High-temperature structure thermal-mechanical coupling topological optimization method considering thermal contact

Abstract

The invention belongs to the field of high-temperature thermal structure optimization design, and discloses a high-temperature structure thermal-mechanical coupling topological optimization method considering thermal contact. The method comprises the following steps: establishing a thermal-mechanical coupling finite element analysis method containing a contact thermal resistance interface; carrying out thermal coupling analysis on the high-temperature structure on the basis of the thermal coupling finite element analysis method containing the contact thermal resistance interface in the steps, and establishing a topological optimization model containing a plurality of constraints; performing sensitivity solving on the objective function and the constraint function of the topological optimization model to obtain a sensitivity column formula; filtering the sensitivity through a density filtering method; and updating variables in the topological optimization model by adopting a moving asymptote optimization algorithm MMA. A contact problem is expanded to a thermal-mechanical coupling structure, fine design of a high-temperature structure containing thermal contact is facilitated, and meanwhile, a regulation and control mechanism of contact thermal resistance to the thermal-mechanical coupling structure is given through an optimization result, so that the fine degree of design of the high-temperature structure containing thermal contact is improved.

Description

Technical Field

[0001] The invention belongs to the field of high-temperature thermal structure optimization design, and in particular relates to a high-temperature structure thermal-mechanical coupling topology optimization method considering thermal contact. Background Art

[0002] Thermal contact resistance is widely present in the fields of nuclear industry, aerospace and microelectronics, and is a key factor affecting heat transfer and temperature gradient inside the structure. In the fields of electronic equipment, integrated circuits, electric vehicles and LED (light-emitting diode) lighting, the management and optimization of thermal contact resistance is crucial to improving the performance and reliability of the equipment. For example, in electronic equipment, by optimizing the structure and materials of the heat sink and using materials with better thermal conductivity to reduce the thermal contact resistance, the heat dissipation effect of the electronic equipment can be improved and its service life can be extended. In addition, in the field of thermal analysis and thermal design, there are some professional software tools such as Icepak, which can simulate and optimize the thermal contact resistance problem. These tools are based on finite element method and computational fluid dynamics (CFD) technology, which can accurately simulate and analyze heat conduction and thermal radiation problems, and provide visual analysis results to help engineers better understand and optimize thermal management solutions. Therefore, thermal contact resistance is an important parameter in the heat conduction process, which is affected by many factors and can be optimized through a variety of measures.

[0003] In high-temperature, heat-contact structures, the influence of contact thermal resistance plays a vital role. Taking the aircraft thermal conduction structure as an example, if the structural design underestimates the contact thermal resistance, it will overestimate the heat protection efficiency of the structure, making the thermal protection system have safety hazards; on the contrary, if the structural design overestimates the contact thermal resistance, it will underestimate the heat protection efficiency of the structure, thus designing a highly redundant structure, which is not conducive to achieving the safety, refinement and low-redundancy design of the structure. Summary of the invention

[0004] The purpose of the present invention is to provide a thermomechanical coupling topology optimization method for high-temperature structures taking thermal contact into consideration in order to solve the above-mentioned problems, thereby improving the problem that the existing topology optimization only considers mechanical contact problems and thus the design of high-temperature structures with thermal contact is not refined enough.

[0005] The technical solution adopted by the present invention is as follows: a method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact, the method comprising the following steps: S100: Establish a thermal-mechanical coupling finite element analysis method for interfaces with contact thermal resistance; S200: performing a thermomechanical coupling analysis of the high-temperature structure based on the thermomechanical coupling finite element analysis method of the contact thermal resistance interface in step S100, establishing a topology optimization model with minimum weight as the goal and structural flexibility and regional maximum temperature as constraints, and using the obtained thermomechanical response data as input to the topology optimization model; S300: Objective function of the topology optimization model in step S200 and constraint functions , Solve the sensitivity and obtain the sensitivity formula; S400: In order to avoid the generation of a checkerboard scene, the sensitivity in step S300 is filtered by a density filtering method; S500: Using the moving asymptote optimization algorithm MMA to update the variables in the topology optimization model, the variables are design variables.

