A curve fiber variable stiffness composite material structure integration optimization method

Abstract

The application discloses a curve fiber variable stiffness composite structure integration optimization method and belongs to the field of composite structure optimization.The application realizes the method as follows: defining and creating an initial "base ply" of a curve fiber variable stiffness composite structure, constructing a number domain representing the existence of each single layer of the "base ply", establishing a curve fiber variable stiffness composite structure integration optimization problem model integrating the number of plies, the thickness of the plies and the curve fiber laying angle; based on a Latin hypercube sampling test, constructing an index form of a mixed correction mode variable fidelity proxy model; adopting a genetic algorithm to perform discrete continuous mixed variable optimization to obtain a preliminary optimization result; reconstructing an optimization problem containing only fiber path parameters as continuous design variables, adopting a sequential quadratic programming algorithm to optimize and solve the reconstructed optimization problem to obtain a curve fiber variable stiffness composite structure optimization result; and through iterative optimization, the curve fiber variable stiffness composite structure integration optimization is realized.

Description

Technical Field

[0001] This invention belongs to the field of composite material structure optimization, and relates to an integrated optimization method for curved fiber variable stiffness composite material structures. Background Technology

[0002] Compared to traditional materials such as steel and aluminum alloys, composite materials have advantages such as high specific strength, high specific stiffness, and strong design flexibility, and have been widely used in important fields such as civil engineering, shipbuilding, aviation, and aerospace. Curved fiber variable stiffness composite structures, by customizing curved fiber paths, can change the spatial distribution of structural stiffness, providing powerful support for lightweight, intelligent, and integrated functional structural design. To fully utilize the mechanical performance advantages of curved fiber variable stiffness composite structures, the design variables can simultaneously include the number of ply layers, ply thickness, and point-by-point customized curved fiber placement angles. Currently, the optimization design of variable stiffness composite structures mostly uses the curved fiber placement angle as a continuous design variable for optimization. A few studies have optimized ply thickness and curved fiber placement angle as continuous design variables, but have neglected process limitations such as the discrete value characteristics of ply thickness. An integrated design method that integrates the number of ply layers, ply thickness, and curved fiber placement angle as variables still needs further research.

[0003] Defining fiber paths in curved fiber variable stiffness composite structures is challenging, requiring sophisticated simulation analysis and a large optimization design space. This makes the optimization design problem, even with only the curved fiber layup angle as a continuous variable, inherently extremely difficult. Furthermore, the simultaneous introduction of discrete ply numbers and thicknesses leads to discontinuous and non-differentiable objective and constraint functions, rendering approximation-based optimization techniques and methods ineffective for solving continuous variable problems. While relaxing discrete variables and combining them with surrogate models can efficiently solve this problem, breaking the discrete value characteristics of the variables makes the optimization results difficult to meet manufacturing requirements and necessitates post-processing. Therefore, it is unsuitable as a general method for optimizing engineering structures. Consequently, there is an urgent need to develop practical optimization methods for efficiently solving this integrated discrete-continuous variable optimization design problem. Summary of the Invention

[0004] To address the issues of limited design variables and low optimization efficiency in existing curved fiber variable stiffness composite structures, this invention provides an integrated optimization method for curved fiber variable stiffness composite structures. It establishes an optimization problem model integrating the number of layups, layup thickness, and curved fiber placement angle. By constructing a variable-fidelity surrogate model for the curved fiber variable stiffness composite structure, a genetic-sequence quadratic programming algorithm is introduced to efficiently optimize the design variables. Under the conditions of satisfying discrete values ​​of layup thickness and fiber curvature process constraints, integrated optimization of curved fiber variable stiffness composite structures is achieved.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] This invention discloses an integrated optimization method for curved fiber variable stiffness composite material structures, comprising the following steps:

[0007] Step 1: To minimize post-processing of the optimization results, define and create an initial "base ply" for the curved fiber variable stiffness composite structure. Optimize the ply thickness to determine the existence of each individual layer. When a single layer within the "base ply" is unnecessary, its thickness is set to a small value to indicate deletion; when a single layer is necessary, its thickness is set to an integer multiple of its baseline thickness to indicate retention. Construct a domain representing the existence of each individual layer within the "base ply," and establish an integrated optimization model for the curved fiber variable stiffness composite structure, incorporating the number of plies, ply thickness, and curved fiber placement angle.

[0008] Step 101: Define and create the initial "base ply" for the curved fiber variable stiffness composite structure. The "base ply" of the curved fiber composite structure consists of multiple composite monolayers. The existence of each monolayer is determined by optimizing the ply thickness. When a monolayer within the "base ply" is a non-essential ply, its thickness is set to a small value to indicate deletion; when a monolayer is an essential ply, its thickness is set to an integer multiple of the monolayer's base thickness to indicate retention. In non-essential plies, since the ply thickness is small, changes in the curved fiber placement angle have a negligible impact on structural performance; therefore, the curved fiber placement angle variable in non-essential plies is set to a constant value. In essential plies, the ply thickness must satisfy the characteristic of discrete values. The discrete ply thickness and the continuous curved fiber placement angle are optimized to improve the performance of the curved fiber variable stiffness composite structure.

[0009] Step 102: Construct the number field based on the "base layer" created in Step 101. and This indicates the range of possible thickness values ​​for the necessary ply. The range of thickness values ​​corresponding to the non-essential ply is represented. The elements in the number field correspond to the existence of each single layer in the "base ply". The specific expressions are shown in equations (1) and (2).

[0010]

[0011]

[0012] In the formula, t i t is the thickness of the i-th layer in the base ply; b z represents the single-layer reference thickness corresponding to the fiber placement equipment, where z is a positive integer; This represents the small thickness associated with unnecessary plies; n represents the number of plies in the "base ply". (Number field) The elements in the middle represent necessary ply thicknesses that are integer multiples of the base thickness of a single layer, and the number field. The middle element indicates that the thickness of the non-essential layer is a small amount.

