Topological optimization method for thermally stable bearing support structure

Abstract

The invention discloses a topological optimization method for a thermal stable bearing support structure, which relates to the field of structure optimization, and comprises the following steps: defining a design domain and a non-design domain, and completing initialization setting; based on the density filtering function and the projection function, converting the design variable into a physical variable; establishing an interpolation model of the elastic coefficient and the heat conductivity coefficient; constructing and assembling a heat transfer matrix and a stiffness matrix according to the finite element mesh model; executing heat transfer simulation to obtain an equivalent thermal load of the unit; statics simulation is executed, and design response is calculated; calculating the sensitivity of the design response to the design variables; establishing an optimization model, solving the optimization model based on a moving asymptote algorithm, and updating design variables; and post-processing an optimization result to generate a support structure with a smooth surface. Aiming at the thermal-mechanical coupling optimization problem under environmental thermal fluctuation, the bearing structure with high specific stiffness and thermal deformation resistance is obtained, and the problems that a traditional method is low in stiffness and prone to failure under large environmental fluctuation are solved.

Description

Technical Field

[0001] The present invention relates to the field of structural optimization, and in particular to a topological optimization method for a thermally stable load-bearing support structure. Background Art

[0002] Structural topology optimization is a structural design method that optimizes the spatial layout of materials point by point, and can design lightweight configurations with optimized load-bearing performance. In actual engineering applications, the deformation of the load-bearing structure is not only affected by external loads, but also by environmental thermal fluctuations. If the influence of environmental thermal fluctuations is ignored in the topology optimization design, the actual load-bearing performance of the optimized design will not be consistent with the design expectations. For example, the lunar rover needs to serve on the lunar surface with a large temperature difference between day and night, and its support structure is subject to two major effects: mechanical deformation caused by external loads and thermal deformation caused by thermal expansion and contraction. Under high temperature differences between day and night, the lunar rover support structure designed by the traditional topology optimization method that does not consider environmental fluctuations is prone to large deformation failure. Therefore, it is necessary to consider the design of thermally stable load-bearing performance structures under environmental thermal fluctuations.

[0003] In the existing topology optimization methods considering thermally stable load-bearing structures, optimization is often performed under given thermal load conditions, that is, the thermal load is irrelevant to the structural topology and the impact of variable temperature environment on structural performance is not considered.

[0004] Therefore, technicians in this field are committed to developing a topology optimization method for a thermally stable load-bearing support structure. Summary of the invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to deal with the adverse effects of thermal loads and environmental thermal fluctuations in the topology optimization design of thermally stable load-bearing structures.

[0006] To achieve the above object, the present invention provides a method for topological optimization of a thermally stable load-bearing support structure, the method comprising the following steps:

[0007] S101: Define the design domain and non-design domain, and complete the initialization settings;

[0008] S103: Converting design variables into physical variables based on density filtering function and projection function;

[0009] S105: establishing an interpolation model of the elastic coefficient and thermal conductivity of the support structure;

[0010] S107: Based on the constructed finite element mesh model, construct and assemble the heat transfer matrix and stiffness matrix of the system;

[0011] S109: Execute heat transfer simulation calculation to obtain the equivalent heat load of the unit according to the temperature field;

[0012] S111: Perform static simulation calculation to calculate the design response of the support structure;

[0013] S113: Calculating the sensitivity of the design response to the design variable;

[0014] S115: establishing an optimization model, solving the optimization model based on a moving asymptote algorithm, and updating the design variables;

[0015] S117: Post-processing the optimization result to generate the support structure with a smooth surface.

[0016] Furthermore, the initialization setting in S101 includes setting material parameters of the support structure, setting load conditions and temperature conditions, and initializing the design variables to indirectly represent the relative density of the structure.

[0017] Further, in S103, the density filtering function is:

[0018]

[0019] in, is the intermediate variable of unit e after density filtering, M e ={i|||X i -X e ||≤r min} is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||,0} is the weight coefficient, μ i is the design variable of unit i, Ω2 is the design domain;

[0020] The projection function is:

[0021]

[0022] Among them, ρ e represents the physical variable of unit e, β is the steepness of the projection, and η is the projection threshold.

