Method and system for topology optimization of temperature-dependent transient thermoelastic structures considering material properties

Abstract

The application discloses a kind of transient thermoelastic structure topology optimization methods considering material property temperature correlation, belong to structural topology optimization technical field.It includes:1) obtaining transient heat conduction and transient thermoelastic static finite element control equation;2) material property temperature correlation transient heat transfer control equation is solved using Newton iteration method and difference method;3) based on SIMP method, the transient thermoelastic structure topology optimization model considering material property temperature correlation and stress constraint is established;4) the sensitivity expression of objective function and constraint function about design variable is derived using adjoint method, and the design variable in topology optimization model is iteratively updated using corresponding optimization algorithm, and the optimal design result under current thermal load condition is obtained.The method provided by the application can accurately reflect the influence of transient thermal effect on material property temperature correlation, and realize the accurate design of structure in the material property temperature correlation thermoelastic structure topology optimization problem under transient thermal load.

Description

Technical Field

[0001] This invention belongs to the field of structural topology optimization technology, and particularly relates to a transient thermoelastic structural topology optimization method and system that considers the temperature-dependent properties of materials. Background Technology

[0002] During high-speed flight, hypersonic vehicles experience a complex and time-varying aerodynamic thermal loads on their surfaces due to the combined effects of multiple factors, including aerodynamic heating, complex flow field structures, and dynamic flight trajectories. These aerodynamic thermal loads cause temperature field disturbances that often lead to changes in material properties, resulting in fluctuations in structural performance.

[0003] In existing research on the structural optimization design of hypersonic vehicles, to avoid the huge computational costs of iterative solutions, it is often assumed that material properties do not change with temperature, or transient thermal loads are simplified into a fixed temperature field. This leads to discrepancies between design conditions and actual service conditions, ultimately resulting in structural designs that are either unsafe or overly conservative. Therefore, there is an urgent need to establish a structural design method that can accurately characterize the changes in material properties with temperature under transient heat transfer conditions. Through higher-precision design, structural safety can be ensured while maximizing the potential of structural service performance. Summary of the Invention

[0004] In view of this, the present invention provides a transient thermoelastic structural topology optimization method and system that considers the temperature correlation of material properties. The topology optimization method provided by the present invention can accurately reflect the influence of transient effects on the temperature correlation of material properties under transient heat transfer, and obtains better design results than the previous thermoelastic topology optimization methods that assume constant material properties and simplify the transient thermal load to a fixed temperature field under transient heat transfer conditions.

[0005] To solve the aforementioned technical problem, the technical solution adopted by the present invention is as follows: A transient thermoelastic structure topology optimization method considering the temperature dependence of material properties includes the following steps: 1) Based on the load conditions and constraint boundary conditions, apply thermal and mechanical boundary conditions to the design target model to obtain the finite element control equations for transient heat conduction and transient thermoelastic static analysis; 2) The transient heat transfer control equations related to material properties and temperature are solved by Newton's iteration method and the finite difference method to obtain the temperature field and material property distribution matrix at each time point. Then, the obtained temperature field and material property distribution matrix are substituted into the transient thermoelastic static analysis finite element control equations to obtain the thermoelastic structural displacement, strain and stress structural response at each time point. 3) Based on the SIMP method, a transient thermoelastic structure topology optimization model considering the temperature dependence of material properties and stress constraints is established to characterize the maximum values ​​of strain energy and stress of the thermoelastic structure in the time domain, and use them as the objective function and constraint function of the established optimization model. 4) Based on the sensitivity information, the maximum values ​​of the objective function and the constraint function of the transient heat transfer process are integrated into the transient thermoelastic structural topology optimization model that considers the temperature-dependent properties of the material properties, so as to obtain the optimal design result under the current thermal load conditions.

[0006] Preferably, the finite element governing equations for transient heat conduction and transient thermoelastic static analysis in step 1) are shown in (1) and (2), respectively: (1) (2) in, The design variable distribution function is given by: T representing the temperature field, C representing the global heat capacity matrix, and K representing the global thermal conductivity matrix; F(t) representing the applied transient thermal load vector, and T(t) representing the temperature field vector at time t. Let K be the derivative of the temperature field vector at time t with respect to time. m It is the overall structural stiffness matrix, U(t) is the displacement vector at time t, and P m It is the mechanical load vector, P th (t) is the equivalent temperature load vector caused by thermal strain.