[0013] Step 103: Based on the numerical domain constructed in Step 102 to represent the existence of each single layer of the curved fiber variable stiffness composite structure, an integrated optimization problem model of the curved fiber variable stiffness composite structure is established, which integrates the number of layups, layup thickness, and curved fiber layup angle, as shown in Equation (3):

[0014]

[0015] In the formula, t represents the discrete ply thickness vector, T is the path function parameter vector related to the curved fiber layup angle, f(t,T) and g(t,T) are the objective function and constraint function, respectively, J0 is the number of constraint functions; κ(T) is the fiber curvature constraint; κ max Maximum allowable fiber curvature constraint; and These are the lower and upper bounds of the path function parameter variables, respectively. is a constant; m is the number of fiber path function parameters in a single layer, and n is the number of layers in the "base layer", i.e., the number of discrete variables. Path function parameters Value and corresponding single-layer thickness t i Related, when At that time, with t i Associated ply retention, single-layer thickness t i The corresponding ply thickness is an integer multiple of the single-layer reference thickness. Takes continuous values ​​within a given interval; when At that time, with t i Related ply deletion, ply thickness set to a small value. at this time Take constant

[0016] Step 2: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the high-fidelity and low-fidelity models of the curved fiber variable stiffness composite material structure. Based on the initial sample points of the high-fidelity and low-fidelity models, the curved fiber variable stiffness composite material structure is analyzed to obtain the response values ​​of the high-fidelity and low-fidelity surrogate models. An exponentially form hybrid modified mode variable fidelity surrogate model is then constructed.

[0017] Step 201: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the low-fidelity model and high-fidelity model of the corresponding curve fiber variable stiffness composite material structure. The number of initial sample points is determined by equations (4) and (5):

[0018]

[0019]

[0020] In the formula, L N With H N , representing the number of sampling points for the low-fidelity model and the high-fidelity model, respectively; nm represents the number of continuous variables; and round(*) is the rounding function. Standard Latin hypersquare sampling is only applicable to continuous variable sampling; therefore, continuous slack variables are used for mixed variable sampling. In [0, 1]... n+nm A continuous set of sample points is constructed in space, where the first n values ​​are related to the discrete ply thickness variable, and the last nm values ​​are related to the continuous curve fiber layup angle variable. The floor function is used to calculate the i-th discrete ply thickness variable in the number domain. The actual value in is calculated using the following formula:

[0021]

[0022] In the formula, x represents the sampled value in the range [0,1] corresponding to the thickness variable of the i-th discrete ply. i This represents the actual sampled value of the i-th discrete ply thickness variable; floor(*) is the floor function; Γ i For number fields and The union of the two sets. The calculation formula for the sampling point of the fiber laying angle variable of the i-th continuous curve is as follows:

[0023]

[0024] In the formula, x represents the sampled value within the range [0,1] corresponding to the fiber laying angle variable of the i-th continuous curve. i This represents the actual sampled value of the fiber laying angle variable for the i-th continuous curve; With x i The upper and lower limits are defined for the fiber placement angle variable of the i-th continuous curved fiber. An initial set of sampling points for discrete continuous design variables is generated using Latin hypersquare sampling, where the sampling points for the low-fidelity model and the high-fidelity model of the curved fiber variable stiffness composite structure are respectively... and

[0025] Step 202: Based on the initial sample points from Step 201, perform a curved fiber variable stiffness composite material structure analysis to obtain the response set Y corresponding to the low-fidelity model. LF The response set Y corresponding to the high-fidelity model HF .

[0026] Step 203: Based on the fidelity model response obtained in Step 202, construct an exponential form hybrid modified mode variable fidelity surrogate model, as shown in the following equation:

[0027]

[0028] In the formula, This is a low-fidelity surrogate model based on Gaussian process regression. δ(X) is the variable fidelity surrogate model constructed; r is the exponential correction factor, and δ(X) is the additive correction term of the surrogate model.

[0029] Step 204: Based on the variable fidelity surrogate model established in step 203, obtain the approximate response f(X) of the surrogate model, replace the objective function in the integrated optimization problem of the curved fiber variable stiffness composite material structure established in step 103 with the approximate objective function, that is, the approximate response f(X) of the variable fidelity surrogate model; replace the constraint function in the original optimization problem with the approximate constraint function constructed by the variable fidelity surrogate model, and obtain the approximate optimization problem model of the curved fiber variable stiffness composite material structure, as shown in equation (9).

[0030]

[0031] In the formula, These are the approximate objective and approximate constraint functions constructed based on the variable fidelity surrogate model, respectively. and These are the lower and upper limits of the curve fiber placement angle associated with the i-th ply, respectively.

[0032] Step 3: For the approximate optimization problem model of the curved fiber variable stiffness composite material structure established in Step 2 based on the surrogate model, a genetic algorithm is used to perform discrete-continuous mixed variable optimization to obtain preliminary optimization results for the curved fiber variable stiffness composite material structure. Based on the optimization results of the genetic algorithm, an optimization problem containing only fiber path parameters as continuous design variables is reconstructed. A sequential quadratic programming algorithm is used to optimize and solve the reconstructed optimization problem, improving the solution accuracy of the curved fiber laying angle, and obtaining the optimization results of the curved fiber variable stiffness composite material structure.

[0033] Step 301: The approximate optimization problem of the curved fiber composite material structure established in Step 204 still involves discrete and continuous design variables. To effectively solve this optimization problem, a genetic algorithm is used to find the discrete and continuous mixed variables of the composite material structure. The adaptive penalty fitness function of the genetic algorithm is:

[0034]

[0035]

[0036]

[0037] In the formula, ò is the penalty factor of the fitness function of the composite material structure, and β j For the j-th constraint The average degree of violation among individuals in the current population, γ is the penalty exponent of the fitness function of the composite structure, and γ is calculated as follows: i With γ f G is a given constant; G is the current generation number; MaxG is the maximum number of generations for the genetic algorithm. This represents the average objective function of individuals within the current population. When using a genetic algorithm to solve the problem, for the layup thickness of the curved fiber variable stiffness composite structure, the genes in the chromosomes are encoded in a discrete manner, using a single-point crossover method as the crossover operator and a basic bit mutation method as the mutation operator; for the curved fiber layup angle, it is encoded in actual parameter form, and a new evolutionary population is generated using a simulated binary crossover operator and a polynomial mutation operator.

