A method for optimizing the temperature control of a composite thermal structure

Abstract

The application provides a composite material thermal structure temperature control optimization design method, comprising the following processes: establishing a composite material equivalent performance parameter library, constructing a composite material equivalent performance rapid prediction model based on the parameter library, establishing a design domain, and determining and initializing design variables; establishing a connection relationship; calculating each specific coefficient and matrix corresponding to the design variables; obtaining the temperature response of the structure and calculating the displacement response of the structure; calculating a response function and a partial derivative vector thereof with respect to the design variables to obtain sensitivity information; iteratively solving an optimization problem, repeatedly calculating until a convergence condition is reached, and the design variable information of the current iteration step is the final optimization result. The optimization design method provided by the application significantly improves the calculation efficiency of the optimization process and effectively coordinates the relationship between the temperature control of the equipment and the load bearing performance of the thermal structure.

Description

Technical Field

[0001] This invention belongs to the field of material structure optimization technology, specifically relating to a method for optimizing the temperature control of composite material thermal structures. 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-maneuverability overload, 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 the extreme high-temperature service environment. 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 structure of hypersonic aircraft. However, the structural form of the reinforcing preform, such as the fiber ratio, weaving angle, and weaving method, significantly affects the thermo-mechanical properties of the composite material.

[0003] In engineering applications, composite thermal structures typically house various functional components, instruments, and other equipment. Under harsh and complex thermo-mechanical environments, ensuring the proper functioning of these components requires not only excellent mechanical load-bearing capacity but also adequate thermal insulation to prevent temperatures in the equipment installation area from exceeding permissible limits. The literature "Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint" (Gao T., Zhang WH & Duysinx P. Struct Multidisc Optim 48, 1075–1088 (2013)) proposes a bi-value coding parameterization method to simultaneously optimize the composite structure configuration and fiber orientation. This method discretizes continuous fiber orientation angles, treating them as materials with different properties, and then utilizes multi-material optimization principles to select the optimal fiber orientation. This optimization method is still geared towards unidirectional fiber-reinforced composite materials and cannot be directly applied to the optimization design of braided composite material structures widely used in engineering. Furthermore, the optimization method with the goal of maximizing structural stiffness has good universality for room temperature structures, but it can produce ill-conditioned structures that cannot meet engineering requirements when optimizing high-temperature thermal structures. Moreover, it does not consider the temperature control problem under complex thermo-mechanical loads.

[0004] To ensure that equipment components installed on composite thermal structures operate at reasonable temperatures, and to seek high-performance, lightweight braided composite thermal structures, this invention establishes an equivalent characterization model of the macroscopic thermo-mechanical properties of composite materials using homogenization methods. This enables cross-scale thermo-mechanical coupling analysis across macro, meso, and micro scales. Based on multi-point constraint modeling technology, this invention establishes the connection relationship between equipment components and composite material support structures, constructs index functions suitable for evaluating the performance of thermal structures under extremely high and non-uniform temperature environments, and constrains the maximum temperature on the components. Ultimately, this achieves the collaborative optimization design of the macroscopic structure of composite materials and braiding process parameters under local temperature control. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that it is difficult to coordinate and optimize the load-bearing performance of composite thermal structures with equipment temperature control under high-temperature conditions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for optimizing the temperature control of composite thermal structures includes the following steps:

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

[0009] According to the structural design requirements, a reasonable design domain is established within the allowable space. The geometry of the design domain should be easy to discretize into a mapping mesh. Loads and constraints that can describe the stress conditions of the structure during service are applied. Design variables, namely topological variables, fiber volume fraction and braiding angle, are determined and initialized based on the finite element model.

[0010] The connection relationship between the connection nodes on each component and the nodes of the composite material support structure is established based on multi-point constraint modeling technology;

[0011] The rational approximation interpolation function and the equivalent performance prediction model of the composite material are used to calculate the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient of the composite material design domain, and then assembled into the overall structural stiffness matrix, thermo-mechanical coupling matrix and thermal conductivity matrix.

[0012] Heat transfer analysis is performed to obtain the temperature response of the structure. The temperature response is then used as input for thermo-mechanical coupling analysis to calculate the displacement response of the structure.

[0013] Based on the temperature response and displacement response, the response functions of structural compliance, mechanical strain energy, and maximum approximate temperature of the component installation area, as well as their partial derivative vectors with respect to design variables, are calculated to obtain sensitivity information;

[0014] 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 partial derivative 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 for the design variables is that the maximum value of the 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 the step of calculating the element elastic matrix, thermal stress coefficient, and thermal conductivity coefficient of the composite material design domain and repeats the calculation until the convergence condition is met.

