A heat dissipation design method based on variable density topology optimization and TPMS lattice

Abstract

The present invention discloses a heat dissipation design method based on the combination of variable-density topology optimization and TPMS lattice. The method includes: inputting a heat dissipation topology optimization model and TPMS expression, as well as the corresponding design domain boundaries and initial parameters; generating a density-mapped mesh for the design domain using a variable-density method; extracting the mesh density, performing an expanded column design on the mesh density, and performing a gradient design on the mesh density; mapping a triple-periodic minimal surface implicit function to the mesh density, and filling the design domain with the triple-periodic minimal surface; re-meshing the surface mesh and repairing the triangular facets to obtain an STL model; performing finite element body meshing, deleting the surface mesh, retaining the body mesh, and exporting an inp file; importing the inp file into simulation software, setting boundary conditions, and performing heat dissipation finite element analysis to complete the heat dissipation optimization design combining topology optimization and triple-periodic minimal surfaces. This method can effectively improve the heat dissipation performance of the structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural optimization and heat dissipation, and in particular relates to a heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice. Background Art

[0002] Structural optimization methods can be categorized into topology optimization, shape optimization, and size optimization. Size optimization is a parametric optimization technique, while shape optimization optimizes the structure's boundaries or shape. Topology optimization is a numerical engineering optimization technique with broad application prospects and may become an indispensable engineering tool for many emerging technologies. Topology optimization involves iteratively finding the optimal material distribution path that meets various performance requirements within a fixed design domain, thereby rationally arranging the materials within the design domain.

[0003] Existing variable-density topology optimization often results in uneven density distributions and makes it difficult to find suitable materials for manufacturing. For heat transfer topology optimization, the objective function is the structure's heat dissipation weakness. By optimizing and calculating the structure's minimum heat dissipation weakness under certain constraints, the density topological distribution for optimal heat dissipation is determined. This density distribution is then processed using bilinear interpolation. Furthermore, triple-periodic minimal surface structures can be modified to adjust their density as needed, which can be combined with the topological structure's mesh density to avoid geometric mutations and address manufacturing difficulties. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and provide a heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice, which combines the lattice with topology optimization to obtain better optimization effects and improve the heat dissipation performance of the structure.

[0005] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0006] A heat dissipation design method based on variable density topology optimization combined with TPMS lattice, including:

[0007] Step 1: Input the thermal topology optimization model and triple-periodic minimal surface TPMS expressions, as well as the corresponding design domain boundaries and initial parameters;

[0008] Step 2: Based on the design domain boundary and initial parameters, the variable density method is used to generate a density mapping grid for the design domain of the heat dissipation topology optimization model to obtain a topology optimization density distribution model;

[0009] Step 3: Extract the mesh density of the topology optimization density distribution model based on the density mapping mesh, expand the mesh density and perform gradient design on the mesh density using the bilinear interpolation method;

[0010] Step 4: Map the implicit function t of the triple periodic minimal surface to the mesh density p obtained in step 3, and fill the design domain with the triple periodic minimal surface to obtain the topology optimization-lattice model;

[0011] Step 5: Re-mesh the topology optimization-lattice model and repair the triangular facets to obtain the STL model;

[0012] Step 6: Perform finite element body meshing on the STL model, delete the surface mesh, retain the body mesh, and export the model inp file;

[0013] Step 7: Import the model inp file into the simulation software, set the boundary conditions and perform heat dissipation finite element analysis to complete the heat dissipation optimization design combining topology optimization and triple periodic minimal surface.

[0014] To optimize the above technical solutions, specific measures taken also include:

[0015] The objective function of the heat dissipation topology optimization model described in step 1 above is the heat dissipation weakness representing heat transfer, and there is a volume constraint for lightweight requirements. At the same time, t in the triple periodic minimal surface expression affects the surface density, and the value range of t is different for different surfaces.

[0016] The above heat dissipation topology optimization model is as follows:

[0017] Find w={w1,w2,...,w n}∈R n

[0018]

[0019]

[0020] KT=P

[0021] 0<w min ≤w e ≤1

[0022] Among them, w is the set of unit variables, R n Represents n real number design variables, C is the heat dissipation weakness, T is the node temperature vector of the structure, T T is the transposed matrix of T, K is the heat conduction matrix of the entire structure, K e is the unit heat conduction matrix, T e is the unit temperature node matrix, is the transposed matrix of the unit temperature node matrix, P is the thermal load vector of the entire structure, v e is the volume of the unit, w eis the unit cell variable, α is the penalty factor, V0 is the total volume of the design domain, f is the material volume fraction, w min =0.001;

[0023] The expression of the triple periodic minimal surface TPMS is as follows:

[0024] f(x,y,z)=cos(X)cos(Y)cos(Z)-sin(X)sin(Y)sin(Z)-t

[0025] Where t is the level set constant, which controls the relative density of the lattice structure, X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L is the size of the control lattice unit, and x, y, z are the coordinates of the high-dimensional physical space;

[0026] And the design domain boundary range in step 1 is x∈[x min ,x max ],y∈[y min ,y max ],z∈[z min ,z max ];

[0027] The initial parameters include the target volume fraction and the penalty factor.

