A method for optimizing the design of a composite thermal structure

Abstract

This application provides a method for optimizing the thermal structure design of composite materials, addressing the problem that composite structures are prone to developing undesirable structural defects under high-temperature loads. The method includes the following steps: establishing a database of equivalent performance parameters for composite materials; constructing a rapid prediction model for the equivalent performance of composite materials based on this database; establishing a design domain; determining and initializing design variables; calculating the specific coefficients and matrices corresponding to the design variables; analyzing, solving, and calculating the sensitivity information of the structural response; iteratively solving the optimization problem until convergence is achieved; and the design variable information of the current iteration step is the final optimization result. The optimization design method provided in this application significantly improves the computational efficiency of the optimization process and effectively coordinates the relationship between the load-bearing capacity and stiffness of thermal structures under high-temperature conditions.

Description

Technical Field

[0001] This application belongs to the field of material structure optimization technology, specifically relating to a method for optimizing the thermal structure of composite materials. Background Technology

[0002] With the rapid development of modern aerospace technology, the service environment of aircraft is becoming increasingly harsh and demanding. Hypersonic aircraft, in particular, often face temperatures exceeding 1,000 degrees Celsius, sometimes even surpassing 2,000 degrees Celsius. These aircraft structures must fulfill service missions such as aerodynamic heating during flight, atmospheric reentry, high-G maneuverability, and ultra-long-range cruise, thus requiring characteristics such as extremely high load-bearing capacity, extreme heat resistance, ultra-high precision, and ultra-lightweight design. Traditional metallic materials are insufficient for these extreme service environments. The development of high-temperature resistant composite materials, such as C / SiC and modified C / C composites, has laid the material foundation for the thermal structures of hypersonic aircraft. However, the structural form of the reinforcing preforms, such as fiber ratio, weaving angle, and weaving method, significantly affects the thermo-mechanical properties of the composite materials.

[0003] Currently, mainstream structural optimization methods are usually geared towards single-phase materials, and the optimized structures often have complex geometric configurations, making them difficult to directly apply to the optimization design of braided composite material structures. Traditional optimization models that aim to maximize structural stiffness have good universality for room temperature structures, but they are difficult to obtain reasonable structures that meet engineering requirements when optimizing high-temperature thermal structures. Traditional cross-scale optimization models involve many variables, have complex calculation processes, and require high computer performance.

[0004] To seek high-performance, lightweight braided composite thermal structures, this application establishes an equivalent characterization model of the macroscopic thermo-mechanical properties of composite materials using homogenization methods, enabling thermo-mechanical coupling analysis across macroscopic, mesoscopic, and microscopic scales. Furthermore, it establishes an explicit mapping relationship between braiding parameters and equivalent thermo-mechanical properties through parametric modeling techniques and neural network methods, constructing an index function suitable for evaluating thermal structure performance under extremely high and non-uniform temperature environments. This achieves collaborative optimization design of macroscopic structures and braiding process parameters. Summary of the Invention

[0005] The purpose of this application is to solve the problem that composite thermal structures are difficult to design for high performance and lightweight under high temperature conditions.

[0006] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0007] A method for optimizing the thermal structure of composite materials includes the following steps:

[0008] Model establishment: Based on the equivalent performance parameter library of composite materials, a neural network is applied to fit the mapping relationship between process parameters and equivalent thermo-mechanical properties to obtain a rapid prediction model for the equivalent performance of composite materials.

[0009] Design variable initialization: Establish the design domain, apply loads and constraints that can describe the stress conditions of the structure during service, and determine and initialize the design variables based on the finite element model, namely topology variables, fiber volume fraction and braiding angle;

[0010] Matrix assembly: The rational approximation interpolation function and the fast prediction model of equivalent properties of composite materials are applied to calculate the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient corresponding to the design variables, and then assembled into the overall structural stiffness matrix, thermo-mechanical coupling matrix and thermal conductivity matrix.

[0011] Sensitivity information: Steady-state heat transfer analysis and thermo-mechanical coupling analysis are performed to solve the corresponding equations to obtain the temperature distribution and displacement distribution of the structure, and the response function and its partial derivative vector with respect to the design variables are calculated to obtain the sensitivity information;

[0012] Solution: Gradient optimization algorithms such as Optimization Criterion Method (OC), Moving Asymptote Method (MMA), Sequential Linear Programming (SLP), and Sequential Quadratic Programming (SQP) are applied to iteratively solve the optimization problem. Design variables are updated based on the aforementioned sensitivity information. To avoid checkerboard patterns and obtain a clear structural configuration, density filtering and projection are performed on the topological variables in the updated design variables. The convergence condition is that the maximum change in the design variables is less than 0.001. If the convergence condition is met, the design variable information of the current iteration step is the final optimization result. If the convergence condition is not met, the process jumps to calculating the element elasticity matrix, thermal stress coefficient, and thermal conductivity coefficient corresponding to the design variables and repeats the calculation until the convergence condition is met.