[0007] Preferably, in step 2), when the material property parameters have temperature-dependent characteristics, the transient heat conduction control equation (1) is solved using the finite difference method, and the finite difference solution is shown in (3): (3) Among them, R k For t k Time equation thermal load, When using the finite difference method, the transient heat transfer time interval t is divided into n time steps. ,and , The subscript k represents the current time node number; When the material properties are nonlinear, the Newton-Raphson iteration method is used to solve for the temperature field, heat capacity matrix, heat conduction matrix, and stiffness matrix at each time point; based on the initial temperature field... The heat conduction array at the initial moment is obtained. Thermal array and stiffness matrix Using this as the initial condition, the first time point is solved through equation (3). tInitial values ​​of temperature field, thermal conductivity matrix, heat capacity matrix, and stiffness matrix 1 , , The initial temperature field for the first time node is calculated using nonlinear methods based on the initial values. (4) in: (5) Next, convergence is determined by iteratively calculating the temperature field difference before and after the process. If the difference is less than the specified value, then convergence is considered satisfied; otherwise, the convergence condition is not met. As an initial condition, repeat the above calculation until starting from the first... m The approximate solution and the first m +1 approximate solution satisfies the convergence condition: (6) Thus, the first time point can be obtained. , , And so on, until the temperature field, heat conduction matrix, and heat capacity matrix at all time points are obtained. , , Subsequently, the temperature fields at each time point are substituted into equation (2), and the stiffness matrix and displacement at each time point are obtained by solving equations (3)-(6) in the same way. , .

[0008] Preferably, in step 3), the P-norm integral is used to characterize the maximum values ​​of strain energy and stress in the time domain of the thermoelastic structure, and a transient thermoelastic structure topology optimization model considering material property temperature dependence and stress constraints is established based on the SIMP method; the transient thermoelastic structure topology optimization model considering material property temperature dependence and stress constraints is as follows: (7) in, A For the design domain area, To design the unit density within the domain, A e For the unit area within the design domain, This is the upper limit of the set volume fraction. This is the upper limit of the set stress constraint.

[0009] Preferably, the P-norm integral is used to characterize the maximum values ​​of strain energy and stress in the time domain of the thermoelastic structure, and the maximum strain energy in the time domain of the structure is... The characterization equation is: (8) in, (9) (10) The P-norm integral equation representing the maximum value of structural stress in the time domain is: (11) in, (12) (13) in, Let be the total strain at time t. Let be the free thermal strain at time t. These are the strain-displacement relationship matrix and the element strain-displacement relationship matrix, respectively. These are the thermal strain-temperature relationship matrix and the element thermal strain-temperature relationship matrix, respectively. These are the total elasticity matrix and the element elasticity matrix, respectively. These are the principal stresses in the x-direction, y-direction, and shear stress of the element, respectively.

[0010] In step 4), the adjoint method is used to solve for the sensitivity analytical expressions of the objective function and constraint functions with respect to the design variables, and Lagrange multipliers are introduced. and Then, the expression for the maximum strain energy in the time domain is: (14) The expression for the sensitivity of the time-domain maximum strain energy to the design variables is: (15) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: (16) (17) in, (18) (19) (20) , (twenty one) Substituting the calculated Lagrange multipliers into equation (15) yields the sensitivity analysis value of the maximum strain energy of the structure in the time domain with respect to the design variables.

[0011] Preferably, in step 4), the adjoint method is used to solve the sensitivity analytical expressions of the objective function and constraint function with respect to the design variables, and Lagrange multipliers are introduced. and Then, the expression for the maximum stress in the time domain is: , (twenty two) The expression for the sensitivity of the time-domain maximum stress to the design variables is: ,(twenty three) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: , (twenty four) (25) in, (26) (27) (28) Substituting the calculated Lagrange multipliers into equation (23) yields the sensitivity analysis value of the maximum time-domain stress of the structure with respect to the design variables.

[0012] This invention provides a transient thermoelastic structure topology optimization system that considers the temperature dependence of material properties, including a module for solving the finite element control equations of the transient thermoelastic structure that are related to the temperature dependence of material properties; The module for solving the control equations of the transient thermoelastic structure with temperature-dependent material properties is based on the finite difference method and Newton's iteration method to obtain the material property distribution and thermal and mechanical structural responses of the transient thermoelastic structure at each time point. On this basis, the expression for the maximum value of the objective function and the maximum value of the constraint function of the transient heat transfer process is integrated into the topology optimization model of the transient thermoelastic structure considering the temperature-dependent material properties, based on sensitivity information, to obtain the optimal design result under the current thermal load conditions.

[0013] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the transient thermoelastic structural topology optimization method considering the temperature dependence of material properties as described in any of the above-described schemes.

[0014] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the transient thermoelastic structural topology optimization method considering material property temperature dependence as described in any of the above schemes.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The transient thermoelastic structure topology optimization method considering the temperature correlation of material properties proposed in this invention can accurately obtain the material property distribution and thermal and mechanical structural response of the transient thermoelastic structure at each time point in the simulation calculation of the transient thermoelastic structure considering the temperature correlation of material properties based on the difference method and Newton's iteration method. On this basis, the maximum value of the structural response in the time domain is characterized by the P-norm integral equation, thereby accurately reflecting the influence of transient effect on the temperature correlation of material properties of transient thermoelastic structure.

