CN114417680B - Topology optimization method, system, device and storage medium for improving dynamic deletion rate - Google Patents

Topology optimization method, system, device and storage medium for improving dynamic deletion rate Download PDF

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CN114417680B
CN114417680B CN202210332696.2A CN202210332696A CN114417680B CN 114417680 B CN114417680 B CN 114417680B CN 202210332696 A CN202210332696 A CN 202210332696A CN 114417680 B CN114417680 B CN 114417680B
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deletion rate
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volume
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CN114417680A (en
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刘沐宇
张强
刘齐民
卢志芳
吴航宇
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Wuhan University of Technology WUT
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Abstract

The invention relates to a topology optimization method, a system, equipment and a storage medium for improving dynamic deletion rate, wherein the method comprises the following steps: establishing an initial structure finite element model and a structure topological optimization mathematical model based on an engineering structure, and determining topological optimization related parameters for improving the dynamic deletion rate; carrying out finite element solution on the initial structure finite element model to obtain element sensitivity, structural stress uniformity, structural volume fraction index and dynamic deletion rate of the current step, and calculating the structure volume of the next step according to the dynamic deletion rate of the current step; solving a sensitivity threshold value according to the volume of the next step structure, and updating the initial structure finite element model according to the unit sensitivity and the sensitivity threshold value; and circularly and iteratively executing the solving and optimizing steps until the optimized structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure. The invention can output the structure with optimal performance.

Description

Topology optimization method, system, device and storage medium for improving dynamic deletion rate
Technical Field
The present invention relates to the field of structure optimization technologies, and in particular, to a topology optimization method, system, device, and storage medium for improving dynamic deletion rate.
Background
The topological optimization is an important branch in the field of structural optimization design, and has become a mature design method after decades of development, and the method has the characteristics of high design efficiency, high design freedom and the like, and is widely applied to engineering structural design and academic research. The topological optimization can delete low-efficiency materials in the structure under certain constraint conditions, and find the optimal distribution of the materials in a design domain, so that the structure with light weight and excellent performance is obtained. At present, people face various problems such as material resource shortage, environmental impact and technical competition, and the advantages of topology optimization make the problems become one of important methods for solving the problems.
The deletion rate is an important parameter for structural topology optimization, and the gradual optimization of the material in each iteration step can be controlled to be an optimal form. However, in the current topology optimization method, the deletion rate is a constant that is fixed and unchanged, but the number of entity units changes dynamically in the structure optimization process, so that the current fixed deletion rate is difficult to match with the dynamic change of the units, and the phenomena of low optimization efficiency, unstable optimization process and even failure in optimization occur. Therefore, it is necessary to improve the way of determining the deletion rate, and to provide a new topology optimization method to accomplish the optimization design goal more efficiently and stably.
Disclosure of Invention
In view of the above, it is necessary to provide a topology optimization method, a system, a device and a storage medium for improving a dynamic deletion rate, so as to solve the problem that a conventional fixed deletion rate topology optimization method cannot effectively delete redundant materials due to low optimization efficiency and unstable optimization.
In order to solve the above problem, in a first aspect, the present invention provides a topology optimization method for improving a dynamic deletion rate, which is applied in a structure optimization design process, and includes:
establishing an initial structure finite element model and a structure topology optimization mathematical model based on an engineering structure, distributing an initial unit state variable value for each unit in the initial structure finite element model, and determining topology optimization related parameters for improving the dynamic deletion rate;
carrying out finite element model on the initial structureFinite element solution to obtain element sensitivity
Figure 882556DEST_PATH_IMAGE001
Degree of structural stress uniformity
Figure 136951DEST_PATH_IMAGE002
Structural volume fraction index
Figure 327761DEST_PATH_IMAGE003
And a first
Figure 817648DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 800516DEST_PATH_IMAGE005
According to said second
Figure 350446DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 28552DEST_PATH_IMAGE006
Calculate the first
Figure 197497DEST_PATH_IMAGE007
Volume of step structure
Figure 566030DEST_PATH_IMAGE008
；
According to the said first
Figure 552441DEST_PATH_IMAGE007
Volume of step structure
Figure 858788DEST_PATH_IMAGE008
Solving for sensitivity threshold
Figure 690478DEST_PATH_IMAGE009
And according to the cell sensitivity
Figure 992146DEST_PATH_IMAGE010
And the sensitivityThreshold value
Figure 274092DEST_PATH_IMAGE009
Updating the initial structure finite element model;
and circularly and iteratively executing the solving and updating steps until the updated structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure.
