Regional variable-thickness optimization design method for curve fiber composite material structure

Abstract

The invention discloses a regional variable-thickness optimization design method for a curve fiber composite material structure, and belongs to the field of composite material structure design. The implementation method comprises the following steps of: establishing an initial'base laying layer 'in different regions for a multi-region composite material structure, and defining an optimization problem mathematical model taking the number of laying layers, the thickness of the laying layers and the fiber laying angle as design variables; constructing a variable fidelity agent model, establishing an approximate problem of an original optimization problem, and solving the approximate optimization problem by using a genetic algorithm; putting forward a variable thickness layer loss mechanism of laying layer local sharing and variation, and correcting all individuals of the genetic algorithm population in order to form a variable thickness design satisfying regional continuity; and dynamically increasing sample points to update the proxy model to form the efficient optimization design method for the hybrid variable stiffness composite material structure fusing the curve fiber laying and the variable thickness layer loss mechanism.

Description

Technical Field

[0001] The invention belongs to the field of composite material structure design, and relates to an optimized design method for variable thickness in different regions of a curved fiber composite material structure. Background Art

[0002] Advanced composite material structures have been widely used in the structures of aerospace aircrafts due to their excellent characteristics such as high specific stiffness, high specific strength, and strong designability. Advanced manufacturing technologies for composite materials such as automated fiber placement break through the straight-line mode of traditional fiber layering, can achieve curve customization of fiber paths, change the spatial distribution of structural stiffness, and are gradually applied to the design and manufacturing of aircraft structures. To fully explore the mechanical property advantages of curved fiber composite structures, the design variables of curved fiber variable stiffness composite structures can simultaneously include the number of plies, ply thickness, and fiber placement angles customized point by point. For the design of large-sized structural components of aircrafts, a multi-region variable thickness composite laminate structure form is mostly adopted to achieve equal stress lightweight design. Integrating curved fiber placement with variable thickness design ideas can further improve the structural efficiency of composite materials and has a broader application prospect.

[0003] In the variable thickness laminate structure, layer loss is caused by uneven distribution of ply thickness, resulting in interruption of fiber continuity and conflicts in fiber placement angles in adjacent regions. As a result, stress concentration occurs at the region boundaries due to the interruption of the force transmission path. Therefore, the constraint design of fiber continuity between regions has become an important property determining the mechanical properties of variable thickness laminates. Therefore, the optimized design of curved fiber hybrid variable stiffness composite structures not only needs to determine the number of plies, ply thickness, and placement angles of the equal thickness laminate regions, but also relies on a variable thickness layer loss mechanism that can effectively maintain fiber continuity between adjacent regions. Currently, there are few research results on the hybrid variable stiffness optimized design that integrates curved fibers with variable thickness layer loss at home and abroad. How to reasonably utilize the advantages of the two variable stiffness methods of curved fiber placement and variable thickness layer loss design to achieve the optimized design of curved fiber composite structures while satisfying constraints such as fiber continuity between adjacent regions still requires the development of efficient optimization methods for solving such problems. Summary of the Invention

[0004] The invention provides an optimized design method for variable thickness in different regions of a curved fiber composite material structure. For a multi-region composite material structure, an initial "basic ply" is created for each region, and based on this, a mathematical model of an optimization problem with the number of plies, ply thickness, and fiber placement angle as design variables is established. A variable fidelity surrogate model is constructed and a genetic algorithm is used to solve the approximate optimization problem corresponding to the surrogate model. A variable thickness layer loss mechanism of ply local sharing and mutation is proposed to correct all individuals in the genetic algorithm population to form a variable thickness design that satisfies regional continuity, thereby achieving the efficient optimization of the hybrid variable stiffness composite material structure.

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

[0006] An optimized design method for variable thickness in regions of a curved fiber composite material structure disclosed by the present invention includes the following steps:

[0007] Step 1: To achieve the synchronous optimization of the number of plies, ply thickness, and laying angle, drawing on the idea of the base structure method in structural topology optimization, an initial "base ply" is created, and the optimal number of plies is obtained by determining the existence of each single ply in the "base ply"; considering the design requirement of fiber continuity between adjacent regions of a multi-region composite material structure, the creation of the "base ply" related to each region is kept consistent. To reasonably express the existence of each single ply in the "base ply", a number field representing the existence of a single ply is defined, and a mathematical model of a hybrid variable stiffness optimization problem integrating curved fibers and variable thickness plies is established.

[0008] Step 101: For a multi-region curved fiber composite laminate structure, an initial "base ply" with the same number of plies is created for each region. Similar to the concept of the base structure in structural topology optimization, the necessary retained single plies and unnecessary redundant single plies in the regionally divided "base ply" are determined through optimization calculations to find the optimal number of plies. Among them, when the corresponding single ply is an unnecessary redundant ply, the ply thickness takes a small thickness value, and the laying angle takes a constant value; when the corresponding single ply is a necessary retained ply, the ply thickness takes an integer multiple of the ply reference thickness, and the laying angle takes continuous values within a given range.

[0009] Step 102: Define the number field Γ according to the initial "base ply" created in Step 101 i (I) and Γ i (II) . Γ i (I) represents the value range of the thickness of the necessary retained single plies, represents the value range of the thickness of the unnecessary redundant plies, and the expressions of the two number fields are as follows:

[0010] Γ i (I) ={t i |t i =z·t b ,z∈N +},i = 1,…,n#(1)

[0011] Γ i (II) ={t i |t i =t b0},i = 1,…,n#(2)

[0012] Among them, t i is the single ply thickness corresponding to the i-th layer in the "base ply"; tb is the reference thickness of the ply; z takes positive integers; t b0 is used to represent the thickness increment of the non-essential redundant ply; n is the number of plies in the "basic ply".