[0016] (2) The transient thermoelastic structure topology optimization model of the present invention, which considers the temperature-dependent material properties, derives the sensitivity analytical expressions of the objective function and constraint function with respect to the design variables through the adjoint method, accurately reflecting the influence of the change of the design variables on the values ​​of the objective function and constraint function, and realizing the accurate design of the transient thermoelastic structure with temperature-dependent material properties under transient heat transfer conditions.

[0017] (3) The transient thermoelastic structure topology optimization method considering the temperature-dependent material properties established in this invention can reasonably select and arrange the transient thermoelastic structure with temperature-dependent material properties according to the load and boundary conditions. The optimization results obtained are all the optimal solutions under the current transient thermal load conditions. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a specific implementation method in Embodiment 1 of the present invention; Figure 2 This is the thermoelastic structure topology optimization model under transient thermal load in Embodiment 1 of the present invention; Figure 3 This is the optimized structure diagram for a heat load duration of 100 s in Embodiment 1 of the present invention; where 3a is the optimized result for a heat load duration of 100 s in Embodiment 1 of the present invention. Figure 3 b is the stress cloud diagram of the optimized result when the thermal load application time is 100 s in Embodiment 1 of the present invention. Figure 3 c represents the time-domain maximum strain energy and time-domain maximum stress variation curves during the optimization process when the thermal load application time is 100 s in Embodiment 1 of the present invention. Figure 3 d is the heat capacity coefficient distribution cloud map of the optimized result when the heat load application time is 100 s in Embodiment 1 of the present invention. Figure 3 e is the thermal conductivity distribution cloud map of the optimized result when the heat load application time is 100 s in Embodiment 1 of the present invention. Figure 3 f is the Young's modulus distribution cloud map of the optimization result when the thermal load application time is 100 s in Embodiment 1 of the present invention; Figure 4 This is an optimized structural diagram of Embodiment 1 of the present invention when the heat load duration is 1500s; wherein Figure 4a represents the optimized result when the thermal load application time is 1500 s in Example 1 of this invention. Figure 4 b is the stress cloud diagram of the optimized result when the thermal load application time is 1500 s in Embodiment 1 of the present invention. Figure 4 c represents the time-domain maximum strain energy and time-domain maximum stress variation curves during the optimization process when the thermal load application time is 1500 s in Embodiment 1 of the present invention. Figure 4 d is the heat capacity coefficient distribution cloud map of the optimized result when the heat load application time is 1500 s in Embodiment 1 of the present invention. Figure 4 e is the thermal conductivity distribution cloud map of the optimized result when the heat load application time is 1500 s in Embodiment 1 of the present invention. Figure 4 f is the Young's modulus distribution cloud map of the optimized result when the thermal load application time is 1500 s in Embodiment 1 of the present invention; Figure 5 This is an optimized structural diagram of Embodiment 1 of the present invention when the heat load duration is 3000s; wherein Figure 5 a represents the optimized result when the thermal load application time is 3000 s in Example 1 of this invention. Figure 5 b is the stress cloud diagram of the optimized result when the thermal load application time is 3000 s in Embodiment 1 of the present invention. Figure 5 c represents the curves showing the changes in maximum strain energy and maximum stress in the time domain during the optimization process when the thermal load application time is 3000 s in Example 1 of this invention. Figure 5 d is the heat capacity coefficient distribution cloud map of the optimized result when the heat load application time is 3000 s in Embodiment 1 of the present invention. Figure 5 e is the thermal conductivity distribution cloud map of the optimized result when the heat load application time is 3000 s in Embodiment 1 of the present invention. Figure 5 f is the Young's modulus distribution cloud map of the optimization result when the thermal load application time is 3000 s in Embodiment 1 of the present invention; Figure 6 This is an optimized structural diagram of Embodiment 1 of the present invention when the heat load duration is 5000s; wherein Figure 6 a represents the optimized result when the thermal load application time is 5000 s in Example 1 of this invention. Figure 6 b is the stress cloud diagram of the optimized result when the thermal load application time is 5000 s in Embodiment 1 of the present invention. Figure 6 c represents the curves showing the changes in maximum strain energy and maximum stress in the time domain during the optimization process when the thermal load application time is 5000 s in Example 1 of this invention. Figure 6 d is the heat capacity coefficient distribution cloud map of the optimized result when the heat load application time is 5000 s in Embodiment 1 of the present invention. Figure 6 e is the thermal conductivity distribution cloud map of the optimized result when the heat load application time is 5000 s in Embodiment 1 of the present invention. Figure 6f is the Young's modulus distribution cloud map of the optimized result when the thermal load application time is 5000 s in Embodiment 1 of the present invention; Figure 7 The maximum strain energy in the time domain for each optimization result under different thermal load durations; Figure 8 The maximum stress in the time domain is the result of each optimization under different thermal load durations. Detailed Implementation