Further, the structure topology optimization mathematical model comprises:
Figure 926790DEST_PATH_IMAGE011
wherein
Figure 437537DEST_PATH_IMAGE012
in order to have an average flexibility of the structure,
Figure 859291DEST_PATH_IMAGE013
and
Figure 187504DEST_PATH_IMAGE014
respectively, the load and the unit displacement vector,
Figure 452132DEST_PATH_IMAGE015
in order to transpose the symbols,
Figure 297729DEST_PATH_IMAGE016
in order to be a constraint condition, the method comprises the following steps of,
Figure 573989DEST_PATH_IMAGE017
in order to optimize the target volume,
Figure 73104DEST_PATH_IMAGE018
is the total number of the entity units,
Figure 565308DEST_PATH_IMAGE019
is as follows
Figure 808070DEST_PATH_IMAGE020
The volume of each unit cell is equal to the volume of each unit cell,
Figure 79783DEST_PATH_IMAGE021
is as follows
Figure 484219DEST_PATH_IMAGE020
The state variable of each unit is changed into a state variable,
Figure 598806DEST_PATH_IMAGE022
represent
Figure 238735DEST_PATH_IMAGE020
The unit is a physical unit which is a unit,
Figure 489587DEST_PATH_IMAGE023
represents
Figure 330505DEST_PATH_IMAGE020
The unit is an empty unit;
the allocating of the initial element state variable value to each element in the initial structure finite element model comprises that the initial element of each element in the initial structure finite element model is a solid element;
the topology optimization related parameters for improving the dynamic deletion rate comprise the minimum deletion rate
Figure 542174DEST_PATH_IMAGE024
And an upper limit of increase of deletion rate
Figure 126739DEST_PATH_IMAGE025
。
Further, the cell sensitivity
Figure 232099DEST_PATH_IMAGE001
The solving process comprises the following steps:
Figure 102971DEST_PATH_IMAGE026
wherein
Figure 660992DEST_PATH_IMAGE027
is as follows
Figure 49248DEST_PATH_IMAGE020
The displacement vector of the node of each unit,
Figure 884480DEST_PATH_IMAGE028
is as follows
Figure 801620DEST_PATH_IMAGE020
A cell stiffness matrix of individual cells.
Further, the structural stress is uniform
Figure 112516DEST_PATH_IMAGE002
The solving process comprises the following steps:
the degree of uniformity of the structural stress by using the coefficient of variation
Figure 773304DEST_PATH_IMAGE002
And (3) solving:
Figure 712310DEST_PATH_IMAGE029
wherein
Figure 331510DEST_PATH_IMAGE030
is a first
Figure 864123DEST_PATH_IMAGE020
The von Mises stress of the individual cells,
Figure 938389DEST_PATH_IMAGE031
is the mean value of von Mises stress of all the entity units in the current iteration step.
Further, the structural volume fraction indicator
Figure 138426DEST_PATH_IMAGE003
The solving process comprises the following steps:
indexing the volume fraction of the structure by means of relative difference quotient
Figure 662949DEST_PATH_IMAGE003
And (3) solving:
Figure 807491DEST_PATH_IMAGE032
wherein
Figure 75661DEST_PATH_IMAGE004
for the current number of iteration steps,
Figure 5571DEST_PATH_IMAGE033
is as follows
Figure 435416DEST_PATH_IMAGE004
The volume of the step structure is increased,
Figure 942620DEST_PATH_IMAGE034
in order to optimize the target volume,
Figure 748902DEST_PATH_IMAGE035
to design the domain volume.
