CN115495863A - Heat dissipation topology optimization method for smooth boundary expression - Google Patents
Heat dissipation topology optimization method for smooth boundary expression Download PDFInfo
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Abstract
A heat dissipation topology optimization method of smooth boundary expression relates to the technical field of structure optimization. Dispersing a heat dissipation topological structure to be optimized into a finite element model, and performing optimization based on a finite element grid to obtain the optimal distribution of materials; converting the discrete optimization into continuous optimization based on an interpolation function, and analyzing by using a heat transfer coefficient obtained by the first interpolation function to obtain unit sensitivity; and realizing projection conversion from the unit sensitivity to the node sensitivity according to the preset corresponding relation between the unit and the node. And determining a key level value according to the node sensitivity, wherein when the node sensitivity part of the node corresponding to the unit is greater than the key level value, the unit is a boundary unit. And performing grid subdivision on the boundary unit, calculating the sensitivity of a new subdivision node by using a second interpolation function, determining the density value of the boundary unit according to the sensitivity of the new subdivision node, determining the volume fraction according to the density values of all units, updating the key level value by using the volume fraction, and finally finding out the key level value meeting the volume constraint.
Description
Technical Field
The invention relates to the technical field of structural optimization, in particular to a heat dissipation topological optimization method for smooth boundary expression.
Background
The topological optimization as a structural optimization design method can fully excavate the potential of materials, save the material to the maximum extent on the premise of meeting design requirements and realize the lightweight design of the structure. The topological optimization design is different from the traditional design iteration 'design-realization' empirical design mode, and a conceptual design structure can be directly obtained, so that the product design period is shortened, the design cost is saved, and the method has very important application value for industrial design. The heat dissipation component is one of important fields of topology optimization application, and the topology optimization design can realize optimization of the heat dissipation performance of the component under given material properties and related constraints, including but not limited to minimizing thermal flexibility, minimizing maximum temperature, minimizing temperature field variance, and the like. It is clearly more attractive to meet the heat dissipation requirements by optimizing the structure, as opposed to using expensive heat dissipation materials.
The conventional heat transfer topology optimization method performs optimization and topology expression based on cells of finite element mesh division, as shown in fig. 1, the boundaries of the optimized structure are expressed in a zigzag form. In addition, most of heat transfer topological optimization results are in dendritic distribution, small-size features are complex, and gray-scale units are enriched, so that the manufacturing difficulty of the dendritic distribution optimization structure in engineering practice is extremely high.
Disclosure of Invention
In order to solve the above problems, the present application provides a heat dissipation topology optimization method expressed by a smooth boundary.
According to a first aspect, an embodiment provides a heat dissipation topology optimization method of smooth boundary expression, including:
dispersing a heat dissipation topological structure to be optimized into a finite element model;
calculating a density field of the heat dissipation topological structure to be optimized based on a finite element model, wherein the density field comprises a plurality of units;
calculating a heat transfer coefficient by using a first interpolation function, updating the finite element analysis model according to the heat transfer coefficient, and determining the element sensitivity of each element according to the updated finite element analysis model; the finite element analysis model is used for solving the finite element model;
according to a preset mapping relation of a plurality of units corresponding to a single node, acquiring unit sensitivity of each unit of the plurality of units to determine node sensitivity of the corresponding single node;
determining a key level value according to the node sensitivity of each node, and when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is all larger than the key level value, determining that the unit is a complete entity unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is larger than the key level value, the unit is a boundary unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is all smaller than the key level value, the unit is a cavity unit;
dividing each boundary unit to obtain a corresponding new division unit, and calculating the sensitivity of a new division node of the new division unit corresponding to each boundary unit by using a second interpolation function; for each boundary unit, the density value of the boundary unit is respectively determined according to the sensitivity of the newly-divided node of the boundary unit;
and determining volume fractions according to the density values of all the units, and updating the key level values according to the volume fractions so as to perform smooth boundary expression meeting volume constraints on the result to be optimized.
In an embodiment, the calculating the density field of the heat dissipation topology to be optimized based on the finite element model includes:
controlling the filtering radius of a finite element model based on a continuous density strategy, carrying out a plurality of iterations on the density field to obtain an iterative optimization target, and when the variance of the optimization target is smaller than a set tolerance, ending the iteration and outputting the density field; the filtering radius is calculated by the following formula:
wherein the content of the first and second substances,rin order to be the radius of the iteration,kfor the number of iterations to be performed,r min is the preset minimum filtering radius,r 0 is a preset initial filtering radius and is a preset initial filtering radius,lpa number of iterations to decay to the minimum filter radius for the set initial filter radius.