[0006] Furthermore, in step S100, the thermal-mechanical coupling finite element analysis method of the contact thermal resistance interface specifically includes: S110: Establish a model with contact interface and establish a Galerkin finite element method that can handle thermal-mechanical coupling structures with contact thermal resistance; S120: Establish a finite element module for thermal analysis involving thermal contact using interface numerical flux: ; in, For the unit, for The neighboring interface unit of the unit, is the heat transfer matrix of the unit in the domain, and are the interface unit heat transfer matrices related to the contact thermal resistance, is the temperature column vector of the cell, is the temperature column vector of the neighboring cells, is the unit thermal load column vector; S130: Finite element module for force analysis involving contact using penalty functions: ; in, For the unit, for The neighboring interface unit of the unit, is the element stiffness matrix in the domain, and are the stiffness matrices of the associated penalty functions on the internal interface elements, is the unit displacement vector, is the displacement column vector of the unit, is the displacement column vector of the neighboring unit; and They are the thermal load vector caused by the temperature field and the boundary surface force load vector respectively.

[0007] It should be noted that the existing technology Galerkin finite element method is a numerical solution technology based on partial differential equations, which solves the problem by dividing the continuous domain into finite elements.

[0008] Furthermore, in step S200, the data obtained include temperature field and displacement field data; As the optimization objective function, the constraints include the structural flexibility constraint function and the maximum structural temperature constraint function ; When the constraints are met and the optimization objective function is minimized, the pseudo-density design variable set of the unit is sought The optimal solution of ; its topology optimization model is as follows: ; ; ; ; in, is the set of pseudo-density design variables of the unit, For the unit, is the cell density, is the number of design variables, is the volume of the unit, is the flexibility constraint, For the Temperature constraints for each region, For softness, is the flexibility limit, For Region Maximum temperature, For Region Temperature limits, is the right boundary of the design variable; Using SIMP interpolation method, the elastic modulus of the material , thermal conductivity Related to the design variables: ; ; in, is the cell density, is the penalty parameter, is the cell density after being penalized, and are the thermal conductivity and elastic modulus of the solid material, respectively.

[0009] Furthermore, the area Maximum temperature pass The norm is aggregated, and in order to make the aggregate temperature approximately equal to the maximum temperature during the iteration process, an adaptive factor is introduced in each iteration step. , the temperature after polymerization as follows: ; ; in, For Region The number of internal nodes, For Region Inner node count, For Region Neidi The node temperature, is the aggregation factor, For the The adaptive factor of the step, For Region Maximum temperature, For the The polymerization temperature during the first step, For Region temperature limit.

[0010] Furthermore, due to and is an implicit function of the design variables, so we introduce , and The accompanying factor is the constraint function in step S200 , The sensitivity is solved, and the sensitivity formula includes: For the objective function Solve for sensitivity: ; in, is the volume ratio column vector, is the pseudo-density design variable set of the unit; By constraining the function , Solve for sensitivity: ; ; in, , and is the adjoint factor, obtained by solving the adjoint equation; is the set of pseudo-density design variables of the unit, is the unit displacement vector, is the heat load column vector, is the thermal conductivity matrix of the structure, is the structural temperature column vector, is the stiffness matrix of the structure, is the flexibility constraint, For the Temperature constraints for each region.

[0011] Furthermore, in step S400, the density after filtering Specifically include: ; in, For unit Filter cells within the radius The distance weight factor is is the cell density within the filter radius, is a natural number; The sensitivity filtering formula is as follows: ; in, represents the objective function or constraint function, For unit The cell density, For cells within the filter radius The distance weight factor.

[0012] Furthermore, in step S500, the convergence condition is set to the change of the design variable in each iteration. , and the constraint function , .

[0013] Furthermore, the model containing the contact interface sets the contact thermal resistance at the junction of the two materials, the material of the design domain is one of the two materials, and the contact thermal resistance is set by a topology optimization model.

[0014] It should be noted that different settings of contact thermal resistance will affect the structural physical field and thus affect the topology optimization results.