[0023] Further, in S105, the elastic coefficient interpolation model of the support structure is:

[0024] E e =E min +ρ e p (E0-E min )

[0025] The thermal conductivity interpolation model of the support structure is:

[0026] κ e =κ min +ρ e p (κ0-κ min )

[0027] Among them, E e is the elastic modulus of unit e after interpolation, κ e is the thermal conductivity of unit e after interpolation, E0 is the Young's modulus of the material, κ0 is the thermal conductivity of the material, E min , κ min In order to avoid the minimum value introduced by the singularity of the finite element solution matrix, p is the penalty coefficient.

[0028] Further, in S107, the heat transfer matrix is:

[0029]

[0030] The stiffness matrix is:

[0031]

[0032] Among them, H is the system heat transfer matrix, K is the system stiffness matrix, B e is the strain matrix of element e, Ω e is the region where unit e is located, and n is the number of units.

[0033] Further, in S109, the equivalent heat load is calculated in the following manner:

[0034]

[0035] Among them, F T is the equivalent heat load, T is the temperature field, ΔT e is the temperature rise of unit e relative to the thermal expansion reference temperature, α is the thermal expansion coefficient of the material, φ is a constant, for three-dimensional problems φ=[1 1 1 0 0 0] T .

[0036] Further, in the S111, in the statics simulation calculation, the statics control equation is:

[0037] K·U-(F T +F M )=0

[0038] Among them, F T is the equivalent heat load, F Mis the force load, U is the displacement field, and K is the stiffness matrix.

[0039] Furthermore, in S111, the design response of the support structure includes thermal flexibility, maximum displacement and structural volume fraction of the support structure under high temperature and low temperature conditions.

[0040] The thermal flexibility is:

[0041]

[0042] The maximum displacement is:

[0043]

[0044] The structure volume fraction is:

[0045]

[0046] Among them, U is the displacement field, K is the stiffness matrix, ρ i Represents the physical variable of unit i.

[0047] Furthermore, the S113 includes the following sub-steps:

[0048] S1131: Calculate the sensitivity of the thermal flexibility to the physical variable field:

[0049]

[0050] S1132: Calculate the sensitivity of the displacement field to the physical variable field:

[0051]

[0052] S1133: Using the chain rule, obtain the sensitivity of the design response relative to the design variable:

[0053] The sensitivity of the thermal flexibility to the design variables is:

[0054]

[0055] The sensitivity of the displacement field to the design variables is:

[0056]

[0057] in, is the adjoint vector, which is obtained by the following formula:

[0058]

[0059] The partial derivative of the equivalent heat load with respect to the physical variable field is:

[0060]

[0061] C is thermal flexibility, U is displacement field, μ e is the design variable, ρ e is the physical variable field of unit e.

[0062] Further, in S115, the optimization model is as follows:

[0063]

[0064] stV≤V *

[0065] U max ≤U *

[0066] H.TP T =0

[0067] K·U-(F T +F M )=0

[0068] 0≤μ e ≤1,e=1,2,…,n

[0069] Among them, γ is the weight coefficient, V * is the upper limit of volume constraint, U * is the upper limit of displacement constraint, C a is the thermal flexibility at the lowest temperature of the temperature field, C b is the thermal flexibility at the highest temperature of the temperature field.

[0070] In a preferred embodiment of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0071] 1. The present invention proposes a method for topological optimization of a support structure taking thermally stable load-bearing into consideration. This method can target the thermal-mechanical coupling optimization problem under environmental thermal fluctuations, carry out topological optimization design of a thermally stable load-bearing structure, obtain a load-bearing structure with high specific stiffness and resistance to thermal deformation under actual thermal environmental fluctuations, improve the load-bearing mechanical bearing performance of the structure under environmental thermal fluctuations, and solve the problem of low stiffness and easy failure of the load-bearing support structure designed by the traditional topological optimization method under large environmental fluctuations.

[0072] 2. The present invention proposes a method for topological optimization of a support structure that takes thermal stability into consideration, which can be used for the design of support structures in thermal fluctuation environments to ensure the thermal stability of the structure while achieving lightweight.