In one embodiment, said calculating a heat transfer coefficient using a first interpolation function, and updating said finite element analysis model based on said heat transfer coefficient comprises:
calculating a heat transfer coefficient in the first interpolation function using a penalty factor greater than a set value, the first interpolation function calculated using the formula:
wherein the content of the first and second substances,k 0 in order to be a heat transfer coefficient,εis 10 -3 ，ρIs a unit density, and has a value range of [0,1 ]]，pIn order to be a penalty factor,kare interpolation coefficients.
In an embodiment, the obtaining unit sensitivity of each unit of the plurality of units according to a preset mapping relationship between the plurality of units and a single node to determine node sensitivity of the corresponding single node includes:
calculating the node sensitivity of the single node by using the following mapping formula:
wherein, the first and the second end of the pipe are connected with each other,ns m is a nodemNode sensitivity ofDegree;Neis the total number of units;iis a firstiEach unit, the value range is [1,Ne]；es i is a firstiCell sensitivity of the individual cells;w i m, a weighting function for the sensitivity of a cell in the set of cells.
In one embodiment, the weighting function of the cell sensitivity field of the plurality of cells is determined by the formula:
wherein, the first and the second end of the pipe are connected with each other,w i m, a weighting function of the cell sensitivity fields of the number of cells,r dist is a nodemThe range of the mapping of (a) to (b),
is a firstiUnit to nodemThe distance of (c).
In an embodiment, the determining a key level value according to the node sensitivity of each node in the heat dissipation topology structure to be optimized includes:
acquiring a lower bound value taking the minimum node sensitivity value in all node sensitivities as an interval, and acquiring an upper bound value taking the maximum node sensitivity value in all node sensitivities as an interval; and updating the lower bound value and the upper bound value by using a dichotomy, and calculating the average value of the updated lower bound value and the updated upper bound value to determine the key horizontal value.
In an embodiment, the dividing each boundary unit to obtain a corresponding new divided unit, and calculating the sensitivity of a new divided node of the new divided unit corresponding to each boundary unit by using a second interpolation function includes:
interpolating the node sensitivity of each boundary unit by using a second interpolation function to obtain the new subdivision node sensitivity corresponding to the new subdivision unit; the second interpolation function is expressed by the following formula:
wherein the content of the first and second substances,ns new (o) For the sensitivity of the new subdivision node of the new subdivision unit, (ii) (ξ i ，η i ) The coordinates of the corresponding node of the border element,icorresponding to the boundary celliThe number of the nodes is equal to the number of the nodes,Cethe total number of nodes corresponding to the boundary cell (a), (b), (c)ξ o ，η o ) For the coordinates of the new partitioning node corresponding to the new partitioning unit,
the node sensitivity corresponding to the border cell.
In one embodiment, for each boundary cell, the boundary cell separately determines its density value according to its newly-subdivided node sensitivity, including:
calculating the percentage of the nodes corresponding to the new subdivision units with the sensitivity of the new subdivision nodes larger than the key level value occupying the nodes of the corresponding boundary units, and determining the density values of the corresponding boundary units according to the percentage; the percentage is calculated using the formula:
wherein, the first and the second end of the pipe are connected with each other,bfor the percentage of the nodes of the new subdivision cell that occupy the nodes of the corresponding border cell(s), (b)ξ o ，η o ) For the coordinates of the node corresponding to the new subdivision unit,ns m for the sensitivity of the new subdivision node of the new subdivision unit,ns key in order to be a key level value,N node is the total number of nodes of the border cell.
In an embodiment, the updating the key level value according to the volume fraction to optimize the heat dissipation topology to be optimized includes:
updating the key level value according to the volume fraction, and updating the current time when the volume fraction is larger than the preset volume fractionHas a lower bound value of
(ii) a When the volume fraction is smaller than the preset volume fraction, updating the upper bound value of the current time to be
(ii) a Wherein the content of the first and second substances,ns key for the value of the key level,B min for the last updated lower bound value,B max the upper bound value is updated last time; and updating the key level value according to the current lower bound value and the current upper bound value.
According to a second aspect, an embodiment provides a computer-readable storage medium having a program stored thereon, the program being executable by a processor to implement the above-mentioned method.