[0015] Specifically, the optimal design method for temperature control of composite thermal structures can be summarized as the following mathematical optimization problem:

[0016] find: χ = {x1, x2, ..., x n ;v f ;γ}

[0017] min:

[0018] st:

[0019]

[0020] 0 < x min ≤x i ≤1

[0021] 30%≤v f ≤60%

[0022] 30°≤γ≤60°

[0023] 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, and γ represents the weave angle. J is the objective function, consisting of two parts, the first being structural compliance. K is used to measure the stiffness performance of a structure under high-temperature thermo-mechanical loads. m Let u be the structural stiffness matrix, and let ν be the structural stiffness matrix under thermal load f. th and mechanical load f m The structural displacement vector under the combined action satisfies the equilibrium equation K m u = f th +f m Thermal load can be achieved through f th =K mthΔT is used to calculate, where K mth The first part is the thermomechanical coupling stiffness matrix, where ΔT is the change in the temperature vector of the structural nodes; the second part is the 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 .

[0024] The temperature in the area where the equipment components are installed needs to be controlled below the allowable temperature T. This is because the temperature in the component installation area... A series of nodal temperatures are needed for measurement. Constraining each nodal individually would introduce a large number of constraint equations, which is detrimental to solving the optimization problem. To address this issue, the KS (Kreisselmeier–Steinhauser) condensation function is introduced to construct a new constraint function to approximate the maximum temperature in the component mounting region, i.e. In the formula, the parameter p determines the approximate function. The greater the approximation of the maximum temperature, the better. The closer it gets to the maximum temperature, the more constraint functions are required. It can be further simplified to a constraint function.

[0025] Specifically, the establishment of the equivalent performance parameter library for composite materials includes the following process: 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 the equivalent performance parameter library for composite materials.

[0026] Specifically, neural networks include radial basis function neural networks and backpropagation (BP) networks.

[0027] Specifically, composite materials include planar braided composite materials, 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.

[0028] Compared with the prior art, the present invention has the following beneficial effects or advantages:

[0029] A rapid characterization and prediction model for the equivalent thermo-mechanical properties of composite materials was established based on parametric modeling techniques and neural network methods, which significantly improved the computational efficiency of the optimization process.

[0030] A new objective function form applicable to thermal structure optimization problems under high temperature environments is proposed, which effectively coordinates the relationship between the load-bearing capacity and stiffness of composite materials under high temperature environments.

[0031] A collaborative optimization method for the thermal structure configuration and process parameters of composite materials under equipment temperature control is proposed, realizing the integrated design of structure-function-multi-physics field, and providing an effective theoretical method for the design of the overall structure. Attached Figure Description

[0032] Figure 1 This is a flowchart of the dynamic optimization design of the composite material structure described in this invention.

[0033] Figure 2 This is a representative volumetric element model of the three-dimensional braided composite material described in the embodiments of the present invention.

[0034] Figure 3 This is a schematic diagram of a multi-point constraint connection according to an embodiment of the present invention.

[0035] Figure 4 This is a schematic diagram of the MBB-like simply supported beam structure described in an embodiment of the present invention.

[0036] Figure 5 This is the result of optimizing a MBB-like simply supported beam structure using the traditional structural design method described in the embodiments of the present invention.

[0037] Figure 6 This is the result of optimizing a MBB-like simply supported beam structure using the optimization method described in this invention. Detailed Implementation

[0038] The technical solution of the present invention will be described below with reference to the embodiments. However, the present invention is not limited to the following embodiments.

[0039] Unless otherwise specified, the experimental and detection methods in the following embodiments are conventional methods; the reagents and materials mentioned are commercially available unless otherwise specified; and the index data are measured using conventional methods unless otherwise specified.

[0040] Example 1

[0041] This embodiment provides an experiment for establishing a library of equivalent performance parameters for three-dimensional four-way braided composite materials.

[0042] like Figure 2As 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 (RVE) 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 RVE model. Figure 2 In the diagram, (a) represents the yarn-scale RVE model.

[0043] Based on the energy method, the thermo-mechanical properties of composite materials are calculated, including the equivalent thermoelastic coefficient, equivalent thermal expansion coefficient, and equivalent thermal conductivity coefficient, and a library of equivalent performance parameters for three-dimensional four-way braided composite materials is established.

[0044] Example 2

[0045] This embodiment provides an experiment on optimizing a MBB-like simply supported beam structure using the optimization design method described in this invention.

[0046] 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.