[0038] Step 302: Based on the optimization results of the genetic algorithm in step 301, a sequential quadratic programming algorithm is used to further optimize the continuous variables. The optimized solution obtained by the genetic algorithm in step 301 is x. GA =(t * ,T * ), where t* is the optimal discrete ply thickness vector corresponding to the solution obtained by the genetic algorithm, T * This represents the optimal curved fiber path parameter vector corresponding to the obtained solution. Considering the randomness of the genetic algorithm, the solution accuracy for continuous variables cannot be guaranteed. Starting from the optimized solution obtained by the genetic algorithm, an optimization problem is established regarding the curved fiber path parameter variables. By further optimizing the continuous fiber angle variables, the solution accuracy for the curved fiber layup angle is improved. Based on the optimized solution of the curved fiber variable stiffness composite material structure obtained by the genetic algorithm, the discrete ply thickness variable is fixed to a constant value t*, and the continuous curved fiber layup angle variable associated with unnecessary plies is fixed to a constant value. Using only the ply-related curved fiber path parameters as continuous variables, the optimization problem for reconstructing curved fiber variable stiffness composite structures is as follows:

[0039]

[0040] In the formula, Let n′ be the vector of curved fiber path parameters associated with the retained plies, and n′ be the number of retained plies. For the above-reconstructed continuous variable optimization problem, Equation (13) holds only when the objective function is related to the curved fiber layup angle. The sequential quadratic programming algorithm is used to optimize and solve Equation (13) to improve the optimization solution accuracy of the curved fiber variable stiffness composite material structure. When the objective function is an independent function of the curved fiber layup angle variable, Equation (13) cannot optimize the curved fiber layup angle of the composite material. Therefore, the optimization problem of Equation (13) needs to be reconstructed so that the objective function is a function of the curved fiber layup angle. For this reason, the most critical constraint is selected from the constraint function set as the new objective function, and the optimization problem of the curved fiber variable stiffness composite material structure is reconstructed as follows:

[0041]

[0042]

[0043] In the formula, J represents the most critical constraint selected from the constraint set; J is the index set corresponding to the constraint set after removing the most critical constraint.

[0044] Step 303: For the optimization problem of the curved fiber variable stiffness composite material structure established in Step 302, the sequential quadratic programming algorithm is used to optimize and solve the problem, and the optimization result of the curved fiber variable stiffness composite material structure is obtained.

[0045] Step 4: Determine whether the optimization result of the curved fiber variable stiffness composite material structure obtained in Step 3 is the optimal solution. If it is the optimal solution, output the optimal solution of the curved fiber variable stiffness composite material structure optimization, and the optimization process ends. If it is not the optimal solution, add the current optimal solution to the sample point set, return to Step 2 to correct the variable fidelity proxy model of the curved fiber variable stiffness composite material structure, and solve the optimization problem of the reconstructed variable stiffness composite material structure according to Step 3 until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, that is, the optimized curved fiber variable stiffness composite material structure is obtained, realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

[0046] Step 401: Obtain the optimal solution for the k-th iteration of the curved fiber variable stiffness composite material structure optimization based on step 303. Compare it with the optimal solution obtained in the (k-1)th iteration The optimization process ends when the distance between two optimal solutions is less than the given convergence control parameter. The stopping criterion formula is as follows:

[0047]

[0048] In the formula, ε is the convergence control parameter.

[0049] Step 402: Based on the judgment result of step 401, if the optimal solution of the fiber-reinforced variable stiffness composite material structure obtained in the k-th iteration does not meet the convergence condition, then the optimal solution of the iteration will be optimized. Add sample point datasets and update the data point set of the fiber-reinforced variable stiffness composite structure curve from step 201. The criterion for adding new sampling points to the data point sets of the low-fidelity model and high-fidelity model of the fiber-reinforced variable stiffness composite structure curve is as follows:

[0050]

[0051] In the formula, and ε is the normalized distance between the current optimal solution and the original data point sets of the low-fidelity and high-fidelity models. LF With ε HF These are the control parameters for adding sample points to the data point sets of the low-fidelity model and high-fidelity model of the curved fiber variable stiffness composite material structure, respectively.

[0052] Step 403: Perform structural response analysis based on the newly sampled data from Step 402, and update the data point sets of the low-fidelity model and the high-fidelity model as follows. Update the curve fiber variable stiffness composite structure response dataset to and Substitute the updated curved fiber variable stiffness composite material structure dataset into step 203 to correct the variable fidelity proxy model.

[0053] Step 404: Update the approximate problem based on the modified variable fidelity surrogate model in Step 403, and return to Steps 301-303 to optimize the approximate problem of curved fiber variable stiffness composite material structure until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, thereby realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

[0054] This invention enables integrated optimization of the number of layups, layup thickness, and curved fiber placement angle in curved fiber variable stiffness composite structures, while satisfying discrete values ​​for layup thickness and fiber curvature process constraints. Through this integrated optimization of curved fiber variable stiffness composite structures, the problems of single design variables and low optimization efficiency in existing curved fiber variable stiffness composite structures can be solved.

[0055] It also includes step five: The curved fiber variable stiffness composite material structure obtained in step four is an integrated optimization result that integrates the number of layups, layup thickness, and curved fiber layup angle variables. It can improve the mechanical properties of the composite material structure, reduce the mass of the composite material structure, and solve the engineering and technical problems in the application field of curved fiber variable stiffness composite material structures while meeting the working conditions.

[0056] Step 5 addresses the engineering challenges in the application of curved fiber variable stiffness composite structures, including: under the process constraints of discrete ply thickness values ​​and fiber curvature limitations, the integrated optimization of the number of ply layers, ply thickness, and curved fiber placement angle in curved fiber variable stiffness composite structures is achieved. The optimization results not only meet the structural strength, stiffness, and quality requirements but also improve the mechanical properties of the composite structure.

[0057] Beneficial effects:

[0058] 1. Existing curved fiber variable stiffness composite material structures suffer from limited design variables and low optimization efficiency. This invention discloses an integrated optimization method for curved fiber variable stiffness composite material structures. It creates an initial "base ply" for the variable stiffness composite material structure, optimizes the thickness of each individual ply to determine its existence, and deleting unnecessary plies by taking a small thickness when a ply is unnecessary, and retaining necessary plies by taking an integer multiple of the base thickness. A domain representing the existence of each individual ply in the "base ply" is constructed, and an integrated optimization problem model for curved fiber variable stiffness composite material structures is established, incorporating the number of plies, ply thickness, and curved fiber placement angle. Based on this integrated optimization problem model, integrated optimization of the number of plies, ply thickness, and curved fiber placement angle is achieved, fully utilizing the mechanical properties of the composite material structure and significantly improving optimization efficiency.

