] in, For the first The unit volume cost of the k-th layer ply material in the region is used to calculate the total structural cost. Through the synergistic optimization of the above five objective functions, the... The algorithm performs parallel search and optimization of structural schemes based on population non-dominated sorting and crowding determination mechanisms, achieving a comprehensive balance between quality, cost, stiffness, stress and stability of the structure.

[0153] In this step, three types of reinforced composite materials with different performance characteristics are selected, and their main mechanical and cost parameters are used for comparative analysis to reflect the impact of material performance differences on structural optimization results. The values ​​of each parameter are only for research significance, as shown in Table 2, which is a schematic diagram of material properties in the embodiments of the present invention.

[0154]

[0155] Table 2

[0156] To achieve efficient optimization of composite material layup structures, this invention integrates a BP neural network with the NSGA-II model. The specific implementation steps of the joint optimization are as follows:

[0157] (1) For the layup optimization problem of variable thickness hybrid composite structures, a discrete vector coding strategy is adopted to formally express the design variables. The input features of each candidate scheme are 110-dimensional vectors, including: 45-layer layup angles, 45-layer layup material types, the number of layup layers in 18 regions, and the region layup thickness. The layup angle is encoded as integers 1–12, corresponding to 0°, ±15°, ±30°, ±45°, ±60°, ±75°, and 90°; the material type is encoded as 1, 2, and 3, distinguishing three different composite materials. To ensure the consistency of the input dimensions, all region layup sequences are extended to 45 layers, and unused layers are filled with 0. The input features are processed by min-max normalization.

[0158] (2) Based on the encoded sequence and finite element simulation performance data, a backpropagation (BP) neural network was constructed to establish a nonlinear mapping relationship between the layered design and structural performance. The network adopts a three-layer hidden layer structure with 10, 10, and 5 neurons respectively, corresponding to a topology of 110–10–10–5–3. The output layer contains three performance indicators: the first-order natural frequency, the maximum stress, and the maximum deformation. The network is trained using the backpropagation algorithm and the mean square error (MSE) is used to minimize the deviation between the predicted value and the finite element result.

[0159] (3) The parameter settings for the NSGA-II algorithm are as follows: number of objective functions to be optimized Population size N=100, maximum number of iterations Crossover probability Individuals participating in the crossover account for a significant portion of the initial population. Probability of mutation .

[0160] (4) Generate an initial population that satisfies manufacturing and buckling constraints based on ioSST encoding; for each individual, first predict the initial population using a BP neural network. At the same time, the quality is calculated through encoding and parsing. With cost NSGA-II performs non-dominated ranking and crowding distance selection on five objectives, retaining high-quality individuals and performing selection, crossover, and mutation to generate a new generation of candidate schemes; iterates to Then, the Pareto optimal layup scheme set is output, which balances frequency, stress, deformation, mass, and cost.

[0161] through After collaborative optimization, the corresponding ioSST values ​​are listed in Table 3. Compared with the traditional SST (Stacking Sequence Table) method, the proposed optimization strategy shows significant advantages in terms of overall structural performance: the first-order natural frequency is increased by approximately 2.44%, the maximum stress is reduced by 29.5%, and the maximum deformation is reduced by 6.91%. Under the condition of introducing two low-cost composite materials with relatively weak mechanical properties for hybrid design, in order to compensate for the lack of local stiffness and stability caused by the substitution of low-performance materials, the number of ply layers in relevant regions is reasonably increased, resulting in a 23.2% increase in structural mass, while the manufacturing cost is still reduced by 8.92%. This achieves the synergistic improvement of multiple performance indicators and the optimized design of high-performance composite material structures under low-cost constraints. The specific numerical results are shown in Table 4.

[0162] <![CDATA[Chromosome ioSST order ]]> <![CDATA[Chromosome ioSST count ]]> <![CDATA[Chromosome ioSST angle ]]> <![CDATA[Chromosome ioSST mat ]]> <![CDATA[Chromosome ioSST map ]]> 5 22 15 Ⅰ 5 4 26 45 ⅠⅠⅠ 5 14 26 -30 Ⅰ 16 17 26 -30 ⅠⅠⅠ 5 7 27 -15 ⅠⅠⅠ 11 3 30 45 ⅠⅠ 10 13 30 0 ⅠⅠ 5 6 31 15 ⅠⅠⅠ 4 18 32 -30 Ⅰ 1 12 33 -15 Ⅰ 5 2 34 45 ⅠⅠⅠ 5 11 35 90 ⅠⅠⅠ 5 8 36 60 ⅠⅠⅠ 5 15 36 -75 ⅠⅠ 1 1 39 30 ⅠⅠⅠ 7 10 42 15 ⅠⅠⅠ 5 16 43 30 ⅠⅠⅠ 4 9 44 75 ⅠⅠ 3 45 ⅠⅠⅠ 5 -15 Ⅰ 12 30 Ⅰ 6 -30 Ⅰ 5 -30 Ⅰ 5 30 Ⅰ 18 -15 Ⅰ 2 45 ⅠⅠⅠ 5 75 ⅠⅠ 3 30 ⅠⅠⅠ 4 15 ⅠⅠⅠ 5 30 ⅠⅠⅠ 3 -75 ⅠⅠ 10 60 ⅠⅠⅠ 5 90 ⅠⅠⅠ 5 45 ⅠⅠⅠ 5 -15 Ⅰ 5 -30 Ⅰ 1 15 ⅠⅠⅠ 4 0 ⅠⅠ 5 45 ⅠⅠ 10 -15 ⅠⅠⅠ 8 -30 ⅠⅠⅠ 5 -30 Ⅰ 9 45 ⅠⅠⅠ 5 15 Ⅰ 5

