A ply library optimization method considering ply process

Abstract

The application relates to a ply library optimization method considering a ply process, relates to the field of computer simulation technology, and mainly comprises the following steps: step S1, defining an optimization target, a design variable and a design constraint through an interactive interface, wherein the optimization target comprises a ply library target and a single ply target, the design variable comprises a ply lay-up layer number, a different ply lay-up range, a different ply lay-up angle and a different angle ply lay-up sequence, and the design constraint comprises a ply constraint and a structure constraint; step S2, solving the set optimization target, the design variable and the ply constraint based on a bottom layer optimization method through a multi-parameter optimization solver; and step S3, outputting an optimization result.

Description

Technical Field

[0001] This application relates to the field of computer simulation technology, and in particular to a method for optimizing a layup library that takes into account layup processes. Background Technology

[0002] In modern aerospace, automotive, and other industries, composite materials are widely used due to their advantages such as high specific strength, high specific modulus, good fatigue resistance, corrosion resistance, and high designability. In the design of composite material structures, layup design is required to fully utilize the performance advantages of composite materials.

[0003] In actual R&D, the optimization problem of composite material layup (library) inherently presents numerous challenges, including a large number of design variables, complex variable types, inter-variable coupling, differences in variable magnitudes, and conflicts between constraints and objective functions. Furthermore, most existing optimization theories and methods only address simplified, idealized optimization models, leading to problems such as high computational load, complex optimization processes, poor universality, and difficulty in obtaining satisfactory results when applied to more complex engineering problems. The special process requirements and engineering constraints inherent in composite material processing and use further increase the difficulty of solving these optimization problems.

[0004] Therefore, this invention considers both process constraints and layup constraints, and optimizes the layup scheme of practical flat-plate composite materials by taking the maximum selected critical buckling load as the optimization objective. Summary of the Invention

[0005] To meet the optimization requirements of composite material layup libraries, this application provides a layup library optimization method that considers layup processes.

[0006] The method for optimizing a ply library considering ply technology provided in this application adopts the following technical solution:

[0007] A method for optimizing a layup library considering layup processes includes the following steps:

[0008] Step S1: Define the optimization objectives, design variables, and design constraints through the interactive interface. The optimization objectives include ply library objectives and individual ply objectives. The design variables include the number of ply layers, the ply coverage of different ply layers, the ply angle of different ply layers, and the ply sequence of ply layers with different angles. The design constraints include ply constraints and structural constraints.

[0009] Step S2: Solve the set optimization objective, design variables and ply constraints using a multi-parameter optimization solver based on the underlying optimization method;

[0010] Step S3: Output the optimization results.

[0011] Preferably, step S2 includes the following steps:

[0012] Step S21, Encoding; including angle encoding, single-layer covering area encoding, and covering order encoding, which provides the foundation for subsequent population evolution iteration, fitness calculation, selection, recombination, mutation, and decoding;

[0013] The angle encoding uses integer 0 to represent 0 degrees, integer 1 to represent 45 degrees, integer 2 to represent 90 degrees, and integer 3 to represent 135 degrees or -45 degrees.

[0014] The single-layer cover area is encoded using binary encoding, where each binary bit 0 or 1 represents whether a structural unit is covered or not.

[0015] The layup order uses mutually exclusive integer encoding, where each value is a non-repeating value from 1 to Ci, used to characterize the layup order, where Ci represents half of the maximum layup number;

[0016] Step S22: Obtain the Pareto optimal solution set using the NSGA-II algorithm;

[0017] Step S23: Perform coupled optimization or multi-level optimization based on the scale of the problem to be solved, starting with strength and then moving to structure.

[0018] Preferably, step S22 includes the following steps:

[0019] Step S221: Initialize the population: Randomly generate an initial population of size N. ;

[0020] Step S222, starting from generation t=0;

[0021] Step S223: Loop begins;

[0022] Step S224: Generate offspring population: For the population Selective, crossover, and mutation operations are performed to obtain a population of offspring of size N. ;

[0023] Step S225, Merge populations: Merge the parent populations and offspring population Merging them yields a population of size 2N. ;

[0024] Step S226: Stratify by non-dominated sorting;

[0025] Step S227: Select a new population: Select individuals from low to high according to the frontier level until the number of selected individuals reaches or exceeds N; if the total number of individuals exceeds N after the current non-dominated set is added, compare the crowding of individuals in the frontier and select individuals with higher crowding until the population is filled.

