A method for optimizing the design of a composite thermal structure

Abstract

The application provides a composite material thermal structure dynamics optimization design method, solves the problem that the composite material structure is difficult to coordinate the dynamics performance and the structure bearing performance under high temperature load, and comprises the following processes: an equivalent performance parameter library of the composite material is established, a rapid prediction model of the equivalent performance of the composite material is constructed based on the parameter library, a design domain is established, a structure statics response analysis and a structure steady heat transfer analysis are performed, a dynamics response is analyzed, sensitivity information is solved, an optimization problem is iteratively solved, and repeated calculation is performed until a convergence condition is reached, and design variable information of a 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 dynamics performance and the structure bearing performance of the composite material under a high temperature environment.

Description

Technical Field

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

[0002] With the rapid development of modern aerospace technology, the service environment of aircraft is becoming increasingly harsh and severe. 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. Therefore, in addition to requiring characteristics such as extremely high load-bearing capacity, extreme heat resistance, ultra-high precision, and ultra-lightweight design, the dynamic challenges they face are becoming increasingly prominent. Traditional metallic materials are insufficient to meet the demands of extreme high-temperature 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 structure of hypersonic aircraft. However, the structural form of their reinforcing preforms, such as fiber ratio, weaving angle, and weaving method, significantly affects the thermo-mechanical properties of the composite materials.

[0003] Current mainstream structural optimization methods are typically 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 structures. Traditional optimization models that aim to maximize the natural frequency of the structure have good universality for room-temperature structures; however, they struggle to obtain reasonable structures that meet engineering requirements when optimizing high-temperature thermal structures. 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 structural configuration and fiber orientation of composite materials. It discretizes continuous fiber orientation angles, treating them as materials with different properties, and then uses multi-material optimization to achieve the optimal fiber orientation selection. This cross-scale optimization model involves many variables, has a complex calculation process, and requires high computer performance.

[0004] 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, 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 invention is to solve the problem that composite materials cannot coordinate dynamic performance and load-bearing capacity of thermal structure in a high-temperature environment with high performance and lightweight design.

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

[0007] A method for optimizing the thermal structure dynamics of composite materials 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] Establish the design domain, apply loads and constraints, and determine and initialize design variables based on the finite element model;

[0010] Perform structural static response analysis, apply rational approximation interpolation function and composite material equivalent performance fast prediction model to calculate the element elastic matrix corresponding to the design variables, and assemble it into the overall structural stiffness matrix;

[0011] Perform structural steady-state heat transfer analysis, apply rational approximation interpolation functions and composite material equivalent performance fast prediction models to calculate the element heat transfer matrix corresponding to the design variables, and assemble it into a structural heat transfer matrix;

[0012] The dynamic response of composite thermal structures under stationary random loads was analyzed using the virtual excitation method and the complete quadratic method.

[0013] Solve the corresponding system of equations and calculate the structural response function and its partial derivative vector with respect to the design variables 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 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 the structural statics analysis step and repeats the calculation until the convergence condition is met.

[0015] Specifically, under stable random excitation and while satisfying certain mass constraints, the composite thermal structure, through simultaneous design of composite material process parameters and macroscopic structural topology, minimizes the root mean square of the displacement response at the degrees of freedom of interest. The dynamic optimization design method for composite thermal structures of this invention can be summarized as the following mathematical optimization problem:

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

[0017] min:

[0018] st:

[0019] 0 < x min ≤x i ≤1

[0020] 30%≤v f ≤60%

[0021] 30°≤γ≤60°

[0022] 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(χ) is the objective function, consisting of two parts: the first part is the root mean square of the displacement response at the degrees of freedom of interest in the structure. Used to measure the thermo-structural dynamic properties of composite materials. ω a and ω b These are the angular frequencies at the start and end points of the random excitation power spectrum, respectively. The first part describes the power spectral density matrix of the displacement response at the degree of freedom of interest; the second part is the mechanical strain energy. K is the structural stiffness matrix, u m For the structure under mechanical load fm The structural displacement vector under action satisfies the equilibrium equation K m u 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 .

[0023] Specifically, the establishment of the equivalent performance parameter library for composite materials includes the following process: extracting process parameters, constructing parameterized representative volume element models, and establishing parameterized unit cell models; 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.

[0024] 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.

[0025] 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.

[0026] Compared with the prior art, the present invention has the following beneficial effects or advantages:

[0027] The composite material thermal structure dynamics optimization design method provided by this invention 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.

[0028] This invention proposes a new objective function form applicable to thermal structure optimization problems under high-temperature environments, which effectively coordinates the relationship between the dynamic properties of composite materials and the structural load-bearing capacity under high-temperature environments. Attached Figure Description

[0029] Figure 1 This is a flowchart of the dynamic optimization design of the composite material structure described in this invention.

[0030] Figure 2This is a representative volumetric element model of the three-dimensional braided composite material described in the embodiments of the present invention.