[0073] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a schematic flow chart of an optimization method according to an embodiment of the present invention;

[0075] Figure 2 is a schematic diagram of a detailed description of the optimization method process of an embodiment of the present invention;

[0076] Figure 3 is a schematic diagram of the working condition of the initial design structure of an embodiment of the present invention;

[0077] Figure 4 It is a schematic diagram of the structure after the initial design and optimized design of an embodiment of the present invention. DETAILED DESCRIPTION

[0078] The following describes several preferred embodiments of the present invention with reference to the drawings in the specification, so that the technical content is clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0079] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[0080] like Figure 1 As shown, in the existing topology optimization methods considering thermally stable load-bearing structures, optimization is often performed under given thermal load conditions, that is, the thermal load is irrelevant to the structural topology and the influence of the variable temperature environment on the structural performance is not considered. The resulting optimized design is likely to be inconsistent with the design expectations. An embodiment of the present invention proposes a topology optimization method for a support structure considering thermally stable load-bearing, while considering the structural optimization design under the combined action of external force loads and environmental thermal fluctuations. The designed support structure achieves lightweight while ensuring excellent thermally stable load-bearing performance. The support structure topology optimization method provided in this embodiment includes the following steps:

[0081] S1: Define the design domain and non-design domain, and complete the initialization settings.

[0082] After defining the design domain and the non-design domain, the system is initialized. The initialization settings include: setting the material parameters of the support structure, setting the load conditions and temperature conditions, and initializing the design variables to indirectly represent the relative density of the structure.

[0083] S2: Based on the density filtering function and projection function, the design variables are converted into physical variables.

[0084] When initializing the design variables, the design variables are used to indirectly represent the relative density of the structure. During the initialization process, if a unit belongs to the area outside the design domain, the corresponding component in the design variable is initialized to 1 and remains unchanged during the subsequent optimization process.

[0085] The density filter function is:

[0086]

[0087] in, is the intermediate variable of unit e after density filtering, M e ={i|||X i -X e ||≤r min} is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||,0} is the weight coefficient, μ i is the design variable of unit i, Ω2 is the design domain;

[0088] The projection function is:

[0089]

[0090] Among them, ρ e represents the physical variable of unit e, β is the steepness of the projection, and η is the projection threshold.

[0091] S3: Establish an interpolation model for the elastic coefficient and thermal conductivity of the bracket structure.

[0092] The elastic coefficient interpolation model of the bracket structure is:

[0093] E e =E min +ρ e p (E0-E min )

[0094] The thermal conductivity interpolation model of the bracket structure is:

[0095] κ e =κ min +ρ e p (κ0-κmin )

[0096] Among them, E e is the elastic modulus of unit e after interpolation, κ e is the thermal conductivity of unit e after interpolation, E0 is the Young's modulus of the material, κ0 is the thermal conductivity of the material, E min , κ min In order to avoid the minimum value introduced by the singularity of the finite element solution matrix, p is the penalty coefficient.

[0097] S4: Based on the constructed finite element mesh model, the heat transfer matrix and stiffness matrix of the system are constructed and assembled.

[0098] The heat transfer matrix is:

[0099]

[0100] The stiffness matrix is:

[0101]

[0102] Among them, H is the system heat transfer matrix, K is the system stiffness matrix, B e is the strain matrix of element e, Ω e is the region where unit e is located, and n is the number of units.

[0103] S5: Perform heat transfer simulation calculations and obtain the equivalent heat load of the unit based on the temperature field.

[0104] The equivalent heat load is calculated as follows:

[0105]

[0106] Among them, F T is the equivalent heat load, T is the temperature field, ΔT e is the temperature rise of unit e relative to the thermal expansion reference temperature, α is the thermal expansion coefficient of the material, φ is a constant, for three-dimensional problems φ=[1 1 1 0 0 0] T .

[0107] S6: Perform static simulation calculations to calculate the design response of the bracket structure.