[0013] Step 103: Based on the number field representing the existence of a single layer of the "basic ply" defined in Step 102, for the composite structure divided into S regions, the mathematical model of the hybrid variable stiffness optimization problem of the curve fiber and variable thickness dropped ply fusion is established as follows:

[0014]

[0015] In the formula, X is the design variable, including the discrete ply thickness variable t and the fiber placement path parameter variable T; t si is the single layer thickness corresponding to the i-th layer in the "basic ply" in region s; T i (p) is the p-th path parameter related to the i-th layer; T i (p) and represent the lower and upper limits of the path parameter respectively, is a constant; m is the number of path function parameters in a single layer; f(X) and g j (X) are the objective function and constraint function of the optimization problem respectively, and J0 is the number of constraint functions. The value of the path parameter T i (p) is related to the minimum value of the single layer thickness of the i-th layer in all regions. When min s {t si}∈Γ i (I) That is, the minimum value of the single layer thickness of the i-th layer in the "basic ply" corresponding to all regions is within the number field Γ i (I) It means that at least one region corresponding to the i-th layer single layer is retained. At this time, T i (p) continuously takes values within the given upper and lower limit intervals; when max s {t si}∈Γ i (II) That is, the maximum value of the single layer thickness of the i-th layer in the "basic ply" corresponding to all regions is within the number field Γ i (II) It means that the i-th layer single layer corresponding to all regions in the "basic ply" is deleted. At this time, T i (p) takes a constant For any two adjacent regions s and s′, assuming that the thickness of all plies in region s′ is less than that in region s, to meet the requirement of fiber continuity, it is necessary to ensure that the thickness of the corresponding single ply in region s′ is a subset of the ply design in region s, that is, to satisfy t s′i -t si ≤0.

[0016] Step 2: Use the finite element analysis method to establish high-fidelity and low-fidelity models of the curve fiber variable stiffness composite structure respectively. Based on the Latin hypercube sampling method, generate initial sample data points corresponding to the high-fidelity and low-fidelity finite element models respectively and conduct structural analysis. According to the structural analysis results, construct a variable-fidelity surrogate model, establish an approximate problem of the original optimization problem, and use the genetic algorithm to solve this approximate optimization problem.

[0017] Step 201: Establish finite element models of the curve fiber variable stiffness composite structure with different mesh sizes, generate high-fidelity and low-fidelity models for structural analysis, and provide model support for the subsequent construction of the variable-fidelity surrogate model.

[0018] Step 202: Based on the Latin hypercube sampling method, generate initial sample points corresponding to the high-fidelity and low-fidelity analysis models of the composite structure established in Step 201 and Conduct finite element analysis of the variable stiffness composite structure accordingly to obtain the structural analysis response data sets corresponding to the high-fidelity and low-fidelity models and

[0019] Step 203: According to the sample points generated in Step 202 and their structural analysis response data, construct a variable-fidelity surrogate model with an exponential form of hybrid correction mode as follows:

[0020]

[0021] In the formula, is the constructed variable-fidelity surrogate model; is the surrogate model of the corresponding low-fidelity analysis model established based on Gaussian process regression; r is the exponential correction factor; δ(X) is the additive correction term of the variable-fidelity surrogate model.

[0022] Step 204: Based on the variable-fidelity surrogate model constructed in Step 203, establish an approximate optimization problem model for the hybrid variable stiffness optimization design of curve fiber and variable thickness dropped plies as shown in the following formula:

[0023]

[0024] In the formula, and respectively represent the approximate objective function and the approximate constraint function constructed using the variable-fidelity surrogate model established in Step 203.

[0025] Step 205: For the approximate optimization problem model established in Step 204, use a genetic algorithm to perform mixed-variable optimization. During the optimization process of the genetic algorithm, it is difficult to consider the fiber breakage phenomenon caused by layer loss in adjacent regions, that is, the inequality constraint t s′i -t si ≤0 (s, s′ = 1, …, S) is not easy to be considered during the execution of the genetic algorithm. This is mainly because the layup design relationship between regions s and s′ is difficult to determine in advance. Therefore, a specific layer-loss mechanism needs to be studied to ensure that any individual in the genetic algorithm population meets the design requirements of fiber continuity in adjacent regions.

[0026] Step Three: Considering that the designs corresponding to the individuals in the genetic algorithm population in Step Two do not meet the design requirements of fiber continuity in adjacent regions, a variable-thickness layer-loss mechanism of layer local sharing and mutation is proposed. After the mutation operation of the genetic algorithm, the variable-thickness layer-loss mechanism is executed to correct all individuals in the genetic algorithm population, so as to form a variable-thickness design that meets the continuity of adjacent regions, improve the overall performance of the structure, and reduce the risk of structural failure.

[0027] Step 301: First, define two groups A and B. The elements in group A include the regions with the thinnest layup thickness in the current design step, otherwise the corresponding regions are divided into the elements of group B. Initialize the region grouping, and all regions are divided into group B.

[0028] Step 302: For the layup design corresponding to any individual in the genetic algorithm population, compare the number of layups in each region of the elements in group B to determine the region with the thinnest current layup thickness, and identify the neighborhood of the thinnest layup region from the elements of group B. Classify the region with the thinnest current layup thickness into group A, and other regions into group B. Share the layup design of the current thinnest layup region with its neighborhood to make the layup design of the thinner layup region a subset of the thicker layup region in its neighborhood, ensuring the continuity of adjacent regions of the structure.