[0019] The technical solutions in specific embodiments of the present invention will be described in detail and completely below. Obviously, the described embodiments are only some specific implementations of the overall technical solution of the present invention, and not all implementations. Based on the overall concept of the present invention, all other embodiments obtained by those skilled in the art fall within the protection scope of the present invention.

[0020] This invention provides a transient thermoelastic structure topology optimization method considering the temperature dependence of material properties, comprising the following steps: 1) Based on the load conditions and constraint boundary conditions, apply thermal and mechanical boundary conditions to the design target model to obtain the finite element control equations for transient heat conduction and transient thermoelastic static analysis; 2) The transient heat transfer control equations related to material properties and temperature are solved by Newton's iteration method and the finite difference method to obtain the temperature field and material property distribution matrix at each time point. Then, the obtained temperature field and material property distribution matrix are substituted into the transient thermoelastic static analysis finite element control equations to obtain the thermoelastic structural displacement, strain and stress structural response at each time point. 3) Based on the SIMP (Solid Isotropic Material with Penalization) method, a transient thermoelastic structure topology optimization model considering the temperature dependence of material properties and stress constraints is established to characterize the maximum values ​​of strain energy and stress of thermoelastic structure in the time domain, and use them as the objective function and constraint function of the established optimization model. 4) Based on the sensitivity information, the maximum values ​​of the objective function and the constraint function of the transient heat transfer process are integrated into the transient thermoelastic structural topology optimization model that considers the temperature-dependent properties of the material properties, so as to obtain the optimal design result under the current thermal load conditions.

[0021] In step 1) of this invention, thermal and mechanical boundary conditions are applied to the design target model based on the load conditions and constraint boundary conditions to obtain the transient heat conduction and transient thermoelastic static analysis finite element control equations, thereby performing finite element analysis on the design model. Further, in this invention, the transient heat conduction and transient thermoelastic static analysis finite element control equations described in step 1) are shown in (1) and (2) respectively: (1) (2) in, The design variable distribution function is given by: T representing the temperature field, C representing the global heat capacity matrix, and K representing the global thermal conductivity matrix; F(t) representing the applied transient thermal load vector, and T(t) representing the temperature field vector at time t. Let K be the derivative of the temperature field vector at time t with respect to time. m It is the overall structural stiffness matrix, U(t) is the displacement vector at time t, and P m It is the mechanical load vector, P th (t) is the equivalent temperature load vector caused by thermal strain.

[0022] In step 2) of this invention, the Newton iteration method and the finite difference method are used to solve the transient heat transfer control equation related to the temperature of the material properties. This invention uses a transient thermoelastic analysis solution module based on the Newton iteration method and the finite difference method, considering the temperature dependence of the material properties, to obtain the material property distribution and structural response at each time point in the transient thermoelastic simulation analysis under the temperature dependence of the material properties. Further, in step 2), when the material property parameters have temperature-dependent characteristics, the finite difference method is used to solve the transient heat conduction control equation (1), and the finite difference solution is shown in (3): (3) Among them, R k For t k Time equation thermal load, When using the finite difference method, the transient heat transfer time interval t is divided into n time steps. ,and , The subscript k represents the current time node number; Equation (3) can obtain the temperature field at each time node under the condition that the initial temperature field x is known. Then, the calculated temperature field is substituted into Equation (2) to complete the thermoelastic simulation solution.

[0023] When the material properties are nonlinear, the Newton-Raphson iteration method is used to solve for the temperature field, heat capacity matrix, heat conduction matrix, and stiffness matrix at each time point; based on the initial temperature field... The heat conduction array at the initial moment is obtained. Thermal array and stiffness matrix Using this as the initial condition, the first time point is solved through equation (3). t Initial values ​​of temperature field, thermal conductivity matrix, heat capacity matrix, and stiffness matrix 1 , , The initial temperature field for the first time node is calculated using nonlinear methods based on the initial values. (4) in: (5) Next, convergence is determined by iteratively calculating the temperature field difference before and after the process. If the difference is less than the specified value, then convergence is considered satisfied; otherwise, the convergence condition is not met. As an initial condition, repeat the above calculation until starting from the first... m The approximate solution and the first m +1 approximate solution satisfies the convergence condition: (6) Thus, the first time point can be obtained. , , And so on, until the temperature field, heat conduction matrix, and heat capacity matrix at all time points are obtained. , , Subsequently, the temperature fields at each time point are substituted into equation (2), and the stiffness matrix and displacement at each time point are obtained by solving equations (3)-(6) in the same way. , .

