A method for microstructure optimization design of fiber-reinforced flexible composite materials

Abstract

This application is applicable to the field of flexible composite material structure design, and provides a fiber-reinforced flexible composite material microstructure optimization design method. Based on the microstructure parameters of the fiber fabric material and the geometric dimensions of the flexible soft substrate material, a representative volume unit geometric model is constructed, and periodic constraints are performed, and finite element calculations are performed to calculate the relative error between the simulated stress-elongation curve and the target stress-elongation curve. With the relative error as the optimization target, a genetic algorithm is used to optimize the microstructure design of the fiber fabric material. This method can search for the optimal microstructure of the fiber fabric material according to the target stress-elongation curve of the fiber-reinforced flexible composite material, thereby effectively reducing the design cost and improving the design efficiency.

Description

Technical Field

[0001] The present application belongs to the field of flexible composite material structure design, and in particular to the microstructure optimization design of flexible soft matrix composite materials. Background Art

[0002] Fiber reinforced flexible composite materials are based on flexible soft materials and fiber fabric structures as reinforcements. Due to their excellent flexibility and lightweight properties, they are widely used in soft robots, flexible actuators, artificial muscles, flexible sensors, wearable devices, flexible deployable structures, aerospace sealing structures, and stratospheric airships. Fiber fabric structures have strong designability, and their microstructures have a great influence on the mechanical properties and sealing properties of fiber reinforced flexible composites. Therefore, in order to ensure that fiber reinforced flexible composites have excellent performance in long-term service, the optimization design of fiber fabric microstructure is of great significance for the design and application of fiber reinforced flexible composites.

[0003] The diversity and complexity of the microstructure of fiber fabrics poses a huge challenge to the design of fiber-reinforced flexible composites. The current design methods make it difficult to design fiber-reinforced flexible composites that meet performance requirements at the microscale. The main difficulty lies in how to automatically construct the mapping relationship between the microstructure optimization variables and the optimization objectives of fiber-reinforced flexible composites, and how to apply periodic boundary conditions. In addition, the matrix of fiber-reinforced flexible composites is a flexible soft material with super-visco-pseudo-elastic properties, and it is also difficult to accurately describe its mechanical behavior.

[0004] These factors greatly increase the difficulty of optimizing the microstructure of fiber-reinforced flexible composites.

[0005] Therefore, it is necessary to propose a new technical solution to overcome the above technical problems and achieve the optimal design of the microstructure of flexible soft matrix composite materials. Summary of the invention

[0006] A fiber-reinforced flexible composite microstructure optimization design method is used to solve the above technical problems. The method can search for the optimal microstructure of fiber fabric materials according to the target stress-elongation curve of the fiber-reinforced flexible composite material, thereby effectively reducing the design cost, improving the design efficiency, and providing guidance for the innovative design of the microstructure of fiber-reinforced flexible composite materials.

[0007] Specifically, the embodiment of the present application provides a method for optimizing the microstructure of a fiber-reinforced flexible composite material, which is characterized by comprising the following steps:

[0008] S1. Setting the optimization parameters of the fiber-reinforced flexible composite material to the microscopic structural parameters of the fiber fabric material, the parameters include: the angle α between the fiber bundles, the cross-sectional radius R of the fiber bundles, and the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles; wherein the initial value of each parameter can be preset or randomly selected;

[0009] S2. Based on the microscopic structural parameters of the fiber fabric material and the geometric dimensions of the flexible soft substrate material given by the optimization algorithm, a representative volume unit geometric model is constructed, and material properties are set for the fiber fabric material and the flexible soft substrate material respectively; wherein the dimensions of the representative volume unit geometric model are larger than a geometric period of the fiber fabric material;

[0010] S3, merging the fiber fabric material and the flexible soft base material, retaining the boundaries of the two, and discretizing the representative volume unit;

[0011] S4, selecting two nodes with the shortest distance on opposite surfaces of the representative volume unit as associated nodes, and applying displacement constraints to the associated nodes; wherein the representative volume unit is a cuboid structure;

[0012] S5. Apply a displacement load in a horizontal direction by coupling a reference point with an end face of the representative volume unit; wherein the horizontal direction is the direction in which the long side of the cross section of the representative volume unit is located;

[0013] S6, extracting the load F and displacement U of the reference point along the horizontal direction, and calculating the simulated stress T and elongation λ of the representative volume unit based on the load F, displacement U and geometric dimensions of the representative volume unit to obtain a simulated stress-elongation curve;

[0014] S7, calculating the relative error between the simulated stress-elongation curve and the target stress-elongation curve, taking the relative error as the optimization target, and using a genetic algorithm to optimize the micro-structure parameters of the fiber fabric material; the target stress-elongation curve is preset;

[0015] S8. When the number of optimizations reaches the set maximum number of optimizations, or the relative error is less than the set threshold, the optimization is terminated; otherwise, steps S2-S7 are repeated.