[0029] Step 303: To reduce the impact of the layer local sharing operation on the layup thickness in adjacent regions, introduce a local mutation operator to make the non-shared layup thickness variables in the "base layup" corresponding to the neighborhood take values within the value range shown in Equation (1) or (2). The mutation probability corresponding to the non-shared and deleted layups in the neighborhood is taken according to Equation (6), and the mutation probability corresponding to the non-shared and retained layups is assigned according to Equation (7), where t s′ is the total layup thickness of the thinnest layup region, t s is the total layup thickness of the neighborhood before the local sharing operation, t s′∩s is the layup thickness of the intersection of the layups in the thinnest layup region and the neighborhood, t dIt is the total thickness of the neighborhood deleted ply after the local sharing operation. The local mutation probabilities shown in Equations (6) and (7) have the equality relationship shown in Equation (8), which probabilistically realizes the consistency of the total thickness of the neighborhood plies before and after the local sharing operation.

[0030]

[0031] P m2 ·(t s -t s′∩s )-t d P m1 =t s ′-t s′∩s #(8)

[0032] Step 304: Determine whether the elements in group B are empty. If it is an empty set, after the ply local sharing and mutation operations, the ply designs corresponding to the relevant individuals in the population at this time can meet the design requirements of fiber continuity in any adjacent region; if B is a non-empty set, repeat the above steps 302 to 303 until B is an empty set, so that the ply design of the multi-region structure of the curved fiber composite material can be gradually carried out in regions, realizing the overall variable-thickness ply removal design of the structure.

[0033] Step 305: After placing the above variable-thickness ply removal mechanism in the genetic algorithm and completing the compilation operator operation, and before calculating the individual fitness, ensure that the variable-thickness design does not damage the established regional connectivity due to the implementation of the genetic operator, and realize the correction of all individuals in the genetic algorithm population, forming a variable-thickness design that meets the continuity of adjacent regions.

[0034] Step Four: According to the optimization results output in Steps Two to Three, judge the convergence of the optimization process. If the current obtained optimization result meets the convergence judgment conditions, output the current optimization result as the final optimized design scheme, and the optimization process ends; if it does not meet the convergence judgment conditions, add the current optimization result to the sample data point set to update the surrogate model, and repeat the above Steps Two to Three until the convergence judgment conditions are met.

[0035] Step 401: In the k-th iteration of the optimization process, after the genetic algorithm and the variable-thickness ply removal mechanism, output the current obtained optimization result X (k) , and compare it with the optimization result X (k-1) obtained in the (k - 1)-th iteration for convergence judgment through the following formula:

[0036]

[0037] where ∈ is the convergence control precision.

[0038] Step 402: According to the convergence judgment in Step 401, if the optimization result obtained in the k-th iteration does not meet the convergence judgment condition, add the current optimization result to the sample data point sets corresponding to the high-fidelity and low-fidelity models, that is Perform finite element analysis on the corresponding high-fidelity and low-fidelity models to obtain the corresponding structural response values Update the structural analysis response data sets corresponding to the high-fidelity and low-fidelity models

[0039] Step 403: Based on the variable-fidelity surrogate model shown in Equation (4), use the updated sample data set to reconstruct and update the surrogate model. Repeat Step 204, 205 and Step Three until the optimal solution of the original optimization problem is obtained, and on the premise of satisfying constraints such as fiber continuity in adjacent regions, realize the optimal design of the curved fiber composite material structure.

[0040] The present invention utilizes the advantages of two variable stiffness methods, namely curved fiber placement and variable thickness layer dropping design. On the premise of satisfying process constraints such as fiber continuity in adjacent regions, it realizes the integrated and efficient optimization of discrete and continuous hybrid variables of the multi-region structure of curved fiber composite materials, effectively improving the mechanical properties of the composite material structure. Through the above optimal design of the curved fiber hybrid variable stiffness composite material structure, it is possible to efficiently determine the number of plies, ply thickness, and placement angle in the equal thickness laminate region, and at the same time effectively solve the design problem of the fiber continuity requirement in adjacent regions.

[0041] It further includes Step Five: The composite material structure obtained in Step Four is a hybrid variable stiffness design form that combines the ideas of curved fiber placement and variable thickness design, which can realize the equal stress lightweight design of the structure, further improve the structural efficiency of the composite material, solve the engineering technical problems in the application field of variable stiffness composite material structures, and have a broader application prospect.

[0042] The engineering technical problems in the application field of variable stiffness composite material structures solved in Step Five include: The optimization of the multi-region variable thickness structure of curved fiber variable stiffness composite materials not only needs to determine the optimal number of plies, ply thickness, and placement angle in the equal thickness region to ensure the overall mechanical properties of the structure, but also needs to avoid the sudden increase in stress caused by the drastic change in the placement angle between adjacent regions and consider problems such as low load transfer efficiency caused by layer dropping.

[0043] Beneficial effects

[0044] 1. The present invention discloses a method for optimizing the design of regional variable thickness of a curved fiber composite material structure. Considering the continuity of fiber placement between adjacent regions, the local sharing and variation technology of plies is proposed on the basis of introducing the concept of "base ply". The plies in the thinnest ply area are shared with the neighborhood to ensure the continuity of fiber changes between adjacent regions. The thickness of non-shared plies in the "base ply" is locally varied to achieve the purpose of keeping the total ply thickness unchanged or changing less than that before the local sharing operation. The ply design of the multi-region structure of the curved fiber variable stiffness composite material is gradually carried out in different regions, and finally a regional variable thickness design form of the overall structure of the composite material is formed.

