A method for layout optimization design of a multi-component composite thermal structural system

Abstract

The application provides a multi-component composite material thermal structure system layout 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, determining and initializing two types of design variables; dividing the component and the design domain boundary into envelope circles, establishing a constraint function according to the envelope circle information and constraint conditions; establishing a connection relationship; 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 multi-component composite material thermal structure system layout optimization design method provided by the application effectively realizes the collaborative optimization design of the macroscopic structure of the composite material, the weaving process parameters and the spatial layout of the component under a high-temperature environment.

Description

Technical Field

[0001] This invention belongs to the field of material structure optimization technology, specifically relating to a layout optimization design method for a multi-component composite material thermal structure system. 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. The aircraft structure 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 the extreme high-temperature service environment. The development of high-temperature resistant composite materials, such as high-temperature ceramic composites, has laid the material foundation for the thermal structure of hypersonic aircraft.

[0003] Various functional components, instruments, and other payloads (referred to as components) are installed on a composite material integral thermal structure platform through a reasonable spatial layout. Both the spatial layout of the components and the configuration of the composite material thermal structure affect the comprehensive mechanical performance of the system. In order to meet the comprehensive mechanical performance and lightweight design requirements of the system, it is necessary to consider the coordinated design of the component spatial layout and structural configuration. The literature "On the multi-component layout design withinertial force" (Zhu, JH, P. Beckers and WH Zhang, Journal of Computational and Applied Mathematics, 2010, 234(7): p.2222-2230) discloses a layout optimization design method for multi-component structural systems. This method combines structural topology optimization and filling layout optimization techniques to achieve coordinated optimization of the spatial layout of components and the configuration of the supporting structure. The literature discloses the use of the finite envelope circle method to solve the interference problems between components and between the boundaries of components and the design area. However, the design problem it addresses is still the pure stiffness optimization design of conventional materials under normal temperature conditions. On the one hand, it cannot characterize the influence of the anisotropic characteristics of the microstructure of braided composite materials on the macroscopic structural performance, and on the other hand, it does not consider the influence of the thermal stress generated by the structure under high temperature conditions on the design results.

[0004] To seek high-performance, lightweight woven composite thermal structures and their synergistic optimization design with component structural layout, a homogenization method was used to establish an equivalent characterization model of the macroscopic thermo-mechanical properties of composite materials, enabling cross-scale thermo-mechanical coupling analysis across macro, meso, and micro scales. A finite envelope circle was used to describe the geometric shape of the components and establish constraint functions. Based on multi-point constraint modeling technology, the connection relationship between each component and the composite material support structure was established. An index function suitable for evaluating the thermal structure performance under extremely high temperature and non-uniform temperature environments was constructed, ultimately achieving synergistic optimization of component spatial layout, composite macrostructure, and weaving process parameters. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that it is difficult to achieve high-performance and lightweight synergistic optimization of the thermal structure and spatial layout of composite materials under high-temperature conditions.

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

[0007] A layout optimization design method for a multi-component composite thermal structure system 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 a design domain, apply loads and constraints that describe the stress conditions of the structure during service, and determine and initialize design variables, namely topological variables, fiber volume fraction and braiding angle, based on the finite element model;

[0010] The boundaries of the component and the design domain are divided into envelope circles. The interference between components and whether the component is located within the design domain can be determined by describing the distance between the envelope circles of the component outline. Based on the center coordinates and the corresponding radius information, the constraints can be written as inequality constraint functions.

[0011] 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;

[0012] Steady-state heat transfer analysis and thermo-mechanical coupling analysis are performed to solve the corresponding equations to obtain the temperature 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 sensitivity information;

[0013] 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 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 step of establishing the connection relationship between each component and the composite material support structure, repeating the calculation until the convergence condition is met.

[0014] Specifically, the layout optimization design method for the multi-component composite material thermal structure system of the present invention can be summarized as the following mathematical optimization problem:

[0015] find:

[0016] min:

[0017] st:

[0018]

[0019] 0 < ρ min ≤ρ i ≤1

[0020] 30°≤γ≤60°

[0021] The optimization model described above includes two types of design variables. The first type of design variable, χ1, describes the overall thermal structure configuration and process parameters of the composite material, and includes the topological variable ρ. i The braiding angle γ; the second type of design variable χ2 is used to describe the position of the installed components, and the position of each component in three-dimensional space is expressed by the coordinates of its geometric center (ξ). jx ξ jy ξ jz ), deflection angle and pitch angle ξ jθ Five variables are used to describe it, N c The number of predefined components. 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 +fm Thermal load can be achieved through f th =K mth ΔT 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 To control the structural load-bearing stiffness, a penalty is imposed. V(χ) i The volumetric material usage of the composite thermal structure needs to be less than the upper limit V. Furthermore, to avoid unreasonable results due to interference between components during the optimization process, an interference constraint g is applied. κ (χ2), Ω i and Ω j These represent the regions where component i and component j are located, respectively. The two regions should never intersect, meaning their intersection Ω is the boundary between them. i ∩Ω j for Furthermore, to avoid singularity in the stiffness matrix, the topological variable ρ is... i The lower limit is set to a very small positive number ρ. min .

[0022] Compared with the prior art, the present invention has the following beneficial effects or advantages:

[0023] 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.