According to the heat dissipation topological optimization method expressed by the smooth boundary and the computer readable storage medium of the embodiment, the heat dissipation topological structure to be optimized is dispersed into a finite element model, and optimization is performed based on a finite element grid to obtain the optimal distribution of materials; converting the discrete optimization into continuous optimization based on an interpolation function, and analyzing by using a heat transfer coefficient obtained by the first interpolation function to obtain unit sensitivity; and realizing projection conversion from unit sensitivity to node sensitivity according to the preset corresponding relation between the units and the nodes. And determining a key level value according to the node sensitivity, wherein when the node sensitivity part of the node corresponding to the unit is greater than the key level value, the unit is a boundary unit. And performing grid subdivision on the boundary unit, calculating the sensitivity of a new subdivision node by using a second interpolation function, determining the density value of the boundary unit according to the sensitivity of the new subdivision node, determining the volume fraction according to the density values of all units, updating the key level value by using the volume fraction, and finally finding out the key level value meeting the volume constraint. According to the traditional heat transfer topological optimization framework based on units, part of small-size features are eliminated, the boundary effect of an optimization result is weakened, and then the conversion from a jagged boundary to a smooth boundary expression is realized by utilizing boundary smoothing processing. The smooth structure topology deletes part of small-size detail features, important detail features are reserved, the performance requirements of the heat dissipation component are met, and meanwhile the manufacturability of an optimization result is improved.
Drawings
FIG. 1 is a diagram illustrating a result of topology boundary optimization in the background art;
FIG. 2 is a flowchart of an embodiment of a method for optimizing a heat dissipation topology using smooth boundary representation;
FIG. 3 is a graph of the optimization results after eliminating some small-sized detail features using a continuity density filtering strategy according to an embodiment;
FIG. 4 is a schematic diagram of a node sensitivity calculation according to an embodiment;
FIG. 5 is a schematic diagram illustrating the subdivision of a border cell according to one embodiment;
FIG. 6 is a diagram of an embodiment of an optimization result after subsequent processing of a density field of an iterative structure;
fig. 7 is a schematic diagram of an embodiment of a heat dissipation topology optimization apparatus with smooth boundary representation.
Detailed Description
The present invention will be described in further detail with reference to the following detailed description and accompanying drawings. Wherein like elements in different embodiments are numbered with like associated elements. In the following description, numerous details are set forth in order to provide a better understanding of the present application. However, those skilled in the art will readily recognize that some of the features may be omitted or replaced with other elements, materials, methods in different instances. In some instances, certain operations related to the present application have not been shown or described in this specification in order not to obscure the core of the present application with unnecessary detail, and it is not necessary for those skilled in the art to describe these operations in detail, so that they may be fully understood from the description in the specification and the general knowledge in the art.
Furthermore, the features, operations, or characteristics described in the specification may be combined in any suitable manner to form various embodiments. Also, the various steps or actions in the method descriptions may be transposed or transposed in order, as will be apparent to one of ordinary skill in the art. Thus, the various sequences in the specification and drawings are for the purpose of clearly describing certain embodiments only and are not intended to imply a required sequence unless otherwise indicated where a certain sequence must be followed.
The numbering of the components as such, e.g., "first", "second", etc., is used herein only to distinguish the objects as described, and does not have any sequential or technical meaning. The term "connected" and "coupled" when used in this application, unless otherwise indicated, includes both direct and indirect connections (couplings).
As one of the common topology optimization methods, the level set method can directly realize smooth expression of the boundary, and the level set method describes the design space by using a level set function with one dimension higher, and the response value of the level set function represents the attribute of the point: a solid, a void, or a boundary. Usually, the intersection of the zero level and the level set function is defined as a structural contour, the set above the zero level represents the solid material distribution region Ω, otherwise, the void distribution regionDAnd/omega, the mathematical model expression is as follows:
wherein the content of the first and second substances,
in the form of a function of the level set,
representing the structural boundaries. Weak materials are also used to replace the material properties of the void region to avoid numerical singularities. In order to evolve the structure contour to realize the flexibility minimization, the sensitivity analysis is used for determining the normal speed of the level set function, the pseudo time is introduced to obtain a Hamilton-Jacobian equation, and the updated level set function is obtained through the solution. However, solving the hamilton-jack equation results in significantly increased computational cost and memory burden, and thus the level set method is difficult to generalize to large scale problems.
The moving deformable component method also enables smooth representation of the boundary and has few design variables to avoid additional computational cost. However, the motion variability component is sensitive to parameters and tends to converge to a sub-optimal or even an infeasible solution, and therefore the computational cost of stealth due to iterative parameter tuning can also be expensive.
