Topological optimization method and system for multi-material thermoelastic structure containing material allowable temperature constraint

Abstract

The invention discloses a multi-material thermoelastic structure topological optimization method and system containing material allowable temperature constraint, and belongs to the technical field of structure topological optimization. Comprising the following steps: 1) acquiring transient heat conduction and transient thermoelasticity static analysis finite element control equations, and performing finite element analysis on a design model; 2) based on a multi-material SIMP method interpolation model and a material domain identification strategy, establishing a material region time domain maximum temperature constraint function and a structure optimization objective function by using a condensation integral function; 3) establishing a multi-material thermoelastic structure topological optimization model containing material allowable temperature constraint; and 4) carrying out iterative updating on the design variables in the topological optimization model by adopting an MMA algorithm to complete the optimization design of the multi-material thermoelastic structure of the design target. According to the method provided by the invention, the maximum temperature of different material areas can be reflected in real time, and the maximum temperature of each material can be controlled within an allowable range in the topological optimization of the multi-material thermoelastic structure under the transient thermal load.

Description

A Method and System for Topology Optimization of Multi-Material Thermoelastic Structures with Allowable Material Temperature Constraints Technical Field

[0001] This invention belongs to the field of structural topology optimization technology, and particularly relates to a method and system for topology optimization of multi-material thermoelastic structures with allowable material temperature constraints. Background Technology

[0002] With technological advancements, thermoelastic structures face increasingly demanding thermal service environments. Single-material topology optimization methods are no longer sufficient to meet the growing requirements for thermal protection, thermal conductivity, and strength. In contrast, multi-material topology optimization offers multiple alternative materials with different properties and selects the most advantageous material for the optimization objective at different locations within the design domain based on loads and boundary conditions, resulting in a superior structural design.

[0003] For thermoelastic structures, temperature is a crucial factor affecting structural safety. High temperatures can cause materials (such as metals) to soften or even melt, leading to structural failure. To ensure safe operation, the maximum temperature of the materials used must be controlled within a safe range. However, existing temperature-constrained topology optimization methods typically consider temperature constraints for a specific spatial domain. In the iterative calculation of multi-material topology optimization, each material subdomain changes continuously with each iteration step. Temperature constraints for a specific spatial domain cannot effectively control the maximum temperature of the continuously changing material domains during optimization. Therefore, establishing a multi-material topology optimization method that can effectively control the maximum temperature of the materials used is of great significance for maximizing the functionality of each material while ensuring structural safety. Accurately identifying the changing range of material subdomains during optimization and expressing their time-domain maximum temperature is a challenge in the allowable temperature constraint problem for materials in multi-material thermoelastic structure topology optimization under transient thermal loads. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for topology optimization of multi-material thermoelastic structures with allowable material temperatures, which can reflect the maximum temperature of different material regions in real time and realize the control of the maximum temperature of each material within the allowable range in the topology optimization of multi-material thermoelastic structures under transient thermal loads.

[0005] To solve the aforementioned technical problem, the technical solution adopted by this invention is as follows: a topology optimization method for multi-material thermoelastic structures with allowable material temperature constraints, comprising the following steps: 1) Applying thermal and mechanical boundary conditions to the design target multi-material thermoelastic model according to the load conditions and constraint boundary conditions, discretizing the design domain using the finite element method to obtain the transient heat conduction and transient thermoelastic static analysis finite element control equations, thereby performing finite element analysis on the design model; the transient heat conduction and transient thermoelastic static analysis finite element control equations are shown in (1) and (2): C +KT(t)=F(t)(1)K m U(t) = P m +P th (t)(2) where C is the global heat capacity matrix, K is the global heat conduction matrix; F(t) is the applied transient heat load vector, and T(t) is 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; 2) Based on the multi-material SIMP interpolation model and material domain identification strategy, the material region time-domain maximum temperature constraint function and structural optimization objective function are established using the condensation integral function; 3) A multi-material thermoelastic structure topology optimization model with allowable material temperature constraints is established; 4) The MMA algorithm is used to iteratively update the design variables in the topology optimization model to complete the optimization design of the multi-material thermoelastic structure with the design objective, and obtain the design result that meets the temperature safety requirements; Steps 1) and 2) are not limited by time order.