[0026] Step S228: Form a new population of size N. ;

[0027] Step S229: Set t = t + 1. If the maximum algebra is not reached, return to step S23; otherwise, end.

[0028] Preferably, step S226 includes the following steps:

[0029] Step S2261: Merge populations For each individual p in the dataset, initialize... and Two sets; among which, Let p represent the set of all individuals dominated by p. This represents the number of individuals that dominate individual p;

[0030] Step S2262, Determining the first level of non-dominated sets: Iterate through each individual p, if... =0, then it is classified into the first level non-dominated set. The first layer of non-dominated set That is, the first frontier and the first front edge The level is set to 1;

[0031] Step S2263: Initialize a queue, first by placing the first layer of leading edge... All individuals are added to the queue, and then processing begins.

[0032] Preferably, step S2263 includes the following steps:

[0033] Step S22631: Set the current leading edge The level k=1;

[0034] Step S22632: Initialize the next frontier Empty;

[0035] Step S22633, Regarding the current frontier For each individual p, iterate through the set of individuals that p governs. Each individual q in the process.

[0036] Preferably, iterate through the set of individuals dominated by p. The methods for each individual q in the dataset include:

[0037] q Subtract 1;

[0038] If q's =0, then add q to the next frontier set. And set its level to k+1;

[0039] Let k = k + 1, and continue processing. This continues until all individuals q are assigned a frontier rank.

[0040] Preferably, the coupled optimization solution method includes the following steps:

[0041] Step S2311: Identify the structural finite element model as structural elements;

[0042] Step S2312: Form a structural unit Map table;

[0043] Step S2313: Randomly initialize the connected components and the tiling order based on the input maximum and minimum tiling numbers;

[0044] Step S2314: Update the finite element model and perform calculations;

[0045] Step S2315: Calculate the internal load and check the stability and stiffness;

[0046] Step S2316: Determine whether the margin requirement is met. If the margin requirement is not met, adjust the number of ply layers at each angle of the structural unit according to the margin and return to step S2314. If the margin requirement is met, determine whether the internal load meets the ply library process constraints. If the ply library process constraints are met, the process ends. If the ply library process constraints are not met, optimize the ply sequence and connected regions and return to step S2314.

[0047] The preferred method for multi-level optimization, which prioritizes strength over structure, includes the following steps:

[0048] Step S2321: Identify the structural finite element model as structural elements;

[0049] Step S2322: Form a structural unit Map table;

[0050] Step S2323: Set attributes using the super layer method;

[0051] Step S2324: Create design variables and constraints, with the optimization objective being minimum weight;

[0052] Step S2325: Solve using the structural optimization solver;

[0053] Step S2326: Determine if the structural weight is optimal. If the structural weight is not optimal, return to step S2324; otherwise, round / fine-tune the ply thickness and ply ratio, and then analyze the adjacent relationships of structural units according to the Map table.

[0054] Step S2327: Optimize the calculation of the number of layers for each angle of the structural unit based on the maximum value of the number of layers for all angles;

[0055] Step S2328: Determine whether the process constraints are met. If yes, calculate the connected region and the corresponding angle based on the adjacent relationship and the number of layers. If no, return to step S2327.

[0056] Step S2329: Optimize the layup sequence to meet the layup library constraints and process constraints;

[0057] Step S23210: Determine whether the ply stack constraint is met. If yes, perform structural stability check; otherwise, return to step S2329.

[0058] Step S23211: Determine whether the structural stability constraints and stiffness constraints are met. If yes, end the process; otherwise, repeat the process optimization cycle.

[0059] Preferably, the ply stack targets include maximum compressive buckling stress of a flat plate, maximum shear buckling stress of a flat plate, maximum flexural buckling stress of a flat plate, minimum absolute value of thermal expansion coefficient, and weighted coupling of multiple targets; the individual ply stack targets include 0 expansion coefficient, infinite longitudinal stiffness, infinite transverse stiffness, infinite torsional stiffness, infinite longitudinal flexural stiffness, infinite transverse flexural stiffness, and infinite in-plane shear stiffness.

