A composite material superstructure design method and system with customizable thermal expansion coefficient and a storage medium

Abstract

The application provides a composite material superstructure design method and system with customizable thermal expansion coefficient, and a storage medium. A target optimization function containing a density field and an angle field is determined according to a microcosmic composition phase of a composite material. An optimization target of the target optimization function is that a thermal expansion coefficient and a structure flexibility related function are minimized. The target optimization function is subjected to density optimization and angle optimization according to a current density field and an angle field, so as to obtain material structure parameters after density optimization and angle optimization. A geometric model of the superstructure is output according to the material structure parameters. The method and system provided by the application calculate mechanical properties and thermal expansion properties in the process of structure optimization, can simultaneously meet the requirements of high mechanical properties and high thermal dimensional stability, and can calculate equivalent properties of the structure through a homogenization method and finite element analysis, can predict the structure properties within a certain error range, and reduces experimental and manufacturing costs.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a method, system, and storage medium for designing composite material superstructures with customizable coefficients of thermal expansion. Background Technology

[0002] With the rapid development of high-end engineering fields, structural components often need to withstand extreme and drastically changing thermal environments during service. Under high-temperature conditions, traditional single materials usually have a fixed and positive coefficient of thermal expansion. Temperature changes will cause the material to undergo unavoidable thermal expansion and contraction, which will lead to structural dimension deviations, interface thermal stress concentration, connection failures, and overall performance degradation. Even small thermal deformations can accumulate into significant systematic errors, and even lead to functional failure.

[0003] Existing technologies attempting to control the coefficient of thermal expansion mainly include material formulation and structural design. While material formulation can reduce thermal expansion to some extent, it is difficult to achieve near-zero expansion, and the preparation process is complex with low design freedom. Structural design, on the other hand, either relies on complex assembly and multi-material interfaces, resulting in system complexity, high cost, and limited reliability. If fixed topological geometric units are used, the adjustable range is limited. Therefore, existing technologies cannot meet the requirement of high thermal dimensional stability under precise control of the coefficient of thermal expansion.

[0004] Therefore, the existing technology needs further improvement. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a method, system and storage medium for designing composite material superstructures with customizable coefficient of thermal expansion, overcoming the defect that the prior art cannot achieve a low coefficient of thermal expansion.

[0006] The technical solution adopted by this invention to solve the technical problem is as follows: In a first aspect, the present invention provides a method for designing composite material superstructures with customizable coefficients of thermal expansion, comprising: The objective optimization function, which includes the density field and the angle field, is determined based on the microstructure of the composite material. Based on the current density field and angle field, the target optimization function is optimized for density and angle to obtain the optimized material structure parameters. The geometric model of the superstructure is output based on the material structural parameters.

[0007] Optionally, the superstructure is composed of multiple units, and the step of determining the objective optimization function including the density field and the angle field based on the microstructure of the composite material includes: Based on the numerical range of the density field, the number of phases and the total number of units in the microstructure of the material, a density field term is constructed. An angle field term is constructed based on the angle of each phase material in each element and the total number of elements in the angle field. Based on the density field term, angle field term, equivalent constitutive matrix of the superstructure, and equivalent thermal expansion coefficient vector of the superstructure, as well as the volume fraction constraint of the objective optimization function and the density and constraint of each phase material in each unit, the objective optimization function is constructed.

[0008] Optionally, the step of performing density optimization and angle optimization on the target optimization function based on the current density field and angle field to obtain the density-optimized and angle-optimized material structure parameters includes: For different multiphase materials, determine the input property parameters; Based on the determined input attribute parameters, construct the constitutive matrix and thermal expansion coefficient vector of each phase material; The equivalent properties of each element are calculated using the SIMP interpolation method for multiphase composite materials and the asymptotic homogenization theory. The density sensitivity and angular sensitivity of each element are determined based on the equivalent properties of each element. Density sensitivity and angle sensitivity were optimized separately to obtain material structural parameters.

[0009] Optionally, the step of calculating the equivalent properties of each element using the SIMP interpolation method and asymptotic homogenization theory for multiphase composite materials includes: The equivalent constitutive matrix and equivalent expansion coefficient vector of each element are calculated using the SIMP interpolation method for multiphase composite materials. Based on the predefined test strain and unit temperature change, as well as the equivalent constitutive matrix and equivalent expansion coefficient vector of each element, the global stiffness matrix, global mechanical load, and global thermal load are determined. The equivalent constitutive matrix and equivalent thermal stress vector of the overall structure are calculated using the asymptotic homogenization theory, as well as the partial derivatives of the equivalent constitutive matrix and equivalent thermal stress vector of the overall structure with respect to the density and angle of each material in each element.