[0028] In step 2 above, the heat dissipation topology optimization model based on the variable density method performs topology optimization iterative updates on the design domain according to the input design domain boundary and initial parameters. The iteration ends when the density change is less than or equal to 0.001, and the final topology optimization density distribution model is obtained.

[0029] In the above step 2, the penalty factor is set to α=3.

[0030] In the above step 3, each grid in the design domain is expanded ten times by a numerical array of the same density, and the numerical values ​​are gradient-modulated using bilinear interpolation.

[0031] The above bilinear interpolation calculation formula is as follows:

[0032]

[0033]

[0034]

[0035] In step 4 above, a mapping relationship between the t value in the implicit function of the triply periodic minimal surface and the mesh density p is established, and the mesh density is mapped to the t value in the triply periodic minimal surface so that the triply periodic minimal surface is filled into the topology optimization density distribution model to obtain the topology optimization-lattice model;

[0036] The mapping relationship between the grid density p and t value is as follows:

[0037] p = -0.007t 2 -0.4118t+0.5008.

[0038] In step 5, the topology optimization-lattice model is redivided into triangular faces, and the model triangular faces are detected and repaired, and the STL file is exported.

[0039] In step 7, the inp file is imported to perform a heat dissipation simulation experiment. By giving boundary conditions and constraints, a temperature distribution cloud diagram of the structure after steady state is obtained.

[0040] The present invention has the following beneficial effects:

[0041] The method of the present invention utilizes a structural heat dissipation topology optimization model. Based on the topology optimization model, a grid density value is derived, and bilinear interpolation processing is performed on the grid density to avoid density transition mutations. The triple periodic minimal surface is mapped to the grid density for filling, so that the porous density value of the triple periodic minimal surface corresponds to the grid density value after topology optimization. The filled structure is grid-repaired, volume grid division is performed, and finally simulation is performed to obtain a structural temperature distribution cloud map.

[0042] 1. The present invention expands the grid density obtained by topology optimization and uses bilinear interpolation to achieve a smooth transition in density between grids, thus avoiding sudden changes during geometric filling.

[0043] 2. Since porous structures can provide a wide range of density variations, the present invention matches the grid density generated by the variable density topology optimization method with the porous density one-to-one, solving the problem that previous topological structures could not be processed.

[0044] 3. The present invention realizes topological optimization from point heat source to boundary heat source by changing the range of heat source;

[0045] 4. The present invention changes the size range of the topological structure density so that the minimum density of the grid structure is 0.2 and the maximum density is 0.7, thereby avoiding the appearance of empty materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A diagram of the topology optimization process implemented for a fixed design domain of the present invention;

[0047] Figure 2 A flow chart for implementing topology optimization and triple-periodic minimal surface fusion design for the present invention;

[0048] Figure 3 This is the rendering of the topology optimization-lattice model of the present invention;

[0049] Figure 4 This is the temperature cloud diagram of the heat dissipation simulation of the model of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0051] Although the steps in the present invention are arranged with numbers, they are not intended to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0052] The present invention discloses a heat dissipation design method based on the combination of variable density topology optimization and TPMS dot matrix, such as Figure 1 and Figure 2 As shown, it includes: taking the original design domain and constraints as input, using heat dissipation as the target of topology optimization, numerically iterating the structure in the specified design domain to obtain a reasonable material density distribution, and then using the grid density and the triple-periodic minimal surface density for mapping to design a topology optimization-lattice optimization model. The method specifically includes the following steps:

[0053] Step 1: Input the thermal topology optimization model and the triple-periodic minimal surface TPMS expression f(x, y, z) = t, as well as the corresponding design domain boundaries and initial parameters;

[0054] The objective function of the heat dissipation topology optimization model described in step 1 is the heat dissipation weakness representing heat transfer, and there is a volume constraint for lightweight requirements. At the same time, t in the triple periodic minimal surface expression affects the surface density, and the value range of t is different for different surfaces.