[0163] Table 3

[0164]

[0165] Table 4

[0166] Ultimately, through multiple generations of iterative evolution, the optimal variable-thickness hybrid composite laminate layup scheme that satisfies buckling factor constraints and manufacturing constraints was obtained, achieving comprehensive optimization of multiple performance indicators.

[0167] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A multi-objective hybrid optimization method for variable-thickness hybrid composite laminates, characterized in that, Includes the following steps: Step 1: Structural region division and parameter definition; Step 2: Generate the initial sequence of the regional ply structure; Step 3: Layer-by-layer construction and sequential optimization of the regional ply structure; Step 4: Improve and optimize the construction of stacked sequence lists; Step 5: Multi-objective optimization and performance proxy integration.

2. The multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 1, characterized in that: In step one, the structure is divided according to different forces. Sub-regions; remember This indicates the number of ply layers in different regions, where Let r be the layer number of the r-th region; remember Indicates the ply sequence of each region, where The ply angle sequence for the r-th region; remember This indicates the ply material for each area, where Let be the layup material sequence for the r-th region.

3. The multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 2, characterized in that: In step two, after the region is divided, the initial sequence of the ply structure for each sub-region is generated: Phase 1: Insert a single layer in the middle of the initial symmetrical ply sequence, and calculate the current buckling factor. ;like If the sequence is successful, it is recorded as a candidate solution; if it fails to meet the requirements, the layup is withdrawn and the process proceeds to the second stage. Second stage: Insert two layers at symmetrical positions above and below the sequence and recalculate. If the buckling factor is still less than 1 at this point, the layup is preserved and intercalation and evaluation are continued until... ; The buckling factor is calculated based on the classical buckling theory of composite laminates, and its expression is: ;in, and They are respectively regions Length and width, and Applying along the region and Compressive load in the direction; , , and It is based on the ply sequence The calculated bending stiffness term, and is the half-wave number of the buckling mode.

4. The multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 3, characterized in that: To ensure that the generated solution meets engineering manufacturability requirements, the candidate layup must satisfy the following manufacturing constraints during the generation process: (1) Structural symmetry constraint: The ply of each region should be symmetrical about the center plane. ; (2) Direction angle ratio constraint: for each typical ply direction, such as The ratio should meet This is to ensure the uniformity of the angle distribution; (3) Constraint on angle variation between adjacent layers: the angle variation between adjacent layers shall not exceed ,Right now ; (4) Angle Discrete Constraint: The allowed ply angles come from a finite discrete set. ; (5) Limit on the number of layers with the same angle: The number of consecutive layers with the same angle shall not exceed 4; (6) Outermost layer consistency constraint: The outermost layer angle of each region should be consistent to ensure the continuity of the upper and lower surfaces; In addition to satisfying the above manufacturing constraints, buckling stability constraints are further introduced, requiring that the buckling factor of each sub-region under the design load meets the following requirements. This is to ensure that the structure does not experience local buckling instability.

5. A multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 3, characterized in that: In step three, based on the initial region generation order obtained in step two, the ply information of the thinnest region is first retained as the basis for subsequent construction, and the initial ply data of the remaining regions are no longer retained. Subsequently, the layered structures of each region are generated sequentially from thinnest to thickest. In this process, manufacturing constraints and buckling factor constraints are satisfied simultaneously, and intercalation mechanisms and regional sequence optimization mechanisms are introduced to generate regional lay-up structures.