[0010] Optionally, before the step of calculating the equivalent properties of each element using the SIMP interpolation method and asymptotic homogenization theory for multiphase composite materials, the method further includes: Calculate the constitutive matrix and thermal expansion coefficient vector of each phase material after rotation in each unit, and calculate the derivatives of the constitutive matrix and thermal expansion coefficient vector with respect to the constitutive matrix based on the rotated constitutive matrix and thermal expansion coefficient vector.

[0011] Optionally, the step of determining the density sensitivity and angular sensitivity of each element based on the equivalent properties of each element includes: Based on the defined objective optimization function, calculate the objective function value, and the density sensitivity and angular sensitivity of the objective function value for each material in each element.

[0012] Optionally, the step of outputting the geometric model of the superstructure based on the material structural parameters includes: Output pixelated patterns of the superstructure based on material structural parameters; The pixelated pattern is smoothed to obtain a geometric model containing superstructure boundaries and fiber paths.

[0013] Secondly, the present invention provides a composite material superstructure design system with a customizable coefficient of thermal expansion, comprising: The objective optimization function definition module is used to determine the objective optimization function, which includes the density field and the angle field, based on the microstructure of the composite material. The structural parameter determination module is used to perform density optimization and angle optimization on the target optimization function based on the current density field and angle field, so as to obtain the material structural parameters after density optimization and angle optimization. The physical structure output module is used to output the geometric model of the superstructure based on the material structure parameters.

[0014] Optionally, the composite material is a continuous fiber reinforced composite material; the density field and angular field of the superstructure are symmetrical, and the superstructure is composed of multiple units, each unit being a single cell.

[0015] Thirdly, this application also discloses a computer storage medium, which is a computer-readable storage medium, wherein a computer program is stored in the computer storage medium, and when the computer program is executed by the computer, the computer is used to execute the aforementioned composite material superstructure design method with customizable thermal expansion coefficient.

[0016] Beneficial effects: This invention provides a method, system, and storage medium for designing composite material superstructures with customizable thermal expansion coefficients. The method involves determining a target optimization function, including density and angle fields, based on the microstructure composition of the composite material; optimizing the target optimization function based on the current density and angle fields to obtain the optimized material structural parameters; and outputting the geometric model of the superstructure based on these parameters. The method and system provided by this invention calculate mechanical and thermal expansion properties during structural optimization, simultaneously meeting the requirements for high mechanical performance and high thermal dimensional stability. Furthermore, this invention can calculate the equivalent performance of the structure through homogenization methods and finite element analysis, predicting structural performance within a certain error range and reducing experimental and manufacturing costs. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the steps of the composite material superstructure design method with customizable thermal expansion coefficient provided by this invention; Figure 2 A flowchart illustrating the steps of a specific embodiment of the superstructure design method provided by the present invention; Figure 3 Convergence curve during the iterative optimization process of the superstructure design method provided by this invention; Figure 4 A pixelated pattern schematic diagram of a specific application embodiment of the superstructure design method provided by the present invention; Figure 5 A schematic diagram of the superstructure in a specific application embodiment of the superstructure design method provided by the present invention; Figure 6 This is a schematic diagram of the design principle of a composite material superstructure system with a customizable coefficient of thermal expansion in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0019] It should be noted that although a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown in the flowchart. The terms "first," "second," etc., used in the specification, claims, and the foregoing drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0020] With the rapid development of high-end engineering fields such as aerospace, precision instruments, optical platforms, and electronic packaging, structural components often need to withstand extreme and drastically changing thermal environments during service. Under such conditions, traditional single materials typically have a fixed and positive coefficient of thermal expansion. Temperature changes inevitably lead to thermal expansion and contraction, causing structural dimensional deviations, interface thermal stress concentration, connection failures, and overall performance degradation. Especially in high-precision scenarios, such as satellite payload supports, optical mirror brackets, precision measuring equipment, and microelectronic packaging, even minute thermal deformations can accumulate into significant system errors, or even lead to functional failure. Therefore, there is an urgent need for a novel structural design method that can actively control thermal expansion behavior and achieve near-zero or customizable coefficients of thermal expansion to ensure that structures maintain high precision and reliability under complex thermal environments.

