A heat dissipation structure topology optimization method based on anisotropic functionally graded unit cell

Abstract

The present application belongs to the technical field of structure optimization, and discloses a heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells, which comprises the following steps: (1) providing anisotropic functionally graded unit cells; (2) obtaining the equivalent heat conduction tensor of the equal-step functionally graded unit cells by using the homogenization method, and then respectively composing a plurality of heat conduction tensor curved surfaces, and fitting the relationship between the design variables of the functionally graded unit cells and the heat conduction tensor thereof by interpolation of the heat conduction tensor curved surfaces through an interpolation function; (3) filling the grid in the design domain by using the functionally graded unit cells, constructing a multi-scale topology optimization design model with the minimum heat dissipation flexibility as the target based on the relationship, and then optimizing the design variables of all the functionally graded unit cells to obtain an optimal topology optimization structure. The present application can not only maintain the heat transfer performance of the cross-type lattice structure unit cells, but also improve the connectivity between the functionally graded unit cells and the manufacturability of the topology optimization structure.

Description

Technical Field

[0001] This invention belongs to the technical field of structural optimization, and more specifically, relates to a method for optimizing the topology of heat dissipation structures based on anisotropic functionally graded cells. Background Technology

[0002] Compared to isotropic unit cells with high thermal conductivity, functionally graded cells (FJCs) with anisotropic thermal conductivity possess superior properties such as lightweight design, controlled heat flow, and efficient heat transfer. They also offer a larger design domain, allowing for optimization and updates to improve structural heat dissipation. The functionally graded multiscale topology optimization method is an intelligent design approach that automatically finds the optimal configuration of FJCs. Its main characteristic is a wider degree of design freedom, enabling the design of complex structures with superior performance and lightweight design. For heat dissipation issues, FJCs can be used to fill macroscopic units, thereby improving the heat transfer performance of topology-optimized structures. Therefore, by improving the FJC multiscale topology optimization method, highly manufacturable topology-optimized heat dissipation structures with excellent thermal conductivity can be designed.

[0003] Regarding multi-scale topology optimization methods for thermal conductivity in functionally graded cells, some research has been conducted by those skilled in the art. For example, reference 1, "MIN K,OH M,KIM C,et al. Topological design of thermalconductors using functionally graded materials[J].Finite Elements in Analysis and Design,2023,220:103947," optimizes the design of a cross-shaped lattice cell by updating its rotation angle and size variables. This method uses a cross-shaped lattice cell as a functionally graded cell, which is prone to connectivity problems between cells after rotation, and the manufacturability of the structure is also reduced. It is necessary to ensure that high thermal conductivity materials are connected between adjacent cells. For multi-scale topology optimization methods based on functionally graded cellular units, some research has been conducted by those skilled in the art, such as in reference 2: "X. Liu, L. Gao, M. Xiao, et al. Kriging-assisted design of functionally graded cellular structures with smoothly-varying lattice unitcells[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 390." This method incorporates algorithms between unit cells to ensure the gradient change in size between adjacent unit cells, improving the connectivity and manufacturability of the structure. However, this method only considers the objective function based on minimizing compliance and does not consider the objective function of minimizing thermal compliance. Furthermore, this method does not add a rotation angle to the unit cell to expand the design domain space of the unit cell. Summary of the Invention

[0004] To address the above-mentioned deficiencies or improvement needs of existing technologies, this invention provides a topology optimization method for heat dissipation structures based on anisotropic functionally graded cells. This method improves upon the traditional cross-shaped lattice structure cell. The improved functionally graded cell can rotate its internal cross-shaped structure according to heat flow transfer requirements to achieve better heat dissipation performance. Furthermore, an external manufacturable wall is provided to ensure the connectivity between cells and the manufacturability of the overall topology optimization structure.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for optimizing the topology of a heat dissipation structure based on anisotropic functionally graded cells is provided, the method comprising the following steps:

[0006] (1) An anisotropic functionally graded unit cell is provided, the functionally graded unit cell comprising a cross-shaped structure and a manufacturable wall, the manufacturable wall being disposed outside the cross-shaped structure; the unit cell comprising x i y i θ i Three design variables, x i It is the ratio of the width of the vertical bars of the cross-shaped structure inside the i-th functionally graded unit cell, y i It is the ratio of the width of the cross-shaped struts inside the i-th functionally graded unit cell, θ i It is the rotation angle of the cross-shaped structure inside the i-th functionally graded unit cell;

