A Robust Topological Optimization Method and System for the Heat Dissipation Path of a CPU Heat Sink

Abstract

The present invention provides a robust topology optimization method and system for the heat dissipation path of a CPU heat sink. The method includes: S1: Presetting boundary conditions and constructing a finite element model of the structural design domain of the CPU heat sink; S2: Initializing the design variables and random variables of the finite element model, and presetting constraint conditions to construct a robust optimization model; S3: Calculating the sensitivity of the design variables and the sensitivity to the random variables; S4: Filtering the sensitivity; S5: Based on the filtered sensitivity, the mean and standard deviation of the objective function, and the constraint conditions, using the moving asymptote method to update the design variables, and determining whether the updated design variables converge. If not, return to step S3 for re-iteration; S6: Based on the converged design variables, obtaining a robust topology optimization model of the heat sink; completing the robust topology optimization of the heat dissipation path of the CPU heat sink. The present invention can enable the heat generated by the CPU to be quickly and efficiently transferred to the heat dissipation part.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural optimization design, and particularly relates to a robust topology optimization method and system for the heat dissipation path of a CPU heat sink. Background Art

[0002] Under the background of the information age, computer technology and Internet technology are becoming increasingly mature, and their application scope is also becoming wider and wider. The demand for computers in fields such as computer-aided systems, artificial intelligence, and data processing is increasing day by day. Every aspect of human society has become inseparable from the assistance of high-frequency microcomputers. Based on this realistic background, it can be inferred that people's application requirements for computer devices will gradually increase, thus putting higher requirements on the performance of computer devices. Computers will surely develop in the direction of miniaturization, intelligence, and higher computing frequencies. The continuous reduction of the volume of computers and the increase in their operating frequencies will inevitably lead to greater energy consumption of computers, increase the heat generation of the CPU, thereby affecting the function of the CPU, reducing the operation accuracy rate, and even causing equipment failure problems. And in practical engineering applications, uncertainty is inevitable. Factors such as material parameters, geometric dimensions, boundary conditions, and external loads may change due to manufacturing errors, environmental changes, and long-term use. Although these changes may seem insignificant, they can profoundly affect the mechanical properties of the CPU and ultimately affect their response and behavior. Therefore, these uncertainties must be considered and solved in structural design and analysis to ensure the robustness and safety of the CPU in an uncertain environment.

[0003] The design of traditional CPU heat sinks is generally obtained through thermodynamic calculations, and its design efficiency and heat dissipation performance have gradually lagged behind the increasing CPU heat dissipation requirements. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a robust topology optimization method and system for the heat dissipation path of a CPU heat sink, which helps the CPU dissipate heat better through a heat sink with better heat dissipation ability and a better heat transfer path.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A robust topology optimization method for the heat dissipation path of a CPU heat sink includes the following steps:

[0007] S1: Preset boundary conditions and construct a finite element model of the structural design domain of the CPU heat sink;

[0008] S2: Initialize the design variables and random variables of the finite element model, and preset constraint conditions to construct a robust optimization model;

[0009] S3: Calculate the sensitivities of the objective function of the robustness optimization model with respect to the design variables and with respect to the random variables;

[0010] S4: Conduct Heaviside filtering on the sensitivities;

[0011] S5: Based on the filtered sensitivities, the mean and standard deviation of the objective function, and the constraint conditions, use the moving asymptote method to update the design variables, and determine whether the updated design variables converge. If not, return to step S3 for re-iteration;

[0012] S6: Based on the converged design variables, obtain the robust topology optimization model of the heat sink;

[0013] S7: Based on the robust topology optimization model of the heat sink, complete the robust topology optimization of the heat dissipation path of the CPU heat sink.