[0060] Preferably, the ply constraints include: symmetry; uniformity; outermost ply at ±45 degrees; uniform distribution of ply at all angles; continuous ply thickness or number of layers; improved buckling behavior; ply group 1: ply in pairs at ±45 degrees; ply group 2: angle variation between adjacent layers is less than 90 degrees; staggered plying: dropped layers should be as close as possible to the middle layer; at least the outermost two layers should be continuous ply; continuous dropped layers: for every 4 dropped layers, at least one layer should completely cover it and the dropped layers should be evenly distributed.

[0061] The structural constraints include: ply continuity between adjacent structural units; identical design of flanges, webs, inserts, and pads; and natural continuity between units with the same ply ratio. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating the tool framework in an embodiment of this application.

[0063] Figure 2 , Figure 3This is a schematic diagram illustrating two optimization result display interfaces in an embodiment of this application.

[0064] Figure 4 This is a schematic diagram illustrating the overall algorithm flow of the solver in an embodiment of this application.

[0065] Figure 5 This is a schematic diagram illustrating the main flow of the coupled optimization solution method in the embodiments of this application.

[0066] Figure 6 This is a schematic diagram illustrating the main flow of a multi-level optimization solution method that prioritizes strength over structure, as described in the embodiments of this application. Detailed Implementation

[0067] The following combination Figures 1-6 This application will be described in further detail.

[0068] Example

[0069] This application discloses a method for optimizing a ply library considering ply technology. This optimization method mainly includes the following steps:

[0070] Step S1: Define the optimization objectives, design variables, and design constraints through the interactive interface. The optimization objectives include the ply library objective and the individual ply objective.

[0071] Step S2: Solve the set optimization objective, design variables and ply constraints using a multi-parameter optimization solver based on the underlying optimization method;

[0072] Step S3: Output the optimization results.

[0073] This method is developed using Python 3.8.3. Through an interactive interface, users can select the structure to be covered, set optimization objectives for different regions, input single-layer material data parameters, select layup constraints and process constraints, solve the set problems using low-level optimization methods, and finally return the optimization results for the current auxiliary material structure and input parameters. Its tool framework flowchart is shown below. Figure 1 As shown.

[0074] The interactive interface allows users to define optimization objectives, design variables, and design constraints, forming the three essential elements of optimization. The solver performs numerical calculations on the created optimization problem and outputs the optimization results. These results can be displayed and viewed in 3D within the tool, or exported as tabular data and stored in a file.

[0075] like Figure 2 and Figure 3As shown, the generated ply library can be easily displayed in the graphics area, or the content of the graphics area can be output as an Excel file; for the actual ply structure, each connected region and ply angle can also be output.

[0076] Among them, the ply stack objectives include maximum compressive buckling stress of a flat plate, maximum shear buckling stress of a flat plate, maximum flexural buckling stress of a flat plate, minimum absolute value of thermal expansion coefficient, and multi-objective coupling by weight; individual ply stack objectives include 0 expansion coefficient, infinite longitudinal stiffness, infinite transverse stiffness, infinite torsional stiffness, infinite longitudinal flexural stiffness, infinite transverse flexural stiffness, and infinite in-plane shear stiffness.

[0077] It should be noted that a single layup objective refers to the objective for a specific structural unit, while a layup library objective is a constraint on the set of structural units formed by these units. These objectives can be coupled into multiple objectives by assigning different weights.

[0078] Ply constraints include: symmetry; uniformity; outermost ply at ±45 degrees; uniform distribution of ply at all angles; thickness or number of consecutive ply layers; improvement of buckling behavior; Ply group 1: paired ply at ±45 degrees; Ply group 2: angle variation between adjacent ply layers less than 90 degrees; staggered plying: dropped ply should be as close as possible to the middle ply; at least the two outermost ply layers should be consecutive ply layers; consecutive dropped plying: at least one of every four dropped ply layers should completely cover it and the dropped ply layers should be evenly distributed.

[0079] It should be noted that the ply constraint does not consider the constraint of structural plying.

[0080] Structural constraints include: ply continuity between adjacent structural units; identical design of flanges, webs, intercalations, and pads; and natural continuity between ply ratios.

[0081] The design variables include the number of ply layers, the coverage range of different ply layers, the coverage angle of different ply layers, and the ply sequence of different angle ply layers. The design constraints include ply constraints and structural constraints.

[0082] For ply library optimization problems considering different structural ply configurations, the design variables shift from a single ply or a mixed ply library from a certain angle to optimizing the total number of plies, the range of each ply, the angle of each ply, and the ply sequence. Under certain conditions, such as when all structural units in a flat plate have the same ply ratio, the two problems mentioned above are equivalent.