[0016] Among them, in step S2, the material properties of the fiber fabric material and the flexible soft substrate material are set, specifically including: the fiber fabric material property is set to elasticity, and the Mooney-Rivlin model is used to define the flexible soft substrate material property; wherein the material properties of the fiber fabric material include: elastic modulus and Poisson's ratio, and the material properties of the flexible soft substrate material include: constitutive parameters of the Mooney-Rivlin model.

[0017] Among them, in step S4, the method for selecting the associated node specifically includes:

[0018] S41. Select any point on the left and right cross sections of the representative volume unit as a node pair, and use the node pair that meets the following conditions as an associated node:

[0019]

[0020] Among them, (x A ,x B )、(y A ,y B )、(z A ,z B ) are the XYZ axis coordinates of point A and point B, respectively, and point A and point B are points on the left and right cross sections;

[0021] S42, randomly selecting a point on the front and rear cross sections of the representative volume unit as a node pair, and taking the node pair that meets the following conditions as an associated node:

[0022]

[0023] Among them, (x C ,x D )、(y C ,y D )、(z C ,z D ) are the XYZ axis coordinates of point C and point D, respectively, and point C and point D are points on the front and rear sections, respectively.

[0024] Wherein, in step S6, the calculation formula of the stress T and the elongation λ is:

[0025]

[0026] Wherein, L, W, and H represent the length, width, and height of the representative volume unit, respectively.

[0027] Wherein, in step S7, the calculation formula of the relative error is:

[0028]

[0029] Wherein, Num represents the number of representative points on the simulated stress-elongation curve and the target stress-elongation curve, and the representative points on the simulated stress-elongation curve correspond one to one to the representative points on the target stress-elongation curve; and They respectively represent the stress values ​​corresponding to the i-th representative points on the simulated stress-elongation curve and the target stress-elongation curve.

[0030] Wherein, step S7 also includes setting the value ranges of various parameters of the fiber fabric material respectively.

[0031] In step S7, the optimization problem is expressed as:

[0032] Find X={α,R,L1,L2}

[0033] Min Y={Error}

[0034] Stα L ≤α≤α U

[0035] R L ≤R≤R U

[0036]

[0037]

[0038] Among them, X represents the variables to be optimized, including the angle α between the fiber bundles, the radius of the fiber bundle cross section R, the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles, α L , α U , R L , R U , They represent the upper and lower bounds of the value ranges of α, R, L1, and L2 respectively; Y represents the optimization target, specifically the relative error Error.

[0039] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0040] The present invention provides a method for optimizing the microstructure of a fiber-reinforced flexible composite material. Based on the microstructure parameters of the fiber fabric material and the geometric dimensions of the flexible soft substrate material, a representative volume unit geometric model is constructed, and periodic constraints are performed, and finite element calculations are performed to calculate the relative error between the simulated stress-elongation curve and the target stress-elongation curve. With the relative error as the optimization target, a genetic algorithm is used to optimize the microstructure parameters of the fiber fabric material. The method can search for the optimal microstructure of the fiber fabric material according to the target stress-elongation curve of the fiber-reinforced flexible composite material, thereby effectively reducing the design cost and improving the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

[0042] Figure 1 It is a flow chart of a method for optimizing the microstructure of a fiber-reinforced flexible composite material provided in an embodiment of the present application;

[0043] Figure 2 is a schematic diagram of the microstructure of a fiber-reinforced flexible composite material provided in an embodiment of the present application;

[0044] FIG3( a ) is a schematic diagram of a selection rule for an associated node provided in an embodiment of the present application;

[0045] FIG3( b ) is a schematic diagram of periodic boundary conditions of a representative volume unit provided in an embodiment of the present application;

[0046] Figure 4 is a calculation diagram of the optimization target Error provided in an embodiment of the present application;

[0047] FIG5( a ) is a curve showing the change of relative error Error with the number of optimizations provided in an embodiment of the present application;

[0048] FIG5( b ) is a stress-elongation curve of the optimal result provided by an embodiment of the present application. DETAILED DESCRIPTION

[0049] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0050] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or combinations thereof.