[0024] In this invention, further, the transient thermoelastic structural topology optimization model considering material property temperature dependence and stress constraints in step 3) is as follows: (7) in, A For the design domain area, To design the unit density within the domain, A e For the unit area within the design domain, This is the upper limit of the set volume fraction. This is the upper limit of the set stress constraint.

[0025] In this invention, the P-norm integral is further used to characterize the maximum value of the transient thermoelastic structural response in the time domain under temperature-dependent material properties. Based on this, the objective function and stress control function of the optimization model are constructed. In this invention, the P-norm integral is used to characterize the maximum values ​​of strain energy and stress in the time domain of the thermoelastic structure, wherein the maximum strain energy in the time domain of the structure... The characterization equation is: (8) in, (9) (10) The P-norm integral equation representing the maximum value of structural stress in the time domain is: (11) in, (12) (13) in, Let be the total strain at time t. Let be the free thermal strain at time t. These are the strain-displacement relationship matrix and the element strain-displacement relationship matrix, respectively. These are the thermal strain-temperature relationship matrix and the element thermal strain-temperature relationship matrix, respectively. These are the total elasticity matrix and the element elasticity matrix, respectively. These are the principal stresses in the x-direction, y-direction, and shear stress of the element, respectively.

[0026] In this invention, further, in step 4), the adjoint method is used to solve for the sensitivity analytical expressions of the objective function and constraint function with respect to the design variables, and Lagrange multipliers are introduced. and Then, the expression for the maximum strain energy in the time domain is: (14) The expression for the sensitivity of the time-domain maximum strain energy to the design variables is: (15) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: (16) (17) in, (18) (19) (20) , (twenty one) Substituting the calculated Lagrange multipliers into equation (15) yields the sensitivity analysis value of the maximum strain energy of the structure in the time domain with respect to the design variables.

[0027] Introducing Lagrange multipliers and Then, the expression for the maximum stress in the time domain is: , (twenty two) The expression for the sensitivity of the time-domain maximum stress to the design variables is: ,(twenty three) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: , (twenty four) (25) in, (26) (27) (28) Substituting the calculated Lagrange multipliers into equation (23) yields the sensitivity analysis value of the maximum time-domain stress of the structure with respect to the design variables.

[0028] This invention provides a transient thermoelastic structure topology optimization system that considers the temperature dependence of material properties, including a module for solving the finite element control equations of the transient thermoelastic structure that are related to the temperature dependence of material properties; The module for solving the control equations of the transient thermoelastic structure with temperature-dependent material properties is based on the finite difference method and Newton's iteration method to obtain the material property distribution and thermal and mechanical structural responses of the transient thermoelastic structure at each time point. On this basis, the expression for the maximum value of the objective function and the maximum value of the constraint function of the transient heat transfer process is integrated into the topology optimization model of the transient thermoelastic structure considering the temperature-dependent material properties, based on sensitivity information, to obtain the optimal design result under the current thermal load conditions.

[0029] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the transient thermoelastic structural topology optimization method considering the temperature dependence of material properties as described in any of the above-described schemes.

[0030] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the transient thermoelastic structural topology optimization method considering material property temperature dependence as described in any of the above schemes.

[0031] It should be noted that the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage) containing computer-usable program code.

[0032] This invention is described in terms of flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowcharts and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0033] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0034] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0035] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0036] To further illustrate the present invention, the technical solutions provided by the present invention will be described in detail below with reference to the embodiments, but they should not be construed as limiting the scope of protection of the present invention.

[0037] Example 1 like Figure 2 The figure shows a temperature-dependent thermoelastic structural topology optimization model for materials subjected to transient thermal loads. The model size is [size missing]. The upper part of the structure is a non-designable region with a thickness of 2mm, indicated in black; the gray area represents the designable region. The upper part bears a uniformly distributed compressive load. q (t) = 5 N / mm and uniformly distributed heat flux load f (t) = 1 W / mm. The lower boundary is a vertical displacement constraint and a 20°C isothermal boundary. Both the left and right sides are adiabatic boundaries. The material used in the design domain is TC4 (Ti-6Al-4V), and the equations for the material's Young's modulus, heat capacity, and thermal conductivity as a function of temperature are as follows: (29) (30) (31) The optimization objective is to minimize the strain energy of the structure under the given material volume fraction (40%) and considering the time-domain maximum stress constraint (not exceeding 46 MPa).

[0038] In this embodiment, the specific implementation process for transient thermoelastic structural topology optimization considering material property temperature dependence is as follows: Figure 1 As shown. To illustrate the technical solution of this embodiment, the steps are described in detail.