[0021] While existing technologies have disclosed solutions for reducing the coefficient of thermal expansion through material formulation design, the ability to control thermal expansion is limited by formulation selection, filler ratio, interfacial bonding, and dispersibility. These solutions can only reduce the coefficient of thermal expansion to a certain extent and cannot achieve a near-zero coefficient of thermal expansion. Furthermore, the preparation process for such material formulation designs is complex; different formulations require post-preparation performance testing to determine the various properties of the material, making prediction impossible and resulting in low design freedom.

[0022] In the prior art, another solution is disclosed, which reduces the overall thermal deformation of the telescope by means of material matching, topology optimization support position, error chain compensation and flexible connection. It belongs to the thermal compensation at the macroscopic structural level. Its thermal stability depends on complex assembly compensation, structural decoupling and multi-material interface design. The system has high complexity, poor scalability, high manufacturing cost and limited reliability.

[0023] Furthermore, existing technologies disclose the use of two metallic materials with different coefficients of thermal expansion to form predefined geometric units, which are arranged periodically in a lattice as unit cells. This method utilizes the difference in thermal expansion between the two materials to obtain an anomalous coefficient of thermal expansion through a geometric amplification effect, and the coefficient of thermal expansion can be customized by adjusting geometric parameters. However, because this approach uses artificially conceived geometric shapes and a fixed topology, the customizable range achievable simply by modifying the geometric dimensions is very limited. Moreover, it does not consider the mechanical properties of the structure and cannot meet the requirements of high specific strength and high specific stiffness in related fields.

[0024] To address the aforementioned issues, this invention provides a method, system, and storage medium for designing composite material superstructures with customizable thermal expansion coefficients. Through topology optimization, the optimal material distribution scheme is found, offering high design freedom and achieving minimum thermal expansion within the target range. Furthermore, mechanical properties are calculated during structural optimization, simultaneously meeting the requirements for high mechanical performance and high thermal dimensional stability. This invention also utilizes homogenization methods and finite element analysis to calculate the equivalent performance of the structure, enabling prediction of structural performance within a certain error range and reducing experimental and manufacturing costs.

[0025] The following description, in conjunction with the accompanying drawings, provides a more detailed account of the composite material superstructure design method, system, and storage medium with customizable thermal expansion coefficient disclosed in this embodiment.

[0026] In a first aspect, the present invention provides a method for designing composite material superstructures with customizable coefficients of thermal expansion, such as... Figure 1 As shown, it includes: Step S1: Determine the target optimization function, which includes the density field and the angle field, based on the microstructure of the composite material; wherein, the optimization objective of the target optimization function is to minimize the correlation function between the coefficient of thermal expansion and the structural flexibility.

[0027] In order to design a superstructure with a near-zero expansion coefficient, this step involves constructing an objective optimization function containing a density field and an angle field, and then performing topology optimization based on the constructed objective optimization function to obtain the designed superstructure. Furthermore, the optimization objective of this step is to construct an objective optimization function that includes optimal mechanical properties and minimum thermal expansion properties, so as to optimize the flexibility while optimizing the thermal expansion coefficient of the structure, and to ensure the mechanical properties of the structure while meeting special thermal expansion requirements.

[0028] In detail, the steps for determining the objective optimization function, which includes the density field and the angle field, based on the microstructure of the composite material include: Step S11: Construct the density field term based on the numerical range of the density field, the number of phases in the total microstructure of the material, and the total number of units.

[0029] Step S12: Construct the angle field term based on the angle of each phase material in each element and the total number of elements in the angle field.

[0030] Step S13: Based on the density field term, angle field term, equivalent constitutive matrix of the superstructure, and equivalent thermal expansion coefficient vector of the superstructure, as well as the volume fraction constraint of the objective optimization function and the density and constraint of each phase in each unit, the objective optimization function is constructed.

[0031] In one implementation, the optimization problem can be expressed as: ; ; ; ; ; in, This refers to the pseudo-density of each phase material in each unit cell, i.e., the density field. This represents the total number of material phases. This represents the total number of units; Let be the angle of each phase material in each element, i.e., the angle field. For isotropic materials, The value does not affect material properties; The equivalent constitutive matrix of the structure; is the vector of the equivalent thermal expansion coefficients of the structure; This is the volume of the unit; For the first The density of the phase material in this unit; The total volume of the design domain; For the first Volume fraction constraints of phase materials; Optimize the function for the target, and define a customizable function about... and The function, and All by and Calculated; For volume fraction constraints; This indicates that the sum of the densities of each phase in each unit is 1.