[0059] 2. The present invention discloses an integrated optimization method for curved fiber variable stiffness composite material structures. Based on the Latin hypersquare sampling experiment, discrete continuous mixed variable sample points are generated, and an exponential form mixed correction mode variable fidelity surrogate model is constructed. Based on the variable fidelity surrogate model, the original optimization problem of curved fiber variable stiffness composite material structure is transformed into an approximate problem, thereby reducing the difficulty of solving the optimization problem and improving the optimization solution efficiency of curved fiber variable stiffness composite material structure.

[0060] 3. The present invention discloses an integrated optimization method for curved fiber variable stiffness composite material structures. It uses a genetic algorithm to optimize and solve the approximate optimization problem of curved fiber variable stiffness composite material structures. Based on the optimization results of the genetic algorithm, it reconstructs the optimization problem of curved fiber variable stiffness composite material structures with only the laying angle of curved fibers as the design variable. It then uses a sequential quadratic programming algorithm to optimize and solve the reconstructed optimization problem, thereby realizing the optimization solution of curved fiber variable stiffness composite material structures and improving the optimization solution accuracy of curved fiber variable stiffness composite material structures.

[0061] 4. The present invention discloses an integrated optimization method for curved fiber variable stiffness composite material structures. The optimized curved fiber variable stiffness composite material structure integrates the optimization results of the number of lay-up layers, lay-up thickness, and curved fiber lay-up angle variables. Under the process constraints of discrete values ​​of lay-up thickness and fiber curvature limitations, the integrated optimization of the number of lay-up layers, lay-up thickness, and curved fiber lay-up angle of the curved fiber variable stiffness composite material structure not only meets the requirements of structural strength, stiffness, and quality, but also improves the mechanical properties of the composite material structure. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating the implementation of an integrated optimization method for curved fiber variable stiffness composite material structures according to the present invention.

[0063] Figure 2 The curved fiber variable stiffness composite laminate provided in the embodiments of the present invention.

[0064] Figure 3 An integrated optimization method for curved fiber variable stiffness composite structures by introducing the concept of "base ply".

[0065] Figure 4(a) shows the low-fidelity analysis model of the curved fiber variable stiffness composite laminate provided in the embodiment of the present invention.

[0066] Figure 4(b) shows the high-fidelity analysis model of the curved fiber variable stiffness composite laminate provided in the embodiment of the present invention. Detailed Implementation

[0067] To make the technical problems solved by this invention and the technical solutions adopted clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to this invention are shown in the accompanying drawings, not all of them.

[0068] The implementation process of the integrated optimization method for curved fiber variable stiffness composite material structure of the present invention is as follows: Figure 1 As shown, to better illustrate the purpose and advantages of the present invention, a curved fiber variable stiffness composite laminate is used as an example. Figure 2 As shown in the figure, the integrated optimization method for curved fiber variable stiffness composite material structure disclosed in this embodiment has the following specific implementation steps:

[0069] Step 1: To minimize post-processing of the optimization results, define and create an initial "base ply" for the curved fiber variable stiffness composite structure. Optimize the ply thickness to determine the existence of each individual layer. When a single layer within the "base ply" is unnecessary, its thickness is set to a small value to indicate deletion; when a single layer is necessary, its thickness is set to an integer multiple of its baseline thickness to indicate retention. Construct a domain representing the existence of each individual layer within the "base ply," and establish an integrated optimization model for the curved fiber variable stiffness composite structure, incorporating the number of plies, ply thickness, and curved fiber placement angle.

[0070] Step 101: Define and create the initial "base ply" of the curved fiber variable stiffness composite structure. The "base ply" of the curved fiber composite structure consists of multiple composite monolayers. The existence of each monolayer is determined by optimizing the ply thickness. When a monolayer within the "base ply" is a non-essential ply, the ply thickness is set to a small value to indicate ply deletion; when a monolayer is an essential ply, the ply thickness is set to an integer multiple of the monolayer's base thickness to indicate ply retention. In non-essential plies, since the ply thickness is small, the change in the curved fiber placement angle within the ply has a negligible impact on structural performance; therefore, the curved fiber placement angle variable in non-essential plies is set to a constant value. In essential plies, the ply thickness must satisfy the characteristic of discrete values. The discrete ply thickness and the continuous curved fiber placement angle are optimized to improve the performance of the curved fiber variable stiffness composite structure, such as... Figure 3 As shown.

[0071] Step 102: Construct the number field based on the "base layer" created in Step 101. and This indicates the range of possible thickness values ​​for the necessary ply. This indicates the range of thickness values ​​corresponding to the non-essential ply. The element values ​​in the number field correspond to the existence of each single layer in the "base ply". The specific expressions are as follows: (1) and (2):

[0072]

[0073]

[0074] In the formula, t i t is the thickness of the i-th layer in the base ply; b For the single-layer reference thickness corresponding to the filament placement equipment, t b =0.127mm, where z is a positive integer; This indicates a small amount of thickness associated with unnecessary ply layups, taken as... n represents the number of layers in the "base layer". Number field The elements in the middle represent necessary ply thicknesses that are integer multiples of the base thickness of a single layer, and the number field. The middle element indicates that the thickness of the non-essential layer is a small amount.

[0075] Step 103: Based on the numerical domain constructed in Step 102 to represent the existence of each single layer of the curved fiber variable stiffness composite structure, an integrated optimization problem model of the curved fiber variable stiffness composite structure is established, which integrates the number of layups, layup thickness, and curved fiber layup angle, as shown in Equation (3):

[0076]

[0077] In the formula, t represents the discrete ply thickness vector, T is the path function parameter vector related to the fiber layup angle, f(t,T) and g(t,T) are the objective function and constraint function, respectively, J0 is the number of constraint functions; κ(T) is the fiber curvature constraint; κ max For the maximum allowable fiber curvature constraint, κ max =4.00m -1 ; and These are the lower and upper bounds of the path function parameter variables, respectively. For constant values, take m represents the number of fiber path function parameters in a single layer, taken as m = 2; n represents the number of layers in the "base layer", i.e., the number of discrete variables. Path function parameters Value and single-layer thickness t i Related, when At that time, with t i The associated ply is retained, and the corresponding ply thickness is an integer multiple of the single-layer reference thickness. Taking continuous values ​​within a given interval, when At that time, with t i Related ply deletion, ply thickness set to a small value. at this time Take constant

[0078] Step 2: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the high-fidelity and low-fidelity models of the curved fiber variable stiffness composite material structure. Based on the initial sample points of the high-fidelity and low-fidelity models, the curved fiber variable stiffness composite material structure is analyzed to obtain the response values ​​of the high-fidelity and low-fidelity surrogate models. An exponentially form hybrid modified mode variable fidelity surrogate model is then constructed.