[0013] Specifically, the method for establishing a database of equivalent performance parameters for composite materials includes the following steps: extracting process parameters, constructing a parameterized representative volume element model, and establishing a parameterized unit cell model; calculating the equivalent thermo-mechanical performance parameters corresponding to the process parameters based on the energy homogenization method, and establishing a database of equivalent performance parameters for composite materials; after updating the design variables, performing density filtering and projection on the updated topology variables.

[0014] Specifically, the neural network includes radial basis function neural networks and backpropagation (BP) networks; the geometry of the design domain is easy to discretize into a mapping mesh; the loads and constraints can describe the stress conditions of the structure during service; and the design variables are topological variables, fiber volume fraction, and braiding angle.

[0015] Specifically, composite materials include planar braided composite materials, machine-woven composite materials, three-dimensional four-way braided composite materials, three-dimensional five-way braided composite materials, three-dimensional six-way braided composite materials, three-dimensional seven-way braided composite materials, etc.

[0016] Compared with the prior art, this application has the following beneficial effects or advantages:

[0017] The composite material thermal structure optimization design method provided in this application establishes a rapid characterization and prediction model of the equivalent thermo-mechanical properties of composite materials based on parametric modeling technology and neural network methods, which significantly improves the computational efficiency of the optimization process.

[0018] This application proposes a new objective function form applicable to thermal structure optimization problems under high temperature environments, which effectively coordinates the relationship between the load-bearing capacity and the stiffness of composite thermal structures under high temperature environments. Attached Figure Description

[0019] Figure 1 This is a flowchart of the composite material thermal structure optimization design method described in this application.

[0020] Figure 2 This is a representative volumetric element model diagram of the three-dimensional braided composite material described in the embodiments of this application.

[0021] Figure 3 This is a schematic diagram of the simply supported beam structure described in the embodiments of this application.

[0022] Figure 4 The result is the optimization of a simply supported beam structure using the traditional structural design method described in the embodiments of this application.

[0023] Figure 5 The result of optimizing a simply supported beam structure using the composite material thermal structure optimization design method described in the embodiments of this application.

[0024] Figure 6 The embodiments described in this application are for Figure 5 The image shows the structure and microstructure of the optimized result after smoothing. Detailed Implementation

[0025] The technical solution of this application will be described below with reference to the embodiments. However, this application is not limited to the following embodiments.

[0026] Unless otherwise specified, the experimental and detection methods in the following embodiments are conventional methods; the index data are conventional measurement methods unless otherwise specified.

[0027] This application provides a method for optimizing the thermal structure design of composite materials, including the following process:

[0028] Model establishment: Based on the equivalent performance parameter library of composite materials, a neural network is applied to fit the mapping relationship between process parameters and equivalent thermo-mechanical properties to obtain a rapid prediction model for the equivalent performance of composite materials.

[0029] Design variable initialization: Establish the design domain, apply loads and constraints that can describe the stress conditions of the structure during service, and determine and initialize the design variables based on the finite element model, namely topology variables, fiber volume fraction and braiding angle;

[0030] Matrix assembly: The rational approximation interpolation function and the fast prediction model of equivalent properties of composite materials are applied to calculate the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient corresponding to the design variables, and then assembled into the overall structural stiffness matrix, thermo-mechanical coupling matrix and thermal conductivity matrix.

[0031] Sensitivity information: Steady-state heat transfer analysis and thermo-mechanical coupling analysis are performed to solve the corresponding equations to obtain the temperature distribution and displacement distribution of the structure, and the response function and its partial derivative vector with respect to the design variables are calculated to obtain the partial derivative information;

[0032] Solution: Gradient optimization algorithms such as Optimization Criterion Method (OC), Moving Asymptote Method (MMA), Sequential Linear Programming (SLP), and Sequential Quadratic Programming (SQP) are applied to iteratively solve the optimization problem. Design variables are updated based on the aforementioned sensitivity information. To avoid checkerboard patterns and obtain a clear structural configuration, density filtering and projection are performed on the topological variables in the updated design variables. The convergence condition is that the maximum change in the design variables is less than 0.001. If the convergence condition is met, the design variable information of the current iteration step is the final optimization result. If the convergence condition is not met, the process jumps to calculating the element elasticity matrix, thermal stress coefficient, and thermal conductivity coefficient corresponding to the design variables and repeats the calculation until the convergence condition is met.