[0039] Step 1: Establishment of the governing equations for temperature-dependent transient thermoelastic simulation of material properties: Figure 2 The diagram shows a topology optimization model of a material property temperature-dependent thermoelastic structure subjected to transient thermal load. Based on the load conditions and constraint boundary conditions, thermal and mechanical boundary conditions are applied to the material property temperature-dependent transient thermoelastic model to obtain the finite element control equations for material property temperature-dependent transient heat conduction and material property temperature-dependent transient thermoelastic static analysis. This allows for finite element analysis of the design model. The finite element control equations for transient heat conduction and transient thermoelastic static analysis are shown in equations (1) and (2): (1) (2) in, The design variable distribution function is given by: T representing the temperature field, C representing the global heat capacity matrix, and K representing the global thermal conductivity matrix; F(t) representing the applied transient thermal load vector, and T(t) representing the temperature field vector at time t. Let K be the derivative of the temperature field vector at time t with respect to time. m It is the overall structural stiffness matrix, U(t) is the displacement vector at time t, and P m It is the mechanical load vector, P th (t) is the equivalent temperature load vector caused by thermal strain.

[0040] Step 2: Solve the temperature-dependent transient thermoelastic simulation control equations for material properties: The transient heat transfer control equation (1) is solved using the finite difference method and Newton's iteration method. The finite difference solution is as follows: (3) Where R k For t k Time equation thermal load, When using the finite difference method, the transient heat transfer time interval t is divided into n time steps. ,and , The subscript k represents the current time node number. Equation (3) can be derived from the given initial temperature field. Under the given conditions, the temperature field at each time point is obtained. Then, the calculated temperature field is substituted into equation (2) to complete the thermoelastic simulation solution.

[0041] When the material properties are nonlinear, the Newton-Raphson iteration method is used to solve for the temperature field, heat capacity matrix, heat conduction matrix, and stiffness matrix at each time point. Initial temperature field The heat conduction array at the initial moment is obtained. Thermal array and stiffness matrix Using this as the initial condition, the initial values ​​of the temperature field, thermal conductivity matrix, heat capacity matrix, and stiffness matrix at the first time point t1 are obtained by solving equation (3). , , The initial temperature field for the first time node is calculated using nonlinear methods based on the initial values. (4) in: (5) Next, convergence is determined by iteratively calculating the temperature field difference before and after the process. If the difference is less than the specified value, then convergence is considered satisfied. If the convergence condition is not met, then... As an initial condition, repeat the above calculation until starting from the first... m The approximation with the first m +1 approximate solution satisfies the convergence condition: (6) Thus, the first time point can be obtained. , , And so on, until the temperature field, heat conduction matrix, and heat capacity matrix at all time points are obtained. , , Subsequently, the temperature fields at each time point are substituted into equation (2), and the stiffness matrix and displacement at each time point are obtained by solving equations (3)-(6) in the same way. , .

[0042] Step 3: Characterize the maximum values ​​of strain energy and stress in the time domain of the thermoelastic structure using the P-norm integral: The characterization equation for the maximum strain energy in the time domain of a structure is: (8) in, (9) (10) The P-norm integral equation representing the maximum value of structural stress in the time domain is: (11) in, (12) (13) Step 4: Establishing the optimization model: A topology optimization model based on the SIMP method is established to minimize the maximum strain energy in the time domain of the structure, while considering the maximum stress constraint in the time domain and the material volume fraction constraint. (7) in, A For the design domain area, To design the unit density within the domain, A e For the unit area within the design domain, This is the upper limit of the set volume fraction. This is the upper limit of the set stress constraint.

[0043] Step 5: Use the adjoint method to solve for the sensitivity expressions of the objective function and constraint functions with respect to the calculation variables: Introducing Lagrange multipliers and Then, the expression for the maximum strain energy in the time domain is: (14) The expression for the sensitivity of the time-domain maximum strain energy to the design variables is: (15) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: (16) (17) in, (18) (19) (20) , (twenty one) Substituting the calculated Lagrange multipliers into equation (15) yields the sensitivity analysis value of the maximum strain energy of the structure in the time domain with respect to the design variables.

[0044] Introducing Lagrange multipliers and Then, the expression for the maximum stress in the time domain is: , (twenty two) The expression for the sensitivity of the time-domain maximum stress to the design variables is: ,(twenty three) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: , (twenty four) (25) in, Substituting the calculated Lagrange multipliers into equation (23) yields the sensitivity analysis value of the maximum time-domain stress of the structure with respect to the design variables.