[0047] A schematic diagram of a MBB-like simply supported beam structure is shown below. Figure 4 As shown, each of the upper and lower skins has a layer that serves as a non-design area, while the middle sandwich layer is the design area. The upper and lower skins primarily function as sealants, bearing the scouring of high-temperature airflow and mechanical loads, while the sandwich layer performs multiple functions including load-bearing, weight reduction, and thermal insulation. A crucial functional component is located in the center of the sandwich layer, and its maximum temperature under temperature loads must be controlled to not exceed 120°C.

[0048] like Figure 3 As shown, the connection relationship between the connection nodes on each component and the nodes of the composite material support structure is established based on the multi-point constraint modeling technique. P1 is a connection node on the component, and its projection point in the support structure is point P1 in element e1. * The displacement of node P1 and the projection point P1 * The displacements are equal, while point P1 * The displacement can be obtained by interpolating the displacement of node e1 of element through shape functions, thereby establishing the multi-point constraint equations: In the formula, For the displacement of component connection node P1, Let e1 be the nodal displacement vector. Let e1 be the interpolation shape function of element e1; each connection node of the component corresponds to a multi-point constraint equation, which can be written in matrix form, i.e., Hu = 0, where the H matrix is ​​determined by the shape function of the connection element and the coordinates of the connection node, and u is the overall displacement vector of the structure.

[0049] A rational approximation interpolation function and a rapid prediction model of the equivalent properties of composite materials are applied to calculate the element elastic matrix, thermal stress coefficient, and thermal conductivity coefficient of the composite material design domain, and then assembled into the overall structural stiffness matrix K. m Thermodynamic coupling matrix K mth and thermal conductivity K th ,

[0050]

[0051]

[0052] In the formula, N is the total number of units, and q D and q β All are penalty factors in the RAMP model, N is the element basis function matrix, and B is the element strain matrix.

[0053] Heat transfer analysis is performed to obtain the temperature response of the structure, and this temperature field is used as input for thermo-mechanical coupling analysis to calculate the displacement response of the structure.

[0054] Calculate the structural compliance c and mechanical strain energy c based on temperature and displacement response. m Maximum approximate temperature of component installation area Isostatic response function and its vector of partial derivatives with respect to design variables;

[0055] The gradient optimization algorithm is applied to iteratively solve the optimization problem. The design variables are updated based on the partial derivative information obtained in the previous step, and the updated topological variables are subjected to density filtering and projection.

[0056] 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 calculation of the coefficients and matrices of the composite material design domain is repeated until the convergence condition is met.

[0057] Optimization results are as follows Figure 6 As shown, the composite material structure has a clear and reasonable configuration, and the braiding angle has also achieved the optimal value. The main force transmission path bypasses the equipment components, which can ensure that the equipment components can work normally under the allowable temperature, thus making it more practical for engineering.

[0058] Example 3

[0059] This embodiment provides an experiment for optimizing a MBB-like simply supported beam structure using the traditional direct optimization method.

[0060] The MBB-like simply supported beam structure and the applied loads and constraints are the same as in Example 2.

[0061] The results of optimizing MBB-like simply supported beam structures using the traditional direct optimization method are as follows: Figure 5 As shown, by Figure 5 It can be seen that the configuration functional components obtained by the direct optimization method are connected to a large number of support structures, resulting in higher temperatures that cannot meet the needs of normal equipment operation.

[0062] As described above, the present invention can be well implemented. The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various changes and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the present invention.

Claims

1. A method for optimizing the temperature control of composite material thermal structures, characterized in that, Includes the following processes: Based on the equivalent performance parameter library of composite materials, a neural network is used to fit the mapping relationship between process parameters and equivalent thermo-mechanical properties to obtain a fast prediction model for the equivalent performance of composite materials; a design domain is established, loads and constraints are applied, and design variables are determined and initialized based on the finite element model; The connection relationship between each component and the composite material support structure is established based on the multi-point constraint modeling method; The rational approximation interpolation function and the fast prediction model of the equivalent properties of the composite material are used to calculate the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient of the composite material design domain, and then assembled into the overall structural stiffness matrix, thermo-mechanical coupling matrix and thermal conductivity matrix. Heat transfer analysis is performed to obtain the temperature response of the structure. The temperature response is then used as input for thermo-mechanical coupling analysis to calculate the displacement response of the structure. Based on the temperature response and displacement response, the response function and its partial derivative vector with respect to the design variables are calculated to obtain the sensitivity information; The gradient optimization algorithm is applied to iteratively solve the optimization problem. The design variables are updated based on the sensitivity information. The convergence conditions of the design variables are preset. The calculation steps of the element elastic matrix, thermal stress coefficient and thermal conductivity coefficient of the composite material design domain are repeated until the convergence conditions are met. 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, 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 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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