[0083] In this embodiment, step S2 includes the following steps:

[0084] Step S21, Encoding; including angle encoding, single-layer covering area encoding, and covering order encoding, which provides the foundation for subsequent population evolution iteration, fitness calculation, selection, recombination, mutation, and decoding;

[0085] Angle encoding uses integer 0 to represent 0 degrees, integer 1 to represent 45 degrees, integer 2 to represent 90 degrees, and integer 3 to represent 135 degrees (or -45 degrees).

[0086] The single-layer cover area is encoded using binary encoding, where each binary bit 0 or 1 represents whether a structural unit is covered or not.

[0087] The layup order is encoded using mutually exclusive integer codes, where each value is a non-repeating value from 1 to Ci, representing the layup order, where Ci represents half of the maximum layup number;

[0088] Step S22: Obtain the Pareto optimal solution set using the NSGA-II algorithm;

[0089] Step S23: Perform coupled optimization or multi-level optimization based on the scale of the problem to be solved, starting with strength and then moving to structure.

[0090] Pre-encoding of angles, single-layer covering regions, and covering order facilitates the use of heuristic population optimization algorithms, providing a foundation for subsequent population evolution iterations, fitness calculations, selection, recombination, mutation, and decoding.

[0091] Reference Figure 4 The core solver obtains the Pareto optimal solution set through the NSGA-II algorithm, and step S22 of the algorithm mainly includes the following steps:

[0092] Step S221: Initialize the population: Randomly generate an initial population of size N. ;

[0093] Step S222, starting from generation t=0;

[0094] Step S223: Loop begins;

[0095] Step S224: Generate offspring population: For the population Selective, crossover, and mutation operations are performed to obtain a population of offspring of size N. ;

[0096] Step S225, Merge populations: Merge the parent populations and offspring population Merge the populations to obtain a population of size 2N;

[0097] Step S226: Stratify by non-dominated sorting;

[0098] Step S227: Select a new population: Select individuals from low to high according to the frontier level until the number of selected individuals reaches or exceeds N; if the total number of individuals exceeds N after the current non-dominated set is added, compare the crowding of individuals in the frontier and select individuals with higher crowding until the population is filled.

[0099] Step S228: Form a new population of size N. ;

[0100] Step S229: Set t = t + 1. If the maximum algebra is not reached, return to step S23; otherwise, end.

[0101] Step S226 includes the following steps:

[0102] Step S2261: Merge populations For each individual p in the dataset, initialize... and Two sets; among which, Let p represent the set of all individuals dominated by p. This represents the number of individuals that dominate individual p;

[0103] Step S2262, Determining the first level of non-dominated sets: Iterate through each individual p, if... =0, then it is classified into the first level non-dominated set. (i.e., the first front edge) ), and the first frontier The level is set to 1;

[0104] Step S2263: Initialize a queue, first by placing the first layer of leading edge... All individuals are added to the queue, and then processing begins.

[0105] Preferably, step S2263 includes the following steps:

[0106] Step S22631: Set the current leading edge The level k=1;

[0107] Step S22632: Initialize the next frontier Empty;

[0108] Step S22633, Regarding the current frontier For each individual p, iterate through each individual q in the set of individuals dominated by p.

[0109] The methods for iterating through each individual q in the set of individuals dominated by p include:

[0110] q Subtract 1;

[0111] If q's =0, then add q to the next frontier. And set its level to k+1;

[0112] Let k = k + 1, and continue processing. This continues until all individuals are assigned a frontier rank.

[0113] Subsequent processing includes: according to the frontier level ( ...) Select individuals; sort individuals at the front edge of the same layer according to their crowding distance to ensure diversity.

[0114] Non-dominated sorting time complexity: Calculating dominance relationships: O(MN²), where (M represents the number of targets and N represents the population size); in the worst case, using front assignment: O(N²).

[0115] Reference Figure 5 The method for solving coupled optimization problems includes the following steps:

[0116] Step S2311: Identify the structural finite element model as structural elements;

[0117] Step S2312: Form a structural unit Map table;

[0118] Step S2313: Randomly initialize the connected components and the tiling order based on the input maximum and minimum tiling numbers;

[0119] Step S2314: Update the finite element model and perform calculations;

[0120] Step S2315: Calculate the internal load and check the stability and stiffness;

[0121] Step S2316: Determine whether the margin requirement is met. If the margin requirement is not met, adjust the number of ply layers at each angle of the structural unit according to the margin and return to step S2314. If the margin requirement is met, determine whether the internal load meets the ply library process constraints. If the ply library process constraints are met, the process ends. If the ply library process constraints are not met, optimize the ply sequence and connected regions and return to step S2314.