[0079] Step 201: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the low-fidelity model and high-fidelity model of the corresponding curve fiber variable stiffness composite material structure. The number of initial sample points is determined by equations (4) and (5):

[0080]

[0081]

[0082] In the formula, L N With H N , representing the number of sampling points for the low-fidelity model and the high-fidelity model, respectively; nm represents the number of continuous variables; and round(*) is the rounding function. Standard Latin hypersquare sampling is only applicable to continuous variable sampling; therefore, continuous slack variables are used for mixed variable sampling. In [0, 1]... n+nm Continuous sampling is performed in space, where the first n values ​​are related to the discrete ply thickness variable, and the last nm values ​​are related to the continuous curve fiber layup angle variable. The specific calculation formula for the i-th discrete ply thickness variable sampling point using the floor function is as follows:

[0083]

[0084] In the formula, x represents the sampled value in the range [0,1] corresponding to the thickness variable of the i-th discrete ply. i This represents the actual sampled value of the i-th discrete ply thickness variable; floor(*) is the floor function; Γ i For number fields and The union of the two sets. The formula for calculating the sampling point of the fiber laying angle variable of the i-th continuous curve is:

[0085]

[0086] In the formula, x represents the sampled value within the range [0,1] corresponding to the fiber laying angle variable of the i-th continuous curve. i This represents the actual sampled value of the fiber laying angle variable for the i-th continuous curve; With x i The upper and lower limits are defined for the fiber placement angle variable of the i-th continuous curve. An initial set of sampling points for the discrete continuous design variables was generated using Latin hypersquare sampling, where the sampling points for the low-fidelity model and the high-fidelity model of the variable stiffness composite material structure with curved fibers are respectively... and

[0087] Step 202: Based on the initial sample points from Step 201, perform a structural analysis of the curved fiber variable stiffness composite material. The low-fidelity analysis model has 625 finite element numbers (25×25), and the high-fidelity analysis model has 10000 finite element numbers (100×100), as shown in Figures 4(a) and 4(b). The response set corresponding to the low-fidelity model is obtained. Response set corresponding to high fidelity model

[0088] Step 203: Construct an exponential form hybrid modified mode variable fidelity surrogate model based on the high-fidelity and low-fidelity model response values ​​obtained in Step 202, as shown in the following equation:

[0089]

[0090] In the formula, This is a low-fidelity surrogate model based on Gaussian process regression. δ(X) is the variable fidelity surrogate model constructed; r is the exponential correction factor, and δ(X) is the additive correction term of the surrogate model.

[0091] Step 204: Based on the variable fidelity surrogate model established in step 203, obtain the approximate response f(X) of the surrogate model, replace the objective function in the integrated optimization problem of the curved fiber variable stiffness composite material structure established in step 103 with the approximate objective function, that is, the approximate response f(X) of the variable fidelity surrogate model; replace the constraint function in the original optimization problem with the approximate constraint function constructed by the variable fidelity surrogate model, and obtain the approximate optimization problem model of the curved fiber variable stiffness composite material structure, as shown in equation (9).

[0092]

[0093] In the formula, These are the approximate objective and approximate constraint functions constructed based on the variable fidelity surrogate model, respectively. and These are the lower and upper limits of the fiber layup angle associated with the p-th ...

[0094] Step 3: For the approximate optimization problem model of the curved fiber variable stiffness composite material structure established in Step 2 based on the surrogate model, a genetic algorithm is used to perform discrete-continuous mixed variable optimization to obtain preliminary optimization results for the curved fiber variable stiffness composite material structure. Based on the optimization results of the genetic algorithm, an optimization problem containing only fiber path parameters as continuous design variables is reconstructed. A sequential quadratic programming algorithm is used to optimize and solve the reconstructed optimization problem, improving the solution accuracy of the curved fiber laying angle, and obtaining the optimization results of the curved fiber variable stiffness composite material structure.

[0095] Step 301: The approximate optimization problem of the curved fiber composite material structure established in Step 204 still involves discrete and continuous design variables. To effectively solve this optimization problem, a genetic algorithm is used to find the discrete and continuous mixed variables of the composite material structure. The adaptive penalty fitness function of the genetic algorithm is:

[0096]

[0097]

[0098]

[0099] In the formula, ò is the penalty factor of the fitness function of the composite material structure, taken as ò = 0.01, β j For the j-th constraint The average degree of violation among individuals in the current population, γ is the penalty exponent of the fitness function of the composite structure, and γ is calculated as follows: i With γ f is a given constant; G is the current generation number, MaxG is the maximum generation number of the genetic algorithm, and MaxG = 100 is taken; This represents the average objective function of individuals within the current population. When solving using a genetic algorithm, for discrete variables, genes in chromosomes are encoded discretely, using a single-point crossover method as the crossover operator and a basic bit mutation method as the mutation operator; for continuous variables, they are encoded in actual parameter form, and a new evolutionary population is generated using a simulated binary crossover operator and a polynomial mutation operator.

[0100] Step 302: Based on the optimization results of the genetic algorithm in step 301, a sequential quadratic programming algorithm is used to further optimize the continuous variables. The optimized solution obtained by the genetic algorithm in step 301 is x. GA =(t * ,T * ), where t* is the optimal discrete ply thickness vector corresponding to the solution obtained by the genetic algorithm, T * This represents the optimal fiber path parameter vector corresponding to the obtained solution. Considering the randomness of the genetic algorithm, the accuracy of solving continuous variables cannot be guaranteed. To improve the accuracy of solving the fiber layup angle, this invention starts from the optimized solution obtained by the genetic algorithm, establishes an optimization problem regarding the fiber path parameter variables, and further optimizes the continuous variables. Based on the optimized solution obtained by the genetic algorithm, the discrete layup thickness variable is fixed at t*, and the continuous layup angle variable associated with unnecessary layups is also fixed as a constant value. Using only the fiber path parameters related to the layup as continuous design variables, the optimization problem is established as follows:

[0101]

[0102] In the formula, Let n′ be the vector of curved fiber path parameters associated with the retained plies, and n′ be the number of retained plies. For the above-reconstructed continuous variable optimization problem, Equation (13) holds only when the objective function is related to the curved fiber layup angle. The sequential quadratic programming algorithm is used to optimize and solve Equation (13) to improve the optimization solution accuracy of the curved fiber variable stiffness composite material structure. When the objective function is an independent function of the curved fiber layup angle variable, Equation (13) cannot optimize the curved fiber layup angle of the composite material. Therefore, the optimization problem of Equation (13) needs to be reconstructed so that the objective function is a function of the curved fiber layup angle. For this reason, the most critical constraint is selected from the constraint function set as the new objective function, and the optimization problem of the curved fiber variable stiffness composite material structure is reconstructed as follows:

[0103]

[0104]

[0105] In the formula, J represents the most critical constraint selected from the constraint set; J is the index set corresponding to the constraint set after removing the most critical constraint.