[0031] Figure 3 This is the result of optimizing the cantilever beam structure using the traditional structural design method described in the embodiments of the present invention.

[0032] Figure 4 The result of optimizing the cantilever beam structure using the optimization method described in this invention. Detailed Implementation

[0033] 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.

[0034] 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.

[0035] Example 1

[0036] This embodiment provides an experiment for establishing a library of equivalent performance parameters for three-dimensional four-way braided composite materials.

[0037] 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.

[0038] The thermo-mechanical properties of composite materials are calculated based on the energy method, including the equivalent thermoelastic coefficient, equivalent thermal expansion coefficient, equivalent thermal conductivity coefficient, equivalent density, and equivalent damping coefficient, and a library of equivalent performance parameters for three-dimensional four-way braided composite materials is established.

[0039] Example 2

[0040] This embodiment provides an experiment on optimizing a cantilever beam structure using the optimization design method described in this invention.

[0041] 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.

[0042] A fixed constraint is applied to the left end boundary of the cantilever beam, and a stable random excitation is applied at the midpoint of the right side in the vertical direction.

[0043] according to Figure 1 The process shown has been optimized as follows:

[0044] The design variables, namely the topology variable x, are determined and initialized based on the finite element model. i Fiber volume fraction ν f And the weaving angle γ; perform structural static response analysis and solve the static equilibrium equation K. m u m =f m By applying the rational approximation interpolation function (RAMP) and the aforementioned fast prediction model for the equivalent properties of composite materials, the element elasticity matrix corresponding to the design variables is calculated, and all element stiffness matrices are assembled to obtain the structural stiffness matrix K. m And calculate the mechanical strain energy c of the structure. m ;

[0045]

[0046] In the formula, N is the total number of units, and q D is the penalty factor in the RAMP model, and B is the element strain matrix.

[0047] Perform a steady-state heat transfer analysis of the structure and solve the heat transfer equation K. th T = f th By applying the rational approximation interpolation function (RAMP) and the aforementioned fast prediction model for the equivalent properties of composite materials, the element heat transfer matrix corresponding to the design variables is calculated, and all element heat transfer matrices are assembled into a structural heat transfer matrix K. th ;

[0048]

[0049] In the formula, N is the total number of units, and q κ ∠ is the penalty factor in the RAMP model, ∠ is the gradient operator, and N is the unit basis function matrix.

[0050] The dynamic response of composite thermal structures under stationary random loads is analyzed using the virtual excitation method and the complete quadratic method, and the dynamic equilibrium equations are solved. In the formula, M, C and K mth These are the mass matrix, damping matrix, and thermo-coupling stiffness matrix, respectively, which can be obtained by assembling the correlation matrices of all elements. p represents the stationary random excitation load on the structure. The power spectral density matrix S of the displacement response is calculated based on the analysis results. u and the root mean square of the displacement response at the degrees of freedom of concern of the structure

[0051] The structural response function, including the root mean square of the displacement response at the degrees of freedom of interest, is calculated using the adjoint method. and mechanical strain energy c m Regarding the sensitivity of the design variables, sensitivity information is obtained.

[0052] 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.

[0053] 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 structural statics analysis step and repeats the calculation until the convergence condition is met.

[0054] Optimization results are as follows Figure 4 As shown, by Figure 4 As can be seen, the optimized design method of the present invention provides a clear and reasonable composite material structure configuration, and the braiding angle has also obtained the optimal value. The resulting structure has a relatively balanced load-bearing capacity and stronger engineering applicability.

[0055] Example 3

[0056] This embodiment provides an experiment on optimizing a cantilever beam structure using a traditional direct optimization method.

[0057] The cantilever beam structure and the applied loads and constraints are the same as in Example 2.

[0058] Traditional direct optimization methods are used to optimize this structure, and the optimization results are as follows: Figure 3 As shown, by Figure 3 It can be seen that the structure obtained by the traditional direct optimization method exhibits a strong-weak phase distribution. Although the dynamic performance is relatively good, the connection in some regions is very weak, resulting in poor mechanical performance.

[0059] 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 thermal structure dynamics of composite materials, characterized in that, The process includes the following: 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. Establish the design domain, apply loads and constraints, and determine and initialize design variables based on the finite element model; Perform structural static response analysis, apply rational approximation interpolation function and the fast prediction model of equivalent performance of the composite material to calculate the element elasticity matrix corresponding to the design variables, and assemble it into the overall structural stiffness matrix; Perform structural steady-state heat transfer analysis, apply rational approximation interpolation function and the fast prediction model of equivalent properties of the composite material to calculate the unit heat transfer matrix corresponding to the design variables, and assemble it into a structural heat transfer matrix; The dynamic response of composite thermal structures under stationary random loads is analyzed using the virtual excitation method and the complete quadratic method. Solve the corresponding system of equations and calculate the structural response function and its partial derivative vector with respect to the design variables to obtain 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, and the process jumps to the structural statics analysis step to repeat the calculation 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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