[0051] It should also be understood that the term “and / or” used in the specification and appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0052] As used in the specification and appended claims of this application, the term "if" can be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [described condition or event] is detected" or "in response to detecting [described condition or event]", depending on the context.

[0053] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", "fourth", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0054] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0055] Figure 1 A flowchart of a method for optimizing the microstructure of a fiber-reinforced flexible composite material provided in an embodiment of the present application is shown. Figure 1 As shown, the fiber-reinforced flexible composite material microstructure optimization design method specifically includes:

[0056] S1. Setting the optimization parameters of the fiber-reinforced flexible composite material to the microscopic structural parameters of the fiber fabric material, the parameters include: the angle α between the fiber bundles, the cross-sectional radius R of the fiber bundles, and the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles; wherein the initial value of each parameter can be preset or randomly selected;

[0057] For detailed settings of each parameter, please refer to Figure 2 ;

[0058] S2. Based on the microscopic structural parameters of the fiber fabric material and the geometric dimensions of the flexible soft substrate material given by the optimization algorithm, a representative volume unit geometric model is constructed, and material properties are set for the fiber fabric material and the flexible soft substrate material respectively; wherein the dimensions of the representative volume unit geometric model are larger than a geometric period of the fiber fabric material;

[0059] The flexible soft substrate material is a rectangular parallelepiped structure, and the geometric dimensions can be set to 5*3*0.7mm.

[0060] Among them, the above-mentioned representative volume unit modeling is parametric modeling, and the changes in the microstructure of the fiber-reinforced flexible composite material can be achieved subsequently by modifying the specific values ​​of the above-mentioned parameters.

[0061] Among them, in step S2, the material properties of the fiber fabric material and the flexible soft substrate material are set, specifically including: the fiber fabric material property is set to elasticity, and the Mooney-Rivlin model is used to define the flexible soft substrate material property; wherein the material properties of the fiber fabric material include: elastic modulus and Poisson's ratio, and the material properties of the flexible soft substrate material include: constitutive parameters of the Mooney-Rivlin model.

[0062] The material properties of the flexible soft matrix can be defined by the material properties of the finite element software ABAQUS or by writing subroutines Uhyper or Umat;

[0063] Specifically, the present application uses the Mooney-Rivlin model provided by the finite element software ABAQUS to define the material properties of the flexible soft matrix, and the material properties of the fiber fabric are set to elasticity. The specific material parameters are shown in Table 1;

[0064] Table 1 Material parameters of flexible soft matrix and fiber bundle

[0065]

[0066] In the above table, they are the constitutive parameters of the Mooney-Rivlin model, as well as the elastic modulus and Poisson's ratio of the fiber fabric material.

[0067] S3, merging the fiber fabric material and the flexible soft base material, retaining the boundaries of the two, and discretizing the representative volume unit;

[0068] The representative volume units are discretized to reduce the number of grids to improve computational efficiency while ensuring computational accuracy.

[0069] Since the cross section of the fiber bundle is circular, a periodic grid cannot be formed. For a non-periodic grid, a script for applying periodic boundary conditions needs to be written. The periodic boundary condition application method is described in the following step S4.

[0070] S4, selecting two nodes with the shortest distance on opposite surfaces of the representative volume unit as associated nodes, and applying displacement constraints to the associated nodes; wherein the representative volume unit is a cuboid structure;

[0071] Among them, the Equation module in ABAQUS is used to impose displacement constraints on the associated nodes;

[0072] The process of determining the associated nodes is shown in Figure 3(a), which specifically includes:

[0073] S41, randomly selecting a point on the left and right cross sections of the representative volume unit as a node pair, and taking the node pair that meets the following conditions as an associated node:

[0074]

[0075] Among them, (x A ,x B )、(y A ,y B )、(z A ,z B ) are the XYZ axis coordinates of point A and point B, respectively, and point A and point B are points on the left and right cross sections, respectively;

[0076] S42, randomly selecting a point on the front and rear cross sections of the representative volume unit as a node pair, and taking the node pair that meets the following conditions as an associated node:

[0077]

[0078] Among them, (x C ,x D )、(y C ,y D )、(z C ,z D ) are the XYZ axis coordinates of point C and point D, respectively, and point C and point D are points on the front and rear sections, respectively.

[0079] In addition, since the representative volume element is modeled through the thickness, there is no need to apply periodic boundary conditions in the thickness direction of the representative volume element. The representative volume element after applying periodic boundary conditions is shown in Figure 3(b).