[0024] A novel objective function form suitable for thermal structure optimization problems under high-temperature environments is proposed, which effectively coordinates the relationship between the thermal structure of composite materials and the spatial layout of components under high-temperature environments.

[0025] A collaborative optimization method for component structural spatial layout, composite material thermal structure configuration, and process parameters was proposed, realizing integrated design of materials, structure, and multiple physics fields, and providing an effective theoretical method for the design of the overall structure. Attached Figure Description

[0026] Figure 1 This is a flowchart of the layout optimization design of the composite material component described in this invention.

[0027] Figure 2 This refers to the representative volume element model and homogenization process of the three-dimensional braided composite material described in the embodiments of the present invention.

[0028] Figure 3 This is an approximate division of the finite envelope circle between the components and the design domain as described in the embodiments of the present invention.

[0029] Figure 4 This is a schematic diagram of a multi-point constraint connection according to an embodiment of the present invention.

[0030] Figure 5 This is a schematic diagram of the cantilever beam structure described in an embodiment of the present invention.

[0031] Figure 6 The layout optimization design method for the multi-component composite material thermal structure system described in this invention is optimized. Figure 5 The result of the cantilever beam structure shown. Detailed Implementation

[0032] 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.

[0033] 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.

[0034] Example 1

[0035] This embodiment provides an experiment for establishing a library of equivalent performance parameters for three-dimensional four-way braided composite materials.

[0036] 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 with the weaving angle and fiber volume fraction as process parameters.

[0037] The thermo-mechanical properties of composite materials are calculated based on the energy homogenization method, including the equivalent thermoelastic coefficient, equivalent thermal expansion coefficient, and equivalent thermal conductivity coefficient. A library of equivalent performance parameters for composite materials is established. A radial basis function neural network is applied to fit the mapping relationship between braiding process parameters and equivalent thermo-mechanical properties, and a library of equivalent performance parameters for three-dimensional four-way braided composite materials is established.

[0038] Example 2

[0039] This embodiment provides an experiment on optimizing a cantilever beam structure using the optimization design method described in this invention.

[0040] 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.

[0041] Cantilever beam structure, such as Figure 5 As shown, there are 3 component structures distributed in the design domain.

[0042] according to Figure 1 The process shown has been optimized as follows:

[0043] 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 condition of the structure during service are applied. Two types of design variables, χ1 and χ2, are determined and initialized based on the finite element model.

[0044] like Figure 3 As shown, the boundaries of components and design domains are divided into envelope circles. The geometry of each component can be approximated by a series of envelope circles. O represents an envelope circle, the first subscript represents the i-th component, the second subscript represents the j-th envelope circle, and O 12 This refers to the second envelope circle on the first component. The design domain of a composite material structure can also be viewed as a component, its geometric profile approximated by a series of envelope circles. Therefore, the interference between components and whether a component is within the design domain can be determined by describing the distance between the envelope circles of the component profiles. Based on the center coordinates and corresponding radius information, the constraints can be written as the following inequality constraint functions.

[0045]

[0046]

[0047] In the formula, (x ik y ik , z ik Let (x) be the coordinates of the center of the k-th envelope circle of the i-th component. jl y jl , z jl Let r be the x-coordinate of the center of the l-th envelope circle of the j-th component. ik Let r be the radius of the k-th envelope circle of the i-th component. jl Let be the radius of the l-th envelope circle of the j-th component, where i = 1, 2, ... N c j = 1, 2, ... N c And i≠j, (x Ωl y Ωl , z Ωl Let r be the coordinates of the center of the l-th envelope circle in the design domain.Ωl Let be the radius of the l-th envelope circle of the design domain.

[0048] like Figure 4 As shown, the displacement 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. 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 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] The rational approximation interpolation function (RAMP) and the above-mentioned rapid prediction model for the equivalent properties of composite materials 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 K. m Thermodynamic coupling matrix K mth and thermal conductivity K th ;

[0050]

[0051] In the formula, N is the total number of units, and q D and q β is the penalty factor in the RAMP model, N is the element basis function matrix, and B is the element strain matrix.

[0052] 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 The sensitivity information is obtained by analyzing the response function and its partial derivative vector with respect to the design variables.

[0053] 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.

[0054] 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 establishing the displacement relationship and repeats the calculation until the convergence condition is met.

[0055] Optimization results are as follows Figure 6 As shown, by Figure 6 It can be seen that the composite material structure has a clear and reasonable configuration, the braiding angle has also obtained the optimal value, and the three components have all found the optimal installation position. There is no mutual interference between the components and they do not exceed the design domain.

[0056] 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 layout of a multi-component composite material thermal structure system, 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 boundaries of the component and design domain are divided into envelope circles. Inequality constraint functions are established based on the center coordinates of the envelope circles, the corresponding radius information, and the constraint conditions. The connection relationship between each component and the composite material support structure is established based on the multi-point constraint modeling method; Steady-state heat transfer analysis and thermo-mechanical coupling analysis are performed to solve the corresponding equations to obtain the temperature 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 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 condition of the design variables is preset. The step of establishing the connection relationship between each component and the composite material support structure is repeated 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, constructing a parameterized representative volume element model, and establishing a parameterized unit cell model; calculating the equivalent thermo-mechanical performance parameters of the composite materials 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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