[0122] Reference Figure 6 The multi-level optimization solution method, which prioritizes strength over structure, includes the following steps:

[0123] Step S2321: Identify the structural finite element model as structural elements;

[0124] Step S2322: Form a structural unit Map table;

[0125] Step S2323: Set attributes using the super layer method;

[0126] Step S2324: Create design variables and constraints, with the optimization objective being minimum weight;

[0127] Step S2325: Solve using the structural optimization solver;

[0128] Step S2326: Determine if the structural weight is optimal. If the structural weight is not optimal, return to step S2324; otherwise, round / fine-tune the ply thickness and ply ratio, and then analyze the adjacent relationships of structural units according to the Map table.

[0129] Step S2327: Optimize the calculation of the number of layers for each angle of the structural unit based on the maximum value of the number of layers for all angles;

[0130] Step S2328: Determine whether the process constraints are met. If yes, calculate the connected region and the corresponding angle based on the adjacent relationship and the number of layers. If no, return to step S2327.

[0131] Step S2329: Optimize the layup sequence to meet the layup library constraints and process constraints;

[0132] Step S23210: Determine whether the ply stack constraint is met. If yes, perform structural stability check; otherwise, return to step S2329.

[0133] Step S23211: Determine whether the structural stability constraints and stiffness constraints are met. If yes, end the process; otherwise, repeat the process optimization cycle.

[0134] This invention provides a layup library optimization method that takes into account layup processes, which solves the pain points of existing composite material structure layup design, such as complex optimization process, poor universality, and difficulty in obtaining satisfactory results. It can improve the accuracy and efficiency of composite material structure layup library design.