[0007] (2) The design variables of the functionally graded unit cell are changed in a consistent step size to obtain a series of functionally graded unit cells with different structures. The equivalent thermal conductivity tensor of the functionally graded unit cell is obtained by using a homogenization method. The multiple thermal conductivity tensors obtained are used to form multiple thermal conductivity tensor surfaces. The thermal conductivity tensor surfaces are interpolated by an interpolation function to fit the relationship between the design variables of the functionally graded unit cell and its thermal conductivity tensor. The relationship can be used to achieve positive prediction from the design variables of the functionally graded unit cell to the thermal conductivity tensor.

[0008] (3) Use the functionally graded cells to fill the grid in the design domain, construct a multi-scale topology optimization design model with the goal of minimizing heat dissipation flexibility based on the relation, and optimize the design variables of all functionally graded cells in the design domain through the multi-scale topology optimization design model to obtain the optimal topology optimization structure.

[0009] The mathematical expression for the multi-scale topology optimization design model is:

[0010]

[0011] In the formula, ρ i Let x be the set of design variables for the i-th functionally graded unit cell in the cell grid, which contains three design variables, x and x'. i y i θ i n is the number of grid cells; Θ is the objective function, representing the overall thermal compliance value of the structure; P is the externally applied thermal load matrix; T is the internal temperature matrix of the structure; K is the global thermal conduction matrix of the structure; v i is the volume percentage of the high thermal conductivity material inside the i-th functionally graded cell; f is the given volume constraint; V0 is the sum of the volumes of all meshes; w is the thickness of the fabricable walls in the outer ring of the functionally graded cell.

[0012] Furthermore, the expanded expression of the objective function of the multi-scale topology optimization design model is as follows:

[0013]

[0014] Among them, T i Let K be the temperature matrix of the i-th functionally graded unit cell. i Let Ω be the thermal conductivity matrix of the i-th functionally graded unit cell, and let Ω be the design domain of the structure.

[0015] Furthermore, K i The expression is:

[0016]

[0017] Among them, κ H Let B be the element heat conduction tensor, and let B be the temperature gradient-temperature matrix.

[0018] Furthermore, κ H The corresponding expression is:

[0019]

[0020] Furthermore, the sensitivity of the objective function of the multi-scale topology optimization design model to the design variables is calculated, and the design variables of each functionally graded cell in the optimization design domain are updated using the MMA method, thereby obtaining the optimal topology optimization structure.

[0021] Furthermore, update the design variable ρ i The method is MMA based on sensitivity information, and the formula for calculating the sensitivity of the objective function is:

[0022]

[0023] Furthermore, step (1) also includes the step of setting the thickness w of the manufacturable wall.

[0024] Furthermore, the equivalent thermal conductivity tensor of a functionally graded unit cell is obtained through a homogenization method, and the corresponding formula is:

[0025]

[0026] Where |Ω| is the volume of the functionally graded unit cell sample, and κ is the thermal conductivity tensor. For the applied temperature gradient field of the test unit, g p (T) represents the unknown temperature gradient field, and Ω represents the design domain space within the homogenization method.

[0027] Furthermore, g p (t i The expression is obtained through the linear elasticity equation:

[0028]

[0029] Where δt represents the virtual temperature field within the design domain in the homogenization method. This refers to the total temperature space.

[0030] Furthermore, the design variables of the functionally graded unit cell samples are varied in a consistent step size. The step size for the bar width ratio is 0.04, ranging from [0, 0.92], and the step size for the angle is 9°, ranging from [0, 171°]. The number of gradient lattice samples constructed based on the functionally graded unit cell is 24*24*20.

[0031] In summary, compared with the prior art, the heat dissipation structure topology optimization method based on anisotropic functionally graded cells provided by the present invention has the following advantages:

[0032] 1. Functionally graded cells can rotate their internal cross-shaped structure according to heat flow requirements to achieve better heat dissipation performance, and an external manufacturable wall can be set to maintain the excellent heat transfer performance of the cross-shaped lattice structure cell, while improving the connectivity between functionally graded cells and the manufacturability of the topology-optimized structure.