[0006] Preferably, the expression for the material domain identification strategy in step 2) is: (3) Wherein, if the thermal conductivity of a certain region is located at the thermal conductivity k of material m (m = 1,2,3) m Add or subtract a small positive number interval This allows us to identify that the area falls within the coverage of material m; where the smaller positive number... The value is 0.0001.

[0007] Preferably, the material domain identification strategy expression is determined based on a multi-material thermal conductivity interpolation model; the density field and thermal conductivity of the multi-material thermal conductivity interpolation model are shown in (4) and (5): (4) (5) Among them: (6) (7) For this multi-material interpolation model, the design variables in the material m subdomain take the following values: (8) In this case, the density and thermal conductivity of the material in this region are respectively: (9).

[0008] Preferably, a mapping algorithm using PDE filtering and Heaviside mapping is used to make the design variables take the value of 0 or 1.

[0009] Preferably, the temperature at the center of the unit is selected as the controlled object; the formula for calculating the temperature at the center of the unit is: (10).

[0010] Where T e T1, T2, T3, T4 are the temperatures of the finite element nodes; N1, N2, N3, N4 are weighting coefficients in the form of shape functions of the finite element nodes, and their magnitudes are positively correlated with the corresponding node temperatures.

[0011] Preferably, in step 2), the constraint function for the highest time-domain temperature reflecting the different material coverage areas is established using the condensation integral function: (11) Where T(x,t) is the temperature field at time t, tf is the duration of the transient thermal load, V is the integration region of the function, and a T The exponent of the integral of temperature condensation, when hour, The strategy for increasing the condensation integral factor with each iteration step is to increase the condensation integral factor value by n for every m iterations, where m and n are set according to the specific numerical example.

[0012] Preferably, the first derivatives of the condensation integral function and the material region time-domain maximum temperature constraint function with respect to the design variables are solved, and the design variables in the topology optimization model are iteratively updated using the MMA algorithm to complete the optimization design of the multi-material thermoelastic structure of the design target.

[0013] This invention provides a topology optimization system for multi-material thermoelastic structures with allowable material temperatures, including a module for constraining the maximum temperature in the time domain of the material coverage area and a module for acquiring temperatures in specific regions. The module for constraining the maximum temperature in the time domain of the material coverage area is used to establish expressions for the maximum temperature in the time domain of each material region and calculate the sensitivity of these expressions. The module for acquiring temperatures in specific regions is used to integrate the expressions for the maximum temperature in the time domain of the material regions into the topology optimization model of the multi-material thermoelastic structure based on the sensitivity information, thereby obtaining a multi-material thermoelastic structure that meets temperature safety requirements.

[0014] 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 multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above schemes.

[0015] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs a multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above embodiments.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The multi-material thermoelastic structure topology optimization method with material allowable temperature constraints proposed in the present invention can accurately reflect the changes in the range of each material domain in the iterative process of multi-material structure topology optimization based on the material domain identification method based on thermal conductivity. On this basis, the material allowable temperature constraint model can accurately reflect the time domain maximum temperature of each material domain and control the maximum temperature of a specific material within its allowable range.

[0017] (2) The material allowable temperature constraint model of the present invention, by deriving the sensitivity of the constraint function, is integrated into the topology optimization model of multi-material thermoelastic structure, and a solution method that meets the generality and robustness required for optimization iteration is established, realizing the safe design of multi-material thermoelastic structure under transient heat transfer conditions.

[0018] (3) The material allowable temperature model established by the present invention can make reasonable selection and arrangement of candidate materials according to the load and boundary conditions, and the maximum temperature of each material in the optimization results is effectively controlled within the allowable range. Attached Figure Description

[0019] Figure 1 is a flowchart of an embodiment of the present invention; Figure 2 is the initial design model of the multi-material thermoelastic cantilever beam in Embodiment 1 of the present invention; Figure 3 is a multi-material interpolation model diagram in Embodiment 1 of the present invention; Figure 4 is a structural diagram of the multi-material thermoelastic cantilever beam in Embodiment 1 of the present invention after topology optimization without considering the allowable temperature constraints of materials; wherein Figure 4a is the topology optimization result, Figure 4b is the change of the maximum temperature of each material region with time in the optimization result, and Figure 4c is the temperature field at the final moment of the optimization result; Figure 5 is a structural diagram of the multi-material thermoelastic cantilever beam in Embodiment 1 of the present invention after topology optimization considering the allowable temperature constraints of materials; wherein Figure 5a is the topology optimization result, Figure 5b is the change of the maximum temperature of each material with the iteration step, Figure 5c is the change of the maximum temperature of each material region with time in the optimization result, and Figure 5d is the temperature field at the final moment of the optimization result. Detailed Implementation

[0020] 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.