[0055] The heat dissipation topology optimization model is as follows:

[0056] Find w={w1,w2,...,w n}∈R n

[0057]

[0058]

[0059] KT=P

[0060] 0<w min ≤we ≤1

[0061] Among them, w is the set of unit variables, R n Represents n real number design variables, C is the heat dissipation weakness, T is the node temperature vector of the structure, T T is the transposed matrix of T, K is the heat conduction matrix of the entire structure, K e is the unit heat conduction matrix, T e is the unit temperature node matrix, is the transposed matrix of the unit temperature node matrix, P is the thermal load vector of the entire structure, v e is the volume of the unit, w e is the unit cell variable, α is the penalty factor, V0 is the total volume of the design domain, f is the material volume fraction, w min =0.001;

[0062] The expression of the triple periodic minimal surface TPMS is as follows:

[0063] f(x,y,z)=cos(X)cos(Y)cos(Z)-sin(X)sin(Y)sin(Z)-t

[0064] Where t is the level set constant, which controls the relative density of the lattice structure, X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L is the size of the control lattice unit, and x, y, z are the coordinates of the high-dimensional physical space;

[0065] And the design domain boundary range in step 1 is x∈[x min ,x max ],y∈[y min ,y max ],z∈[z min ,z max ];

[0066] The initial parameters include the target volume fraction and the penalty factor.

[0067] Step 2: Based on the design domain boundary and initial parameters, the variable density method is used to generate a density mapping grid for the design domain of the heat dissipation topology optimization model to obtain a topology optimization density distribution model;

[0068] In step 2, the heat dissipation topology optimization model based on the variable density method performs topology optimization iterative updates on the design domain according to the input design domain boundary and initial parameters. The iteration ends when the density change is less than or equal to 0.001, and the final topology optimization density distribution model is obtained.

[0069] In the iterative calculation of topology optimization, the density of each material unit is used as a design variable, and the density of each unit is continuously updated and the related performance is calculated to finally obtain the optimal material density distribution, where the density of each unit ranges from 0.2 to 0.7, such as Figure 1 As shown;

[0070] In step 2, the penalty factor is set to α = 3, which can reduce the generation of intermediate density units and transform the discretization problem into a continuous problem.

[0071] Step 3: Extract the mesh density of the topology optimization density distribution model based on the density mapping mesh, expand the mesh density and perform gradient design on the mesh density using the bilinear interpolation method;

[0072] In step 3, in order to prevent large numerical gradients between the initial grids, which would cause geometric mutations in subsequent filling, each grid in the design domain is expanded ten times by a numerical array of the same density to avoid geometric mutations due to excessive density gradients, and the numerical values ​​are gradient-processed using bilinear interpolation to ensure geometric continuity.

[0073] The calculation formula of bilinear interpolation is as follows:

[0074]

[0075]

[0076]

[0077] Step 4: Map the implicit function t of the triple periodic minimal surface to the mesh density p obtained in step 3, and fill the design domain with the triple periodic minimal surface to obtain the topology optimization-lattice model;

[0078] In step 4, a mapping relationship between the t value and the mesh density p in the implicit function of the triply periodic minimal surface is established, and the mesh density in step 3 is mapped to the t value in the triply periodic minimal surface so that the triply periodic minimal surface is filled into the topology optimization density distribution model. The STL format file is exported to obtain the topology optimization-lattice model.

[0079] like Figure 3 As shown, the mapping relationship between the grid density p and t value is as follows:

[0080] p = -0.007t 2 -0.4118t+0.5008

[0081] Step 5: Re-mesh the topology optimization-lattice model and repair the triangular facets to obtain the STL model;

[0082] In step 5, the topology optimization-lattice filling model obtained in step 4 is redivided into triangular faces to make the surface mesh distribution more uniform. At the same time, the model triangular faces are detected and repaired to prevent the generation of overlapping triangular faces, bad holes and redundant shells, and the STL file is exported.

[0083] Step 6: Perform finite element body meshing on the STL model, delete the surface mesh, retain the body mesh, and export the model inp file;

[0084] In step 6, the STL model processed in step 5 is divided into a volume mesh. Since the surface mesh is evenly distributed at this time, the quality of the volume mesh adaptively generated based on the surface mesh is also improved. The surface mesh is deleted, the volume mesh is retained, and the inp file is exported.

[0085] Step 7: Import the model inp file into the simulation software, set the boundary conditions and perform heat dissipation finite element analysis to complete the heat dissipation optimization design combining topology optimization and triple periodic minimal surface.

[0086] In step 7, import the inp file to perform heat dissipation simulation experiments. By giving boundary conditions and constraints, the temperature distribution cloud of the structure after steady state is obtained, as shown in the figure below: Figure 4 shown.