[0106] Step 303: For the continuous variable optimization problem established in step 302, the sequential quadratic programming algorithm is used to optimize and solve the problem, and the optimization results of the curved fiber variable stiffness composite material structure are obtained.

[0107] Step 4: Determine whether the optimization result of the curved fiber variable stiffness composite material structure obtained in Step 3 is the optimal solution. If it is the optimal solution, output the optimal solution of the curved fiber variable stiffness composite material structure optimization, and the optimization process ends. If it is not the optimal solution, add the current optimal solution to the sample point set, return to Step 2 to correct the variable fidelity proxy model of the curved fiber variable stiffness composite material structure, and solve the optimization problem of the reconstructed variable stiffness composite material structure according to Step 3 until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, that is, the optimized curved fiber variable stiffness composite material structure is obtained, realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

[0108] Step 401: Obtain the optimal solution for the k-th iteration of the curved fiber variable stiffness composite material structure optimization based on step 303. Compare it with the optimal solution obtained in the (k-1)th iteration The optimization process ends when the distance between two optimal solutions is less than the given convergence control parameter. The stopping criterion formula is as follows:

[0109]

[0110] In the formula, ε is the convergence control parameter, and in this invention, ε = 0.001.

[0111] Step 402: Based on the judgment result of step 401, if the optimal solution of the fiber-reinforced variable stiffness composite material structure obtained in the k-th iteration does not meet the convergence condition, then the optimal solution of the iteration will be optimized. Add sample point datasets and update the data point set of the fiber-reinforced variable stiffness composite structure curve from step 201. The criterion for adding new sampling points to the data point sets of the low-fidelity model and high-fidelity model of the fiber-reinforced variable stiffness composite structure curve is as follows:

[0112]

[0113] In the formula, and ε is the normalized distance between the new data point and the original data point sets of the low-fidelity and high-fidelity models. LF With ε HF The control parameter ε is set to add sample points to the data point sets of the low-fidelity model and high-fidelity model of the curved fiber variable stiffness composite material structure, respectively. LF =0.001, ε HF =0.001.

[0114] Step 403: Perform structural response analysis based on the newly sampled data from Step 402, and update the data point sets for both the low-fidelity and high-fidelity models. Update the response dataset to and Substitute the updated dataset into step 200 to correct the variable fidelity proxy model.

[0115] Step 404: Update the approximate problem based on the modified variable fidelity surrogate model in Step 403, and return to Steps 301-303 to optimize the approximate problem of curved fiber variable stiffness composite material structure until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, thereby realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

[0116] against Figure 2 The curved fiber-reinforced variable stiffness composite laminate shown is subjected to distributed loads. To maximize the critical buckling load, integrated optimization of the number of ply layers, ply thickness, and layup angle is performed. The parameters of the single-layer composite material are E1 = 134 GPa, E2 = 7.71 GPa, and G... 12 =G 13 = 4.31 GPa, G 23 =2.76 GPa, v 12 =v 13 =0.301, v 23 =0.396, where E1 and E2 are the elastic moduli in the X and Y directions, respectively, and v 12 v 13 v 23Given the material's Poisson's ratio and the single-layer reference thickness t. b =0.127mm, the length and width of the variable stiffness composite laminate are both a=100mm. Low-fidelity and high-fidelity analysis models were established, with the low-fidelity analysis model having 625 finite element numbers (25×25) and the high-fidelity analysis model having 10000 finite element numbers (100×100), as shown in Figures 4(a) and 4(b). Using the number of layups, layup thickness, and layup angle as design variables, the maximum fiber curvature radius was limited to 4.00m. -1 The maximum number of ply layers is 16, and the optimization results are shown in Table 1. Starting from different "base plies", the optimal plies obtained all meet the process constraints and can provide scheme guidance for practical engineering applications.

[0117] Table 1

[0118]

[0119] It also includes step five: The curved fiber variable stiffness composite material structure obtained in step four is an integrated optimization result that integrates the number of layups, layup thickness, and curved fiber layup angle variables. It can improve the mechanical properties of the composite material structure, reduce the mass of the composite material structure, and solve the engineering and technical problems in the application field of curved fiber variable stiffness composite material structures while meeting the working conditions.

[0120] Step 5 addresses the engineering challenges in the application of curved fiber variable stiffness composite structures, including: under the process constraints of discrete ply thickness values ​​and fiber curvature limitations, the integrated optimization of the number of ply layers, ply thickness, and curved fiber placement angle in curved fiber variable stiffness composite structures is achieved. The optimization results not only meet the structural strength, stiffness, and quality requirements but also improve the mechanical properties of the composite structure.

[0121] The above are merely specific steps of the present invention and do not constitute any limitation on the scope of protection of the present invention. It can be extended to the field of structural optimization of curved fiber variable stiffness composite materials. All technical solutions formed by equivalent transformations or substitutions fall within the scope of protection of the present invention. The parts of the present invention not described in detail are well-known technologies to those skilled in the art.