[0015] Furthermore, the cell density The range is: ,in, is the right boundary of the design variable.

[0016] Furthermore, the constraint function , is an implicit function of the design variables.

[0017] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. Extending the contact problem to the thermo-mechanical coupling structure is conducive to the refined design of high-temperature structures with thermal contact. At the same time, the optimization results can provide the control mechanism of contact thermal resistance on the thermo-mechanical coupling structure. The method is not limited to geometric models, and can be applied to any geometric model of two-dimensional or three-dimensional structure heat protection with thermal contact. At the same time, the method is not limited to the optimization model. It can not only carry out optimization design based on the lightweight optimization model with flexibility and temperature constraints developed by this patent, but also incorporate design-related influencing factors such as stress, displacement, and temperature variance into the optimization model according to design requirements.

[0018] 2. By setting up a thermomechanical coupling analysis module containing contact thermal resistance, the contact thermal resistance is set between two materials, and the distribution of materials in the iterative design domain is used to obtain the optimal structural model, so that the method of the present invention has better convergence and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of the method of the present invention; Figure 2 The model of the contact thermal resistance interface and the schematic diagram of the boundary structure of the present invention; Figure 3 It is an iteration history diagram of a double-layer cantilever beam structure according to an embodiment of the present invention; Figure 4 Optimal structural model diagram for an embodiment of the present invention; Figure 5 It is a line graph of the optimal volume change under different contact thermal resistances of an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0021] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0022] like Figure 1 As shown, a thermal-mechanical coupling topology optimization method for a high-temperature structure considering thermal contact comprises the following steps: S100: Establish a thermal-mechanical coupling finite element analysis method for a contact thermal resistance interface; the thermal-mechanical coupling finite element analysis method for a contact thermal resistance interface specifically includes: S110: Establish a model with contact interface and establish a Galerkin finite element method that can handle thermal-mechanical coupling structures with contact thermal resistance; S120: Establish a finite element module for thermal analysis involving thermal contact using interface numerical flux: ; in, For the unit, for The neighboring interface unit of the unit, is the heat transfer matrix of the unit in the domain, and are the interface unit heat transfer matrices related to the contact thermal resistance, is the temperature column vector of the cell, is the temperature column vector of the neighboring cells, is the unit thermal load column vector; S130: Finite element module for force analysis involving contact using penalty functions: ; in, For the unit, for The neighboring interface unit of the unit, is the element stiffness matrix in the domain, and are the stiffness matrices of the associated penalty functions on the internal interface elements, is the displacement column vector of the unit, is the displacement column vector of the neighboring unit; and They are the thermal load vector caused by the temperature field and the boundary surface force load vector respectively.

[0023] S200: performing a thermomechanical coupling analysis of the high-temperature structure based on the thermomechanical coupling finite element analysis method of the contact thermal resistance interface in step S100, establishing a topology optimization model with minimum weight as the goal and structural flexibility and regional maximum temperature as constraints, and using the obtained thermomechanical response data as input to the topology optimization model; The data obtained include temperature field and displacement field data; weight function As the optimization objective function, the constraints include the structural flexibility constraint function and the maximum structural temperature constraint function ; When the constraints are met and the optimization objective function is minimized, the pseudo-density design variable set of the unit is sought The optimal solution of ; its topology optimization model is as follows: ; ; ; ; in, is the pseudo-density design variable set of the unit, For the unit, is the cell density, is the number of design variables, is the volume of the unit, is the flexibility constraint, For the Temperature constraints for each region, For softness, is the flexibility limit, For Region Maximum temperature, For Region Temperature limits, is the right boundary of the design variable; the constraint function , is an implicit function of the design variables.

[0024] Using SIMP interpolation method, the elastic modulus of the material , thermal conductivity Related to the design variables: ; ; in, is the cell density, is the penalty parameter, is the cell density after being penalized, and are the thermal conductivity and elastic modulus of the solid material, respectively.