[0014] Preferably, in step S1, the boundary conditions include the first kind of boundary condition, the second kind of boundary condition, and the third kind of boundary condition, where

[0015] The first kind of boundary condition is as follows:

[0016]

[0017] The second kind of boundary condition is as follows:

[0018]

[0019] The third kind of boundary condition is as follows:

[0020]

[0021] Among them, T(x, y, z, t) is the temperature of any element at any time t, is the function of the change of the initial temperature of the heat sink with time, λ is the thermal conductivity of the element in the x, y, and z directions, n is the direction vector of the element, q(t) is the heat flux density, is the convective heat transfer coefficient, T ∞ is the ambient temperature.

[0022] Preferably, in step S2,

[0023] The design variable is the element density of the finite element model of the CPU heat sink structure design domain;

[0024] The random variable is the elastic modulus of the CPU heat sink material;

[0025] The constraint condition is the volume constraint.

[0026] Preferably, in step S2, the method for constructing the robustness optimization model is as follows:

[0027] Based on the improved SIMP variable density method model, obtain the elastic modulus as the random variable;

[0028] Based on the boundary conditions, construct a heat conduction model using the variational approach;

[0029] Based on the random variable, the design variable, the constraint condition, and the heat conduction model, construct a robustness optimization model.

[0030] Preferably, in step S3, the method for calculating the sensitivity of the objective function to the design variable is as follows:

[0031] Calculate the sensitivity of the mean value of the objective function to the design variable and to the random variable;

[0032] Based on the sensitivity of the mean value of the objective function to the design variable and to the random variable, calculate the sensitivity of the standard deviation of the objective function to the design variable;

[0033] Based on the sensitivity of the mean value and the standard deviation of the objective function to the design variable and the robustness coefficient, obtain the sensitivity of the objective function to the design variable.

[0034] A robustness topology optimization system for the heat dissipation path of a CPU heat sink, used to implement the above method, includes:

[0035] A finite element model construction module, used to preset boundary conditions and construct a finite element model of the structural design domain of the CPU heat sink;

[0036] An optimization model construction module, used to initialize the design variable and the random variable of the finite element model, preset the constraint condition, and construct a robustness optimization model;

[0037] A sensitivity calculation module, used to calculate the sensitivity of the objective function of the robustness optimization model to the design variable and to the random variable;

[0038] A filtering module, used to perform Heaviside filtering on the sensitivity;

[0039] An update convergence module, used to update the design variable using the moving asymptote method based on the filtered sensitivity, the mean value and the standard deviation of the objective function, and the constraint condition, and determine whether the updated design variable converges. If not, return to the sensitivity calculation module for re-iteration;

[0040] A topology optimization model construction module, used to obtain a robustness topology optimization model of the heat sink based on the converged design variable;

[0041] A heat dissipation path optimization module, configured to perform robust topology optimization on the heat dissipation path of the CPU heat sink based on the heat sink robustness topology optimization model.

[0042] Preferably, in the optimization model construction module,

[0043] The design variable is the element density of the finite element model of the CPU heat sink structure design domain;

[0044] The random variable is the elastic modulus of the CPU heat sink material;

[0045] The constraint condition is volume constraint.

[0046] Preferably, the optimization model construction module includes a model construction unit for constructing a robust optimization model, and the model construction unit includes:

[0047] A random variable acquisition subunit, configured to obtain an elastic modulus as the random variable based on an improved SIMP variable density method model;

[0048] A heat conduction model construction subunit, configured to construct a heat conduction model by using the variational approach based on the boundary conditions;

[0049] An optimization model construction subunit, configured to construct a robust optimization model based on the random variable, the design variable, the constraint condition, and the heat conduction model.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a heat sink with better heat dissipation ability and a better heat transfer path to help the CPU dissipate heat better. The present invention proposes a heat sink robustness topology optimization model, and the optimized heat dissipation path of the model can enable the heat generated by the CPU to be quickly and efficiently transmitted to the heat dissipation part. This heat dissipation path ensures that the heat sink material has high heat transfer performance and has become an important way for the heat sink structure design. The present invention selects the elastic modulus as an uncertain random variable and studies the influence of the change of the elastic modulus on the CPU heat dissipation topology structure. Description of the Drawings