The results of heat transfer topology optimization are often expressed dendritic and therefore the detailed features of the structure are complex. The expression capability of the level set method and the mobile deformable component method for detailed features is inferior, but the details of an optimization result obtained by a classical density-based topological optimization method are too complex, and the actual manufacturing is not facilitated.
The method is based on a classical SIMP (Solid Isotropic Material with Penalification model, which is a common density-stiffness interpolation model) interpolation model topology optimization framework, only uses a continuous density filtering strategy to control the radius size in the optimization process, and executes subsequent processing on a density field of an iterative structure. The continuous density filtering strategy is firstly used for eliminating the detail features with the small size in the optimization process, and then the subsequent processing is carried out on the density field of the iterative structure, so that the detail features with the small size can be further eliminated, and the necessary feature structures are reserved and the connectivity of the structure is not changed. By using the method, the radius size is controlled by using a continuous density filtering strategy only in the optimization process, and the density field after iteration is finished is subjected to post-processing, so that high calculation cost and huge memory burden are avoided.
Referring to fig. 2, an embodiment of the present application provides a method for optimizing a heat dissipation topology with smooth boundary expression, which includes the following steps.
Step S100: and dispersing the heat dissipation topological structure to be optimized into a finite element model.
In some embodiments, a topological optimization design space is established in consideration of actual needs of the heat dissipation component, a topological structure to be optimized is discretized to generate a finite element model, and an optimization target, boundary conditions, convergence conditions and initial values of relevant parameters are set.
Step S200: and calculating a density field of the heat dissipation topological structure to be optimized based on the finite element model.
In some embodiments, the filtering radius used per iteration is controlled based on a continuity density strategy to control the bandwidth of the grayscale cells at the structure boundaries. Wherein the filtering radius used by the iterative loop is obtained according to the following formula:
wherein the content of the first and second substances,rin order to be the radius of the iteration,kin order to be the number of iterations,r min is a preset minimum filtering radius,r 0 is a preset initial filtering radius and is a preset initial filtering radius,lpa number of iterations to decay to the minimum filter radius for the set initial filter radius. In some embodiments, the preset minimum filtering radius and the preset initial filtering radius are set in step S100 according to initial values of parameters.
In some embodiments, the finite element model is used to calculate the temperature field of the heat dissipation topological structure to be optimized, the element sensitivity is calculated based on the temperature field of the heat dissipation topological structure to be optimized, and the density field is updated by using the calculated element sensitivity. When the density field is updated each time, the current filtering radius needs to be updated, a new density filtering mapping matrix is established until the optimization iteration meets the given convergence condition, namely the variance of the optimization target is smaller than the set tolerance, the optimization cycle is ended, and the final density field is output. Wherein the density field comprises a plurality of cells.
Referring to fig. 3, steps S100 to S200 are graphs of optimization results after eliminating some small-sized detail features by using a continuous density filtering strategy in the optimization process.
Step S300: cell acuity is determined and node acuity for individual nodes is determined based on the cell acuity.
In some embodiments, a heat transfer coefficient is calculated using a first interpolation function, the finite element analysis model is updated based on the heat transfer coefficient, and a cell sensitivity for each cell is determined based on the updated finite element analysis model. And acquiring the unit sensitivity of each unit of the plurality of units according to the preset mapping relation of the plurality of units corresponding to the single node so as to determine the node sensitivity of the corresponding single node.
In some embodiments, a penalty factor greater than a set value is used in the first interpolation function to calculate the heat transfer coefficient, so that the penalty effect on the intermediate density is increased, and the islanding phenomenon of the result after the smoothing treatment is avoided. That is, in calculating the cell sensitivities of individual cells throughout the density field, a large penalty factor needs to be applied to calculate the heat transfer coefficient to prevent the presence of isolated cells. Wherein the first interpolation function is represented by the following formula:
wherein the content of the first and second substances,k 0 in order to be a heat transfer coefficient,εis 10 -3 ，ρIs a unit density, and has a value range of [0,1 ]]，pIn order to be a penalty factor,kare interpolation coefficients.
In some embodiments, after the unit sensitivity of each unit is calculated, each unit corresponds to a node according to a preset mapping relationship of a plurality of units corresponding to one node, wherein some units correspond to the same node. A cell sensitivity field is acquired for each cell to determine a node sensitivity for a corresponding node of each cell. Referring to fig. 4, a plurality of cells covered in a circle all correspond to a node corresponding to the center of the circle, and then cell sensitivity fields of all the cells covered in the circle are acquired, and the node sensitivity of the node corresponding to the center of the circle is determined according to the cell sensitivity fields of the cells. In some embodiments, it is also possible that a single unit can map out a single node. Wherein the node sensitivity of a single node is calculated by using the following mapping formula:
wherein the content of the first and second substances,ns m is a nodemNode acuity of (a);Neis the total number of units;iis as followsiEach unit, the value range is [1,Ne]；es i is as followsiCell sensitivity of the individual cells;w i m, is a weighted function of the sensitivity of the cells in the set of cells.