[0021] This invention provides a topology optimization method for multi-material thermoelastic structures with allowable material temperature constraints, comprising the following steps: 1) Applying thermal and mechanical boundary conditions to the multi-material thermoelastic model of the design target according to the load conditions and constraint boundary conditions, discretizing the design domain using the finite element method to obtain the transient heat conduction and transient thermoelastic static analysis finite element control equations, thereby performing finite element analysis on the design model; the transient heat conduction and transient thermoelastic static analysis finite element control equations are shown in (1) and (2): C +KT(t)=F(t)(1)K m U(t) = P m +P th (t)(2) where C is the global heat capacity matrix, K is the global heat conduction matrix; F(t) is the applied transient heat load vector, and T(t) is the temperature field vector at time t. K is the time derivative of the temperature field vector at time t. 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; 2) Based on the multi-material SIMP interpolation model and material domain identification strategy, the material region time-domain maximum temperature constraint function and structural optimization objective function are established using the condensation integral function; 3) A multi-material thermoelastic structure topology optimization model with allowable material temperature constraints is established; 4) The MMA algorithm is used to iteratively update the design variables in the topology optimization model to complete the optimization design of the multi-material thermoelastic structure with the design objective, and obtain the design result that meets the temperature safety requirements; Steps 1) and 2) are not limited by time order.

[0022] In this invention, the expression for the material domain identification strategy is further defined as follows: (3) Wherein, if the thermal conductivity of a certain region is located at the thermal conductivity k of material m (m = 1,2,3) m Add or subtract a small positive number interval This allows us to identify that the area falls within the coverage of material m; where the smaller positive number... The value is 0.0001. Furthermore, based on the multi-material thermal conductivity interpolation model, the material domain identification strategy expression is determined, assuming that the thermoelastic model design domain contains N subdomains, which are occupied by empty materials and N-1 types of materials. At this time, the density field and thermal conductivity of the multi-material interpolation model are shown in (4) and (5): (4) (5) Among them: (6) (7) For this multi-material interpolation model, the design variables in the material m subdomain take the following values: (8) In this case, the density and thermal conductivity of the material in this region are respectively: (9).

[0023] For multi-material topology optimization methods based on SIMP, design variables can take intermediate values, not just 0 or 1. Intermediate variables can lead to the presence of more than one material within a finite cell, causing errors in material domain identification. To address this issue, this invention further employs a mapping algorithm based on PDE filtering and Heaviside mapping, allowing design variables to take values ​​of 0 or 1. Specifically: First, a partial differential filter based on Helmholtz-type partial differential equations is used to smooth the original design variable field. In equation (12), These are the smoothed design variables. The PDE filter radius is related to the standard filter radius as follows: (13) of which Let be the filtering radius. Then, the smoothed field is truncated and mapped using a large-threshold Heaviside projection to obtain the mapped field of the design variables. The Heaviside function is: In equation (14), To design the mapping field of variable xi, It is a parameter that determines the sharpness of the mapping function. The threshold value is used.

[0024] For multi-material finite element models, nodes at the interface belong to two different material regions simultaneously. If node temperature is the controlled object, the node temperature at the interface will be controlled by multiple constraint functions simultaneously, which may cause computational difficulties in optimizing the model. Therefore, in this invention, the temperature at the element center is further selected as the controlled object; the formula for calculating the element center temperature is: (10).

[0025] Where T eT1, T2, T3, and T4 are the temperatures of the finite element nodes; N1, N2, N3, and N4 are weighting coefficients in the form of finite element node shape functions, whose magnitudes are positively correlated with the corresponding node temperatures to avoid large errors between the calculated element center point temperatures and the maximum node temperatures.

[0026] Therefore, the time-domain maximum temperature control function for the area covered by the m-th material can be obtained. The expression is: In equation (15), For the nth i A finite element at t j Temperature at time t j N represents discrete time points in the time domain. c Subdomain occupied by material m The number of finite elements. N j It represents the number of discrete time points. T The exponent of the integral of temperature condensation, when hour, Therefore, the allowable temperature constraint model for materials, which aims to control the maximum temperature of a specific material within its allowable range, is as follows: (16) where m is the allowable temperature of material m.