[0025] The area Maximum temperature pass norm for aggregation, the temperature after aggregation as follows: ; ; in, For Region The number of internal nodes, For Region Inner node count, For Region Neidi The node temperature, is the aggregation factor, For the The adaptive factor of the step, For Region Maximum temperature, For the The polymerization temperature during the first step, For Region temperature limit.

[0026] S300: Objective function of the topology optimization model in step S200 and constraint functions , Solve the sensitivity and obtain the sensitivity formula; The sensitivity formula includes: For the objective function Solve for sensitivity: ; in, is the volume ratio column vector, is the pseudo-density design variable set of the unit; By constraining the function , Solve for sensitivity: ; ; in, , and is the adjoint factor, obtained by solving the adjoint equation; is the pseudo-density design variable set of the unit, is the unit displacement vector, is the heat load column vector, is the thermal conductivity matrix of the structure, is the structural temperature column vector, is the stiffness matrix of the structure, is the flexibility constraint, For the Temperature constraints for each region.

[0027] S400: filtering the sensitivity in step S300 by density filtering method; Density after filtering (i.e. physical density) specifically includes: ; in, For unit Filter cells within the radius The distance weight factor is is the cell density within the filter radius, is a natural number; The sensitivity filtering formula is as follows: ; in, represents the objective function or constraint function, For unit The cell density, For the unit, is the number of design variables, is the density after filtering, For unit Filter cells within the radius The distance weight factor.

[0028] S500: Use the moving asymptote optimization algorithm (MMA) to update the variables in the topology optimization model, and set the convergence condition to the change of the design variable in each iteration. , and the constraint function , .

[0029] Example like Figures 2 to 5 As shown in Figure 2, a topological optimization study was conducted on a cantilever beam structure with a double layer of contact thermal resistance. Figure 2 As shown in the figure, the contact thermal resistance is set at the interface between material 1 and material 2, and the design domain is material 2. The lightweight optimization model, the contact thermal resistance is set to , optimize the iteration history as Figure 3 As shown in the figure, as the iteration proceeds, the distribution of material 2 in the design domain becomes clearer. When the iteration reaches 208, the result converges, and the temperature and constraints satisfy the set constraints at the same time. Finally, the following is obtained: Figure 4 The optimal configuration shown in FIG. 1 verifies that the method proposed in this embodiment has good convergence and stability. Figure 5 It can be seen that with the increase of contact thermal resistance, the volume ratio of the optimal structure decreases first and then increases, indicating that the appropriate contact thermal resistance can not only take into account the mechanical and thermal performance, but also is conducive to the lightweight of the structure. Therefore, the method proposed in this embodiment is not only applicable to the topology optimization research of thermal-mechanical coupling structures with thermal contact, but also the law research obtained by this method also provides technical support for the rational use of contact thermal resistance in structural design.

[0030] This embodiment extends the contact problem to the thermo-mechanical coupling structure, which is not only applicable to the topology optimization problem of mechanical contact, but also can handle the heat transfer topology optimization with only thermal contact, and the thermo-mechanical coupling topology optimization problem with thermal contact or combined force-heat contact. At the same time, the optimization method proposed in this embodiment is not limited to the cantilever beam structure in this embodiment, and any two-dimensional and three-dimensional structure with thermal contact can be optimized by the method proposed in this embodiment. At the same time, this method is not limited to the lightweight optimization model proposed in this embodiment, and can be applied to most optimization models proposed in the existing thermo-mechanical coupling topology optimization, such as the fixed volume optimization model with the minimum flexibility target, the lightweight model with stress and temperature as constraints, etc.

[0031] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A thermal-mechanical coupling topology optimization method for high-temperature structures considering thermal contact, characterized in that: The method comprises the following steps: S100: Establish a thermal-mechanical coupling finite element analysis method for interfaces with contact thermal resistance; S200: performing a thermomechanical coupling analysis of the high-temperature structure based on the thermomechanical coupling finite element analysis method of the contact thermal resistance interface in step S100, establishing a topology optimization model with minimum weight as the goal and structural flexibility and regional maximum temperature as constraints, and using the obtained thermomechanical response data as input to the topology optimization model; S300: Objective function of the topology optimization model in step S200 and constraint functions , Solve the sensitivity and obtain the sensitivity formula; S400: filtering the sensitivity in step S300 by density filtering method; S500: Use the moving asymptote optimization algorithm (MMA) to update the variables in the topology optimization model.