In some embodiments, the weighting function for the cell sensitivity field for a number of cells is determined by the following equation:
wherein, the first and the second end of the pipe are connected with each other,w i m, a weighting function of the cell sensitivity fields of the number of cells,r dist is a nodemThe range of the mapping of (a) to (b),
is as followsiUnit to nodemThe distance of (c).
In some embodiments, a finite element analysis model, which is a general process of conventional topology optimization, is used to solve the finite element model. The method specifically comprises the following steps: based on the density field determined in step S200, the heat transfer coefficients of the units in the density field are calculated by using the first interpolation function, and after the heat transfer coefficients of the units are calculated, the structural response analysis is performed on the heat transfer coefficients by using the finite element model. After the structural response analysis is completed, the temperature field of the topological structure with the heat dissipation and the unit sensitivity of each unit are calculated, and the density field is updated by using the unit sensitivity at the moment. During the update of the density field, the sensitivity of the cells other than the individual cells is calculated.
Step S400: determining a complete entity cell, a boundary cell and a hole cell.
In some embodiments, a key level value is determined according to the node sensitivity of each node, and when the node sensitivity of a node corresponding to a unit in the heat dissipation topological structure to be optimized is all greater than the key level value, the unit is a complete entity unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is larger than a key level value, the unit is a boundary unit; and when the node sensitivity of the corresponding node of one unit in the heat dissipation topological structure to be optimized is less than the key level value, the unit is a cavity unit.
In some embodiments, the minimum node sensitivity value of all the node sensitivities is obtained as a lower bound value of an interval, and the maximum node sensitivity value of all the node sensitivities is obtained as an upper bound value of the interval; and updating the lower bound value and the upper bound value by using a dichotomy, and calculating the average value of the updated lower bound value and the updated upper bound value to determine a key horizontal value. And determining a key level value based on the node sensitivity value of each mapped node to ensure that the volume fractions before and after the smoothing treatment are consistent. Firstly initializing one-dimensional search maximum node sensitivity as an upper bound value by utilizing a dichotomyB max Minimum node sensitivity is a lower bound valueB min Continuously updating and iterating the upper bound value and the lower bound value by using a dichotomy, wherein the key level value isB max AndB min average value of (a).
In some embodiments, since one unit corresponds to four nodes, two adjacent units will have the same two nodes, and thus a single unit corresponds to multiple nodes in the whole heat dissipation topology to be optimized. Based on the above, if the node sensitivity values of all nodes corresponding to a certain cell are smaller than the key level value, the cell is a hole cell; if the node sensitivity values of all nodes corresponding to a certain unit are greater than the key level value, all the units are complete entity units; if the node sensitivity value of all nodes corresponding to a certain cell is partially greater than the key level value, the cell is a boundary cell.
Step S500: the key level values are updated cyclically.
In some embodiments, each boundary unit is respectively subdivided to obtain a corresponding new subdivision unit, and the sensitivity of a new subdivision node of the new subdivision unit corresponding to each boundary unit is calculated by using a second interpolation function; for each boundary unit, the density value of the boundary unit is respectively determined according to the sensitivity of the newly-divided node of the boundary unit; and determining volume fractions according to the density values of all the units, and updating the key level value according to the volume fractions.
In some embodiments, referring to fig. 5, the boundary cells determined in step S400 are subdivided, that is, each boundary cell is subdivided to obtain new subdivided cells. The node sensitivity of each of the border cell corresponding nodes (i.e., the original nodes in fig. 5) is interpolated using a second interpolation function to determine a new split node sensitivity of the new split cell corresponding to the new split node (i.e., the new nodes in fig. 5). Wherein the second interpolation function is represented by the following formula:
wherein the content of the first and second substances,ns new (o) For the sensitivity of the new subdivision node of the new subdivision unit, (ii) (ξ i ，η i ) Is the coordinate of the corresponding node of the border element,iis corresponding to the boundary celliThe number of the nodes is equal to the number of the nodes,Cethe total number of nodes corresponding to the boundary cell (a), (b), (c)ξ o ，η o ) For the coordinates of the new partitioning node corresponding to the new partitioning unit,
the node sensitivity corresponding to the border cell.