Further, said first step
Figure 517007DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 648911DEST_PATH_IMAGE005
The solving process comprises the following steps:
based on the structural stress uniformity
Figure 377833DEST_PATH_IMAGE002
And structural volume fraction index
Figure 863172DEST_PATH_IMAGE003
For the second step, by means of a sine function
Figure 626728DEST_PATH_IMAGE004
Solving the step dynamic deletion rate:
Figure 663955DEST_PATH_IMAGE036
wherein
Figure 270385DEST_PATH_IMAGE006
is as follows
Figure 418470DEST_PATH_IMAGE004
The dynamic rate of deletion is stepped up to,
Figure 36533DEST_PATH_IMAGE024
in order to minimize the rate of deletion,
Figure 120027DEST_PATH_IMAGE025
an upper limit is added to the erasure rate.
Further, the method according to the second aspect
Figure 89120DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 431108DEST_PATH_IMAGE005
Calculate the first
Figure 903678DEST_PATH_IMAGE007
Volume of step structure
Figure 282707DEST_PATH_IMAGE037
The method comprises the following steps:
Figure 473517DEST_PATH_IMAGE038
。
further, the unit sensitivity is determined according to the unit sensitivity
Figure 104349DEST_PATH_IMAGE001
And the sensitivity threshold
Figure 697004DEST_PATH_IMAGE009
Optimizing the initial structure finite element model in terms of size, comprising:
when the cell sensitivity of any cell
Figure 246935DEST_PATH_IMAGE001
Greater than the sensitivity threshold
Figure 778236DEST_PATH_IMAGE009
If so, converting the unit into an entity unit;
when the cell sensitivity of any cell
Figure 337393DEST_PATH_IMAGE001
Less than the sensitivity threshold
Figure 784555DEST_PATH_IMAGE009
Then the cell is converted to an empty cell.
Further, the preset constraint condition includes: the structure volume reaches the optimized target volume;
the preset convergence condition comprises the following steps:
Figure 646332DEST_PATH_IMAGE039
wherein
Figure 811734DEST_PATH_IMAGE012
the value of the objective function, i.e. the average compliance of the structure,
Figure 33637DEST_PATH_IMAGE004
for the number of steps of the current iteration,
Figure 335305DEST_PATH_IMAGE040
is the tolerance of convergence and is,
Figure 227038DEST_PATH_IMAGE040
are integers.
In a second aspect, the present invention further provides a topology optimization system for improving a dynamic deletion rate, which is applied to a structure optimization design process, and includes:
the system comprises an establishing module, a dynamic deletion rate improving module and a dynamic deletion rate improving module, wherein the establishing module is used for establishing an initial structure finite element model and a structure topology optimization mathematical model based on an engineering structure, allocating initial unit state variable values for each unit in the initial structure finite element model and determining related parameters of topology optimization for improving the dynamic deletion rate;
a solving module for carrying out finite element solving on the initial structure finite element model to obtain element sensitivity
Figure 755102DEST_PATH_IMAGE010
Degree of structural stress uniformity
Figure 390483DEST_PATH_IMAGE002
Structural volume fraction index
Figure 77816DEST_PATH_IMAGE003
And a first step of
Figure 530663DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 811603DEST_PATH_IMAGE005
According to said second
Figure 985095DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 526935DEST_PATH_IMAGE005
Calculate the first
Figure 885104DEST_PATH_IMAGE007
Volume of step structure
Figure 246815DEST_PATH_IMAGE008
；
An update module for updating according to the second
Figure 489578DEST_PATH_IMAGE007
Volume of step structure
Figure 761290DEST_PATH_IMAGE008
Solving for sensitivity threshold
Figure 165727DEST_PATH_IMAGE009
And according to the cell sensitivity
Figure 14734DEST_PATH_IMAGE001
And the sensitivity threshold
Figure 185821DEST_PATH_IMAGE009
Updating the initial structure finite element model;
and the output module is used for circularly and iteratively executing the solving and updating steps until the updated structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure.