[0087] Typical implementation examples of the present invention are as follows:

[0088] The embodiment adopts a three-periodic minimal surface D surface, whose function expression is:

[0089] f(x,y,z)=cos(X)cos(Y)cos(Z)-sin(X)sin(Y)sin(Z)-t

[0090] The design domain ranges from x∈[0,40], y∈[0,40], and z∈[0,10], with target volume fractions v=0.3, v=0.4, v=0.5, and v=0.6, respectively. The density distribution calculated using the variable density method for heat dissipation topology optimization can be substituted into the fitting formula to calculate the corresponding structural parameters. This method achieves the generation of a three-periodic minimal surface porous structure with a solid configuration based on a heat dissipation topology optimization structure.

[0091] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0092] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A heat dissipation design method based on variable density topology optimization combined with TPMS lattice, characterized in that: include: Step 1: Input the thermal topology optimization model and triple-periodic minimal surface TPMS expressions, as well as the corresponding design domain boundaries and initial parameters; The heat dissipation topology optimization model is as follows: Find w={w1,w2,...,w n }∈R n KT=P 0<w min ≤in e ≤1 Among them, w is the set of unit variables, R n Represents n real number design variables, C is the heat dissipation weakness, T is the node temperature vector of the structure, T T is the transposed matrix of T, K is the heat conduction matrix of the entire structure, K e is the unit heat conduction matrix, T e is the unit temperature node matrix, is the transposed matrix of the unit temperature node matrix, P is the thermal load vector of the entire structure, v e is the volume of the unit, w e is the unit cell variable, α is the penalty factor, V0 is the total volume of the design domain, f is the material volume fraction, w min =0.001; The expression of the triple periodic minimal surface TPMS is as follows: f(x,y,z)=cos(X)cos(Y)cos(Z)-sin(X)sin(Y)sin(Z)-t Where t is the level set constant, which controls the relative density of the lattice structure, X = 2πx / L, Y = 2πy / L, Z = 2πz / L, L is the size of the control lattice unit, and x, y, z are the coordinates of the high-dimensional physical space; And the design domain boundary range in step 1 is x∈[x min ,x max ],y∈[y min ,y max ],z∈[z min ,z max ]; The initial parameters include the target volume fraction and penalty factor; Step 2: Based on the design domain boundary and initial parameters, the variable density method is used to generate a density mapping grid for the design domain of the heat dissipation topology optimization model to obtain a topology optimization density distribution model; Step 3: Extract the mesh density of the topology optimization density distribution model based on the density mapping mesh, expand the mesh density and perform gradient design on the mesh density using the bilinear interpolation method; Step 4: Map the implicit function t of the triple periodic minimal surface to the mesh density p obtained in step 3, and fill the design domain with the triple periodic minimal surface to obtain the topology optimization-lattice model; Step 5: Re-mesh the topology optimization-lattice model and repair the triangular facets to obtain the STL model; Step 6: Perform finite element body meshing on the STL model, delete the surface mesh, retain the body mesh, and export the model inp file; Step 7: Import the model inp file into the simulation software, set the boundary conditions and perform heat dissipation finite element analysis to complete the heat dissipation optimization design combining topology optimization and triple periodic minimal surface.

2. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: The objective function of the heat dissipation topology optimization model described in step 1 is the heat dissipation weakness representing heat transfer, and there is a volume constraint for lightweight requirements. At the same time, t in the triple periodic minimal surface expression affects the surface density, and the value range of t is different for different surfaces.

3. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: In step 2, the heat dissipation topology optimization model based on the variable density method performs topology optimization iterative updates on the design domain according to the input design domain boundary and initial parameters. The iteration ends when the density change is less than or equal to 0.001, and the final topology optimization density distribution model is obtained.

4. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 3 is characterized in that: In step 2, α=3 is used as the penalty factor.

5. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: In step 3, each grid in the design domain is enlarged ten times by a numerical array of the same density, and the numerical values ​​are gradient-modulated using bilinear interpolation.

6. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 5 is characterized in that: The calculation formula of bilinear interpolation is as follows:

7. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: In step 4, a mapping relationship between the t value in the implicit function of the triply periodic minimal surface and the mesh density p is established, and the mesh density is mapped to the t value in the triply periodic minimal surface so that the triply periodic minimal surface is filled into the topology optimization density distribution model to obtain the topology optimization-lattice model; The mapping relationship between the grid density p and t value is as follows: p=-0.007t 2 -0.4118t+0.5008。 8. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: In step 5, the topology optimization-lattice model is redivided into triangular faces, and the model triangular faces are detected and repaired, and the STL file is exported.

9. The heat dissipation design method based on the combination of variable density topology optimization and TPMS lattice according to claim 1 is characterized in that: In step 7, the inp file is imported to perform a heat dissipation simulation experiment. By giving boundary conditions and constraints, a temperature distribution cloud diagram of the structure after steady state is obtained.

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