In some embodiments, after a plurality of new split units are split for each boundary unit, the density values of the boundary units corresponding to the new split units are determined according to the node sensitivity of the new split nodes corresponding to the new split units. After the boundary cells are determined according to the key level values, the boundary cells remain unchanged, but each boundary cell needs to be subdivided to determine the density value of each boundary cell. The method specifically comprises the following steps: and acquiring new subdivision nodes of the new subdivision units with the sensitivity of the new subdivision nodes higher than the key level value, and determining the density values of the boundary units according to the percentages of the new subdivision nodes occupying the nodes of the corresponding boundary units. Wherein the percentage is calculated using the formula:
wherein the content of the first and second substances,bfor the percentage of the nodes of the new subdivision cell occupying the nodes of the corresponding boundary cell, (ii) aξ o ，η o ) For the coordinates of the node corresponding to the new subdivision unit,ns m for the sensitivity of the new subdivision node of the new subdivision unit,ns key in order to be a key level value,N node is the total number of nodes of the border cell.
In some embodiments, in calculating the density value for each of the border cells, the volume fraction is determined collectively from the density values of all of the cells.
In some embodiments, when a cell is determined to be a fully physical cell, the density value of the cell is determined accordingly, wherein the density value of the fully physical cell is 1. When the cell is determined to be a hole cell, the density value of the cell is determined accordingly, wherein the density value of the hole cell is 0. Therefore, the density values of all the units in the whole heat dissipation topological structure to be optimized can be determined only by calculating the density values of the boundary units.
And obtaining an optimization target of the updated finite element model, and updating the key level value according to the volume fraction when the optimization target does not meet the convergence condition. When the volume fraction is larger than the preset volume fraction, updating the current lower bound value into the current lower bound value by utilizing the dichotomy
(ii) a When the volume fraction is smaller than the preset volume fraction, updating the upper bound value of the current time into the upper bound value by utilizing a dichotomy
(ii) a Wherein the content of the first and second substances,ns key in order to be a key level value,B min for the last updated lower bound value,B max the upper bound value is updated last time; when the volume fraction and the preset volume fraction meet the set tolerance, updating the key level value to bens key I.e. keeping the key level value calculated in step S400 unchanged.
In some embodiments, the tolerance between the calculated volume fraction and the preset volume fraction is a minimum value:
wherein the content of the first and second substances,epresentation unite，NeThe total number of the cells is represented,ρ e presentation uniteThe density of (a) of (b),v e presentation uniteThe volume of (a) to (b),V 0 is a pre-set volume fraction of the total volume,εfor the established convergence threshold, 10 is generally taken -9 。
In some embodiments, after calculating the key level value satisfying the set volume fraction, the cells above the key level value are completely solid materials, the cells below the key level value are voids, and the cells equal to the key level value are boundary cells.
Referring to fig. 6, steps S300 to S400 are diagrams illustrating an optimization result after performing subsequent processing on the density field of the iterative structure.
In the heat dissipation topology optimization method for smooth boundary expression, after the optimization iteration is finished, the boundary smooth expression post-processing technology for realizing the zigzag-smooth boundary conversion is applied, and the key point is to realize the conversion of the structural topology expression paradigm based on units and nodes. And moreover, by matching with a continuity density filtering strategy and a rear boundary smooth expression post-processing technology, the aim of eliminating partial small-size detail features in multiple stages can be achieved, and the manufacturability of an optimization result is further improved. The boundary smoothing post-processing technology is used after optimization iteration, so that the impression of the post-processing technology on the optimization process is avoided, the robustness of heat transfer topology optimization is ensured, and the high calculation cost caused by repeated execution in the optimization process is avoided in the form of decoupling of post-processing and optimization iteration, so that the method is easier to expand to a large-scale problem.
Referring to fig. 7, the present application further provides a heat dissipation topology optimization apparatus 700 with smooth boundary representation, which includes a memory 710 and a processor 720, which are described in detail below.
The memory 710 is used to store programs.
The processor 720 is configured to execute the program of the memory to implement the heat dissipation topology optimization method of the smooth boundary expression in the embodiment of the present application.
In some embodiments, the processor 710 first discretizes the heat dissipation topology to be optimized into a finite element model, and then calculates a density field of the heat dissipation topology to be optimized based on the finite element model. After obtaining the density field, processor 710 calculates a heat transfer coefficient using the first interpolation function, updates the finite element analysis model based on the heat transfer coefficient, and determines a cell sensitivity for each cell based on the updated finite element analysis model. The processor 710 stores a preset mapping relationship of a plurality of units corresponding to a single node, and the processor 710 obtains a unit sensitivity field of each of the plurality of units to determine a node sensitivity of the corresponding single node.