[0027] In this invention, a constraint function reflecting the highest time-domain temperature of different material-covered regions is further established using the condensation integral function: (11) Where T(x,t) is the temperature field at time t, tf is the duration of the transient thermal load, V is the integration region of the function, and aT is the exponent of the temperature condensation integral. hour, The strategy for increasing the condensation integral factor with each iteration step is to increase the condensation integral factor value by n for every m iterations, where m and n are set according to the specific numerical example.

[0028] In this invention, the first derivatives of the condensation integral function and the material region time-domain maximum temperature constraint function with respect to the design variables are solved. The MMA algorithm is then used to iteratively update the design variables in the topology optimization model, completing the optimization design of the multi-material thermoelastic structure with the design objective. The specific implementation process of the topology optimization of the multi-material thermoelastic structure with allowable material temperature constraints in this invention is shown in Figure 1.

[0029] This invention provides a topology optimization system for multi-material thermoelastic structures with allowable material temperatures, including a module for constraining the maximum temperature in the time domain of the material coverage area and a module for acquiring temperatures in specific regions. The module for constraining the maximum temperature in the time domain of the material coverage area is used to establish expressions for the maximum temperature in the time domain of each material region and calculate the sensitivity of these expressions. The module for acquiring temperatures in specific regions is used to integrate the expressions for the maximum temperature in the time domain of the material regions into the topology optimization model of the multi-material thermoelastic structure based on the sensitivity information, thereby obtaining a multi-material thermoelastic structure that meets temperature safety requirements.

[0030] 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 multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above schemes.

[0031] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs a multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above embodiments.

[0032] 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.

[0033] 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, create means for implementing the functions specified in one or more blocks of the flowcharts and / or one or more blocks of the block diagrams.

[0034] 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 that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0035] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0036] 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.

[0037] 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.

[0038] Example 1 In this example, the method includes the following steps: determining the design objectives and load conditions of the designed structure. As shown in Figure 2, the structure is 120mm long and 80mm high, fixed at the left end, and subjected to a concentrated load F of 10N at the middle of the right end, directed vertically downwards. Simultaneously, a constant heat source q(t) with a heat generation rate of 100W / s is located at the point of concentrated load application, and the load application time is 1200 s. The left side of the model is a isothermal heat dissipation boundary with a specified temperature of 0℃, and the remaining sides are adiabatic boundaries. The design domain contains three design materials. The property parameters of the three design materials and the empty material region are shown in Table 1. Under the given material content (material 1: 10%, material 2: 10%, material 3: 10%, total material volume 30%) and allowable material temperatures, design the optimal structural topology to minimize the strain energy of the structure.

[0039] Table 1 Material Properties

[0040] Specifically, in order to illustrate the technical solution of this embodiment, the steps are described in detail.

[0041] Step 1: Multi-material region identification: As shown in Figure 3, when the model contains four materials, three sets of design variable fields x1, x2, and x3 are defined. In this case, the density field and thermal conductivity interpolation of the four-material model are expressed as: (17) (18) Among them, Here, k is density, and k is thermal conductivity. X is the coordinate of the point within the defined domain. and These represent the density field and thermal conductivity of the void phase, respectively. and (i = 1,2,3) represent the density field and thermal conductivity of material i. P is a penalty factor that causes the values ​​of the design variables to tend towards the upper or lower bound. As shown in Figure 3, the design variable fields x1 and x2 divide the design domain into three subdomains. , , , These are occupied by empty material, material 1, material 2, and material 3, respectively. For the three subdomains... , (i = 1,2,3).

[0042] In this case, if the thermal conductivity of a certain region is at the level of the thermal conductivity k of material m (m = 1, 2, 3) m Add or subtract a small positive number interval This allows us to identify the region as belonging to the coverage area of ​​material m. The smaller positive number is 0.0001. The formula for the material domain identification strategy based on thermal conductivity is: (3) Step 2: Maximum temperature constraint function of the material region: The maximum temperature is approximated as the condensation integral of the temperature field in the time and spatial domains: (11) Where T(x,t) is the temperature field at time t, obtained by solving the transient heat transfer control equation. f Let V be the duration of the transient thermal load, V be the integration region of the function, and a be the time of application of the transient thermal load. T The exponent of the integral of temperature condensation, when hour, The strategy for increasing the condensation integral factor with each iteration step is to increase it by a certain value after each certain number of iterations.