[0080] S5. Apply a displacement load in a horizontal direction by coupling a reference point with an end face of the representative volume unit; wherein the horizontal direction is the direction in which the long side of the cross section of the representative volume unit is located;

[0081] For details, see Figure 2 As shown, direction 1 is the horizontal direction.

[0082] Specifically, the reference point is a reference point in the finite element software ABAQUS. By coupling the reference point with the end face of the representative volume unit, the displacement of the end face can be controlled by setting the displacement of the reference point.

[0083] Specifically, the displacement load is 1 mm, the tensile strain is 20%, and the displacement of the other end of the representative volume unit in the tensile direction is ensured to be 0.

[0084] It can be seen that the above steps S1-S5 construct representative volume units based on the finite element processing method and apply periodic boundary conditions. The above processes can be written in the form of Python scripts respectively.

[0085] S6, extracting the load F and displacement U of the reference point along the horizontal direction, and calculating the simulated stress T and elongation λ of the representative volume unit based on the load F, displacement U and geometric dimensions of the representative volume unit to obtain a simulated stress-elongation curve;

[0086] This step can also be written in the form of a Python script.

[0087] Wherein, the calculation formula of the stress T and the elongation λ is:

[0088]

[0089] Wherein, L, W, and H represent the length, width, and height of the representative volume unit, respectively. Specifically, L=5 mm, W=3 mm, and H=0.7 mm can be set.

[0090] In summary, in steps S1-S6, Python scripts for representative volume unit construction, periodic boundary condition application, and stress and elongation calculation are written. Next, we only need to write a MATLAB program, call the finite element software ABAQUS to execute the above Python script, and update the variables to be optimized through the optimization algorithm. Please refer to the subsequent steps for details.

[0091] S7, calculating the relative error between the simulated stress-elongation curve and the target stress-elongation curve, taking the relative error as the optimization target, and using a genetic algorithm to optimize the micro-structure parameters of the fiber fabric material; the target stress-elongation curve is preset;

[0092] The calculation formula of the relative error is:

[0093]

[0094] Wherein, Num represents the number of representative points on the simulated stress-elongation curve and the target stress-elongation curve, and the representative points on the simulated stress-elongation curve correspond one to one to the representative points on the target stress-elongation curve; and represent the stress values ​​corresponding to the i-th representative points on the simulated stress-elongation curve and the target stress-elongation curve respectively;

[0095] Before optimization, the value ranges of various parameters of the fiber fabric material need to be preset. The value ranges of various parameters are shown in Table 2;

[0096] Table 2 Value range of optimization variables

[0097]

[0098]

[0099] When performing the first optimization, the initial value of each parameter to be optimized is set, such as by random selection, and the set initial value should be within the value range of each parameter to be optimized.

[0100] Specifically, in order to simplify the optimization process, L1 and L2 may be set equal.

[0101] Specifically, the optimization problem is expressed as:

[0102] Find X={α,R,L1,L2}

[0103] Min Y={Error}

[0104] Stα L ≤α≤α U

[0105] R L ≤R≤R U

[0106]

[0107]

[0108] Among them, X represents the variables to be optimized, including the angle α between the fiber bundles, the radius of the fiber bundle cross section R, the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles, α L , α U , R L , R U , They represent the upper and lower bounds of the value ranges of α, R, L1, and L2 respectively; Y represents the optimization target, specifically the relative error Error.

[0109] The finite element calculation results of the simulated stress-elongation curve, the target stress-elongation curve, and the optimization target calculation are shown in the figure below. Figure 4 shown.

[0110] Specifically, a genetic algorithm is used for optimization, and the population size is set to 100, the crossover probability is set to 0.75, and the evolutionary generations are set to 1000.

[0111] S8. When the number of optimizations reaches the set maximum number of optimizations, or the relative error is less than the set threshold, the optimization is terminated; otherwise, steps S2-S7 are repeated.

[0112] Among them, the maximum number of optimization times and the threshold can be set in advance according to actual conditions.

[0113] After the optimization is completed, the optimal microstructure of the fiber-reinforced flexible composite material is output.

[0114] Among them, after multiple optimizations, the relative error Error changes with the number of optimizations and the optimal result stress-elongation curve are as follows: Figure 5(a) and 5(b) shown.