In some embodiments, after determining the node sensitivity of each node, the processor 710 determines a key level value according to the node sensitivity of each node, and when the node sensitivity of a node corresponding to a unit in the to-be-optimized heat dissipation topology is greater than the key level value, the unit is a complete entity unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is larger than the key level value, the unit is a boundary unit; and when the node sensitivity of the node corresponding to one unit in the heat dissipation topological structure to be optimized is less than the key level value, the unit is a cavity unit.
The processor 710 divides each boundary cell to obtain a corresponding new divided cell. Processor 710 calculates a new partition node acuity for the new partition unit corresponding to each of the boundary units using a second interpolation function. For each boundary unit, the density value of the boundary unit is respectively determined according to the sensitivity of the new subdivision node, the processor 710 determines the volume fraction according to the density values of all the units, and updates the key level value according to the volume fraction so as to perform smooth boundary expression meeting the volume constraint on the result to be optimized.
Those skilled in the art will appreciate that all or part of the functions of the various methods in the above embodiments may be implemented by hardware, or may be implemented by computer programs. When all or part of the functions of the above embodiments are implemented by a computer program, the program may be stored in a computer-readable storage medium, and the storage medium may include: a read only memory, a random access memory, a magnetic disk, an optical disk, a hard disk, etc., and the program is executed by a computer to realize the above functions. For example, the program may be stored in a memory of the device, and when the program in the memory is executed by the processor, all or part of the functions described above may be implemented. In addition, when all or part of the functions in the above embodiments are implemented by a computer program, the program may be stored in a storage medium such as a server, another computer, a magnetic disk, an optical disk, a flash disk, or a removable hard disk, and may be downloaded or copied to a memory of a local device, or may be version-updated in a system of the local device, and when the program in the memory is executed by a processor, all or part of the functions in the above embodiments may be implemented.
The present invention has been described in terms of specific examples, which are provided to aid in understanding the invention and are not intended to be limiting. For a person skilled in the art to which the invention pertains, several simple deductions, modifications or substitutions may be made according to the idea of the invention.
Claims (10)
1. A heat dissipation topology optimization method for smooth boundary expression is characterized by comprising the following steps:
dispersing a heat dissipation topological structure to be optimized into a finite element model;
calculating a density field of the heat dissipation topological structure to be optimized based on a finite element model, wherein the density field comprises a plurality of units;
calculating a heat transfer coefficient by using a first interpolation function, updating the finite element analysis model according to the heat transfer coefficient, and determining the element sensitivity of each element according to the updated finite element analysis model; the finite element analysis model is used for solving the finite element model; according to a preset mapping relation of a plurality of units corresponding to a single node, acquiring unit sensitivity of each unit of the plurality of units to determine node sensitivity of the corresponding single node;
determining a key level value according to the node sensitivity of each node, and when the node sensitivity of a node corresponding to a unit in the heat dissipation topological structure to be optimized is all larger than the key level value, the unit is a complete entity unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is larger than the key level value, the unit is a boundary unit; when the node sensitivity of a node corresponding to one unit in the heat dissipation topological structure to be optimized is all smaller than the key level value, the unit is a cavity unit;
dividing each boundary unit to obtain a corresponding new division unit, and calculating the sensitivity of a new division node of the new division unit corresponding to each boundary unit by using a second interpolation function; for each boundary unit, the density value of the boundary unit is respectively determined according to the sensitivity of the newly-divided node of the boundary unit;
and determining volume fractions according to the density values of all the units, and updating the key level values according to the volume fractions so as to perform smooth boundary expression meeting volume constraints on the result to be optimized.
2. The method for optimizing a heat dissipation topology by smoothing a boundary representation as recited in claim 1, wherein the calculating a density field of the heat dissipation topology to be optimized based on a finite element model comprises:
controlling the filtering radius of a finite element model based on a continuous density strategy, carrying out a plurality of iterations on the density field to obtain an iterative optimization target, and when the variance of the optimization target is smaller than a set tolerance, ending the iteration and outputting the density field; the filtering radius is calculated by the following formula:
wherein the content of the first and second substances,rin order to be the radius of the iteration,kfor the number of iterations to be performed,r min is a preset minimum filtering radius,r 0 is a preset initial filtering radius and is a preset initial filtering radius,lpa number of iterations to decay for the set initial filter radius to the minimum filter radius.