[0033] Specifically, the composite material thermal structure optimization design method of this application can be summarized as the following mathematical optimization problem:

[0034] find: χ = {x1, x2, ..., x n ;v f ;γ}

[0035] min:

[0036] st:

[0037] 0 < x min ≤x i ≤1

[0038] 30%≤v f ≤60%

[0039] 30°≤γ≤60°

[0040] In the formula, χ is the design variable, which includes the topological variable x that describes the macroscopic material layout. i and weaving process parameter variables (ν) f ,γ), where ν f γ represents the fiber volume fraction, γ represents the weave angle; J is the objective function, consisting of two parts, the first part being structural compliance. Used to measure the stiffness performance of a structure at high temperatures, K is the structural stiffness matrix, and u is the structural stiffness under thermal load f. th and mechanical load f m The structural displacement vector under the combined action satisfies the equilibrium equation Ku = f th+ f m The second part is mechanical strain energy. u m For the structure only under mechanical load f m The structural displacement vector under action satisfies the equilibrium equation Ku m =f m Based on the penalty function Φ(t), the mechanical strain energy c m A penalty is applied to control the structural bearing stiffness. M(χ) is the mass constraint function of this mathematical optimization model, and ρ f and ρ m V represents the density of the fiber and the matrix material, respectively. i For unit volume, This represents the upper limit of the allowable material mass. Simultaneously, to avoid singularities in the stiffness matrix, the topological variable x... i The lower limit is set to an extremely small positive number x. min .

[0041] Specifically, the method for establishing a database of equivalent performance parameters for composite materials includes the following steps: extracting process parameters, constructing a parameterized representative volume element model, and establishing a parameterized unit cell model; calculating the equivalent thermo-mechanical performance parameters corresponding to the process parameters based on the energy homogenization method, and establishing a database of equivalent performance parameters for composite materials; after updating the design variables, performing density filtering and projection on the updated topology variables.

[0042] Specifically, the neural network includes radial basis function neural networks and backpropagation (BP) networks; the geometry of the design domain is easy to discretize into a mapping mesh; the loads and constraints can describe the stress conditions of the structure during service; and the design variables are topological variables, fiber volume fraction, and braiding angle.

[0043] Specifically, composite materials include planar braided composite materials, machine-woven composite materials, three-dimensional four-way braided composite materials, three-dimensional five-way braided composite materials, three-dimensional six-way braided composite materials, three-dimensional seven-way braided composite materials, etc.

[0044] Example 1

[0045] This embodiment provides an experiment for establishing a library of equivalent performance parameters for three-dimensional four-way braided composite materials.

[0046] like Figure 2 As shown, the weaving process parameters of the three-dimensional four-way braided composite material are extracted, including the fiber volume fraction ν. f Based on the weaving process characteristics, parameterized representative volume element models are constructed at both the yarn and fiber scales, along with the weaving angle γ. A parameterized unit cell model is then established using the weaving angle and fiber volume fraction as process parameters. Figure 2 In the diagram, (b) represents the fiber-scale representative volume element (RVE) model. Figure 2 In the diagram, (a) represents the yarn-scale RVE model.

[0047] Based on the energy homogenization method, the equivalent thermo-mechanical properties at the fiber scale are first calculated and used as material parameters of the yarn in the yarn model. Then, the energy homogenization method is applied again to calculate the equivalent thermo-mechanical properties of the three-dimensional four-way braided composite material, and a library of equivalent performance parameters of the three-dimensional four-way braided composite material is established.

[0048] Example 2

[0049] This embodiment provides an experiment for optimizing a simply supported beam structure using the optimization design method described in this application.

[0050] Based on the equivalent performance parameter library of three-dimensional four-directional braided composite materials established in Example 1, a radial basis function neural network is used to fit the mapping relationship between braiding process parameters and equivalent thermo-mechanical properties to obtain a rapid prediction model for the equivalent performance of composite materials.

[0051] Simply supported beam structure, such as Figure 3 As shown, a forced convection boundary is applied to the upper surface of the simply supported beam structure to simulate the aerodynamic heating process. At the same time, a uniform pressure of 1 MPa is applied to the upper surface, and a natural convection boundary is applied to the lower surface. A fixed constraint is applied to one end of the lower surface, and only the vertical degree of freedom is constrained at the other end.

[0052] according to Figure 1 The process shown has been optimized as follows:

[0053] The design variable x, i.e. the topology variable x, is determined and initialized based on the finite element model. i Fiber volume fraction ν f And the weaving angle γ, using the rational approximation interpolation function (RAMP) and the aforementioned fast prediction model for the equivalent properties of composite materials, calculate the element elastic matrix corresponding to the current design variables. thermal stress coefficient and thermal conductivity And assembled into an integral structural stiffness matrix K mThermodynamic coupling matrix K mth and thermal conductivity K th ;

[0054]

[0055]

[0056]

[0057] In the formula, N is the total number of units, and q D q β and q κ All are penalty factors in the RAMP model, ▽ is the gradient operator, N is the element basis function matrix, and B is the element strain matrix.