[0108] In statics simulation calculation, the statics control equation is:

[0109] K·U-(F T +F M )=0

[0110] Among them, F T is the equivalent heat load, F M is the force load, U is the displacement field, and K is the stiffness matrix.

[0111] The design response of the bracket structure includes the thermal flexibility, maximum displacement and structural volume fraction of the bracket structure under high and low temperature conditions. The specific calculation is as follows:

[0112] Thermal flexibility is:

[0113]

[0114] The maximum displacement is:

[0115]

[0116] The structural volume fraction is:

[0117]

[0118] Among them, U is the displacement field, K is the stiffness matrix, ρ i is the physical variable of unit i.

[0119] S7: Calculate the sensitivity of the design response to the design variables.

[0120] When designing the sensitivity of the response to the design variables, the following sub-steps are involved:

[0121] S71: Calculate the sensitivity of thermal flexibility to the field of physical variables:

[0122]

[0123] S72: Calculate the sensitivity of the displacement field to the physical variable field:

[0124]

[0125] S73: Combined with the chain rule, the sensitivity of the design response to the design variable is obtained:

[0126] The sensitivity of thermal flexibility to design variables is:

[0127]

[0128] The sensitivity of the displacement field to the design variables is:

[0129]

[0130] in, is the adjoint vector, which is obtained by the following formula:

[0131]

[0132] The partial derivative of the equivalent heat load to the physical variable field is:

[0133]

[0134] C is thermal flexibility, U is displacement field, μ e is the design variable, ρ e is the physical variable field of unit e.

[0135] S8: Establish an optimization model, solve the optimization model based on the moving asymptote algorithm, and update the design variables.

[0136] The following optimization model is established:

[0137]

[0138] stV≤V *

[0139] U max ≤U *

[0140] H.TP T =0

[0141] K·U-(F T +F M )=0

[0142] 0≤μ e ≤1,e=1,2,…,n

[0143] Among them, γ is the weight coefficient, V * is the upper limit of volume constraint, U * is the upper limit of displacement constraint, C a is the thermal flexibility at the lowest temperature of the temperature field, C b is the thermal flexibility at the highest temperature of the temperature field.

[0144] S9: Post-process the optimization results to generate a bracket structure with a smooth surface.

[0145] The present invention aims at the problem that the topology optimization method of thermally stable load-bearing structure in the prior art performs structural optimization design under given thermal load conditions without considering the influence of thermal load related to the configuration and environmental thermal fluctuations, and the obtained optimized design is easily inconsistent with the design expectations. The present invention proposes a topology optimization method for a thermally stable load-bearing bracket structure, which considers the thermally stable load-bearing performance under environmental thermal fluctuations, and obtains a lightweight bracket structure with high specific stiffness and thermal deformation resistance under environmental temperature fluctuations. Based on the variable density topology optimization method, an interpolation model of structural elastic modulus and thermal conductivity and a thermomechanical coupling simulation model considering high temperature and low temperature environments are established; an optimization model considering high temperature and low temperature working conditions is proposed, and the optimization model takes structural thermal flexibility as the optimization target and structural volume fraction and displacement as constraints; the sensitivity of each design response is derived by the adjoint method; the moving asymptote method is used to update the design variables according to each design response, and iterative optimization is performed to finally obtain a bracket structure that meets the requirements of thermally stable load-bearing performance. The present invention proposes a method for topological optimization of a support structure taking thermally stable load-bearing into consideration. This method can target the thermal-mechanical coupling optimization problem under environmental thermal fluctuations, carry out topological optimization design of a thermally stable load-bearing structure, and obtain a load-bearing structure with high specific stiffness and resistance to thermal deformation under actual thermal environment fluctuations. This solves the problem that the load-bearing support structure designed by the traditional topological optimization method has low stiffness and easy failure under large environmental fluctuations.

[0146] The present invention is described in detail below in conjunction with the preferred embodiments of the present invention.