[0045] 2. The present invention discloses a method for optimizing the variable thickness of curved fiber composite materials in different regions. By integrating the layer dropping mechanism into the mixed variable optimization strategy of the curved fiber variable stiffness composite material structure, the optimization of the number of layers, layer thickness and laying angle in the equal thickness region and the coordinated layer dropping design in the variable thickness region are achieved. Thus, a mixed variable stiffness optimization design method for the multi-region structure of curved fiber composite materials is formed, which is beneficial to expanding the utilization space of the curved fiber composite material structure and providing theoretical methods and technical support for its practical application in engineering structures.

[0046] 3. The invention discloses a method for optimizing the design of a curved fiber composite material structure with variable thickness in different regions. By defining the concept of "base ply", the number of plies, ply thickness, and laying angle of equal thickness laminates are determined, and the design requirements of fiber continuity in adjacent regions are satisfied. Since the design parameters are directly used as discrete and continuous variables, a mathematical model for mixed variable optimization problems is established in combination with process constraints, and the optimization results do not require excessive post-processing. The process constraints are organically combined with the optimization model and optimization strategy to effectively promote the implementation of the processing technology.

[0047] 4. The present invention discloses a method for optimizing the design of variable thickness in different regions of a curved fiber composite material structure, which belongs to the field of composite material structure design. The implementation method of the present invention is as follows: for a multi-region composite material structure, an initial "base ply" is created in different regions, and a mathematical model of the optimization problem with the number of plies, ply thickness, and fiber placement angle as design variables is defined; a variable fidelity proxy model is constructed to establish an approximate problem of the original optimization problem, and a genetic algorithm is used to solve the approximate optimization problem; a variable thickness layer dropping mechanism of local ply sharing and variation is proposed, and all individuals in the genetic algorithm population are modified accordingly to form a variable thickness design that satisfies regional continuity; sample points are dynamically added to update the proxy model, forming an efficient optimization design method for a hybrid variable stiffness composite material structure that integrates curved fiber placement and a variable thickness layer dropping mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1This is a flowchart of a method for optimizing the design of a variable-thickness structure in regions of a curved fiber composite material structure according to the present invention.

[0049] Figure 2 This is a two-region variable-stiffness composite laminate provided by an embodiment of the present invention. Detailed implementation manners

[0050] To make the technical problems solved by the present invention and the adopted technical solutions clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the invention and are not intended to limit the present invention. Additionally, it should be noted that, for the sake of convenience of description, only parts related to the present invention are shown in the drawings instead of all the content.

[0051] The implementation process of a method for optimizing the design of a variable-thickness structure in regions of a curved fiber composite material structure according to the present invention is as Figure 1 shown. Taking a two-region variable-stiffness composite laminate as an example, as Figure 2 shown, the purpose and advantages of a method for optimizing the design of a variable-thickness structure in regions of a curved fiber composite material structure disclosed by the present invention are described. The specific implementation steps are as follows:

[0052] Step 1: To achieve the synchronous optimization of the ply number, ply thickness, and laying angle, referring to the idea of the base structure method in structural topology optimization, an initial "base ply" is created. The optimal ply number is obtained by determining the existence of each single ply in the "base ply". Considering the design requirement of fiber continuity between adjacent regions of a multi-region composite material structure, the creation of the "base ply" related to each region is kept consistent. To reasonably express the existence of each single ply in the "base ply", a number field representing the existence of a single ply is defined, and a mathematical model of a hybrid variable-stiffness optimization problem integrating curved fibers and variable-thickness dropped plies is established.

[0053] Step 101: For a multi-region curved fiber composite laminate structure, an initial "base ply" with the same ply number is created for each region. Similar to the concept of the base structure in structural topology optimization, the necessary retained single plies and non-necessary redundant single plies in the region-divided "base ply" are determined through optimization calculations to find the optimal ply number. Among them, when the corresponding single ply is a non-necessary redundant ply, the ply thickness takes a small thickness value, and the laying angle takes a constant value; when the corresponding single ply is a necessary retained ply, the ply thickness takes an integer multiple of the ply reference thickness, and the laying angle continuously takes values within a given range.

[0054] Step 102: According to the initial "base ply" created in Step 101, the number fields Γ i (I) and Γ i (II) . Γ i (I)Represents the value range of the single-layer thickness that must be retained, Represents the value range of the non-essential redundant ply thickness. The two value range expressions are as follows:

[0055] Γ i (I) ={t i |t i =z·t b ,z∈N +},i = 1,…,n#(1)

[0056] Γ i (II) ={t i |t i =t b0},i = 1,…,n#(2)

[0057] Where, t i is the single-layer thickness corresponding to the i-th layer in the "basic ply"; t b is the ply reference thickness, determined by the corresponding fiber placement equipment, taking t b =0.127mm; z takes positive integers; t b0 is used to represent the small thickness of the non-essential redundant ply, taking t b0 =0.01t b ; n is the number of plies in the "basic ply".