[0033] 2. The equivalent thermal conductivity tensor of functionally graded cells under multiple different design variables is obtained by homogenization method. The dataset composed of design variables and thermal conductivity tensor is interpolated by interpolation function to obtain the relationship between design variables and their thermal conductivity tensor, thereby realizing the positive prediction from the design variables of functionally graded cells to their equivalent thermal conductivity tensor.

[0034] 3. This invention introduces a functionally graded unit cell with anisotropic thermal conductivity, which expands the design domain of the topology-optimized structure and improves its heat dissipation performance.

[0035] 4. The functionally graded unit cell (FJC) includes three design variables: x, y, and θ. x represents the width ratio of the vertical bars of the cross-shaped structure within the FJC, y represents the width ratio of the horizontal bars, and θ represents the rotation angle of the cross-shaped structure. Updating the design variables x and y alters the heat transfer performance of the FJC in two mutually perpendicular layered structures. When heat conduction is required in a certain direction, the volume of high thermal conductivity material with a bar width ratio can be appropriately increased. The outer layer of the FJC is surrounded by a manufacturable wall to improve inter-cell connectivity and the overall manufacturability of the structure. Increasing w improves the thermal conductivity and manufacturability of the structure. By changing θ, the cross-shaped structure inside the FJC rotates, while the outer manufacturable wall does not participate in the rotation, maintaining connectivity. Attached Figure Description

[0036] Figure 1This is a flowchart of a heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells provided by the present invention;

[0037] Figure 2 This is a schematic diagram of the anisotropic functionally graded unit cell involved in the present invention;

[0038] Figure 3 This is a schematic diagram of the heat conduction boundary conditions constructed in this invention;

[0039] Figure 4 yes Figure 3 A schematic diagram and detailed diagram of the functionally graded cell filling after design variable optimization when w is 2% in the boundary conditions;

[0040] Figure 5 yes Figure 3 A schematic diagram of functionally graded cell filling after design variable optimization when w is 4% in the boundary conditions. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0042] Please see Figure 1 This invention provides a method for optimizing the topology of a heat dissipation structure based on anisotropic functionally graded cells. The method mainly includes the following steps:

[0043] Step 1: Provide an anisotropic functionally graded unit cell, wherein the functionally graded unit cell includes a cross-shaped structure and a manufacturable wall, the manufacturable wall being substantially U-shaped and disposed outside the cross-shaped structure; the unit cell includes x i y i θ i Three design variables, x i It is the ratio of the width of the vertical bars of the cross-shaped structure inside the i-th functionally graded unit cell, y i It is the ratio of the width of the cross-shaped struts inside the i-th functionally graded unit cell, θ i It is the rotation angle of the cross-shaped structure inside the i-th functionally graded unit cell.

[0044] The anisotropic functionally graded cell is a highly manufacturable anisotropic functionally graded cell with excellent thermal conductivity. It has the advantage of layered heat dissipation, can better conduct heat flow through the rotation of the cross-shaped structure within the cell, and has excellent inter-cell connectivity and overall structural manufacturing performance.

[0045] In this embodiment, such as Figure 2 As shown, the black area represents a high thermal conductivity material, while the remaining white area represents a low thermal conductivity material. This means the thermal conductivity of the material within the cross-shaped structure is greater than that of the filling material between the cross-shaped structure and the manufacturable wall. This functionally graded unit cell (FJC) offers the advantage of layered heat dissipation, enhancing heat flow conduction by rotating the cross-shaped structure within the cell. Furthermore, it exhibits excellent inter-cell connectivity and overall structural manufacturability. The FJC contains three design variables: x, y, and θ, where x represents the ratio of the vertical bar width of the cross-shaped structure within the FJC to the vertical bar width. Figure 2 l in y1 y is the percentage of the width of the cross-shaped struts within the functionally graded unit cell, corresponding to Figure 2 l in y2 θ is the rotation angle of the cross-shaped structure inside the functionally graded cell (FJC). The heat transfer performance of the FJC in two mutually perpendicular layered structures is changed by updating the design variables x and y. When heat conduction is required in a certain direction, the volume of high thermal conductivity material with a rod width ratio can be appropriately increased. The FJC is surrounded by a manufacturable wall to improve inter-cell connectivity and the overall manufacturability of the structure; w is the thickness of the manufacturable wall. Increasing w improves the thermal conductivity and manufacturability of the structure. By changing θ, the cross-shaped structure inside the FJC rotates, while the outer manufacturable wall does not participate in the rotation, maintaining connectivity. The thickness w of the manufacturable wall is set according to manufacturing requirements and minimum length requirements.