[0135] The above are all preferred embodiments of this application and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for optimizing a layup library considering layup processes, characterized in that, Includes the following steps: Step S1: Define the optimization objectives, design variables, and design constraints through the interactive interface. The optimization objectives include ply library objectives and individual ply objectives. The design variables include the number of ply layers, the ply coverage of different ply layers, the ply angle of different ply layers, and the ply sequence of ply layers with different angles. The design constraints include ply constraints and structural constraints. Step S2: Solve the set optimization objective, design variables and ply constraints using a multi-parameter optimization solver based on the underlying optimization method; Step S3: Output the optimization results; Step S2 includes the following steps: Step S21, Encoding; including angle encoding, single-layer cover area encoding, and cover order encoding, which provides the foundation for subsequent population evolution iteration, fitness calculation, selection, recombination, mutation, and decoding; The angle encoding uses integer 0 to represent 0 degrees, integer 1 to represent 45 degrees, integer 2 to represent 90 degrees, and integer 3 to represent 135 degrees or -45 degrees. The single-layer cover area is encoded using binary encoding, where each binary bit 0 or 1 represents whether a structural unit is covered or not. The layup order uses integer mutual exclusion encoding, where each value is a non-repeating value from 1 to Ci, used to characterize the layup order, where Ci represents half of the maximum layup number; Step S22: Obtain the Pareto optimal solution set using the NSGA-II algorithm; Step S23: Perform coupled optimization or multi-level optimization based on the scale of the problem to be solved, starting with strength and then moving to structure. Step S22 includes the following steps: Step S221: Initialize the population: Randomly generate an initial population of size N. ; Step S222, starting from generation t=0; Step S223: Loop begins; Step S224: Generate offspring population: For the population Selective, crossover, and mutation operations are performed to obtain a population of offspring of size N. ; Step S225, Merge populations: Merge the parent populations and offspring population Merging them yields a population of size 2N. ; Step S226: Stratify by non-dominated sorting; Step S227: Select a new population: Select individuals from low to high according to the frontier level until the number of selected individuals reaches or exceeds N; if the total number of individuals exceeds N after the current non-dominated set is added, compare the crowding of individuals in the frontier and select individuals with higher crowding until the population is filled. Step S228: Form a new population of size N. ; Step S229: Set t = t + 1. If the maximum algebra is not reached, return to step S23; otherwise, end. Step S226 includes the following steps: Step S2261: Merge populations For each individual p in the dataset, initialize... and Two sets; where, Let p represent the set of all individuals dominated by p. This represents the number of individuals that dominate individual p; Step S2262, Determining the first level of non-dominated sets: Iterate through each individual p, if... =0, then it is classified into the first level non-dominated set. The first layer of non-dominated set That is, the first frontier and the first front edge The level is set to 1; Step S2263: Initialize a queue, first by placing the first layer of leading edge... All individuals are added to the queue, and then processing begins; Step S2263 includes the following steps: Step S22631: Set the current leading edge The level k=1; Step S22632: Initialize the next frontier Empty; Step S22633, regarding the current frontier For each individual p, iterate through the set of individuals that p governs. Each individual q in; The method for solving coupled optimization problems includes the following steps: Step S2311: Identify the structural finite element model as structural elements; Step S2312: Form a structural unit Map table; Step S2313: Randomly initialize the connected components and the tiling order based on the input maximum and minimum tiling numbers; Step S2314: Update the finite element model and perform calculations; Step S2315: Calculate the internal load and check the stability and stiffness; Step S2316: Determine whether the margin requirement is met. If the margin requirement is not met, adjust the number of ply layers at each angle of the structural unit according to the margin and return to step S2314. If the margin requirement is met, determine whether the internal load meets the ply library process constraints. If the ply library process constraints are met, the process ends. If the ply library process constraints are not met, optimize the ply sequence and connected regions and return to step S2314. The multi-stage optimization solution method, which prioritizes strength over structure, includes the following steps: Step S2321: Identify the structural finite element model as structural elements; Step S2322: Form a structural unit Map table; Step S2323: Set attributes using the super layer method; Step S2324: Create design variables and constraints, with the optimization objective being minimum weight; Step S2325: Solve using the structural optimization solver; Step S2326: Determine if the structural weight is optimal. If the structural weight is not optimal, return to step S2324; otherwise, round / fine-tune the ply thickness and ply ratio, and then analyze the adjacent relationships of structural units according to the Map table. Step S2327: Optimize the calculation of the number of layers for each angle of the structural unit based on the maximum value of the number of layers for all angles; Step S2328: Determine whether the process constraints are met. If yes, calculate the connected region and the corresponding angle based on the adjacent relationship and the number of layers. If no, return to step S2327. Step S2329: Optimize the layup sequence to meet the layup library constraints and process constraints; Step S23210: Determine whether the ply stack constraint is met. If yes, perform structural stability check; otherwise, return to step S2329. Step S23211: Determine whether the structural stability constraints and stiffness constraints are met. If yes, end the process; otherwise, repeat the process optimization cycle.

2. The method for optimizing a layup library considering layup processes according to claim 1, characterized in that, Traverse the set of individuals dominated by p The methods for each individual q in the dataset include: q Subtract 1; If q's =0, then add q to the next frontier. And set its level to k+1; Let k = k + 1, and continue processing. This continues until all individuals q are assigned a frontier rank.

3. The method for optimizing a layup library considering layup processes according to claim 1, characterized in that, The ply stack targets include maximum compressive buckling stress of a flat plate, maximum shear buckling stress of a flat plate, maximum flexural buckling stress of a flat plate, minimum absolute value of thermal expansion coefficient, and weighted coupling of multiple targets; the individual ply stack targets include 0 expansion coefficient, infinite longitudinal stiffness, infinite transverse stiffness, infinite torsional stiffness, infinite longitudinal flexural stiffness, infinite transverse flexural stiffness, and infinite in-plane shear stiffness.

4. The method for optimizing a layup library considering layup processes according to claim 1, characterized in that, The ply constraints include: symmetry; uniformity; outermost ply at ±45 degrees; uniform distribution of ply at all angles; thickness or number of consecutive ply layers; improved buckling behavior; Ply group 1: paired occurrences at ±45 degrees; Ply group 2: angle variation between adjacent layers less than 90 degrees; staggered plying: dropped layers should be as close as possible to the middle layer; at least the outermost two layers should be consecutive ply layers; consecutive dropped layers: for every 4 dropped layers, at least one layer should completely cover it and the dropped layers should be evenly distributed; The structural constraints include: ply continuity between adjacent structural units; identical design of flanges, webs, inserts, and pads; and natural continuity between ply ratios.

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