In a third aspect, the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the topology optimization method for improving dynamic deletion rate when executing the computer program.
In a fourth aspect, the present invention further provides a computer storage medium, in which a computer program is stored, and the computer program, when executed by a processor, implements the steps in the topology optimization method for improving dynamic deletion rate as described above.
The beneficial effects of adopting the above embodiment are:
in the invention, in the structure optimization design process of the building material, an improved dynamic deletion rate calculation method is constructed by considering the structure volume fraction index and the structure stress uniformity, and a topological optimization method calculation process for improving the dynamic deletion rate is established, so that a finite element solution can be carried out on an initial structure finite element model according to a structure topological optimization mathematical model, the dynamic deletion rate is calculated according to the stress condition of the structure in each iteration step, and the problem that the traditional fixed deletion rate cannot be dynamically changed and optimization failure is possibly caused is solved. And then optimizing the finite element model of the building material according to the dynamic deletion rate, outputting the optimized topological structure of the building material, and effectively reducing the use of redundant materials through a reasonable optimized structure, thereby not only meeting the requirements of actual engineering, but also ensuring the optimal performance of the structure. The optimization method in the invention requires fewer iteration steps, and has high calculation efficiency and good stability.
Drawings
FIG. 1 is a flowchart illustrating an embodiment of a topology optimization method for improving dynamic deletion rate according to the present invention;
FIG. 2 is a field diagram of a cantilever design in an embodiment of the present invention;
FIG. 3(a) is a graph of the calculation result of the fixed erasure rate in an embodiment of the present invention;
FIG. 3(b) is a graph of improved dynamic erasure rate calculations in an embodiment provided by the present invention;
FIG. 4 is a graph comparing structure strain energy change history of a fixed erasure rate topology optimization method and a topology optimization method for improving dynamic erasure rate according to an embodiment of the present invention;
fig. 5 is a graph comparing the unit deletion amount history of the topology optimization method with a fixed deletion rate and the topology optimization method with an improved dynamic deletion rate according to an embodiment of the present invention;
FIG. 6 is a schematic structural diagram of an embodiment of a topology optimization system for improving dynamic erasure rate according to the present invention;
fig. 7 is an electronic device provided by the present invention.
Detailed Description
The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and which together with the embodiments of the invention serve to explain the principles of the invention and not to limit its scope.
In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise. Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
The present invention provides a topology optimization method, system, device and storage medium for improving dynamic deletion rate, which are described below.
Referring to fig. 1, fig. 1 is a schematic flow chart of an embodiment of a topology optimization method for improving dynamic deletion rate according to the present invention, and an embodiment of the present invention discloses a topology optimization method for improving dynamic deletion rate, which is applied to a structure optimization design process, and includes:
step S101: establishing an initial structure finite element model based on an engineering structure and a structural topological optimization mathematical model, distributing an initial unit state variable value for each unit in the initial structure finite element model, and determining topological optimization related parameters for improving the dynamic deletion rate;
it should be noted that the topology optimization method of the present invention is applicable to the minimum compliance topology optimization design of any engineering structure, and in a specific embodiment of the present invention, the engineering structure includes a building material that can be stressed, such as a cantilever beam. The initial structure finite element model based on the engineering structure comprises a cantilever beam finite element model.