[0058] Step 103: Based on the value range representing the existence of the single layer of the "basic ply" defined in Step 102, for the composite structure divided into S regions, the mathematical model of the hybrid variable stiffness optimization problem of the curve fiber and variable thickness layup fusion is established as follows:

[0059]

[0060] In the formula, x is the design variable, including the discrete ply thickness variable t and the fiber placement path parameter variable T; t si is the single-layer thickness corresponding to the i-th layer in the "basic ply" in region s; T i (p) is the p-th path parameter related to the i-th layer; T i (p) And respectively represent the lower and upper limits of the path parameter, taking T i (p) =0° and is a constant value, taking m is the number of path function parameters in a single layer, taking m = 2; f(X) and g j (X) are the objective function and constraint function of the optimization problem respectively, and J0 is the number of constraint functions. The path parameter Ti (p) The value is related to the minimum value of the single-layer thickness of the i-th layer in all regions. When min s {t si}∈Γ i (I) When it is the case, that is, the minimum value of the single-layer thickness of the i-th layer in the "base laying layer" corresponding to all regions takes values in the number field Γ i (I) It means that at least one single layer corresponding to a region is retained. At this time, T i (p) takes continuous values within the given upper and lower limit intervals; when max s {t si}∈Γ i (II) When it is the case, that is, the maximum value of the single-layer thickness of the i-th layer in the "base laying layer" corresponding to all regions takes values in the number field Γ i (II) It means that all single layers of the i-th layer corresponding to all regions in the "base laying layer" are deleted. At this time, T i (p) takes a constant For any two adjacent regions s and s′, assuming that the thickness of all laying layers in region s′ is less than that in region s, to meet the requirement of fiber continuity, it is necessary to ensure that the single-layer thickness corresponding to region s′ is a subset of the laying layer design of region s, that is, to satisfy t s′i -t si ≤0.

[0061] Step 2: Use the finite element analysis method to establish high-fidelity and low-fidelity models of the curve fiber variable stiffness composite material structure respectively. Based on the Latin hypercube sampling method, generate initial sample data points corresponding to the high-fidelity and low-fidelity finite element models respectively and conduct structural analysis. According to the structural analysis results, construct a variable-fidelity surrogate model, establish an approximate problem of the original optimization problem, and use the genetic algorithm to solve this approximate optimization problem.

[0062] Step 201: Establish finite element models of the curve fiber variable stiffness composite material structure with different mesh scales, generate high-fidelity and low-fidelity models for structural analysis, and provide model support for the subsequent construction of the variable-fidelity surrogate model.

[0063] Step 202: Based on the Latin hypercube sampling method, generate initial sample points corresponding to the high-fidelity and low-fidelity analysis models of the composite material structure established in Step 201 and Conduct finite element analysis of the variable stiffness composite material structure accordingly to obtain the structural analysis response data sets corresponding to the high-fidelity and low-fidelity models and

[0064] Step 203: Construct an exponential-form hybrid modified mode variable-fidelity surrogate model based on the sample points generated in Step 202 and their structural analysis response data, as follows:

[0065]

[0066] In the formula, is the constructed variable-fidelity surrogate model; is the surrogate model of the corresponding low-fidelity analysis model established based on Gaussian process regression; r is the exponential correction factor; δ(X) is the additive correction term of the variable-fidelity surrogate model.

[0067] Step 204: Based on the variable-fidelity surrogate model constructed in Step 203, establish an approximate optimization problem model for the hybrid variable-stiffness optimization design of curve fiber and variable-thickness delamination, as shown in the following formula:

[0068]

[0069] In the formula, and respectively represent the approximate objective function and the approximate constraint function constructed using the variable-fidelity surrogate model established in Step 203.

[0070] Step 205: For the approximate optimization problem model established in Step 204, use the genetic algorithm to perform hybrid variable optimization. In the process of optimizing and solving using the genetic algorithm, it is difficult to consider the fiber interruption phenomenon caused by delamination in adjacent regions, that is, the inequality constraint t s′i -t si ≤0 (s, s′ = 1,…, S) is not easy to be considered in the execution process of the genetic algorithm. This is mainly because it is difficult to determine in advance the layup design relationship between regions s and s′. Therefore, it is necessary to study a specific delamination mechanism to make any individual in the genetic algorithm population meet the design requirements of fiber continuity in adjacent regions.

[0071] Step Three: Considering that the designs corresponding to the individuals in the genetic algorithm population in Step Two do not meet the design requirements of fiber continuity in adjacent regions, propose a variable-thickness delamination mechanism of layup local sharing and mutation. After the mutation operation of the genetic algorithm, execute the variable-thickness delamination mechanism to correct all individuals in the genetic algorithm population, so as to form a variable-thickness design that meets the continuity of adjacent regions, improve the overall performance of the structure, and reduce the risk of structural failure.

[0072] Step 301: First, define two groups A and B, where the elements in group A include the regions with the thinnest layup thickness in the current design step, otherwise the corresponding regions are divided into the elements in group B. Initialize the region grouping, and all regions are divided into group B.

[0073] Step 302: For the ply design corresponding to any individual in the genetic algorithm population, compare the number of plies in each area of ​​the elements in group B, determine the area with the thinnest current ply thickness, and identify the neighborhood of the thinnest ply area from the elements in group B. Classify the area with the thinnest current ply thickness into group A, and the other areas into group B. Share the ply design of the current thinnest ply area with its neighborhood, so that the ply design of the thinner ply area is a subset of the thicker ply area in its neighborhood, and ensure the continuity of adjacent areas of the structure.