[0032] Step S2: Perform density optimization and angle optimization on the target optimization function based on the current density field and angle field to obtain the material structure parameters after density optimization and angle optimization.

[0033] In step S1 above, the objective optimization function has been defined, constraints have been given, and parameters, mesh, design variables, and boundary conditions have been initialized for the objective optimization function.

[0034] In detail, the initialization parameters include optimization parameters, physical parameters, and solver parameters. Optimization parameters include the maximum number of iterations and convergence tolerance; physical parameters include the material elastic modulus and filter radius; and solver parameters include the type of finite element solver. The mesh is used to discretize the design domain and create a finite element mesh. Design variables are defined core variables and assigned initial values. Core variables can be element density or thickness. Filters are used to introduce filtering mechanisms to prevent numerical instability. Therefore, in this step, the continuous problem with infinite degrees of freedom is transformed into a discrete problem with finite degrees of freedom through meshing. Design variables represent material distribution, filters ensure solution stability, boundary conditions simulate real-world conditions, and parameters control the solution process, thereby establishing a computational environment for topology optimization.

[0035] In practical implementation, in addition to periodic boundary conditions, other types of boundary conditions can also be applied to the superstructure, such as constraints and loads. For example, macroscopic boundary conditions can be applied to specific scenarios.

[0036] Furthermore, the superstructure in this embodiment is a periodically arranged microscopic unit cell superstructure, which can be arranged into any macroscopic structure. The step of performing density optimization and angle optimization on the target optimization function based on the current density field and angle field to obtain the density-optimized and angle-optimized material structure parameters includes: Step S21: Determine the input property parameters for different multiphase materials.

[0037] In this step, for orthotropic materials, the maximum number of property parameters that need to be input for each phase material includes... , , , , , For isotropic materials, only input is required. , , .in, For elastic modulus, Shear modulus Poisson's ratio, The coefficient of thermal expansion is... and These represent the elastic modulus in the fiber direction and perpendicular to the fiber direction, respectively.

[0038] Step S22: Based on the determined input attribute parameters, construct the constitutive matrix and thermal expansion coefficient vector of each phase material.

[0039] Based on the above input attribute parameters, the constitutive matrix of each phase material can be constructed. and the vector of thermal expansion coefficients .

[0040] Step S23: Calculate the equivalent properties of each element using the SIMP interpolation method for multiphase composite materials and the asymptotic homogenization theory.

[0041] Furthermore, before the step of calculating the equivalent properties of each element using the SIMP interpolation method and asymptotic homogenization theory for multiphase composite materials, the method further includes: Calculate the constitutive matrix and thermal expansion coefficient vector of each phase material after rotation in each unit, and calculate the derivatives of the constitutive matrix and thermal expansion coefficient vector with respect to the constitutive matrix based on the rotated constitutive matrix and thermal expansion coefficient vector.

[0042] In detail, before performing interpolation, the angle field is first determined. Calculate the constitutive matrix of each phase material after rotation in each element. and the vector of thermal expansion coefficients The calculation method is as follows: ; ; ; in, For rotation matrix, For cell index, For material index.

[0043] Based on the above formulas, we can derive the constitutive matrix and the thermal expansion coefficient vector regarding... The derivatives of are respectively and This is used for subsequent sensitivity calculations. For isotropic materials, The value has no effect, so no rotation is needed; just use it directly. and That's all, they are for The derivative is 0.

[0044] Furthermore, the step of calculating the equivalent properties of each element using the SIMP interpolation method and asymptotic homogenization theory for multiphase composite materials includes: Step S24: Using the SIMP interpolation method for multiphase composite materials, calculate the equivalent constitutive matrix and equivalent expansion coefficient vector of each element.

[0045] Material interpolation is performed to obtain the equivalent constitutive matrix and equivalent thermal expansion coefficient vector for each element: ; ; in This is a penalty factor.

[0046] This invention is based on the traditional SIMP method, but improves upon it by using orthogonal anisotropic constitutive model and equivalent thermal expansion coefficient calculations. This makes it well applicable to the design scheme and preserves the penalty factor in the traditional method, minimizing the density intermediate terms that do not conform to physical reality.