Claims

1. An integrated optimization method for curved fiber variable stiffness composite material structures, characterized in that: Includes the following steps, Step 1: Define and create the initial "base ply" of the curved fiber variable stiffness composite structure. Optimize the solution to determine the existence of each individual layer by solving for its thickness. When an individual layer in the "base ply" is unnecessary, the ply thickness is set to a small value to indicate deletion; when an individual layer is necessary, the ply thickness is set to an integer multiple of the base thickness to indicate retention. Construct a domain representing the existence of each individual layer in the "base ply". Establish an integrated optimization problem model for the curved fiber variable stiffness composite structure, incorporating the number of plies, ply thickness, and curved fiber placement angle. The implementation method for step one is as follows: Step 101: Define and create the initial "base ply" of the curved fiber variable stiffness composite structure; the "base ply" of the curved fiber composite structure consists of multiple composite monolayers. The existence of each monolayer is determined by optimizing the ply thickness; when a monolayer in the "base ply" is a non-essential ply, the ply thickness is set to a small value to indicate ply deletion; when a monolayer is an essential ply, the ply thickness is set to an integer multiple of the monolayer reference thickness to indicate ply retention; in non-essential plies, since the ply thickness is a small value, the change in the curved fiber placement angle within the ply has a negligible impact on structural performance, so the curved fiber placement angle variable in non-essential plies is set to a constant value; in essential plies, the ply thickness must satisfy the characteristic of discrete values. The discrete ply thickness and the continuous curved fiber placement angle are optimized to improve the performance of the curved fiber variable stiffness composite structure; Step 102: Construct the number field based on the "base layer" created in Step 101. and , This indicates the range of possible thickness values ​​for the necessary ply. This represents the range of thickness values ​​corresponding to unnecessary plies. The elements in the number field correspond to the existence of each single layer in the "base ply". The specific expression is as follows: , As shown; In the formula, For the first layer of the base layer Layer thickness; For the single-layer reference thickness corresponding to the filament placement equipment, It is a positive integer; Indicates a small amount of thickness associated with unnecessary ply layups; Represents the number of layers in a "base layer"; number field The elements in the middle represent necessary ply thicknesses that are integer multiples of the base thickness of a single layer, and the number field. The middle element indicates that the thickness of an unnecessary layer is a small value; Step 103: Based on the numerical domain constructed in Step 102 to represent the existence of each single layer in the curved fiber variable stiffness composite structure, establish an integrated optimization problem model for the curved fiber variable stiffness composite structure that integrates the number of layups, layup thickness, and curved fiber layup angle, as shown in the equation. As shown: In the formula, Represents a discrete ply thickness vector. The path function parameter vector related to the laying angle of the curved fiber. and These are the objective function and the constraint function, respectively. The number of constraint functions; For fiber curvature constraint; Maximum allowable fiber curvature constraint; and These are the lower and upper bounds of the path function parameter variables, respectively. It is a constant value; This represents the number of fiber path function parameters in a single layer. The number of plies in the "base layer", i.e., the number of discrete variables; path function parameters. Value and corresponding single-layer thickness Related, when At that time, and Associated ply retention, single-layer thickness The corresponding ply thickness is an integer multiple of the single-layer reference thickness. Takes continuous values ​​within a given interval; when At that time, and Related ply deletion, ply thickness set to a small value. ,at this time Take constant ; Step 2: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the high-fidelity model and low-fidelity model of the curved fiber variable stiffness composite material structure; based on the initial sample points of the high-fidelity and low-fidelity models, the curved fiber variable stiffness composite material structure is analyzed to obtain the response values ​​of the high-fidelity and low-fidelity surrogate models of the composite material structure, and an exponential form of mixed correction mode variable fidelity surrogate model is constructed. Step 3: For the approximate optimization problem model of the curved fiber variable stiffness composite material structure established in Step 2 based on the surrogate model, a genetic algorithm is used to perform discrete continuous mixed variable optimization to obtain the preliminary optimization results of the curved fiber variable stiffness composite material structure; based on the optimization results of the genetic algorithm, an optimization problem containing only fiber path parameters as continuous design variables is reconstructed, and a sequential quadratic programming algorithm is used to optimize and solve the reconstructed optimization problem to obtain the optimization results of the curved fiber variable stiffness composite material structure. Step 4: Determine whether the optimization result of the curved fiber variable stiffness composite material structure obtained in Step 3 is the optimal solution. If it is the optimal solution, output the optimal solution of the curved fiber variable stiffness composite material structure optimization, and the optimization process ends. If it is not the optimal solution, add the current optimal solution to the sample point set, return to Step 2 to correct the variable fidelity proxy model of the curved fiber variable stiffness composite material structure, and solve the optimization problem of the reconstructed variable stiffness composite material structure according to Step 3 until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, that is, the optimized curved fiber variable stiffness composite material structure is obtained, realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

2. The integrated optimization method for curved fiber variable stiffness composite material structures as described in claim 1, characterized in that: It also includes step five: The curved fiber variable stiffness composite material structure obtained in step four is an integrated optimization result that integrates the number of lay-ups, lay-up thickness, and curved fiber lay-up angle variables. It can meet the structural strength, stiffness, and quality requirements under the process constraints of discrete lay-up thickness and fiber curvature limitations, and can also improve the mechanical properties of composite material structures.

3. The integrated optimization method for curved fiber variable stiffness composite material structures as described in claim 2, characterized in that: The second step is implemented as follows: Step 201: Based on the Latin hypersquare sampling experiment, mixed variable sampling is performed using continuous relaxation variables to generate initial sample points for the low-fidelity model and high-fidelity model of the corresponding curve fiber variable stiffness composite material structure; the number of initial sample points is determined by the formula... , Sure: In the formula, and These represent the number of sampling points for the low-fidelity model and the high-fidelity model, respectively. The number of continuous variables, This is a rounding function; the standard Latin hypersquare sampling technique is only applicable to continuous variable sampling, therefore, continuous slack variables are used for mixed variable sampling; in Construct continuous sample points in space, where the first The values ​​are related to the discrete ply thickness variable, and then... The first value is related to the fiber placement angle variable of the continuous curve; the floor function is used to calculate the first value. A discrete ply thickness variable in the number domain The actual value in is calculated using the following formula: In the formula, Indicates the first Each discrete ply thickness variable corresponds to Sampled values ​​within the range, Indicates the first The actual sampled values ​​of the discrete ply thickness variable; It is a rounding function; For number fields and The union of; for the first The calculation formula for the sampling points of the fiber layup angle variable of a continuous curve is as follows: In the formula, Indicates the first The corresponding fiber laying angle variables of a continuous curve Sampled values ​​within the range, Indicates the first The actual sampled values ​​of the fiber laying angle variable of a continuous curve; and For the first The upper and lower limits of the fiber laying angle variable of a continuous curve; The initial set of sampling points for discrete continuous design variables is generated using Latin hypersquare sampling. The sampling points for the low-fidelity model and the high-fidelity model of the curved fiber variable stiffness composite material structure are respectively... and ; Step 202: Based on the initial sample points from Step 201, perform a curve fiber variable stiffness composite material structure analysis to obtain the response set corresponding to the low-fidelity model. Response set corresponding to high fidelity model ; Step 203: Based on the fidelity model response obtained in Step 202, construct an exponential form hybrid modified mode variable fidelity surrogate model, as shown in the following equation: In the formula, This is a low-fidelity surrogate model based on Gaussian process regression. The variable fidelity proxy model was constructed. As an index correction factor, For the additive correction term in the proxy model; Step 204: Based on the variable fidelity surrogate model established in Step 203, obtain the approximate response of the surrogate model. The objective function in the integrated optimization problem of the curve fiber variable stiffness composite material structure established in step 103 is replaced with an approximate objective function, namely the approximate response of the variable fidelity surrogate model. The constraint functions in the original optimization problem are replaced with approximate constraint functions constructed by the variable fidelity surrogate model to obtain an approximate optimization problem model for the curved fiber variable stiffness composite material structure, as shown in the equation. As shown; In the formula, , These are the approximate objective and approximate constraint functions constructed based on the variable fidelity surrogate model, respectively. and These are the lower and upper limits of the curve fiber placement angle associated with the i-th ply, respectively.