[0045] Step 6: The MMA algorithm is used to iteratively update the macroscopic and microscopic design variables in the topology optimization model to complete the optimization design of the temperature-dependent transient thermoelastic structure of the target material properties. Figures 3, 4, 5, and 6 show the optimization results of the proposed method under heat load durations of 100 s, 1500 s, 3000 s, and 5000 s, respectively. Each set of optimization results includes stress cloud diagrams, iteration history curves, and distribution cloud diagrams of specific heat capacity, thermal conductivity, and elastic modulus under the final temperature field. It can be seen that there are significant differences in the material layout of the optimized structure under different heat load durations. The maximum strain energies in the time domain for each optimization result are 405.3 J, 680.5 J, 898.6 J, and 1197.3 J, respectively. The differences in the final temperature field of the optimized configuration result in different distributions of specific heat capacity, thermal conductivity, and elastic modulus. This indicates that the transient effect of heat load has a significant impact on the structural configuration, structural response, and material property distribution of the optimized results. Furthermore, the maximum equivalent stress in the time domain of all optimized results does not exceed 46 MPa, verifying the effectiveness of the stress constraint in the proposed method. To verify the performance variation law of the optimized results under different thermal load durations, multi-condition thermal load duration simulation analysis was carried out for all optimized configurations. Figures 7 and 8 show the maximum strain energy and maximum stress in the time domain of each optimized structure under different thermal load durations, respectively. As shown in Figure 7, under the four load conditions, each optimized structure can obtain the optimal value of the objective function under its corresponding design condition. For example, under the 100-second transient heating condition, the topology optimization design based on the 100-second duration has the minimum objective function value; similarly, when the actual thermal load duration is 3000 seconds, the topology optimization design corresponding to the 3000-second condition outperforms other design schemes. As shown in Figure 8, each optimized structure only meets the stress constraint requirements under its corresponding transient thermal load condition; when the optimized structure is subjected to non-design thermal load conditions, its maximum stress in the time domain will exceed the stress constraint limit of 46 MPa.

[0046] The above results lead to the conclusion that, for the topology optimization problem of thermoelastic structures with temperature-dependent material properties under transient thermal loads, the transient effect of thermal load has a significant impact on the material layout, structural mechanical properties, and material property distribution of the optimization results. If there is a deviation between the designed thermal load condition and the actual service condition, the maximum stress of the optimized structure will fail to meet the stress safety limit requirements.

[0047] The proposed method, under different thermal load durations, not only achieves effective control of the time-domain maximum stress but also obtains the optimal objective function value for each designed thermal load duration. This demonstrates that the method can accurately characterize the influence of transient thermal load effects, thus validating the effectiveness of the proposed method.

[0048] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A transient thermoelastic structural topology optimization method considering the temperature dependence of material properties, characterized in that, Includes the following steps: 1) Based on the load conditions and constraint boundary conditions, apply thermal and mechanical boundary conditions to the design target model to obtain the finite element control equations for transient heat conduction and transient thermoelastic static analysis; 2) The transient heat transfer control equations related to material properties and temperature are solved by Newton's iteration method and the finite difference method to obtain the temperature field and material property distribution matrix at each time point. Then, the obtained temperature field and material property distribution matrix are substituted into the transient thermoelastic static analysis finite element control equations to obtain the thermoelastic structural displacement, strain and stress structural response at each time point. 3) Based on the SIMP method, a transient thermoelastic structure topology optimization model considering the temperature dependence of material properties and stress constraints is established to characterize the maximum values ​​of strain energy and stress of the thermoelastic structure in the time domain, and use them as the objective function and constraint function of the established optimization model. 4) Based on the sensitivity information, the maximum values ​​of the objective function and the constraint function of the transient heat transfer process are integrated into the transient thermoelastic structural topology optimization model that considers the temperature-dependent properties of the material properties, so as to obtain the optimal design result under the current thermal load conditions.

2. The topology optimization method according to claim 1, characterized in that, The transient heat conduction and transient thermoelastic static analysis finite element governing equations described in step 1) are shown in (1) and (2) respectively: ， (1) ， (2) in, The design variable distribution function is given by: T representing the temperature field, C representing the global heat capacity matrix, and K representing the global thermal conductivity matrix; F(t) representing the applied transient thermal load vector, and T(t) representing the temperature field vector at time t. Let K be the derivative of the temperature field vector at time t with respect to time. m It is the overall structural stiffness matrix, U(t) is the displacement vector at time t, and P m It is the mechanical load vector, P th (t) is the equivalent temperature load vector caused by thermal strain.