[0074] Step 303: In order to reduce the impact of the local ply sharing operation on the ply thickness in the adjacent area, a local mutation operator is introduced to make the non-shared ply thickness variable in the "base ply" corresponding to the neighborhood take values ​​within the range shown in equation (1) or (2). The mutation probability corresponding to the non-shared and deleted ply in the neighborhood is taken according to equation (6), and the mutation probability corresponding to the non-shared and retained ply is assigned according to equation (7), where t s′ is the total thickness of the ply in the thinnest ply area, t s is the total thickness of the ply in the neighborhood before the local sharing operation, t s′∩s is the ply thickness of the intersection of the thinnest ply area and the neighboring ply, t d is the total thickness of the ply deleted in the neighborhood after the local sharing operation. The local mutation probabilities shown in equations (6) and (7) have the equation relationship shown in equation (8), which achieves the consistency of the total thickness of the neighborhood ply before and after the local sharing operation in terms of probability.

[0075]

[0076] P m2 ·(t s -t s′∩s )-t d P m1 =t s′ -t s′∩s #(8)

[0077] Step 304: Determine whether the elements in group B are empty. If it is an empty set, after local ply sharing and mutation operations, the ply design corresponding to the relevant individuals in the population can meet the design requirements of fiber continuity in any adjacent region. If B is a non-empty set, repeat the above steps 302 to 303 until B is an empty set, so that the ply design of the multi-region structure of the curved fiber composite material can be gradually implemented by region, realizing the overall variable thickness layer loss design of the structure.

[0078] Step 305: The variable thickness layer dropping mechanism is placed in the genetic algorithm after the compilation operator operation is completed and before the individual fitness calculation, so that the variable thickness design does not destroy the established regional connectivity due to the implementation of the genetic operator, and all individuals in the genetic algorithm population are corrected to form a variable thickness design that satisfies the continuity of adjacent regions.

[0079] Step 4: According to the optimization results output from steps 2 to 3, the convergence of the optimization process is judged. If the current optimization result meets the convergence judgment condition, the current optimization result is output as the final optimization design solution, and the optimization process ends. If the convergence judgment condition is not met, the current optimization result is added to the sample data point set to update the proxy model, and the above steps 2 to 3 are repeated until the convergence judgment condition is met.

[0080] Step 401: In the kth iteration of the optimization process, after the genetic algorithm and the variable thickness layer dropping mechanism, the current optimization result X is output. (k) , and combine it with the optimization result X obtained in the (k-1)th iteration (k-1) The convergence is judged by the following formula:

[0081]

[0082] Where ∈ is the convergence control accuracy, and ∈=0.001 is taken.

[0083] Step 402: According to the convergence judgment of step 401, if the optimization result obtained by the kth iteration does not meet the convergence judgment condition, the current optimization result is added to the sample data point set corresponding to the high and low fidelity models, that is, Perform finite element analysis on high and low fidelity models to obtain corresponding structural response values Update the structural analysis response datasets corresponding to high and low fidelity models

[0084] Step 403: Based on the variable fidelity proxy model shown in formula (4), the proxy model is reconstructed and updated using the updated sample data set. Steps 204, 205 and step 3 are repeated until the optimal solution of the original optimization problem is obtained, and the optimal design of the curved fiber composite material structure is achieved under the premise of satisfying constraints such as the continuity of fibers in adjacent regions.

[0085] against Figure 2 The two-region variable stiffness composite laminate subjected to distributed load is shown in the figure. The fiber direction changes linearly along the x-axis. The fiber angle θ at any position of the composite single layer is as shown in formula (10), where a represents the length of the laminate, T0 and T1 are fiber path parameters, which represent the angle between the fiber at the origin and at x = a / 2 and the x-axis, respectively. The parameters of the single-layer composite material are: elastic modulus E1 = 134 GPa, E2 = 7.71 GPa, shear modulus G 12 =G 12 =4.31GPa, G 22 =2.76GPa, material Poisson's ratio v 12 =v 13 =0.13, v 23= 0.396, the single-layer reference thickness t b0 = 0.127 mm, the side length of the two-region variable stiffness composite laminate is a = 100 mm. For this two-region composite laminate, low-fidelity and high-fidelity finite element analysis models are established. The number of finite elements in the low-fidelity analysis model is 625 (25×25), and the number of finite elements in the high-fidelity analysis model is 10,000 (100×100). With maximizing the critical buckling load as the design goal, the maximum fiber curvature radius is limited to 4.00 m -1 、the equivalent maximum number of plies is 16, and a regional variable thickness optimization is carried out with the integrated number of plies, ply thickness, and laying angle as design variables. Starting from the "basic plies" with two different numbers of plies, the optimization results are shown in Table 1. When the number of "basic plies" increases from less to more, the design space also increases accordingly, and it is easier to obtain an optimized design with a higher critical buckling load.

[0086]

[0087] Table 1

[0088]

[0089] It also includes Step Five: The composite material structure obtained in Step Four is a hybrid variable stiffness design form that combines the idea of curved fiber placement and variable thickness design, which can achieve the equal stress lightweight design of the structure, further improve the efficiency of the composite material structure, solve the engineering technical problems in the application field of variable stiffness composite material structures, and has a broader application prospect.

[0090] The engineering technical problems in the application field of variable stiffness composite material structures solved in Step Five include: The optimization of the multi-region variable thickness structure of curved fiber variable stiffness composite materials not only needs to determine the optimal number of plies, ply thickness, and laying angle within the equal thickness region to ensure the overall mechanical properties of the structure, but also needs to avoid the sudden increase in stress caused by the drastic change in the laying angle between adjacent regions and consider problems such as low load transfer efficiency caused by layer loss.