[0047] Furthermore, combining the derivatives obtained earlier, we can derive their partial derivatives with respect to each material at each element angle, which are respectively: and .

[0048] Step S25: Determine the global stiffness matrix, global mechanical load, and global thermal load based on the predefined test strain and unit temperature change, as well as the equivalent constitutive matrix and equivalent expansion coefficient vector of each element.

[0049] Based on the predefined test strain and unit temperature change, and the previously calculated effective properties of the elements, the element stiffness matrix is ​​calculated using the finite element method. Unit mechanical load and unit thermal load And assemble them into a global stiffness matrix. Global mechanical load and global thermal load Meanwhile, the following partial derivatives can be derived: , , , .

[0050] Then, according to the equilibrium equation: ; ; The displacement field under mechanical load is obtained by solving separately. and displacement field under thermal load .

[0051] Step S26: Calculate the equivalent constitutive matrix and equivalent thermal stress vector of the overall structure using the asymptotic homogenization theory, as well as the partial derivatives of the equivalent constitutive matrix and equivalent thermal stress vector of the overall structure with respect to the density and angle of each material in each element.

[0052] Based on the asymptotic homogenization theory, the equivalent constitutive matrix of the overall structure can be calculated. and equivalent thermal stress vector And their partial derivatives with respect to the density and angle of each material in each element: , , , .

[0053] Then, according to the following equation: ; It can be calculated At the same time, it is deduced that , .

[0054] Step S24: Determine the density sensitivity and angular sensitivity of each element based on the equivalent properties of each element.

[0055] The displacement field under mechanical load was calculated. and displacement field under thermal load .

[0056] Specifically, the steps of determining the density sensitivity and angular sensitivity of each element based on its equivalent properties include: Based on the defined objective optimization function, calculate the objective function value, and the density sensitivity and angular sensitivity of the objective function value for each material in each element.

[0057] Calculate the objective function value based on the defined objective optimization function. The objective function values ​​for density sensitivity and angular sensitivity of each material in each element are respectively... , .

[0058] Step S25: Optimize the density sensitivity and angle sensitivity respectively to obtain the material structure parameters.

[0059] The material structure parameters are obtained by optimizing the calculated density sensitivity and angle sensitivity separately. Sensitivity refers to the rate of change in the overall structure's performance when the mesh density is increased or decreased slightly. It's conceivable that the order of density and angle optimization can be changed; for example, optimizing the angle first, then the density; or prioritizing density optimization until convergence, then focusing on angle optimization until convergence, without alternating; or changing the alternating strategy to parallel optimization, performing one finite element analysis and then simultaneously optimizing both design variables using their sensitivities.

[0060] In detail, a sensitivity filtering method can be used to process density sensitivity, and based on the filtered sensitivity, the design variables can be updated using an optimization criterion method. This ensures that the volume fraction constraint is met.

[0061] For angle optimization, the following process is used to process angle sensitivity. First, a sensitivity filtering method is used to process the angle sensitivity. The sensitivity after filtering is recorded as: .

[0062] Subsequently, the angle sensitivity needs to be limited. This is because, in the angle optimization process of the fiber-reinforced phase, the angle variable describes the local orientation of orthotropic materials, and such materials are susceptible to rotational changes. With rotation (or When the angle increment is not limited in numerical optimization, the equivalent stiffness, thermal expansion, and other constitutive properties are completely consistent, meaning the material orientation has a π-period equivalent. Therefore, the following situation may occur: the algorithm's update is... But when Greater than At that time, the update is actually equivalent to rotating by a small angle in the opposite direction (e.g., This can cause the optimization direction to reverse, resulting in jumps, oscillations, or even non-convergence in the angle field.

[0063] In detail, when the angle change exceeds half a cycle, the mathematically defined "update direction" no longer aligns with the material physics-based "optimal direction," disrupting the stability and continuity of the optimization process. Therefore, to ensure the physical consistency and numerical stability of the angle update, each angle increment needs to be strictly limited to a certain range. to Within this range, optimization should always proceed in the direction of the true decrease in material properties, avoiding the problem of equivalent direction reversal.

[0064] The following is the limiting formula for angular sensitivity: ; The result after limiting exist Within the range, and the normalization step eliminates the sensitivity scale differences in different iteration steps, avoiding update instability caused by excessively high or low sensitivity.