[0051] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1 It is a flowchart of the robust topology optimization method for the heat dissipation path of the CPU heat sink in the embodiment of the present invention;

[0053] Figure 2 Schematic diagram of the design domain, boundary conditions, and the relationship between the heat source and the heat sink for the embodiments of the present invention;

[0054] Figure 3 Schematic diagram of the optimization result for the embodiments of the present invention. Detailed implementation manners

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0057] Embodiment 1

[0058] As Figure 1 shown, a robustness topology optimization method for the heat dissipation path of a CPU heat sink includes the following steps:

[0059] S1: Preset boundary conditions and construct a finite element model of the structural design domain of the CPU heat sink;

[0060] Further implementation manners lie in that, in step S1, the boundary conditions include the first type of boundary conditions, the second type of boundary conditions, and the third type of boundary conditions, where

[0061] The first type of boundary conditions is as follows:

[0062]

[0063] The second type of boundary conditions is as follows:

[0064]

[0065] The third type of boundary conditions is as follows:

[0066]

[0067] where T(x, y, z, t) is the temperature of any element at any time t, is the function of the initial temperature of the heat sink changing with time, λ is the thermal conductivity of the element along the x, y, and z directions, n is the direction vector of the element, q(t) is the heat flux density, is the convective heat transfer coefficient, T ∞ is the ambient temperature.

[0068] S2: Initialize the design variables and random variables of the finite element model, preset the constraint conditions, and construct a robustness optimization model;

[0069] A further implementation manner lies in that, in step S2,

[0070] The design variable ρ e is the element density of the finite element model of the CPU heat sink structure design domain;

[0071] The random variable x (k) is the elastic modulus of the CPU heat sink material;

[0072] The constraint condition is the volume constraint.

[0073] In this embodiment, the constraint condition is:

[0074]

[0075] wherein, V d * is the volume ratio, and V is the overall volume of the heat sink.

[0076] In this embodiment, the initialized parameters further include the filtering radius r min for density and sensitivity filtering, the robustness index β, the penalty factor p for the SIMP variable density method interpolation model, the heat source position, size, and temperature.

[0077] A further implementation manner lies in that, in step S2, the method for constructing the robustness optimization model is:

[0078] Based on the improved SIMP variable density method model, obtain the elastic modulus E i , as the random variable x (k) ;

[0079] In this embodiment, change the elastic modulus E i = E i (ρ e ) = E min + ρ e p E 0

[0080] to: E i = E i (ρ e ) = E min + ρ e p (E 0 - E min ), ρ e ∈ [0, 1].

[0081] It is equivalent to stipulating the minimum elastic modulus of the material. This method is well applied in the topological optimization of the heat transfer model and can be considered as the distribution of two material phases: a good heat conductor and another conductor with poor heat transfer ability. According to the expected performance of the designed heat sink, the calculated constraint conditions are used for program simulation design to obtain the optimal material distribution of the heat sink.

[0082] Based on the boundary conditions, a variational formulation is used to construct a heat conduction model;

[0083] In this embodiment, the variational formulation is that in the admissible temperature field satisfying the three types of boundary conditions and initial conditions, the true temperature field makes the following functional take the minimum value.

[0084]

[0085] Among them, I is an intermediate variable, Ω is the unit volume domain, ρ is the material density, Q is the internal heat source density of the object, T is the temperature of the heat sink, and λ x , λ y , λ z are the thermal conductivities in the x, y, and z directions.

[0086] In actual problem handling, it is difficult to satisfy the second and third types of boundary conditions in advance. Therefore, these two conditions can be coupled into the functional.

[0087]

[0088] In the formula, s2 and s3 are the unit heat conduction planes, is the coupled heat flux density, is the coupled convective heat transfer coefficient, and A is the unit area.