3. The topology optimization method according to claim 2, characterized in that, In step 2), when the material property parameters have temperature-dependent characteristics, the transient heat conduction control equation (1) is solved using the finite difference method. The finite difference solution is shown in (3): , (3) Among them, R k For t k Time equation thermal load, When using the finite difference method, the transient heat transfer time interval t Divided into n time steps ,and , The subscript k represents the current time node number; When the material properties are nonlinear, the Newton-Raphson iteration method is used to solve for the temperature field, heat capacity matrix, heat conduction matrix, and stiffness matrix at each time point; based on the initial temperature field... The heat conduction array at the initial moment is obtained. thermal array and stiffness matrix Using this as the initial condition, the first time point is solved through equation (3). t Initial values ​​of temperature field, thermal conductivity matrix, heat capacity matrix, and stiffness matrix 1 , , The initial temperature field for the first time node is calculated using nonlinear methods based on the initial values. ， (4) in: , (5) Next, convergence is determined by iteratively calculating the temperature field difference before and after the process. If the difference is less than the specified value, then convergence is considered satisfied; otherwise, the convergence condition is not met. As an initial condition, repeat the above calculation until starting from the first... m The approximate solution and the first m +1 approximate solution satisfies the convergence condition: ， (6) Thus, the first time point can be obtained. , , And so on, until the temperature field, heat conduction matrix, and heat capacity matrix at all time points are obtained. , , Subsequently, the temperature fields at each time point are substituted into equation (2), and the stiffness matrix and displacement at each time point are obtained by solving equations (3)-(6) in the same way. , .

4. The topology optimization method according to claim 1, characterized in that, In step 3), the P-norm integral is used to characterize the maximum values ​​of strain energy and stress in the time domain of the thermoelastic structure. A transient thermoelastic structure topology optimization model considering temperature dependence of material properties and stress constraints is established based on the SIMP method. The transient thermoelastic structure topology optimization model considering temperature dependence of material properties and stress constraints is as follows: ， (7) in, A For the design domain area, Let Ae be the element density within the design domain, and Ae be the element area within the design domain. This is the upper limit of the set volume fraction. This is the upper limit of the set stress constraint.

5. The topology optimization method according to claim 4, characterized in that, maximum strain energy in the time domain of the structure The characterization equation is: , (8) in, (9) (10) The P-norm integral equation representing the maximum value of structural stress in the time domain is: ， (11) in, ， (12) ， (13) in, Let be the total strain at time t. Let be the free thermal strain at time t. These are the strain-displacement relationship matrix and the element strain-displacement relationship matrix, respectively. These are the thermal strain-temperature relationship matrix and the element thermal strain-temperature relationship matrix, respectively. These are the total elasticity matrix and the element elasticity matrix, respectively. These are the principal stresses in the x-direction, y-direction, and shear stress of the element, respectively.

6. The topology optimization method according to claim 5, characterized in that, In step 4), the adjoint method is used to solve for the sensitivity analytical expressions of the objective function and constraint functions with respect to the design variables, and Lagrange multipliers are introduced. and Then, the expression for the maximum strain energy in the time domain is: ， (14) The expression for the sensitivity of the time-domain maximum strain energy to the design variables is: ，(15) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: ， (16) ， (17) in, ， (18) ， (19) ， (20) ， (21) Substituting the calculated Lagrange multipliers into equation (15) yields the sensitivity analysis value of the maximum strain energy of the structure in the time domain with respect to the design variables.

7. The topology optimization method according to claim 5, characterized in that, In step 4), the adjoint method is used to solve for the sensitivity analytical expressions of the objective function and constraint functions with respect to the design variables, and Lagrange multipliers are introduced. and Then, the expression for the maximum stress in the time domain is: ， (22) The expression for the sensitivity of the time-domain maximum stress to the design variables is: ，(23) After simplification, the equations for calculating Lagrange multipliers can be obtained as follows: ， (24) ， (25) in, ， (26) ， (27) ，(28) Substituting the calculated Lagrange multipliers into equation (23) yields the sensitivity analysis value of the maximum time-domain stress of the structure with respect to the design variables.

8. A transient thermoelastic structural topology optimization system considering the temperature dependence of material properties, characterized in that, Includes a module for solving the governing equations of transient thermoelastic structures with temperature-dependent material properties; The module for solving the control equations of the transient thermoelastic structure with temperature-dependent material properties is based on the finite difference method and Newton's iteration method to obtain the material property distribution and thermal and mechanical structural responses of the transient thermoelastic structure at each time point. On this basis, the expression for the maximum value of the objective function and the maximum value of the constraint function of the transient heat transfer process is integrated into the topology optimization model of the transient thermoelastic structure considering the temperature-dependent material properties, based on sensitivity information, to obtain the optimal design result under the current thermal load conditions.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it performs the transient thermoelastic structural topology optimization method that considers the temperature dependence of material properties as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it performs the transient thermoelastic structural topology optimization method considering the temperature dependence of material properties as described in any one of claims 1-7.

Images