4. The integrated optimization method for curved fiber variable stiffness composite material structures as described in claim 3, characterized in that: The method for implementing step three is as follows: Step 301: The approximate optimization problem of the curved fiber composite material structure established in Step 204 still involves discrete and continuous design variables. To effectively solve this optimization problem, a genetic algorithm is used to find the discrete and continuous mixed variables of the composite material structure. The adaptive penalty fitness function of the genetic algorithm is: In the formula, The penalty factor for the fitness function of composite material structures. For the first Constraints The average degree of violation among individuals in the current population. The penalty exponent for the fitness function of composite material structures. In the calculation formula and Given a constant; For the current generation, This represents the maximum number of generations in the genetic algorithm. The average value of the objective function of individuals in the current population; when solving using a genetic algorithm, for the layup thickness of the curved fiber variable stiffness composite material structure, the genes in the chromosome are encoded in a discrete manner, and the single-point crossover method is used as the crossover operator, and the basic bit mutation method is used as the mutation operator; for the curved fiber layup angle, it is encoded in actual parameter form, and a new evolutionary population is generated using the simulated binary crossover operator and the polynomial mutation operator; Step 302: Based on the optimization results of the genetic algorithm in step 301, the continuous variables are further optimized using a sequential quadratic programming algorithm; the optimized solution obtained by the genetic algorithm in step 301 is... ,in This represents the optimal discrete ply thickness vector corresponding to the solution obtained by the genetic algorithm. This represents the optimal curve fiber path parameter vector corresponding to the obtained solution. Considering the randomness of the genetic algorithm, the solution accuracy for continuous variables cannot be guaranteed. Starting from the optimized solution obtained by the genetic algorithm, an optimization problem regarding the curve fiber path parameter variables is established. By further optimizing the continuous fiber angle variables, the solution accuracy for the curve fiber layup angle is improved. Based on the optimized solution of the curve fiber variable stiffness composite material structure obtained by the genetic algorithm, the discrete layup thickness variable is fixed as a constant value. The fiber layup angle variable associated with the non-essential layup is fixed as a constant. By retaining only the ply-related curved fiber path parameters as continuous variables, the optimization problem of the curved fiber variable stiffness composite structure is reconstructed as follows: In the formula, This is a vector of curved fiber path parameters associated with the retained layup. To preserve the number of layers; for the above-described continuous variable optimization problem, the formula is only valid when the objective function is related to the fiber layup angle of the curve. The equation is valid, and the sequential quadratic programming algorithm is used to apply it. Optimization is performed to improve the accuracy of optimization solutions for curved fiber variable stiffness composite structures; when the objective function is an independent function of the curved fiber layup angle variable, the equation... Since it is impossible to optimize the fiber layup angle of composite material curves, it is necessary to modify the formula. The optimization problem is reconstructed so that the objective function is a function of the curved fiber laying angle. Therefore, the most critical constraint is selected from the constraint function set as the new objective function, and the optimization problem of the curved fiber variable stiffness composite material structure is reconstructed as follows: In the formula, The most critical constraint selected from the constraint set; The set of indices corresponding to the constraint set after removing the most critical constraint; Step 303: For the optimization problem of the curved fiber variable stiffness composite material structure established in Step 302, the sequential quadratic programming algorithm is used to optimize and solve the problem, and the optimization result of the curved fiber variable stiffness composite material structure is obtained.

5. The integrated optimization method for curved fiber variable stiffness composite material structures as described in claim 3, characterized in that: Step four is implemented as follows: Step 401: Obtain the first step based on step 303. The optimal solution for the iterative optimization of subcurved fiber variable stiffness composite material structures , and the first The optimal solution obtained in the second iteration The optimization process ends when the distance between two optimal solutions is less than the given convergence control parameter. The stopping criterion formula is as follows: In the formula, These are the convergence control parameters; Step 402: Based on the result of step 401, if the first... If the optimization solution for the fiber-reinforced variable stiffness composite material structure obtained in the second iteration does not meet the convergence condition, then the optimal solution obtained in the next iteration will be optimized. Add sample point datasets and update the data point set of the curve fiber variable stiffness composite material structure in step 201; the judgment condition for adding new sampling points to the data point sets of the low-fidelity model and high-fidelity model of the corresponding curve fiber variable stiffness composite material structure is: In the formula, and The normalized distance between the current optimal solution and the original data point sets of the low-fidelity and high-fidelity models. and These are the control parameters for adding sample points to the data point sets of the low-fidelity model and high-fidelity model of the curved fiber variable stiffness composite material structure, respectively. Step 403: Perform structural response analysis based on the newly sampled data from Step 402, and update the data point sets of the low-fidelity model and the high-fidelity model as follows. , Update the curve fiber variable stiffness composite structure response dataset to and Substitute the updated curve fiber variable stiffness composite material structure dataset into step 203 to correct the variable fidelity proxy model; Step 404: Update the approximate problem based on the modified variable fidelity surrogate model in Step 403, and return to Steps 301-303 to optimize the approximate problem of curved fiber variable stiffness composite material structure until the optimal solution of the curved fiber variable stiffness composite material structure optimization problem is obtained, thereby realizing the integrated optimization of the curved fiber variable stiffness composite material structure.

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