The structure topology optimization mathematical model comprises:
Figure 702253DEST_PATH_IMAGE041
wherein
Figure 418536DEST_PATH_IMAGE012
in order to have an average flexibility of the structure,
Figure 754840DEST_PATH_IMAGE042
and
Figure 729618DEST_PATH_IMAGE014
respectively, the load and the unit displacement vector,
Figure 834977DEST_PATH_IMAGE015
in order to transpose the symbols,
Figure 456582DEST_PATH_IMAGE016
in order to be a constraint condition, the method comprises the following steps of,
Figure 545761DEST_PATH_IMAGE017
in order to optimize the target volume,
Figure 402859DEST_PATH_IMAGE043
is the total number of the entity units,
Figure 752937DEST_PATH_IMAGE019
is as follows
Figure 670078DEST_PATH_IMAGE020
The volume of each unit cell is equal to the volume of each unit cell,
Figure 980974DEST_PATH_IMAGE021
is as follows
Figure 517128DEST_PATH_IMAGE020
The state variable of each unit is changed into a state variable,
Figure 597080DEST_PATH_IMAGE022
represents
Figure 685121DEST_PATH_IMAGE020
The unit is a solid unit which is composed of a plurality of units,
Figure 607947DEST_PATH_IMAGE023
represents
Figure 338006DEST_PATH_IMAGE020
The unit is an empty unit;
and then assigning an initial element state variable value to each element in the initial structure finite element model, wherein the initial element of each element in the initial structure finite element model is a solid element, that is, all element state variables are 1 in the first iteration.
Wherein the topology optimization related parameters for improving the dynamic deletion rate comprise the minimum deletion rate
Figure 272464DEST_PATH_IMAGE024
And an upper limit of increase of deletion rate
Figure 406773DEST_PATH_IMAGE025
。
Step S102: carrying out finite element solution on the initial structure finite element model to obtain element sensitivity
Figure 426681DEST_PATH_IMAGE010
Structural stress uniformity
Figure 960431DEST_PATH_IMAGE002
Structural volume fraction index
Figure 879888DEST_PATH_IMAGE003
And a first
Figure 575312DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 82517DEST_PATH_IMAGE005
And according to the first
Figure 29744DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 938794DEST_PATH_IMAGE006
Calculate the first
Figure 195332DEST_PATH_IMAGE007
Volume of step structure
Figure 924254DEST_PATH_IMAGE008
；
It can be understood that the displacement of each degree of freedom of the node can be obtained by performing finite element solution on the initial structure finite element model, and then subsequent parameters can be solved according to the displacement of each degree of freedom of the node.
In one embodiment of the invention, the cell sensitivity
Figure 534227DEST_PATH_IMAGE001
The solving process comprises the following steps:
Figure 907570DEST_PATH_IMAGE026
wherein
Figure 210376DEST_PATH_IMAGE027
is as follows
Figure 426593DEST_PATH_IMAGE020
The displacement vector of the node of each unit,
Figure 699312DEST_PATH_IMAGE028
is as follows
Figure 317375DEST_PATH_IMAGE020
A cell stiffness matrix of individual cells.
In one embodiment of the invention, the degree of structural stress uniformity
Figure 525502DEST_PATH_IMAGE002
The solving process comprises the following steps:
degree of structural stress uniformity by using coefficient of variation
Figure 369962DEST_PATH_IMAGE002
And (3) solving:
Figure 321737DEST_PATH_IMAGE029
wherein
Figure 794307DEST_PATH_IMAGE030
is as follows
Figure 173335DEST_PATH_IMAGE020
The von Mises stress of the individual cells,
Figure 488779DEST_PATH_IMAGE031
is the mean value of von Mises stress of all the entity units in the current iteration step.
Wherein,
Figure 244246DEST_PATH_IMAGE002
the larger the structure stress distribution, the more uneven the structure stress distribution, and the influence of unreal numerical values caused by stress concentration can be reduced by adopting the variation coefficient to calculate the structure stress uniformity, so that the structure stress uniformity is reflected more truly.
In one embodiment of the invention, the structure volume fraction indicator
Figure 836901DEST_PATH_IMAGE003
The solving process comprises the following steps:
index structure volume integral number by means of relative difference quotient
Figure 996618DEST_PATH_IMAGE003
And (3) solving:
Figure 674724DEST_PATH_IMAGE032
wherein, in the process,
Figure 233881DEST_PATH_IMAGE004
for the current number of iteration steps,
Figure 805677DEST_PATH_IMAGE033
is as follows
Figure 792087DEST_PATH_IMAGE004
The volume of the step structure is increased,
Figure 691910DEST_PATH_IMAGE034
in order to optimize the target volume,
Figure 398966DEST_PATH_IMAGE035
to design the domain volume.