[0058] Steady-state heat transfer analysis and thermo-mechanical coupling analysis were performed separately to solve the corresponding equations and obtain the temperature and displacement distribution of the structure. Based on these data, the structural compliance c and mechanical strain energy c were calculated. m From the partial derivative vector of the design variables, sensitivity information is obtained.

[0059]

[0060]

[0061] The gradient optimization algorithm is applied to iteratively solve the optimization problem. The design variables are updated based on the sensitivity information obtained in the previous step, and density filtering and projection are performed on the updated topological variables.

[0062] The convergence condition is that the maximum value of the change in the design variable is less than 0.001. If the convergence condition is met, the design variable information of the current iteration step is the final optimization result. If the convergence condition is not met, the process jumps to the step of calculating the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient corresponding to the design variable and repeats the calculation until the convergence condition is met.

[0063] Optimization results are as follows Figure 5 As shown, by Figure 5 It can be seen that the optimization design method described in this application not only causes the structural compliance and mechanical compliance to decrease steadily and gradually approach the minimum value during the iteration process, but also forms a reasonable and effective force transmission path after the optimized material distribution.

[0064] This embodiment also smoothed the optimization results to obtain the macrostructure and composite material microstructure as follows: Figure 6 As shown.

[0065] Example 3

[0066] This embodiment provides an experiment to optimize a simply supported beam structure with the traditional structural compliance as the optimization target.

[0067] The simply supported beam structure and the applied loads and constraints are the same as in Example 2.

[0068] The structure was optimized with the compliance of traditional structures as the optimization objective. The optimization results are as follows: Figure 4 As shown, by Figure 4 It is evident that methods that optimize traditional structural compliance not only experience violent oscillations during the iteration process, but also result in a highly disordered material distribution and the absence of effective force transmission paths.

[0069] As described above, this application can be well implemented. The above embodiments are merely descriptions of preferred embodiments of this application and are not intended to limit the scope of this application. Without departing from the spirit of this application, all changes and improvements made by those skilled in the art to the technical solutions of this application should fall within the protection scope defined by this application.

Claims

1. A method for optimizing the thermal structure of composite materials, characterized in that, Includes the following processes: Model establishment: Based on the equivalent performance parameter library of composite materials, a neural network is applied to fit the mapping relationship between process parameters and equivalent thermo-mechanical properties to obtain a rapid prediction model for the equivalent performance of composite materials. Design variable initialization: Establish the design domain, apply loads and constraints, and determine and initialize design variables based on the finite element model; Matrix assembly: The rational approximation interpolation function and the fast prediction model of the equivalent properties of the composite material are used to calculate the unit elastic matrix, thermal stress coefficient and thermal conductivity coefficient corresponding to the design variables, and then assembled into the overall structural stiffness matrix, thermo-mechanical coupling matrix and thermal conductivity matrix. Sensitivity information: Steady-state heat transfer analysis and thermo-mechanical coupling analysis are performed to solve the corresponding governing equations to obtain the temperature distribution and displacement distribution of the structure, and the response function and its partial derivative vector with respect to the design variables are calculated to obtain the sensitivity information; Solution: Set convergence conditions for the design variables, apply gradient optimization algorithm to iteratively solve the optimization problem, update the design variables based on the sensitivity information, jump to the matrix assembly step and repeat the calculation until the convergence condition is reached. The design variable information of the current iteration step is the final optimization result.

2. The optimization design method according to claim 1, characterized in that, The convergence condition is that the maximum value of the change in the design variable is less than 0.

001.

3. The optimization design method according to claim 1, characterized in that, The establishment of the equivalent performance parameter library for composite materials includes the following process: extracting process parameters and constructing a parameterized representative volume element model; calculating the equivalent thermo-mechanical performance parameters corresponding to the process parameters based on the energy homogenization method, and establishing the equivalent performance parameter library for composite materials.

4. The optimization design method according to claim 1, characterized in that, After updating the design variables, density filtering and projection are performed on the topology variables in the updated design variables.

5. The optimization design method according to claim 1, characterized in that, The neural network includes radial basis function neural networks and backpropagation (BP) networks.

6. The optimization design method according to claim 1, characterized in that, The geometry of the design domain is easy to discretize into a mapped mesh, the loads and constraints can describe the stress conditions of the structure during service, and the design variables are topological variables, fiber volume fraction, and braiding angle.

7. The optimization design method according to claim 1, characterized in that, The gradient optimization algorithms include optimization criterion method, moving asymptote method, sequential linear programming, and sequential quadratic programming.

8. The optimization design method according to claim 1, characterized in that, The composite materials include planar braided composite materials, machine-woven composite materials, three-dimensional four-way braided composite materials, three-dimensional five-way braided composite materials, three-dimensional six-way braided composite materials, and three-dimensional seven-way braided composite materials.

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