[0147] In the prior art, the topology optimization method of thermally stable load-bearing structure is considered. The structure optimization design is performed under given thermal load conditions, but the influence of the thermal load related to the configuration and the environmental thermal fluctuation is not considered. The obtained optimized design is likely to be inconsistent with the design expectation. The present invention proposes a topology optimization method of a thermally stable load-bearing support structure. The thermally stable load-bearing performance under environmental thermal fluctuation is considered to obtain a lightweight support structure with high specific stiffness and thermal deformation resistance under environmental temperature fluctuation. Specifically, the method proposed in the preferred embodiment of the present invention includes the following steps:

[0148] Step 1: Define the design domain and non-design domain, and set the material parameters.

[0149] like Figure 2 As shown in the figure, for a given initial design structure of the bracket, this method is used to optimize the thermal stability of the load-bearing design. The working environment temperature of the bracket structure is 93K~423K. The non-design domain is defined as Ω1 and the design domain is defined as Ω2. The design domain structure is discretized into a grid of 241×65×33 units, and the Young's modulus of the material is set to E0=60000MPa, the Poisson's ratio is 0.33, the heat transfer coefficient is 237W / (m·K), and the thermal expansion coefficient is 0.000023K. -1 .

[0150] Step 2: Set up load cases and temperature cases.

[0151] For the non-design domain Ω1, the specified thermal-mechanical coupling condition is applied. The condition diagram is as follows: Figure 3 As shown in the figure. For heat transfer loads, two working conditions, high temperature and low temperature, are considered, and two ambient temperatures are set to 93K and 423K respectively; for static loads, one end of the bracket is fixed and the other end is subjected to vertical force.

[0152] Step 3: Initialize design variables.

[0153] Initialize the design variables, design variables μ=(μ1,μ2,…,μ n ), which is used to indirectly indicate the relative density of the structure, where n is the total number of units.

[0154] During the initialization process, if the unit i belongs to the region Ω1 where the non-design domain is located, the component μ in μ is i It is initialized to 1 and remains unchanged during subsequent optimization.

[0155] Step 4: Density filtering and projection.

[0156] Based on density filtering and projection function, the design variable μ is transformed into a physical variable ρ = (ρ1, ρ2, …, ρ n ).

[0157] The density filtering formula is as follows:

[0158]

[0159] in, is the intermediate variable of unit e after density filtering, M e ={i|||X i -X e ||≤r min} is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||,0} is the weight coefficient, μ i is the design variable of unit i, and Ω2 is the design domain.

[0160] The projection function formula is as follows:

[0161]

[0162] Among them, ρe represents the physical variable of unit e, β is the steepness of the projection, and η is the projection threshold.

[0163] Step 5: Establish the elastic coefficient and thermal conductivity interpolation model.

[0164] Based on the SIMP formula, the elastic coefficient and thermal conductivity interpolation model of the overall structure is established:

[0165] E e =E min +ρ e p(E0-E min )

[0166] κ e =κ min +ρ e p(κ0-κ min )

[0167] Among them, E e , κ e are the elastic modulus and thermal conductivity of unit e after interpolation; E0 is the Young's modulus of the material; κ0 is the thermal conductivity of the material; E min , κ min To avoid the minimum value introduced by the singularity of the finite element solution matrix; p is the penalty coefficient. In this embodiment, E min , κ min Take 1e-6 and P take 3.

[0168] Step 6: Assemble the heat transfer matrix and stiffness matrix.

[0169] Based on the constructed finite element mesh, construct and assemble the heat transfer matrix and stiffness matrix of the system:

[0170]

[0171] Among them, H is the system heat transfer matrix, K is the system stiffness matrix, B e is the strain matrix of the unit, Ω e is the region where unit e is located, and n is the number of units.

[0172] Step 7: Perform heat transfer simulation to obtain equivalent heat load.

[0173] Calculate the equivalent heat load when the ambient temperature is low temperature 93K and high temperature 423K Perform heat transfer simulation calculations. The heat transfer governing equation is:

[0174] H.TP T =0

[0175] Where T is the temperature field, P T is the equivalent temperature load.

[0176] The equivalent heat load of the unit is obtained according to the temperature field:

[0177]

[0178] Where, ΔT e is the temperature rise of the unit relative to the thermal expansion reference temperature, φ is a constant, for three-dimensional problems φ=[1 11 0 0 0] T ; α is the thermal expansion coefficient of the material.