6. The multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 5, characterized in that: The intercalation mechanism achieves interlayer continuity and overall symmetry through symmetrical or locally asymmetrical intercalation; this intercalation mechanism uses buckling factor To determine the evaluation criteria, the system calculates the results promptly after each interpolation. And based on this, decide whether to accept intercalation or continue iteration; when When, save the current sequence as a candidate; if If the buckling constraint is satisfied or the iteration limit is reached, then continue to execute the next round of intercalation and judgment until the buckling constraint is satisfied or the iteration limit is reached; The intercalation process is divided into two cases based on the parity of the number of layers in the previous region: A: Even-numbered layers A1: Divide the previous region sequence into symmetrical front and rear halves. Select an intercalation position in the front half to insert a new layer and merge them to generate a complete sequence. Calculate... ;like If so, then save the sequence; if Cancel the intercalation and proceed to the next step; A2: Interpolate again in the first half, replace the second half with the updated mirror image of the first half, merge to generate the complete sequence, and recalculate. ;like If so, save and end; Otherwise, continue iterating until... Or it may reach its limit; B: Odd-numbered layer cases B1: Divide the sequence into two parts, making the first part one layer longer than the second part; directly mirror the first part to generate a new second part and merge them into a complete sequence, then calculate... ;like If, then save; if Proceed to the next step; B2: While maintaining the first half with one more layer, first mirror the first half to generate a temporary second half, then insert a layer into the first half to form a new complete sequence, and recalculate. ;like If the condition is met, save the result; otherwise, continue the loop iteration until the condition is met. Or it may reach the iteration limit.

7. A multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 5, characterized in that: The steps of the region optimization mechanism are as follows: (1) For the current region to be generated Calculate the previous region Buckling factor under the current boundary conditions ; (2) If Continue tracing back to the region Until the first one is found area ; (3) Move the current area Insert into region Then, it serves as a new starting point for generation; (4) For the inserted region and its subsequent regions, the layers are regenerated based on the previous region's layer sequence to ensure interlayer continuity and overall stability; (5) Update the generation order of all subsequent regions according to the new regional order, and calculate the buckling factor of each region. To verify stability; (6) Repeat the above steps until all regions are generated in order of increasing thickness, forming a final stable and continuous multi-region layered structure.

8. A multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 5, characterized in that: During the generation process, the system simultaneously performs the determination of manufacturing constraints and buckling factor constraints, wherein the manufacturing constraints include the following: (1) Structural symmetry constraint: The ply of each region should be symmetrical about the center plane. ; (2) Direction angle ratio constraint: for each typical ply direction, such as The ratio should meet This is to ensure the uniformity of the angle distribution; (3) Regional inter-layer consistency constraints: If the region The number of layers is less than the area ,but To maintain the nested relationship between regions; (4) Constraint on angle variation between adjacent layers: the angle variation between adjacent layers shall not exceed ,Right now ; (5) Angle Discrete Constraint: The allowed ply angles come from a finite discrete set. ; (6) Limit on the number of layers with the same angle: The number of consecutive layers with the same angle shall not exceed 4; (7) Outermost layer consistency constraint: The outermost layer angle of each region should be consistent to ensure the continuity of the upper and lower surfaces; (8) Continuity constraint of interrupted layers: In the interrupted area, there should be at least one continuous layer every three layers to maintain the continuity of the local structure.

9. A multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 5, characterized in that: In step four, based on the multi-region feasible layup generated in step three, an improved optimization stacking sequence table (ioSST) is constructed to uniformly express the layup sequence, layup angle, material type and thickness information of each region, thereby realizing a standardized interface between the optimization algorithm and the performance prediction model. The construction steps are as follows: (1) Chromosome : Used to represent the number of each sub-region, and sorted in order from thinnest to thickest, with a length of . an integer vector; (2) Chromosomes : Used to describe the number of ply layers in each sub-region, corresponding one-to-one with the region number; (3) Chromosomes : Used to describe the complete ply angle sequence of the thickest region, with a length of an integer vector; (4) Chromosomes : Used to describe the complete ply material sequence of the thickest region, with the same length as the angle sequence, indicating the material type corresponding to each ply; (5) Chromosomes : A region number used to identify the first occurrence of each ply, with a length of . an integer vector; where the first... The digit indicates the first position. The earliest area numbering system introduced for layer-by-layer plying was the one that was first introduced.

10. A multi-objective hybrid optimization method for variable thickness hybrid composite laminates according to claim 9, characterized in that: In step five, the ioSST stacked sequence list constructed in step four is combined with the NSGA-II multi-objective evolutionary algorithm and the BP neural network intelligent agent model to form a multi-objective optimization module for composite laminates. The BP neural network was trained using finite element simulation samples and was used to establish structural design variables. The nonlinear mapping relationship between performance response and the training of the BP intelligent agent model allows for rapid prediction of structural response, including the first-order natural frequency, during optimization iterations. Maximum stress With maximum deformation This significantly reduces the cost of finite element analysis. The optimization process is driven by the NSGA-II algorithm, which realizes global search and multi-objective balance. NSGA-II evaluates and screens candidate structural schemes based on BP prediction results, and completes the iterative optimization of multi-region variable thickness hybrid composite laminate. The optimization objectives include five categories of performance metrics: (1) First-order frequency objective function: ; (2) Objective function for maximum stress: ; (3) Objective function for maximum deformation: ； (4) Structural quality objective function: ; in It is the first Region 1 Density of the ply material It is the first Region 1 The thickness of a single layer of plywood material. It is the first The ply area of ​​each region; (5) Structural cost objective function: ； in It is the first Region 1 Unit volume cost of layered materials.

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