[0046] Step 2: The design variables of the functionally graded cells are varied in a consistent step size to obtain a series of functionally graded cells with different structures. The equivalent thermal conductivity tensor of the functionally graded cells is obtained using a homogenization method. The obtained thermal conductivity tensors are used to form multiple thermal conductivity tensor surfaces. The thermal conductivity tensor surfaces are interpolated using an interpolation function to fit the relationship between the design variables of the functionally graded cells and their thermal conductivity tensors. The relationship is used to achieve a positive prediction from the design variables of the functionally graded cells to the thermal conductivity tensors.

[0047] The thermal conductivity tensor of a functionally graded cell under different design variables was calculated using a homogenization method. All thermal conductivity tensors are assembled into multiple thermal conductivity tensor surfaces. Interpolation calculations are performed on the thermal conductivity tensor surfaces using interpolation functions to achieve positive prediction of thermal conductivity tensors from design variables to functionally graded cells.

[0048] The equivalent thermal conductivity tensor of a functionally graded unit cell is obtained through homogenization, and the corresponding formula is:

[0049]

[0050] Where |Ω| is the volume of the functionally graded unit cell sample, and κ is the thermal conductivity tensor. For the applied temperature gradient field of the test unit, g p (T) represents the unknown temperature gradient field, and Ω represents the design domain space within the homogenization method.

[0051] g p (t i The expression is obtained through the linear elasticity equation:

[0052]

[0053] Where δt represents the virtual temperature field within the design domain in the homogenization method. This refers to the total temperature space.

[0054] The lattice unit cell is a highly manufacturable functionally graded unit cell, which is achieved by updating the internal design variable x. i y i and θ i This system achieves thermal flow control and heat dissipation in the topology-optimized structure; by controlling the width w of the manufacturable walls, the manufacturability and connectivity of the functionally graded unit cell (FJC) are improved. The design variables for the FJC samples are varied with a consistent step size: the rod width ratio is 0.04 (range [0, 0.92]), and the angle is 9° (range [0, 171°]). The number of gradient lattice samples constructed from the FJC is 24*24*20. By varying the three design variables with equal step sizes, a series of FJCs with different structures are obtained. The equivalent thermal conductivity tensor of each FJC is calculated using a homogenization method.

[0055] Step 3: Fill the mesh in the design domain with the functionally graded cells. Based on the relationship, construct a multi-scale topology optimization design model with the goal of minimizing heat dissipation compliance. Optimize the design variables of all functionally graded cells in the design domain through the multi-scale topology optimization design model to obtain the optimal topology optimization structure.

[0056] The mathematical expression for the multi-scale topology optimization design model is:

[0057]

[0058] In the formula, ρ i Let x be the set of design variables for the i-th functionally graded unit cell in the cell grid, which contains three design variables, x and x'. i y i θ i , where x i It is the ratio of the width of the vertical bars of the cross-shaped structure inside the i-th functionally graded unit cell, y iIt is the ratio of the width of the cross-shaped struts inside the i-th functionally graded unit cell, θ i Θ is the rotation angle of the cross-shaped structure inside the i-th functionally graded unit cell; n is the number of grid cells; Θ is the objective function, representing the overall thermal compliance value of the structure; P is the externally applied thermal load matrix; T is the internal temperature matrix of the structure; K is the global thermal conduction matrix of the structure; v i is the volume percentage of the high thermal conductivity material inside the i-th functionally graded cell; f is a given volume constraint; V0 is the sum of the volumes of all meshes; w is the thickness of the outer fabricable walls in the functionally graded cell, used to improve the connectivity and fabrication between cells.

[0059] The expanded expression of the objective function of the multi-scale topology optimization design model is:

[0060]

[0061] Among them, T i Let K be the temperature matrix of the i-th functionally graded unit cell. i Let Ω be the thermal conductivity matrix of the i-th functionally graded unit cell, and let Ω be the design domain of the structure.

[0062] K i The expression is:

[0063]

[0064] Among them, κ H Let B be the element heat conduction tensor, and let B be the temperature gradient-temperature matrix.