[0115] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0116] In the embodiments provided in the present application, it should be understood that the disclosed devices / network equipment and methods can be implemented in other ways. For example, the device / network equipment embodiments described above are merely schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0117] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0118] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for optimizing the microstructure of a fiber-reinforced flexible composite material, characterized in that: The following steps are involved: S1. Setting the optimization parameters of the fiber-reinforced flexible composite material to the microscopic structural parameters of the fiber fabric material, the parameters include: the angle α between the fiber bundles, the cross-sectional radius R of the fiber bundles, and the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles; wherein the initial value of each parameter can be preset or randomly selected; S2. Based on the microscopic structural parameters of the fiber fabric material and the geometric dimensions of the flexible soft substrate material given by the optimization algorithm, a representative volume unit geometric model is constructed, and material properties are set for the fiber fabric material and the flexible soft substrate material respectively; wherein the dimensions of the representative volume unit geometric model are larger than a geometric period of the fiber fabric material; S3, merging the fiber fabric material and the flexible soft base material, retaining the boundaries of the two, and discretizing the representative volume unit; S4, selecting two nodes with the shortest distance on opposite surfaces of the representative volume unit as associated nodes, and applying displacement constraints to the associated nodes; wherein the representative volume unit is a cuboid structure; S5. Apply a displacement load in a horizontal direction by coupling a reference point with an end face of the representative volume unit; wherein the horizontal direction is the direction in which the long side of the cross section of the representative volume unit is located; S6, extracting the load F and displacement U of the reference point along the horizontal direction, and calculating the simulated stress T and elongation λ of the representative volume unit based on the load F, displacement U and geometric dimensions of the representative volume unit to obtain a simulated stress-elongation curve; S7, calculating the relative error between the simulated stress-elongation curve and the target stress-elongation curve, taking the relative error as the optimization target, and using a genetic algorithm to optimize the micro-structure parameters of the fiber fabric material; the target stress-elongation curve is preset; S8. When the number of optimizations reaches the set maximum number of optimizations, or the relative error is less than the set threshold, the optimization is terminated, otherwise, steps S2-S7 are repeated; In step S4, the method for selecting the associated node specifically includes: S41. Select any point on the left and right cross sections of the representative volume unit as a node pair, and use the node pair that meets the following conditions as an associated node: min[\sqrt {{({x}_{A}-{x}_{B})}^{2}+{({y}_{A}-{y}_{B})}^{2}+{({z}_{A}-{z}_{B})}^{2}}] ; in, , , are the XYZ axis coordinates of point A and point B, respectively, and point A and point B are points on the left and right cross sections; S42, randomly selecting a point on the front and rear cross sections of the representative volume unit as a node pair, and taking the node pair that meets the following conditions as an associated node: min[\sqrt {{({x}_{C}-{x}_{D})}^{2}+{({y}_{C}-{y}_{D})}^{2}+{({z}_{C}-{z}_{D})}^{2}}] ; in, , , are the XYZ axis coordinates of point C and point D respectively, and point C and point D are points on the front and rear sections respectively.

2. The method according to claim 1, characterized in that In step S2, material properties are set for the fiber fabric material and the flexible soft substrate material, specifically including: the fiber fabric material property is set to elasticity, and the Mooney-Rivlin model is used to define the flexible soft substrate material property; wherein the material properties of the fiber fabric material include: elastic modulus and Poisson's ratio, and the material properties of the flexible soft substrate material include: constitutive parameters of the Mooney-Rivlin model.

3. The method according to claim 1, characterized in that In step S6, the calculation formula of the stress T and the elongation λ is: ， ； Wherein, L, W, and H represent the length, width, and height of the representative volume unit, respectively.

4. The method according to claim 1, characterized in that In step S7, the calculation formula of the relative error is: ； Wherein, Num represents the number of representative points on the simulated stress-elongation curve and the target stress-elongation curve, and the representative points on the simulated stress-elongation curve correspond one to one to the representative points on the target stress-elongation curve; and They respectively represent the stress values ​​corresponding to the i-th representative points on the simulated stress-elongation curve and the target stress-elongation curve.

5. The method according to claim 1, characterized in that Step S7 also includes setting the value ranges of the parameters of the fiber fabric material respectively.

6. The method according to claim 1, characterized in that In step S7, the optimization problem is expressed as: Among them, X represents the variables to be optimized, including the angle α between the fiber bundles, the radius of the fiber bundle cross section R, the side lengths L1 and L2 of the quadrilateral formed by the fiber bundles, α L , α U , R L , R U , L1 L , L1 U , L2 L , L2 U , respectively represent the upper and lower bounds of the value range of α, R, L1, and L2; Y represents the optimization target, specifically the relative error Error.

Images