[0089] Variational extremum seeking It is obtained that,

[0090] Furthermore, it is obtained that:

[0091]

[0092] In the formula, N is the shape matrix.

[0093] Similar to the finite element equilibrium equation model, can be rewritten as where is the finite element global node temperature vector, F is the global heat load vector, is the global thermal conductivity matrix.

[0094] Based on random variables, design variables, constraint conditions, and the heat conduction model, a robustness optimization model is constructed:

[0095] min J = μ + βσ

[0096]

[0097] where J is the objective function, β is the robustness coefficient, ρ e is the design variable, v e is the element volume, V d * is the constrained volume ratio, is the finite element global nodal temperature vector, F is the global heat load vector, is the global thermal conductivity matrix. For isotropic materials, the conductivity is the same in all directions. μ and σ are the mean and standard deviation of the objective function respectively, and the specific solution formulas are as follows:

[0098] μ(ρ,x) = U T (ρ,x)K(ρ,x)U(ρ,x)

[0099]

[0100] where x represents the random variable, nx represents the number of random variables, σ xi represents the standard deviation corresponding to the xi-th random variable.

[0101] S3: Calculate the sensitivity of the objective function of the robustness optimization model to the design variables and to the random variables.

[0102] Furthermore, in the implementation manner, in step S3, the method for calculating the sensitivity of the objective function to the design variables is:

[0103] Calculate the sensitivity of the mean value of the objective function to the design variables and to the random variables;

[0104]

[0105] Based on the sensitivity of the mean value of the objective function to the design variables and to the random variables, calculate the sensitivity of the standard deviation of the objective function to the design variables;

[0106] where,

[0107] Based on the sensitivity of the mean value and the standard deviation of the objective function to the design variables and the robustness coefficient, obtain the sensitivity of the objective function to the design variables.

[0108]

[0109] where, N e represents the number of elements, represents the physical field, k 0 represents the element stiffness matrix; k min represents the minimum stiffness matrix; p represents the penalty factor of the SIMP method; u i represents the element displacement.

[0110] S4: Perform Heaviside filtering on the sensitivity:

[0111]

[0112] where η (d) , η (i) , η (e) are three prediction truncation thresholds set to 0.3, 0.5, 0.7 respectively, θ represents the nonlinear degree of the mapping function, θ = 0 means it satisfies a linear relationship, represents the dilated physical field, represents the intermediate physical field, represents the eroded physical field; the present invention only considers the intermediate physical field;

[0113] Calculate the filtered density field using convolutional density filtering:

[0114]

[0115] where n j represents the coordinate vector of the center point of the j-th element, w(n j ) = r min - ||n j - n e || is a linear weight function, ||·|| represents the 2-norm and Ξ e = {j|||n j - n e || ≤ r min} represents the neighborhood set of the elements centered on the circular region specified by the filter radius r min , v j represents the element volume, ρ j represents the element density.

[0116] S5: Based on the filtered sensitivity, the mean and standard deviation of the objective function, and the constraint conditions, update the design variables using the moving asymptote method, and determine whether the updated design variables converge. If not, return to step S3 and iterate k = k + 1 times;

[0117] S6: Based on the converged design variables, obtain the robust topology optimization model of the heat sink;

[0118] S7: Based on the robust topology optimization model of the heat sink, complete the robust topology optimization of the heat dissipation path of the CPU heat sink.

[0119] Use the MATLAB program software to analyze the program and output the results, and evaluate the performance and effect of two-dimensional topology optimization. Import the file containing the three-dimensional topology optimization program into the MATLAB environment, run the three-dimensional topology optimization program, and implement the optimization algorithm by executing 169 lines of code. Analyze the program output results and give the final robust topology optimization model of the heat sink.