[0179] Step 8: Perform static simulation.

[0180] Combined with the equivalent thermal load calculated in step 7, static simulation calculation is performed to obtain the thermal deformation U caused by thermal-mechanical coupling conditions under low temperature 93K and high temperature 423K. a , U b .

[0181] The governing equations for statics are:

[0182] K·U-(F T +F M )=0

[0183] Among them, F M is the force load, U is the displacement field, U is the displacement field, and K is the stiffness matrix.

[0184] Step 9: Calculate the design responses of the structure.

[0185] Calculate the thermal flexibility C of the structure at low and high temperatures a , C b , structure volume fraction V and maximum displacement

[0186]

[0187] Step 10: Sensitivity analysis of objective function and constraint function.

[0188] Calculate the sensitivity of the design response to the design variables.

[0189] Calculate the thermal flexibility C of the structure to the physical variable field ρ e Sensitivity:

[0190]

[0191] in, is the adjoint vector, which is obtained by the following formula:

[0192]

[0193] Calculate the equivalent heat load on the physical variable field ρ e The partial derivative of :

[0194]

[0195] Calculate the structural displacement field U for the physical variable field ρ e Sensitivity:

[0196]

[0197] Finally, the chain rule is combined to obtain the sensitivity of the design response to the design variable. For example, the thermal flexibility C is sensitive to the design variable μ e The sensitivity is:

[0198]

[0199] Displacement field U versus design variable μ e The sensitivity is:

[0200]

[0201] Among them, ρ e is the physical variable field of unit e, ρ k is the physical variable field of unit k.

[0202] Step 11: The MMA algorithm solves the optimization model and updates the design variables.

[0203] An optimization model is established, and the design variable μ is updated based on the moving asymptote algorithm (MMA algorithm).

[0204] The optimization model is as follows:

[0205]

[0206] stV≤V *

[0207] U max ≤U *

[0208] H.TP T =0

[0209] K·U-(F T +F M )=0

[0210] 0≤μ e ≤1,e=1,2,…,n

[0211] Among them, γ is the weight coefficient, V * is the upper limit of volume constraint, U * is the upper limit of displacement constraint, Ca is the thermal flexibility at the lowest temperature of the temperature field, C b is the thermal flexibility at the highest temperature of the temperature field. In this embodiment, γ is 0.5, V * Take 0.3, U * Take 1.00mm.

[0212] Step 12: Determine whether it converges

[0213] Determine whether the iteration converges. If all constraints are satisfied and the relative change of the objective function is less than 1% for 10 consecutive steps, go to step 13; otherwise, go to step 4.

[0214] Step 13: Optimize structure post-processing

[0215] The support optimization results are post-processed to generate a smooth surface lunar rover support structure, such as Figure 4 The reference design volume is 9298cm 3 , thermal flexibility is 6964J; the optimized design volume is 7440cm 3 , thermal flexibility is 2387J, achieving a 20% weight reduction and a 66% reduction in thermal flexibility.

[0216] The method for topological optimization of a support structure considering thermally stable load-bearing proposed in the embodiment of the present invention can carry out topological optimization design of a thermally stable load-bearing structure for the thermal-mechanical coupling optimization problem under environmental thermal fluctuations, obtain a load-bearing structure with high specific stiffness and thermal deformation resistance under actual heating environment, and improve the load-bearing mechanical bearing performance of the structure under environmental thermal fluctuations. In production implementation, the present invention can be used for the design of support structures in thermally fluctuating environments to ensure the thermal load-bearing stability of the structure, while also achieving lightweight structures.

[0217] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for topological optimization of a thermally stable support structure, characterized in that: The method comprises the following steps: S101: Define the design domain and non-design domain, and complete the initialization settings; S103: converting the design variables into physical variables based on the density filtering function and the projection function; S105: establishing an interpolation model of the elastic coefficient and thermal conductivity of the support structure; S107: Based on the constructed finite element mesh model, construct and assemble the heat transfer matrix and stiffness matrix of the system; S109: Execute heat transfer simulation calculation to obtain the equivalent heat load of the unit according to the temperature field; S111: Perform static simulation calculation to calculate the design response of the support structure; S113: Calculating the sensitivity of the design response to the design variable; S115: establishing an optimization model, solving the optimization model based on a moving asymptote algorithm, and updating the design variables; S117: Post-processing the optimization result to generate the support structure with a smooth surface.