In one embodiment of the invention, the second
Figure 497372DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 779318DEST_PATH_IMAGE005
The solving process comprises the following steps:
based on the degree of structural stress uniformity
Figure 166437DEST_PATH_IMAGE002
And structural volume fraction index
Figure 942763DEST_PATH_IMAGE003
By means of sine function
Figure 364517DEST_PATH_IMAGE004
Solving the step dynamic deletion rate:
Figure 427151DEST_PATH_IMAGE036
wherein
Figure 691779DEST_PATH_IMAGE006
is as follows
Figure 865272DEST_PATH_IMAGE004
The dynamic rate of deletion is stepped on to the extent that,
Figure 141532DEST_PATH_IMAGE024
in order to minimize the rate of deletion,
Figure 516013DEST_PATH_IMAGE025
an upper limit is added to the erasure rate.
By making the unit stress distribution uniform
Figure 877724DEST_PATH_IMAGE002
And structural volume fraction index
Figure 854907DEST_PATH_IMAGE003
The influence of the multiplication method and the unit deletion rate is comprehensively considered, the optimal dynamic deletion rate of each iteration step can be obtained, and compared with the traditional fixed deletion rate mode, the optimization efficiency and quality of the method are greatly improved.
And according to
Figure 985674DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 514745DEST_PATH_IMAGE005
The solving process of the method can be known to adopt a larger deleting rate when the structural stress is uniformly distributed in the early stage of optimization and the structural residual volume is larger than the target volume, and adopt a smaller deleting rate when the structural stress is uniformly distributed and the structural residual volume approaches the target volume in the later stage of optimization, and the dynamic change is carried out along with iteration, so that the material deleting process is carried out efficiently, and compared with the traditional fixed deleting rate topological optimization method, the method has higher calculation efficiency and better stability.
In one embodiment of the invention, according to
Figure 629331DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 410205DEST_PATH_IMAGE005
Calculate the first
Figure 270845DEST_PATH_IMAGE007
Volume of step structure
Figure 846183DEST_PATH_IMAGE008
The method comprises the following steps:
Figure 448066DEST_PATH_IMAGE038
。
step S103: according to the first
Figure 909263DEST_PATH_IMAGE007
Volume of step structure
Figure 280202DEST_PATH_IMAGE008
Solving for sensitivity threshold
Figure 432966DEST_PATH_IMAGE009
And according to cell sensitivity
Figure 522144DEST_PATH_IMAGE010
And sensitivity threshold
Figure 503876DEST_PATH_IMAGE009
Updating the initial structure finite element model according to the size of the initial structure finite element model;
wherein according to the first
Figure 463741DEST_PATH_IMAGE007
Volume of step structure
Figure 912040DEST_PATH_IMAGE008
Solving for sensitivity threshold
Figure 98302DEST_PATH_IMAGE009
In the design process, all units in the design domain need to be sequenced according to the sensitivity level of the units to determine
Figure 759091DEST_PATH_IMAGE007
Volume of step structure
Figure 229255DEST_PATH_IMAGE008
Having the number of units according to
Figure 582876DEST_PATH_IMAGE007
Volume of step structure
Figure 115489DEST_PATH_IMAGE008
The number of physical cells that are present determines the sensitivity threshold, for example, if there are 1000 cells in the design domain, and the cell sensitivity is ranked as:
Figure 455334DEST_PATH_IMAGE044
if, if
Figure 389792DEST_PATH_IMAGE008
Corresponding to a design with 700 physical units, then
Figure 648735DEST_PATH_IMAGE045
。
In one embodiment of the invention, the sensitivity is based on the cell
Figure 668644DEST_PATH_IMAGE001
And sensitivity threshold
Figure 795869DEST_PATH_IMAGE009
Updating the initial structure finite element model according to the size of the initial structure finite element model, comprising:
when the cell sensitivity of any cell
Figure 850412DEST_PATH_IMAGE001
Greater than a sensitivity threshold
Figure 545836DEST_PATH_IMAGE009
If so, converting the unit into an entity unit, namely changing the unit state variable of the unit into 1;
when the cell sensitivity of any cell
Figure 928407DEST_PATH_IMAGE001
Less than a sensitivity threshold
Figure 469110DEST_PATH_IMAGE009
Then the cell is converted to an empty cell, i.e. the cell state variable for the cell is changed to 0.