[0120] Based on the matlab program development software. Through the existing APP design environment in MATLAB, a simple and clear APP interface is designed. This software can update the design variables to solve the optimization problem of the heat sink by inputting the number of elements along the xyz axes, the constraint volume ratio, the penalty parameter, the filtering radius, and the random variables of the given optimization model, and draw the corresponding iteration images and topology maps based on the robust topology optimization design method.

[0121] Example Two

[0122] In this embodiment, the size of the finite element model is selected as the common size of the CPU heat sink of a notebook computer, which is 80mm×80mm×20mm. It is discretized into 160×160×40 hexahedral isoparametric elements. The size of the heat source is 40mm×40mm, and the positional relationship between the heat source and the heat sink is as Figure 2 shown. The heat source is set to a constant temperature of 80°C, and the surrounding temperature is set to room temperature of 20°C. This model is considered to use copper as the material composition of the CPU radiator. The medium between the radiator structures is air, and the parameters of the two media are shown in Table 1. The filtering radius is selected as five times the element size. The allowable volume fraction V * of Material 1 in the robust topology optimization model of the heat sink is 0.4. The mean value of the elastic modulus is 200Gpa, and the coefficient of variation is 10%. Finally, the optimized 3D model of the heat sink is obtained. The optimization results are shown in Table 2, Figure 3 as shown.

[0123] Table 1

[0124]

[0125] Table 2

[0126]

[0127] Example Three

[0128] A robust topology optimization system for the heat dissipation path of a CPU heat sink and a method for implementation, including:

[0129] A finite element model construction module, used to preset boundary conditions and construct a finite element model of the structural design domain of the CPU heat sink;

[0130] An optimization model construction module, which is used to initialize the design variables and random variables of the finite element model, preset the constraint conditions, and construct a robustness optimization model;

[0131] A sensitivity calculation module, which is used to calculate the sensitivity of the objective function of the robustness optimization model to the design variables and to the random variables;

[0132] A filtering module, which is used to perform Heaviside filtering on the sensitivity;

[0133] An update convergence module, which is used to update the design variables by using the moving asymptotes method based on the filtered sensitivity, the mean and standard deviation of the objective function, and the constraint conditions, and to judge whether the updated design variables converge. If not, it returns to the sensitivity calculation module for re-iteration;

[0134] A topology optimization model construction module, which is used to obtain a robustness topology optimization model of the heat sink based on the converged design variables;

[0135] A heat dissipation path optimization module, which is used to complete the robustness topology optimization of the heat dissipation path of the CPU heat sink based on the robustness topology optimization model of the heat sink.

[0136] A further implementation manner lies in that, in the optimization model construction module,

[0137] The design variable is the element density of the finite element model of the CPU heat sink structure design domain;

[0138] The random variable is the elastic modulus of the CPU heat sink material;

[0139] The constraint condition is the volume constraint.

[0140] A further implementation manner lies in that the optimization model construction module includes a model construction unit, which is used to construct a robustness optimization model. The model construction unit includes:

[0141] A random variable acquisition subunit, which is used to obtain the elastic modulus as a random variable based on the improved SIMP variable density method model;

[0142] A heat conduction model construction subunit, which is used to construct a heat conduction model by using the variational formulation based on the boundary conditions;

[0143] An optimization model construction subunit, which is used to construct a robustness optimization model based on the random variables, design variables, constraint conditions, and heat conduction model.