[0065] Subsequently, the angle sensitivity after limiting was processed by density weighting as follows: ; in, The parameters are set to ensure that the angle update amplitude is concentrated in the high-density region, avoiding the problem that the sensitivity may be amplified in the low-density region due to the normalization operation.

[0066] Subsequently, to ensure the convergence of the angle: ; in, This represents the current iteration step. This represents the maximum number of allowed iterations.

[0067] Finally, the angle variable is updated using gradient descent: ; Various convergence conditions can be used to determine whether the iterative process has converged. Classic convergence conditions include, for example, the change in the objective function value being less than a preset threshold or the maximum change in the design variable being less than a preset threshold. If convergence is achieved, the process proceeds to the next step; if convergence is not achieved, the iteration continues until the optimal density sensitivity and optimal angle sensitivity density and angle values ​​are obtained.

[0068] In this step, the optimal material distribution scheme is determined by using topology optimization, resulting in a high degree of design freedom. Theoretically, it is possible to truly achieve the maximum, specific (e.g., 0 thermal expansion), and minimum thermal expansion coefficients within the possible range. Furthermore, this invention can calculate the equivalent performance of the superstructure under design through homogenization methods and finite element analysis, enabling prediction of structural performance within a predetermined error range and reducing experimental and manufacturing costs.

[0069] Step S3: Output the geometric model of the superstructure based on the material structure parameters.

[0070] Based on the material structure parameters calculated in the above steps, the superstructure is reconstructed to obtain the corresponding structural pattern. Since this structural image is based on mesh elements and uses pseudo-density as the design variable, the output structure is a pixelated pattern with intermediate density values, meaning that the elements do not contain only one type of material. This does not conform to the actual situation in the physical world and is therefore unmanufacturable. Furthermore, the fiber angle field is also discretized and cannot directly represent the path of continuous fibers. Therefore, the pixelated pattern needs to be smoothed to obtain clear and smooth structural boundaries and smooth fiber paths.

[0071] Furthermore, the step of outputting the geometric model of the superstructure based on the material structural parameters includes: Step S31: Output the pixelated pattern of the superstructure based on the material structure parameters.

[0072] Step S32: Smooth the pixelated pattern to obtain a geometric model containing superstructure boundaries and fiber paths.

[0073] In practical implementation, the superstructure uses continuous fiber composite materials, which are not only ideal materials for lightweight structures with superior mechanical properties, but can also be manufactured using continuous fiber 3D printing technology, thus having strong practical value.

[0074] In this step, "material distribution (density)" and "fiber orientation (angle)" are treated as two independent design variables, simultaneously controlling the mechanical and thermal expansion properties of the structure. Compared to traditional methods that only optimize material distribution, this invention significantly increases design freedom, enabling microstructures to search for optimal solutions in a higher-dimensional design space.

[0075] The following example, using a specific application embodiment of a continuous fiber-reinforced composite superstructure with zero thermal expansion coefficient, further illustrates the design method provided by this invention in more detail.

[0076] The materials used in the structure consider fiber-reinforced phase, matrix phase, and unreacted phase, where the volume fraction of the fiber-reinforced phase and matrix phase is constrained to be [missing information]. 0.2, The following are the material property parameters: Fiber-reinforced phase: ; Matrix phase: ; The empty phase employs near-zero stiffness and near-zero coefficient of thermal expansion to avoid numerical singularities. ; The parameters above do not represent the properties of the materials actually used in manufacturing and are dimensionless.

[0077] The objective optimization function defined in this embodiment is as follows: ; in, and The objective function, with weights denoted as , maximizes the elastic modulus while keeping the coefficient of thermal expansion zero in both the horizontal and vertical directions.

[0078] In this embodiment, the design domain is a square unit cell, discretized into a 96×96 square grid. Since this implementation considers a superstructure, periodic boundary conditions are applied. In practical implementations, the unit cell can also be other regular shapes, such as hexagons, triangles, etc.

[0079] For isotropic materials , , Terms that are irrelevant to the objective function are 0, therefore the relevant terms (i.e. , , and Isotropic materials are often more easily optimized. In addition, isotropic materials have consistent properties in different directions, making it easier and more accurate to predict their behavior, thus making them easier to apply.