[0043] Step 3: Multi-material thermoelastic topology optimization model with allowable material temperature constraints: Apply thermal and mechanical boundary conditions to the multi-material thermoelastic model, and discretize it using the finite element method to obtain the finite element governing equations for transient heat conduction and transient thermoelastic static analysis: C +KT(t)=F(t)(1)K m U(t) = P m +P th (t)(2) where C is the global heat capacity matrix, K is the global heat conduction matrix; F(t) is the applied transient heat load vector, and T(t) is the temperature field vector at time t. K is the time derivative of the temperature field vector at time t. 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; based on the temperature field and displacement field obtained from simulation calculations, the condensation integral of the structural strain energy in the time domain can be expressed as: (19) Among them: For the actual strain at time t, Let be the initial strain caused by the temperature field at time t. The integral factor for strain energy condensation.

[0044] Combining the temperature constraint model in step 2, a structural topology optimization model is established using the method described in this paper to minimize the maximum time-domain strain energy of the structure while considering the allowable temperature constraint of the material, for the problem of optimizing the stiffness of thermoelastic structures under transient thermal loads. (20) Step 4: Solve for the first derivatives of the objective function and constraint function with respect to the design variables in the optimization model: According to the method of adjoint variables, the first derivative of the maximum strain energy in the time domain with respect to the design variables is: (21) Then, the values ​​of the Lagrange multipliers are calculated using equations (22) and (23): (twenty two) (23) The maximum temperature condensation integral is also solved using the sensitivity method of local maximum response. The analytical expression of the structural maximum temperature condensation integral with respect to the design variables at time t is: (twenty four) (25) Thus, the analytical expression of the condensation integral function at maximum temperature with respect to the design variables can be obtained as follows: (26) (27) (28) Thus, the equation for calculating the Lagrange multipliers can be obtained as follows: (29) Among them: and These are the Lagrange multipliers for strain energy and maximum temperature, respectively; The equivalent thermal load and temperature field relationship matrix is ​​obtained by substituting the calculated Lagrange multipliers into equations (21) and (26) respectively to obtain the time-domain maximum strain energy and the first derivative of the material time-domain maximum temperature condensation integral function with respect to the design variables.

[0045] Step 5: The design variables are iteratively updated using the MMA algorithm to complete the optimization design of the target thermoelastic structure. The optimization results with and without considering the allowable material temperature constraints when the thermal load working time is 800 s are shown in Figures 4 and 5, respectively. As can be seen from Figure 4(a), the global configuration of the optimized structure is similar to the results of minimizing the strain energy of the thermoelastic structure in previous studies. The material with the highest elastic modulus is placed closest to the load. The material with the second highest elastic modulus forms the main force transmission path. The material with the lowest elastic modulus is placed at the edge of the main force transmission path. This material allocation scheme is beneficial to improving the structural stiffness. The strain energy of the optimized structure is 467.39 J. However, as can be seen from Figure 4(b), the highest temperature of stainless steel reaches its allowable temperature at 112 s and reaches 1028.3℃ at the end, exceeding its allowable temperature. Figure 4(c) shows the temperature distribution of the optimized structure at the end. To ensure the safe operation of the optimized structure, the highest temperature of the materials used should be controlled within its allowable range. As shown in Figure 5(a), the allowable temperature constraint on materials led to a significant change in the material distribution scheme of the optimized structure. The aluminum alloy, appearing near the load location, facilitated heat dissipation. Compared to the optimized structure without allowable temperature constraints, the strain energy increased from 467.39 J to 485.17 J, an increase of 3.8%. The change in material distribution weakened the stiffness of the optimized structure. Figure 5(b) shows the convergence curve of the constraint function iteration. As shown in Figure 5(c), the highest time-domain temperatures of the three materials were 500℃, 800℃, and 174.1℃, respectively. Figure 5(d) shows the temperature distribution of the optimized structure at the end of the process. The results in Figure 5 indicate that although the stiffness of the optimized structure was slightly reduced, the highest temperature of the materials used was effectively controlled within its allowable range.