[0065] The rotated functionally graded unit cell exhibits different thermal conductivity in each direction, displaying anisotropic thermal conductivity properties and possessing a larger design domain space. H The corresponding expression is:

[0066]

[0067] Update design variable ρ i The method used is MMA based on sensitivity information. The sensitivity calculation process of the objective function is as follows:

[0068]

[0069] The properties and design variables of the functionally graded cells are updated and optimized using the MMA method. Then, the obtained functionally graded cells are sequentially filled into the macroscopic mesh to obtain the final multi-scale, highly manufacturable heat dissipation topology optimization structure.

[0070] In this embodiment, the sensitivity of the objective function of the multi-scale topology optimization design model to the design variables is calculated. The design variables of each functionally graded cell in the optimization design domain are updated using the MMA method, so that the final topology optimization structure has better heat dissipation performance. The mesh is divided, loads and constraints are set, and the thermal conductivity tensor and design variables of the functionally graded cells are updated and optimized based on the MMA method. Then, the obtained functionally graded cells are sequentially filled into the macroscopic mesh to obtain the final multi-scale highly manufacturable heat dissipation topology optimization structure.

[0071] The present invention will be further described in detail below with reference to specific embodiments.

[0072] Example 1

[0073] In this embodiment, the topology optimization design domain, thermal load, and temperature boundary conditions are as follows: Figure 3 As shown, the design domain of the structure is square; the thermal load is uniformly distributed on the design domain, and the midpoint of the upper boundary is the Dirichlet boundary Γ. D A fixed temperature is maintained at this boundary, while all other boundaries are Newman boundaries. N There is no heat conduction, meaning there is no heat transfer or heat conversion. The corresponding formula is:

[0074]

[0075] T=0,Γ D

[0076]

[0077] Copper with a thermal conductivity of 400 W / (m·K) was selected as the high thermal conductivity material, and PDMS with a thermal conductivity of 0.16 W / (m·K) was selected as the low thermal conductivity material. The entire macroscopic region was divided into 40×40 unit meshes, and the volume constraint was set to 0.45.

[0078] like Figure 1 As shown, the heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells provided in Embodiment 1 of the present invention includes the following steps:

[0079] Step 1: Apply constraints and loads to provide functionally graded cells (FJCs), set the manufacturable wall thickness w of the FJCs, obtain a series of FJCs with different configurations, and calculate their equivalent thermal conductivity tensors using a homogenization method.

[0080] Specifically, it includes the following sub-steps:

[0081] (1.1) According to Figure 3 Apply thermal loads and temperature boundary conditions to create a design domain space, and set constraints, namely a volume constraint of 0.45.

[0082] (1.2) To address the connectivity and manufacturability issues of cross-shaped lattice structure cells, functionally graded cells are provided, such as... Figure 2 As shown, this functionally graded cell is used as the functionally graded cell for subsequent topology optimization.

[0083] The manufacturability wall thickness w was set to 2% and 4% of the microstructure size, respectively, for topology optimization structure comparison.

[0084] The design variables for functionally graded unit cell samples are varied in a consistent step size, with the bar width ratio taking a step size of 0.04 and the angle taking a step size of 9°.

[0085] When w = 2%, the bar width ratio ranges from [0, 0.96] to [0, 171°]. The number of gradient lattice samples constructed based on functionally graded cells is 25*25*20.

[0086] When w = 4%, the bar width ratio ranges from [0, 0.92] to [0, 171°], and the number of gradient lattice samples constructed according to the functionally graded unit cell is 24*24*20.

[0087] (1.3) The equivalent thermal conductivity tensor of functionally graded cells with equal step size is obtained by using the homogenization method.

[0088] By varying the three design variables in equal increments, a series of functionally graded cells with different structures are obtained. The equivalent thermal conductivity tensor of each functionally graded cell is calculated using a homogenization method.

[0089] The multi-scale topology optimization model obtains the equivalent thermal conductivity tensor of a functionally graded unit cell through a homogenization method, and the corresponding formula is:

[0090]

[0091] Where |Ω| is the volume of the functionally graded unit cell sample, and κ is the thermal conductivity tensor. For the applied temperature gradient field of the test unit, g p (T) represents the unknown temperature gradient field, and Ω represents the design domain space within the homogenization method.