[0080] Therefore, in this case, forced symmetry constraints were added to the density field and the angle field: after each update of the density field, it is symmetricized; after each update of the angle field, it is also symmetricized. It is worth noting that the symmetry treatment for the angle field differs from that for the density field; it is not a simple numerical symmetry, but a geometric symmetry. See the appendix for details. Figure 3 The fiber-reinforcing phase (i.e., the red area with black line segments) in the image, for example, the orientation angle of a certain unit on the left half of the unit cell is... Then, at the symmetrical position on the right half, the angle value is... .

[0081] The specific symmetry can be compared to the symmetry of a square, meaning it has four axes of symmetry, including two diagonals and the line connecting the midpoints of the two opposite sides. This updated approach to enforce constraints on design variables is simple and efficient, ensuring that the structure's equivalent constitutive matrix and equivalent thermal expansion coefficient vector are isotropic.

[0082] Subsequently, iterative operations were performed, and the structure converged after 136 iterations. The convergence condition was that the maximum change in the design variables was less than 0.01. The following are the equivalent constitutive matrix and equivalent thermal expansion coefficient vector of the structure. These data show that the structure is isotropic.

[0083] ; The superstructure has an equivalent coefficient of thermal expansion of 0.36 and an equivalent Young's modulus of 1.09. This shows that, compared to the raw materials, the coefficient of thermal expansion is very close to 0, and the modulus of the structure is not significantly reduced. (Convergence process reference) Figure 1 and Figure 2 .Depend on Figure 3 As shown, this case demonstrates good convergence and satisfies the constraints on the volume fraction of each material.

[0084] like Figure 4 The diagram shows the structure after visualizing the final calculated density and angle field data. It can be seen that the structure has high symmetry, and the fiber orientation exhibits good neighborhood consistency and consistency with the structural orientation.

[0085] like Figure 5 This is a schematic diagram of the structure after post-processing. From... Figure 5 It can be concluded that after smoothing the pixelated pattern of the visualized superstructure, the designed superstructure has smooth boundaries and contains complete fiber paths.

[0086] This invention proposes an angle update limiting method for orthotropic materials. Normalization ensures the physical consistency and numerical stability of the angle update, avoiding orientation reversal caused by excessive angle changes. Subsequent operations further ensure the effectiveness and convergence of the angle update. This method guarantees the continuity, convergence, and spatial consistency of the fiber orientation field in the optimization process.

[0087] Furthermore, the design method provided by this invention applies forced symmetry operations to the density field and the angle field, taking into account the special requirement of geometric symmetry for the angle field, ensuring that the final unit cell meets the isotropic requirement in terms of equivalent performance. This symmetry-based constraint method is simple and effective, significantly improving the manufacturability and engineering applicability of the structure, while avoiding the problem of needing to add complex mathematical constraints in traditional methods.

[0088] Secondly, this invention provides a composite material superstructure design system with a customizable coefficient of thermal expansion, such as... Figure 6 As shown, it includes: The objective optimization function definition module 610 is used to determine an objective optimization function containing density field and angle field based on the microstructure of the composite material; wherein, the optimization objective of the objective optimization function is to minimize the sum of the squares of the thermal expansion coefficients and the structural compliance; its function is as described in step S1.

[0089] The structural parameter determination module 620 is used to perform density optimization and angle optimization on the target optimization function based on the current density field and angle field to obtain the material structural parameters after density optimization and angle optimization; its function is as described in step S2.

[0090] The physical structure output module 630 is used to output the geometric model of the superstructure according to the material structure parameters, and its function is as described in step S3.

[0091] In one implementation, the composite material is a continuous fiber reinforced composite material; the density field and angular field of the superstructure are symmetrical, and the unit cells constituting the superstructure are single cells.

[0092] Thirdly, this application also discloses a computer storage medium, which is a computer-readable storage medium, wherein a computer program is stored in the computer storage medium, and when the computer program is executed by the computer, the computer is used to execute the aforementioned composite material superstructure design method with customizable thermal expansion coefficient.

[0093] This invention provides a method, system, and storage medium for designing composite material superstructures with customizable thermal expansion coefficients. The method involves determining a target optimization function, including density and angle fields, based on the microstructure composition of the composite material; optimizing the target optimization function based on the current density and angle fields to obtain the optimized material structural parameters; and outputting the geometric model of the superstructure based on these parameters. The method and system provided by this invention calculate mechanical and thermal expansion properties during structural optimization, simultaneously meeting the requirements for high mechanical performance and high thermal dimensional stability. Furthermore, this invention can calculate the equivalent performance of the structure through homogenization methods and finite element analysis, predicting structural performance within a certain error range and reducing experimental and manufacturing costs.