2. A method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 1, characterized in that: In step S100, the thermal-mechanical coupling finite element analysis method of the contact thermal resistance interface specifically includes: S110: Establish a model with contact interface and establish a Galerkin finite element method that can handle thermal-mechanical coupling structures with contact thermal resistance; S120: Establish a finite element module for thermal analysis involving thermal contact using interface numerical flux: ； in, For the unit, for The neighboring interface unit of the unit, is the heat transfer matrix of the unit in the domain, and are the interface unit heat transfer matrices related to the contact thermal resistance, is the temperature column vector of the cell, is the temperature column vector of the neighboring cells, is the unit thermal load column vector; S130: Finite element module for force analysis involving contact using penalty functions: ； in, For the unit, for The neighboring interface unit of the unit, is the element stiffness matrix in the domain, and are the stiffness matrices of the associated penalty functions on the internal interface elements, is the displacement column vector of the unit, is the displacement column vector of the neighboring unit; and They are the thermal load vector caused by the temperature field and the boundary surface force load vector respectively.

3. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 1, characterized in that: In step S200, the data obtained include temperature field and displacement field data; As the optimization objective function, the constraints include the structural flexibility constraint function and the maximum structural temperature constraint function ; When the constraints are met and the optimization objective function is minimized, the pseudo-density design variable set of the unit is sought The optimal solution of ; its topology optimization model is as follows: ； ； ； ； in, is the set of pseudo-density design variables of the unit, For the unit, is the cell density, is the number of design variables, is the volume of the unit, is the flexibility constraint, For the Temperature constraints for each region, For softness, is the flexibility limit, For Region Maximum temperature, For Region Temperature limits, is the right boundary of the design variable; Using SIMP interpolation method, the elastic modulus of the material , thermal conductivity Related to the design variables: ； ； in, is the cell density, is the penalty parameter, is the cell density after being penalized, and are the thermal conductivity and elastic modulus of the solid material, respectively.

4. A method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 3, characterized in that: The area Maximum temperature pass norm for aggregation, the temperature after aggregation as follows: ； ； in, For Region The number of internal nodes, For Region Inner node count, For Region Neidi The node temperature, is the aggregation factor, For the The adaptive factor of the step, For Region Maximum temperature, For the The polymerization temperature during the first step, For Region temperature limit.

5. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 1, characterized in that: The sensitivity formula includes: For the objective function Solve for sensitivity: ； in, is the volume ratio column vector, is the set of pseudo-density design variables for the unit; By constraining the function , Solve for sensitivity: ； ； in, , and is the adjoint factor, obtained by solving the adjoint equation; is the set of pseudo-density design variables of the unit, is the unit displacement vector, is the heat load column vector, is the thermal conductivity matrix of the structure, is the structural temperature column vector, is the stiffness matrix of the structure, is the flexibility constraint, For the Temperature constraints for each region.

6. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 1, characterized in that: In step S400, the density after filtering Specifically include: ； in, For unit Filter cells within the radius The distance weight factor is is the cell density within the filter radius, is a natural number; The sensitivity filtering formula is as follows: ； in, represents the objective function or constraint function, For unit The cell density, For the unit, is the number of design variables, is the density after filtering, For unit Filter cells within the radius The distance weight factor.

7. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 1, characterized in that: In step S500, the convergence condition is set as the change of the design variable in each iteration. , and the constraint function , .

8. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 2, characterized in that: The model containing the contact interface sets the contact thermal resistance at the junction of the two materials, the material of the design domain is one of the two materials, and the contact thermal resistance is set by a topology optimization model.

9. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 3, characterized in that: The cell density The range is: ,in, is the right boundary of the design variable.

10. The method for thermal-mechanical coupling topology optimization of high-temperature structures considering thermal contact according to claim 3, characterized in that: The constraint function , is an implicit function of the design variables.

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