[0046] 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 method for topology optimization of multi-material thermoelastic structures with allowable material temperatures, characterized in that, The steps include: 1) Applying thermal and mechanical boundary conditions to the multi-material thermoelastic model of the design target according to the load conditions and constraint boundary conditions, discretizing the design domain using the finite element method to obtain the transient heat conduction and transient thermoelastic static analysis finite element control equations, thereby performing finite element analysis on the design model; the transient heat conduction and transient thermoelastic static analysis finite element control equations are shown in (1) and (2): C +KT(t)=F(t)(1)K m U(t) = P m +P th (t)(2) where C is the global heat capacity matrix, K is the global heat conduction matrix; F(t) is the applied transient heat load vector, and T(t) is 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; 2) Based on the multi-material SIMP interpolation model and material domain identification strategy, the maximum time-domain temperature constraint function and structural optimization objective function of the material region are established using the condensation integral function; 3) A topology optimization model of a multi-material thermoelastic structure with allowable material temperature constraints is established; 4) The MMA algorithm is used to iteratively update the design variables in the topology optimization model to complete the optimization design of the multi-material thermoelastic structure with the design objective, and obtain the design result that meets the temperature safety requirements; Steps 1) and 2) are not subject to any time order.

2. The topology optimization method according to claim 1, characterized in that, The expression for the material domain identification strategy in step 2) is: (3) Wherein, if the thermal conductivity of a certain region is located at the thermal conductivity k of material m (m = 1,2,3) m Add or subtract a small positive number interval This allows us to identify that the area falls within the coverage of material m; where the smaller positive number... The value is 0.0001.

3. The topology optimization method according to claim 2, characterized in that, The material domain identification strategy expression is determined based on the multi-material thermal conductivity interpolation model; the density field and thermal conductivity of the multi-material thermal conductivity interpolation model are shown in (4) and (5): （4） （5） in: （6） (7) For this multi-material interpolation model, the design variables in the material m subdomain take the following values: (8) In this case, the density and thermal conductivity of the material in this region are respectively: （9）。 4. The topology optimization method according to claim 1, characterized in that, The PDE filtering and Heaviside mapping algorithm is used to make the design variables take the values ​​of 0 or 1.

5. The topology optimization method according to claim 1, characterized in that, The temperature at the center of the unit is selected as the controlled object; the formula for calculating the temperature at the center of the unit is: (10) Where T e T1, T2, T3, T4 are the temperatures of the finite element nodes; N1, N2, N3, N4 are weighting coefficients in the form of shape functions of the finite element nodes, and their magnitudes are positively correlated with the corresponding node temperatures.

6. The topology optimization method according to claim 1, characterized in that, In step 2), the constraint function for the highest time-domain temperature reflecting the different material coverage areas is established using the condensation integral function: (11) Where T(x,t) is the temperature field at time t, tf is the duration of the transient thermal load, V is the integration region of the function, and a T The exponent of the integral of temperature condensation, when hour, The strategy for increasing the condensation integral factor with each iteration step is to increase the condensation integral factor value by n for every m iterations, where m and n are set according to the specific numerical example.

7. The topology optimization method according to claim 6, characterized in that, The first derivatives of the condensation integral function and the material region time-domain maximum temperature constraint function with respect to the design variables are obtained. The MMA algorithm is then used to iteratively update the design variables in the topology optimization model, thereby completing the optimization design of the multi-material thermoelastic structure with respect to the design objective.

8. A topology optimization system for multi-material thermoelastic structures with allowable material temperature constraints, characterized in that: It includes a module for constraining the maximum temperature in the time domain of the material coverage area and a module for acquiring the temperature of a specific area. The module for constraining the maximum temperature in the time domain of the material coverage area is used to establish the maximum temperature constraint expression in the time domain of each material region and calculate the sensitivity of the maximum temperature constraint expression in the time domain of the material region. The module for acquiring the temperature of a specific area is used to integrate the maximum temperature constraint expression in the time domain of the material region into the topology optimization model of the multi-material thermoelastic structure based on the sensitivity information, so as to obtain a multi-material thermoelastic structure that meets the temperature safety requirements.

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 multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above schemes.

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 multi-material thermoelastic structure topology optimization method with material allowable temperature constraints as described in any of the above schemes.

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