[0094] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the following claims.

[0095] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application.

Claims

1. A method for designing composite material superstructures with customizable coefficients of thermal expansion, characterized in that, include: The objective optimization function, which includes the density field and the angle field, is determined based on the microstructure of the composite material. Based on the current density field and angle field, the target optimization function is optimized for density and angle to obtain the optimized material structure parameters. The geometric model of the superstructure is output based on the material structural parameters.

2. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 1, characterized in that, The superstructure is composed of multiple units; the step of determining the objective optimization function, which includes density and angle fields, based on the microstructure of the composite material includes: Based on the numerical range of the density field, the number of phases and the total number of units in the microstructure of the material, a density field term is constructed. An angle field term is constructed based on the angle of each phase material in each element and the total number of elements in the angle field. Based on the density field term, angle field term, equivalent constitutive matrix of the superstructure, and equivalent thermal expansion coefficient vector of the superstructure, as well as the volume fraction constraint of the objective optimization function and the density and constraint of each phase material in each unit, the objective optimization function is constructed.

3. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 1, characterized in that, The step of performing density optimization and angle optimization on the target optimization function based on the current density field and angle field to obtain the density-optimized and angle-optimized material structure parameters includes: For different multiphase materials, determine the input property parameters; Based on the determined input attribute parameters, construct the constitutive matrix and thermal expansion coefficient vector of each phase material; The equivalent properties of each element are calculated using the SIMP interpolation method for multiphase composite materials and the asymptotic homogenization theory. The density sensitivity and angular sensitivity of each element are determined based on the equivalent properties of each element. Density sensitivity and angle sensitivity were optimized separately to obtain material structural parameters.

4. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 3, characterized in that, The steps for calculating the equivalent properties of each element using the SIMP interpolation method for multiphase composite materials and the asymptotic homogenization theory include: The equivalent constitutive matrix and equivalent expansion coefficient vector of each element are calculated using the SIMP interpolation method for multiphase composite materials. Based on the predefined test strain and unit temperature change, as well as the equivalent constitutive matrix and equivalent expansion coefficient vector of each element, the global stiffness matrix, global mechanical load, and global thermal load are determined. The equivalent constitutive matrix and equivalent thermal stress vector of the overall structure are calculated using the asymptotic homogenization theory, as well as the partial derivatives of the equivalent constitutive matrix and equivalent thermal stress vector of the overall structure with respect to the density and angle of each material in each element.

5. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 4, characterized in that, Before the step of calculating the equivalent properties of each element using the SIMP interpolation method and asymptotic homogenization theory for multiphase composite materials, the method further includes: Calculate the constitutive matrix and thermal expansion coefficient vector of each phase material after rotation in each unit, and calculate the derivatives of the constitutive matrix and thermal expansion coefficient vector with respect to the constitutive matrix based on the rotated constitutive matrix and thermal expansion coefficient vector.

6. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 3, characterized in that, The steps for determining the density sensitivity and angular sensitivity of each element based on its equivalent properties include: Based on the defined objective optimization function, calculate the objective function value, and the density sensitivity and angular sensitivity of the objective function value for each material in each element.

7. The method for designing composite material superstructures with customizable thermal expansion coefficients according to claim 1, characterized in that, The step of outputting the geometric model of the superstructure based on the material structure parameters includes: Output pixelated patterns of the superstructure based on material structural parameters; The pixelated pattern is smoothed to obtain a geometric model containing superstructure boundaries and fiber paths.

8. A composite material superstructure design system with customizable coefficient of thermal expansion, characterized in that, include: The objective optimization function definition module is used to determine the objective optimization function, which includes the density field and the angle field, based on the microstructure of the composite material. The structural parameter determination module is used to perform density optimization and angle optimization on the target optimization function based on the current density field and angle field, so as to obtain the material structural parameters after density optimization and angle optimization. The physical structure output module is used to output the geometric model of the superstructure based on the material structure parameters.

9. The composite material superstructure design system with customizable thermal expansion coefficient according to claim 8, characterized in that, The composite material is a continuous fiber reinforced composite material; the density field and angular field of the superstructure are symmetrical, and the superstructure is composed of multiple units, each of which is a single cell.

10. A computer storage medium, wherein the storage medium is a computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a computer, enables the computer to perform the composite material superstructure design method with customizable thermal expansion coefficient as described in any one of claims 1-7.

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