[0144] The embodiments described above are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A robust topology optimization method for a CPU heat sink heat dissipation path, characterized in that: The following steps are involved: S1: Preset boundary conditions and build a finite element model of the CPU heat sink structure design domain; In step S1, the boundary conditions include first-type boundary conditions, second-type boundary conditions and third-type boundary conditions, wherein: The first type of boundary conditions are as follows: The second type of boundary conditions is as follows: The third type of boundary conditions is as follows: Where T(x,y,z,t) is the temperature of any element at any time t, is the function of the initial temperature of the heat sink changing with time, λ is the thermal conductivity of the element along the x, y, and z directions, n is the direction vector of the element, q(t) is the heat flux density, is the convective heat transfer coefficient, T ∞ is the ambient temperature; S2: Initialize the design variables and random variables of the finite element model, preset constraints, and build a robust optimization model; S3: Calculating the sensitivity of the objective function of the robust optimization model to the design variables and the sensitivity to the random variables; S4: performing Heaviside filtering on the sensitivity; S5: Based on the filtered sensitivity, the mean and standard deviation of the objective function and the constraint conditions, the moving asymptote method is used to update the design variables, and it is determined whether the updated design variables converge. If not, return to step S3 and iterate again; S6: Based on the converged design variables, the robust topology optimization model of the heat sink is obtained; S7: Based on the heat sink robust topology optimization model, complete the robust topology optimization of the CPU heat sink heat dissipation path.

2. The robust topology optimization method for the heat dissipation path of a CPU heat sink according to claim 1, characterized in that: In step S2, The design variable is the unit density of the finite element model of the CPU heat sink structure design domain; The random variable is the elastic modulus of the CPU heat sink material; The constraint condition is a volume constraint.

3. The robust topology optimization method for the heat dissipation path of a CPU heat sink according to claim 1, characterized in that: In step S2, the method for constructing a robustness optimization model is: Based on the improved SIMP variable density method model, the elastic modulus is obtained as the random variable; Based on the boundary conditions, a heat conduction model is constructed using a variational method; A robustness optimization model is constructed based on the random variables, the design variables, the constraints and the heat conduction model.

4. The robust topology optimization method for the heat dissipation path of a CPU heat sink according to claim 1, characterized in that: In step S3, the method for calculating the sensitivity of the objective function to the design variables is: Calculating the sensitivity of the mean of the objective function to the design variables and the sensitivity to the random variables; Calculate the sensitivity of the standard deviation of the objective function to the design variable based on the sensitivity of the mean of the objective function to the design variable and the sensitivity to the random variable; Based on the sensitivity of the objective function mean and standard deviation to the design variables and the robustness coefficient, the sensitivity of the objective function to the design variables is obtained.

5. A robust topology optimization system for a CPU heat sink heat dissipation path, used to implement the method described in any one of claims 1 to 4, characterized in that: include: Finite element model building module, used to preset boundary conditions and build a finite element model of the CPU heat sink structure design domain; The optimization model building module is used to initialize the design variables and random variables of the finite element model, preset constraints, and build a robust optimization model; A sensitivity calculation module, used for calculating the sensitivity of the objective function of the robustness optimization model to the design variables and the sensitivity to the random variables; A filtering module, used for performing Heaviside filtering on the sensitivity; An update convergence module, used to update the design variables using a moving asymptote method based on the filtered sensitivity, the mean and standard deviation of the objective function and the constraint conditions, and determine whether the updated design variables converge. If not, return to the sensitivity calculation module for re-iteration; Topology optimization model building module, used to converge design variables and obtain the robust topology optimization model of the heat sink; The heat dissipation path optimization module is used to complete the robust topology optimization of the heat dissipation path of the CPU heat sink based on the heat sink robust topology optimization model.

6. The robust topology optimization system for the heat dissipation path of a CPU heat sink according to claim 5, characterized in that: In the optimization model construction module, The design variable is the unit density of the finite element model of the CPU heat sink structure design domain; The random variable is the elastic modulus of the CPU heat sink material; The constraint condition is a volume constraint.

7. The robust topology optimization system for the heat dissipation path of a CPU heat sink according to claim 5, characterized in that: The optimization model construction module includes a model construction unit for constructing a robust optimization model, and the model construction unit includes: A random variable acquisition subunit, used to obtain elastic modulus as the random variable based on an improved SIMP variable density method model; A heat conduction model construction subunit is used to construct a heat conduction model based on the boundary conditions by using a variational method; The optimization model construction subunit is used to construct a robust optimization model based on the random variables, the design variables, the constraint conditions and the heat conduction model.

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