[0092] g p (t i The value is obtained through the linear elasticity equation, and the corresponding expression is:

[0093]

[0094] Where δt represents the virtual temperature field within the design domain in the homogenization method. This refers to the total temperature space.

[0095] Step two involves assembling all the thermal conductivity tensors obtained by the homogenization method into multiple thermal conductivity tensor surfaces. Interpolation functions are then used to interpolate these surfaces to fit the relationship between the functionally graded cell design variables and their thermal conductivity tensors. This relationship is then used to achieve a forward prediction from the design variables to the thermal conductivity tensors of the functionally graded cell. For any range of design variables, the predicted thermal conductivity tensors and their partial derivatives for the corresponding lattice structure cell are obtained.

[0096] Step 3: Divide the design domain into 40×40 grids, set volume constraint functions, use the minimization of heat dissipation flexibility as the objective function, and then construct a multi-scale topology optimization model based on the relational formula. Calculate the sensitivity of the objective function of the multi-scale topology optimization model to the design variables, and use the MMA method to update the design variables of each functionally graded cell in the optimization design domain, so that the final topology optimization structure has better heat dissipation performance.

[0097] Specifically, it includes the following sub-steps:

[0098] (3.1) The mathematical expression of the multi-scale topology optimization model of the heat dissipation structure based on anisotropic functionally graded unit cells is as follows:

[0099]

[0100] In the formula, ρ i Let x be the set of design variables for the i-th functionally graded unit cell in the cell grid, which contains three design variables, x and x'. i y i θ i , where x i It is the ratio of the width of the vertical bars of the cross-shaped structure inside the i-th functionally graded unit cell, y i It is the ratio of the width of the cross-shaped struts inside the i-th functionally graded unit cell, θ i Θ is the rotation angle of the cross-shaped structure inside the i-th functionally graded unit cell; n is the number of grid cells; Θ is the objective function, representing the overall thermal compliance value of the structure; P is the externally applied thermal load matrix; T is the internal temperature matrix of the structure; K is the global thermal conduction matrix of the structure; v i is the volume percentage of the high thermal conductivity material inside the i-th functionally graded cell; f is a given volume constraint; V0 is the sum of the volumes of all meshes; w is the thickness of the outer fabricable walls in the functionally graded cell, used to improve the connectivity and fabrication between cells.

[0101] The expanded expression of the objective function of the multi-scale topology optimization model is as follows:

[0102]

[0103] Among them, T iLet K be the temperature matrix of the i-th functionally graded unit cell. i Let Ω be the thermal conductivity matrix of the i-th functionally graded unit cell, and let Ω be the design domain of the structure.

[0104] K i The expression is:

[0105]

[0106] Among them, κ H Let B be the element heat conduction tensor, and let B be the temperature gradient-temperature matrix.

[0107] κ H The corresponding expression is:

[0108]

[0109] The rotated functionally graded unit cell generally exhibits anisotropic thermal conductivity properties, which allows for a wider design domain.

[0110] (3.2) Calculate the sensitivity of the heat dissipation compliance objective function to the design variables. The expression for the sensitivity of the objective function to the design variables is:

[0111]

[0112] (3.3) The properties and design variables of the functionally graded unit cell are updated and optimized based on the MMA method. Then, the obtained functionally graded unit cells are sequentially filled into the macroscopic mesh to obtain the final multi-scale highly manufacturable heat dissipation topology optimization structure, such as... Figure 4 and Figure 5 As shown.

[0113] Please see Figures 2 to 5 The invention will be further illustrated with the optimized heat dissipation structure.

[0114] Figure 4 The manufacturable wall thickness is set to w = 2%, which occupies 2% of the macroscopic unit grid size, and the rod width ratio is controlled within the range of [0.1, 0.96]. Figure 5 The manufacturable wall thickness is set to w = 4%, which occupies 4% of the macroscopic unit grid size, and the rod width ratio is controlled within the range of [0.1, 0.92]. In terms of performance comparison, Figure 4 The heat dissipation flexibility is less than 14300. Figure 5 The thermal flexibility of 14800 indicates that the larger the w, the worse the structure's heat dissipation performance. However, due to the introduction of manufacturable walls, from Figure 4 As can be seen from the detailed diagrams, the highly thermally conductive materials can all be connected, and the connectivity between microstructures and the manufacturability of the overall structure are both enhanced.

[0115] Those skilled in the art will readily understand that the above description is merely 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 within the scope of protection of the present invention.