2. The method according to claim 1, characterized in that The initialization settings in S101 include setting material parameters of the support structure, setting load conditions and temperature conditions, and initializing the design variables to indirectly represent the relative density of the structure.

3. The method according to claim 2, characterized in that In the S103, the density filtering function is: in, is the intermediate variable of unit e after density filtering, M e ={i|||X i -X e ||≤r min } is a unit e with r min is the radius of the neighborhood, X i With X e are the center coordinates of unit i and unit e, respectively, H ie =max{r min -||X i -X e ||,0} is the weight coefficient, μ i is the design variable of unit i, Ω2 is the design domain; The projection function is: Among them, ρ e represents the physical variable of unit e, β is the steepness of the projection, and η is the projection threshold.

4. The method according to claim 3, characterized in that In S105, the elastic coefficient interpolation model of the support structure is: BY e =E min +ρ e p (E0–E min ) The thermal conductivity interpolation model of the support structure is: k e =k min +r e p (k0-k min ) Among them, E e is the elastic modulus of unit e after interpolation, κ e is the thermal conductivity of unit e after interpolation, E0 is the Young's modulus of the material, κ0 is the thermal conductivity of the material, E min , κ min In order to avoid the minimum value introduced by the singularity of the finite element solution matrix, p is the penalty coefficient.

5. The method according to claim 4, characterized in that In S107, the heat transfer matrix is: The stiffness matrix is: Among them, H is the system heat transfer matrix, K is the system stiffness matrix, B e is the strain matrix of element e, Ω e is the region where unit e is located, and n is the number of units.

6. The method according to claim 5, characterized in that In S109, the equivalent heat load is calculated in the following manner: Among them, F T is the equivalent heat load, T is the temperature field, ΔT e is the temperature rise of unit e relative to the thermal expansion reference temperature, α is the thermal expansion coefficient of the material, φ is a constant, for three-dimensional problems φ=[1 1 1 0 0 0] T .

7. The method according to claim 6, characterized in that In the S111, in the statics simulation calculation, the statics control equation is: K·U-(F T +F M )=0 Among them, F T is the equivalent heat load, F M is the force load, U is the displacement field, and K is the stiffness matrix.

8. The method according to claim 7, characterized in that In S111, the design response of the support structure includes thermal flexibility, maximum displacement and structural volume fraction of the support structure under high temperature and low temperature conditions. The thermal flexibility is: The maximum displacement is: The structure volume fraction is: Among them, U is the displacement field, K is the stiffness matrix, ρ i Represents the physical variable of unit i.

9. The method according to claim 8, characterized in that The S113 includes the following sub-steps: S1131: Calculate the sensitivity of the thermal flexibility to the physical variable field: S1132: Calculate the sensitivity of the displacement field to the physical variable field: S1133: Combining the chain rule to obtain the sensitivity of the design response relative to the design variable: The sensitivity of the thermal flexibility to the design variables is: The sensitivity of the displacement field to the design variables is: in, is the adjoint vector, which is obtained by the following formula: The partial derivative of the equivalent heat load with respect to the physical variable field is: C is thermal flexibility, U is displacement field, μ e is the design variable, ρ e is the physical variable field of unit e, ρ k is the physical variable field of unit k.

10. The method according to claim 9, characterized in that In S115, the optimization model is as follows: s.t.V≤V * IN max ≤U * H·T-P T =0 K·U-(F T +F M )=0 0≤μ e ≤1,e=1,2,…,n Among them, γ is the weight coefficient, V * is the upper limit of volume constraint, U * is the upper limit of displacement constraint, C a is the thermal flexibility at the lowest temperature of the temperature field, C b is the thermal flexibility at the highest temperature of the temperature field.

Images