[0091] The above are only the specific steps of the present invention and do not constitute any limitation to the protection scope of the present invention; it can be extended and applied to the field of curved fiber variable stiffness composite material structure optimization. Any technical solutions formed by equivalent transformation or equivalent replacement belong to the scope of the power protection of the present invention.

[0092] In summary, the above is only the preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for optimizing the design of a curved fiber composite material structure with variable thickness in different regions, characterized in that: The following steps are involved: Step 1: Establish a mathematical model for the hybrid variable stiffness optimization problem of curved fiber and variable thickness layer loss fusion; Step 2: using the finite element analysis method, establishing a high-fidelity finite element model of the curved fiber variable stiffness composite material structure and a low-fidelity finite element model of the curved fiber variable stiffness composite material structure; Generate initial sample data points for a high-fidelity finite element model based on a Latin hypercube sampling method, perform structural analysis using the high-fidelity finite element model, and obtain structural analysis results of the high-fidelity finite element model; generating initial sample data points for a low-fidelity finite element model based on a Latin hypercube sampling method, and performing structural analysis using the low-fidelity finite element model to obtain structural analysis results of the low-fidelity finite element model; A variable-fidelity proxy model is constructed according to the structural analysis results of the high-fidelity finite element model and the structural analysis results of the low-fidelity finite element model; Step 3: Based on the variable fidelity proxy model constructed in step 2, an approximate model of the optimization problem in step 1 is established, and a genetic algorithm is used to solve the approximate optimization problem. During the solution process, a variable thickness layer dropping mechanism of local ply sharing and mutation is used to correct all individuals in the genetic algorithm population to meet the design requirements of fiber continuity in adjacent areas. Step 4: According to the optimization result outputted in step 3, the convergence of the optimization process is judged. If the current optimization result meets the convergence judgment condition, the current optimization result is outputted as the final optimization design scheme, and the optimization process ends. If the convergence judgment condition is not met, the current optimization result is added to the sample data point to update the variable fidelity proxy model, and step three is entered again until the convergence judgment condition is met to obtain the final optimized design solution.

2. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 1, characterized in that: In the step 1, a number field representing the existence of a single layer is defined, and a method for establishing a mathematical model for a hybrid variable stiffness optimization problem of a fusion of curved fiber and variable thickness layer loss is as follows: Step 101, facing the multi-region curved fiber composite laminate structure, each region creates an initial "base layer" with the same number of layers, and determines the necessary single layers and unnecessary redundant single layers in the "base layer" of each region through optimization calculation to achieve the optimization of the optimal number of layers; wherein, when the corresponding single layer is a unnecessary redundant layer, the single layer thickness is a small value, and the laying angle is a constant value; when the corresponding single layer is a necessary reserved layer, the single layer thickness is an integer multiple of the layer reference thickness, and the laying angle is continuously taken within a given range; Step 102, based on the initial "base layer" created in step 101, define the number field Γ i (I) With Γ i (II) , Γ i (I) Indicates the necessary range of values ​​for the single layer thickness, Γ i (II) The value domain of the non-essential redundant ply thickness is represented by the following two domain expressions: Γ i (I) ={t i |t i =z·t b ,z∈N + },i=1,…,n Γ i (II) ={t i |t i =t b0 },i=1,…,n Among them, t i is the single layer thickness corresponding to the i-th layer in the "base layer"; t b is the base thickness of the ply; z is a positive integer; t b0 It is used to indicate the thickness of unnecessary redundant plies; n is the number of plies in the "base ply"; Step 103, based on the existence number field of the "base ply" single layer defined in step 102, for the composite material structure divided into S regions, a mathematical model of the hybrid variable stiffness optimization problem of the fusion of curved fiber and variable thickness layer loss is established as follows: Where X is the design variable, including the discrete ply thickness variable t and the fiber placement path parameter variable T; t si T represents the single layer thickness corresponding to the i-th layer in the “base layer” in region s; i (p) is the pth path parameter associated with the i-th layer; T i (p) and Respectively represent the lower and upper limits of the path parameters, is a constant; m is the number of path function parameters in a single layer; f(X) and g j (X) are the objective function and constraint function of the optimization problem, J0 is the number of constraint functions, and the path parameter T i (p) The value of is related to the minimum single layer thickness of the i-th layer in all regions. s {t si }∈Γ i (I) When the thickness of the i-th single layer in the "base layer" corresponds to the minimum value of all regions in the number domain Γ i (I) The value in the middle means that at least one region corresponding to the i-th layer is retained. At this time, T i (p) Continuously take values ​​within the given upper and lower limits; when max s {t si }∈Γ i (II) When the thickness of the i-th single layer in the "base layer" corresponds to the maximum value of all regions in the number domain Γ i (II) The value in the middle means that the i-th single layer corresponding to all areas in the "base layer" is deleted. At this time, T i (p) Take constant For any two adjacent regions s and s′, assuming that the thickness of all plies in the s′ region is smaller than that in the s region, in order to meet the fiber continuity requirements, it is necessary to ensure that the thickness of the corresponding single layer in the s′ region is a subset of the ply design in the s region, that is, to satisfy t s′i -t si ≤0.

3. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 2, characterized in that: In the step 2, the method for constructing the variable fidelity proxy model is: Step 201, establishing a finite element model of a curved fiber variable stiffness composite material structure with different grid scales, and generating a high- and low-fidelity model for structural analysis; Step 202, based on the Latin hypercube sampling method, generates initial sample points of the high and low fidelity analysis model of the composite material structure established in step 201 and Based on this, finite element analysis of variable stiffness composite structures is performed to obtain structural analysis response data sets corresponding to high and low fidelity models. and Step 203, based on the sample points and their structural analysis response data generated in step 202, construct an exponential hybrid modified mode variable fidelity proxy model, as shown below: In the formula, For the constructed variable fidelity proxy model; is the proxy model corresponding to the low-fidelity analysis model established based on Gaussian process regression; r is the exponential correction factor; δ(X) is the additive correction term of the variable-fidelity proxy model.

4. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 3, characterized in that: In step 3, the approximate optimization problem model established is: In the formula, and They respectively represent the approximate objective function and the approximate constraint function constructed using the variable-fidelity proxy model established in step 203 .

5. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 4, characterized in that: In the step 3, according to the established approximate optimization problem model, a genetic algorithm is used to perform mixed variable optimization. In the genetic algorithm optimization solution process, it is necessary to determine a variable thickness layer dropping mechanism so that any individual in the genetic algorithm population meets the design requirements of fiber continuity in adjacent regions; The variable thickness layer dropping mechanism is: Step 301: In the genetic algorithm optimization process, it is difficult to consider the fiber interruption phenomenon caused by the loss of layers in adjacent regions, that is, the inequality constraint t s′i -t si ≤0(s,s′=1,…,S) is not easy to be considered in the execution process of the genetic algorithm. This is mainly because the relationship between the ply design of area s and s′ is difficult to determine in advance. Therefore, it is necessary to study a specific variable thickness layer dropping mechanism. First, two groups A and B are defined, where the elements in group A contain the thinnest ply thickness area in the current design step, otherwise the corresponding area is divided into the elements of group B. The area grouping is initialized, and all areas are divided into group B; Step 302: for the ply design corresponding to any individual in the genetic algorithm population, compare the number of plies in each area of ​​the elements in group B, determine the area with the thinnest current ply thickness, identify the neighborhood of the thinnest ply area from the elements in group B, classify the area with the thinnest current ply thickness into group A, and classify other areas into group B; share the ply design of the current thinnest ply area with its neighborhood, so that the ply design of the thinner ply area is a subset of the thicker ply area in its neighborhood, and ensure the continuity of adjacent areas of the structure; Step 303: In order to reduce the impact of the local ply sharing operation on the ply thickness in the adjacent area, a local mutation operator is introduced to make the non-shared ply thickness variable in the "base ply" corresponding to the neighborhood take values ​​within the value range. The mutation probability corresponding to the non-shared and deleted ply in the neighborhood is P m1 , the mutation probability corresponding to the non-shared and reserved ply is P m2 , where t s′ is the total thickness of the ply in the thinnest ply area, t s is the total thickness of the ply in the neighborhood before the local sharing operation, t s′∩s is the ply thickness of the intersection of the thinnest ply area and the neighboring ply, t d Total thickness of the ply removed from the neighborhood after the local sharing operation; P m2 ·(t s -t s′∩s )-t d P m1 =t s′ -t s′∩s Step 304, determine whether the elements in group B are empty. If it is an empty set, after local ply sharing and mutation operations, the ply design corresponding to the relevant individuals in the population meets the design requirements of fiber continuity in any adjacent region. If B is a non-empty set, repeat the above steps 302 to 303 until B is an empty set, so that the ply design of the multi-region structure of the curved fiber composite material is gradually carried out by region, realizing the overall variable thickness layer loss design of the structure.

6. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 4, characterized in that: In step 3, the method for solving the approximate optimization problem using a genetic algorithm is: The variable thickness layer dropping mechanism is placed after the compilation operator operation in the genetic algorithm is completed and before the individual fitness calculation, so that the variable thickness design does not destroy the established regional connectivity due to the implementation of the genetic operator, and all individuals in the genetic algorithm population are corrected to form a variable thickness design that satisfies the continuity of adjacent regions.

7. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 6, characterized in that: In step 4, the method for judging the convergence of the optimization process is: Step 401: In the kth iteration of the optimization process, after the genetic algorithm and the variable thickness layer dropping mechanism, the current optimization result X is output. (k) , and combine it with the optimization result X obtained in the (k-1)th iteration (k-1) The convergence is judged by the following formula: Where, ∈ is the convergence control accuracy; Step 402: According to the convergence judgment in step 401, if the optimization result obtained in the kth iteration does not meet the convergence judgment condition, the current optimization result is added to the sample data point set corresponding to the high and low fidelity models, that is, Perform finite element analysis on high and low fidelity models to obtain corresponding structural response values Update the structural analysis response datasets corresponding to high and low fidelity models Step 403, based on the variable fidelity proxy model shown in formula (4), the proxy model is reconstructed and updated using the updated sample data set, and steps 204, 205 and step 3 are repeated until the optimal solution of the original optimization problem is obtained, and the optimal design of the curved fiber composite material structure is achieved under the premise of satisfying constraints such as the continuity of fibers in adjacent regions.

8. The method for optimizing the design of a curved fiber composite material structure with regional variable thickness according to claim 7, characterized in that: The composite material structure obtained in step four is a hybrid variable stiffness design form that integrates curved fiber placement and variable thickness design ideas. The optimal number of layers, layer thickness and placement angle in the equal thickness area are obtained to ensure the overall mechanical properties of the structure. At the same time, the stress surge caused by the drastic change of the placement angle between adjacent areas and the low force transmission efficiency caused by layer loss are avoided. The equal stress lightweight design of the structure can be achieved, further improving the efficiency of the composite material structure.

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