Claims

1. A method for optimizing the topology of a heat dissipation structure based on anisotropic functionally graded cells, characterized in that, The method includes the following steps: (1) An anisotropic functionally graded unit cell is provided, the functionally graded unit cell comprising a cross-shaped structure and a manufacturable wall, the manufacturable wall being disposed outside the cross-shaped structure; the unit cell comprising x i y i θ i Three design variables, x i It is the ratio of the width of the vertical bars of the cross-shaped structure inside the i-th functionally graded unit cell, y i It is the ratio of the width of the cross-shaped struts inside the i-th functionally graded unit cell, θ i It is the rotation angle of the cross-shaped structure inside the i-th functionally graded unit cell; (2) The design variables of the functionally graded unit cell are changed in a consistent step size to obtain a series of functionally graded unit cells with different structures. The equivalent thermal conductivity tensor of the functionally graded unit cell is obtained by using a homogenization method. The multiple thermal conductivity tensors obtained are used to form multiple thermal conductivity tensor surfaces. The thermal conductivity tensor surfaces are interpolated by an interpolation function to fit the relationship between the design variables of the functionally graded unit cell and its thermal conductivity tensor. The relationship can be used to achieve positive prediction from the design variables of the functionally graded unit cell to the thermal conductivity tensor. (3) Use the functionally graded cells to fill the grid in the design domain, construct a multi-scale topology optimization design model with the goal of minimizing heat dissipation flexibility based on the relation, and optimize the design variables of all functionally graded cells in the design domain through the multi-scale topology optimization design model to obtain the optimal topology optimization structure. The mathematical expression for the multi-scale topology optimization design model is: In the formula, ρ i Let x be the set of design variables for the i-th functionally graded unit cell in the cell grid, which contains three design variables, x and x'. i y i θ i n is the number of grid cells; Θ is the objective function, representing the overall thermal compliance value of the structure; P is the externally applied thermal load matrix; T is the internal temperature matrix of the structure; K is the global thermal conduction matrix of the structure; v i is the volume percentage of the thermally conductive material inside the i-th functionally graded cell; f is the given volume constraint; V0 is the sum of the volumes of all meshes; w is the thickness of the fabricable walls in the outer ring of the functionally graded cell.

2. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 1, characterized in that: The expanded expression of the objective function of the multi-scale topology optimization design model is: Among them, T i Let K be the temperature matrix of the i-th functionally graded unit cell. i Let Ω be the thermal conductivity matrix of the i-th functionally graded unit cell, and let Ω be the design domain of the structure.

3. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 2, characterized in that: K i The expression is: Among them, κ H Let B be the element heat conduction tensor, and let B be the temperature gradient-temperature matrix.

4. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 3, characterized in that: κ H The corresponding expression is:

5. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 3, characterized in that: The sensitivity of the objective function of the multi-scale topology optimization design model to the design variables is calculated. The design variables of each functionally graded cell in the optimization design domain are updated using the MMA method, thereby obtaining the optimal topology optimization structure.

6. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 5, characterized in that: Update design variable ρ i The method is MMA based on sensitivity information, and the formula for calculating the sensitivity of the objective function is:

7. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in any one of claims 1-6, characterized in that: Step (1) also includes the step of setting the thickness w of the manufacturable wall.

8. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 7, characterized in that: The equivalent thermal conductivity tensor of a functionally graded unit cell is obtained through homogenization, and the corresponding formula is: Where |Ω| is the volume of the functionally graded unit cell sample, and κ is the thermal conductivity tensor. For the applied temperature gradient field of the test unit, g p (T) represents the unknown temperature gradient field, and Ω represents the design domain space within the homogenization method.

9. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in claim 8, characterized in that: g p (t i The expression is obtained through the linear elasticity equation: Where δt represents the virtual temperature field within the design domain in the homogenization method. This refers to the total temperature space.

10. The heat dissipation structure topology optimization method based on anisotropic functionally graded unit cells as described in any one of claims 1-6, characterized in that: The design variables of the functionally graded unit cell samples are varied in a consistent step size. The step size of the rod width ratio is 0.04, ranging from [0, 0.92], and the step size of the angle is 9°, ranging from [0, 171°]. The number of gradient lattice samples constructed based on the functionally graded unit cell is 24*24*20.

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