3. The method of claim 1, wherein the calculating a heat transfer coefficient using a first interpolation function and updating the finite element analysis model based on the heat transfer coefficient comprises:
calculating a heat transfer coefficient in the first interpolation function using a penalty factor greater than a set value, the first interpolation function being represented by the following equation:
wherein the content of the first and second substances,k 0 in order to be a heat transfer coefficient,εis 10 -3 ，ρIs a unit density, and has a value range of [0,1 ]]，pIn order to be a penalty factor,kare interpolation coefficients.
4. The method for optimizing heat dissipation topology expressed by smooth boundaries according to claim 1, wherein the obtaining unit sensitivity of each unit of the plurality of units according to a preset mapping relationship of the plurality of units to a single node to determine node sensitivity of the corresponding single node comprises:
calculating the node sensitivity of the single node by using the following mapping formula:
wherein the content of the first and second substances,ns m is a nodemNode sensitivity of (a);Neis the total number of units;iis a firstiThe number of the units is one,the value range is [1 ],Ne]；es i is as followsiA cell sensitivity of the individual cells;w i m, a weighted function of the cell sensitivities of several cells.
5. The method for smoothing the representation of a boundary for heat dissipation topology optimization of claim 4, wherein the weighting function of the cell sensitivities of the number of cells is determined by the formula:
wherein the content of the first and second substances,w i m, is a weighted function of the cell sensitivities of the number of cells,r dist is a nodemThe range of the mapping of (a) to (b),
is a firstiUnit to nodemThe distance of (c).
6. The method for optimizing heat dissipation topology by smoothing boundary expression according to claim 1, wherein the determining a key level value according to node sensitivity of each node in the heat dissipation topology to be optimized comprises:
acquiring a lower bound value of an interval of the minimum node sensitivity value in all node sensitivities and an upper bound value of an interval of the maximum node sensitivity value in all node sensitivities; and updating the lower bound value and the upper bound value by using a dichotomy, and calculating the average value of the updated lower bound value and the updated upper bound value to determine the key horizontal value.
7. The method for optimizing heat dissipation topology with smooth boundary representation according to claim 1, wherein the dividing each boundary cell to obtain a corresponding new divided cell, and calculating a new division node sensitivity of the new divided cell corresponding to each boundary cell by using a second interpolation function comprises:
interpolating the node sensitivity of each boundary unit by using a second interpolation function to obtain the sensitivity of a new subdivision node corresponding to the new subdivision unit; the second interpolation function is expressed by the following formula:
wherein, the first and the second end of the pipe are connected with each other,ns new (o) For the sensitivity of the new subdivision node of the new subdivision unit, (ii) (ξ i ，η i ) The coordinates of the corresponding node of the border element,iis corresponding to the boundary celliThe number of the nodes is one,Cethe total number of nodes corresponding to the boundary cell(s) ((ξ o ，η o ) For the coordinates of the new partitioning node corresponding to the new partitioning unit,
the node acuity corresponding to the border cell.
8. The method for optimizing heat dissipation topology by smoothing boundary expression of claim 1, wherein for each boundary cell, the boundary cell determines its density value according to its newly-divided node acuity, comprising:
calculating the percentage of the nodes corresponding to the new subdivision units with the sensitivity of the new subdivision nodes higher than the key level value occupying the nodes of the corresponding boundary units, and determining the density values of the corresponding boundary units according to the percentage; the percentage is calculated using the following formula:
wherein the content of the first and second substances,bfor the percentage of the nodes of the new subdivision cell occupying the nodes of the corresponding boundary cell, (ii) aξ o ，η o ) Coordinates of nodes corresponding to the new subdivision unit，ns m For the sensitivity of the new subdivision node of the new subdivision unit,ns key in order to be a key level value,N node is the total number of nodes of the border cell.
9. The method according to claim 6, wherein the updating the key level value according to the volume fraction to perform the smooth boundary expression satisfying the volume constraint on the result to be optimized comprises:
updating the key level value according to the volume fraction, and when the volume fraction is larger than the preset volume fraction, updating the current lower bound value to be
(ii) a When the volume fraction is smaller than the preset volume fraction, updating the upper bound value of the current time to be
(ii) a Wherein the content of the first and second substances,ns key for the value of the key level,B min for the last updated lower bound value,B max the upper bound value of the last update; and updating the key level value according to the current lower bound value and the current upper bound value.
10. A computer-readable storage medium, characterized in that the medium has stored thereon a program which is executable by a processor to implement the method according to any one of claims 1-9.
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