Step S104: and circularly and iteratively executing the solving and updating steps until the updated structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure.
In one embodiment of the present invention, the preset constraint condition includes: the structure volume reaches the optimized target volume;
it can be understood that, in the iteration process, if the structure volume of a certain step is the same as the optimization target volume, the structure finite element model updated in the current iteration step can be considered to reach the preset constraint condition.
The preset convergence condition comprises the following steps:
Figure 378160DEST_PATH_IMAGE046
wherein
Figure 978905DEST_PATH_IMAGE012
the value of the objective function, i.e. the average compliance of the structure,
Figure 832461DEST_PATH_IMAGE004
for the current number of iteration steps,
Figure 301488DEST_PATH_IMAGE040
is the tolerance of convergence and is,
Figure 65045DEST_PATH_IMAGE040
are integers.
It can be understood that the preset convergence condition means that the change of the objective function value in the last 10 iterations is very small and tends to be smooth, i.e. the objective function reaches convergence.
And when the preset constraint condition and the preset convergence condition are reached, ending the iteration process and outputting an updated model, wherein the updated model comprises the optimal topological structure of the engineering structure.
In the invention, in the structure optimization design process of the building material, an improved dynamic deletion rate calculation method is constructed by considering the structure volume fraction index and the structure stress uniformity, and a topological optimization method calculation process for improving the dynamic deletion rate is established, so that a finite element solution can be carried out on an initial structure finite element model according to a structure topological optimization mathematical model, the dynamic deletion rate is calculated according to the stress condition of the structure in each iteration step, and the problem that the traditional fixed deletion rate cannot be dynamically changed and optimization failure is possibly caused is solved. And then optimizing the finite element model of the building material according to the dynamic deletion rate, outputting the optimized topological structure of the building material, and effectively reducing the use of redundant materials through a reasonable optimized structure, thereby not only meeting the requirements of actual engineering, but also ensuring the optimal performance of the structure. The optimization method in the invention requires fewer iteration steps, and has high calculation efficiency and good stability.
For a more convenient understanding of the present invention, reference is made to an embodiment of the present invention, referring to fig. 2, and fig. 2 is a diagram illustrating a cantilever design according to an embodiment of the present invention.
1) Establishing a cantilever beam finite element model, applying load and boundary conditions, solidifying the left end of the figure 2, and enabling the middle point of the cantilever end to be acted by the load F =100N and to be downward. The designed domain has a length of 80mm and a height of 50mm, and is divided into 80 × 50 grids, and 4000 square units are designed. Measuring elastic modulus to 100GPa, taking Poisson's ratio to 0.3, and establishing topological optimization mathematical model
Figure 102271DEST_PATH_IMAGE047
Setting related parameters of topological optimization method for improving dynamic deletion rate and volume constraint
Figure 318489DEST_PATH_IMAGE017
Taking out the mixture of 0.4 percent,
Figure 341939DEST_PATH_IMAGE024
taking out the weight of the mixture of 0.02,
Figure 960003DEST_PATH_IMAGE025
taking 0.02, the dynamic deletion rate is [0.02,0.04 ]]And varied within the interval.
2) Performing finite element solution to obtain element sensitivity
Figure 168130DEST_PATH_IMAGE001
The unit sensitivity calculation method comprises the following steps:
Figure 871644DEST_PATH_IMAGE026
(ii) a And determining the degree of structural stress uniformity
Figure 682474DEST_PATH_IMAGE002
Structural volume fraction index
Figure 420623DEST_PATH_IMAGE003
And calculating the current step deletion rate
Figure 799652DEST_PATH_IMAGE005
And according to
Figure 131407DEST_PATH_IMAGE005
Calculating next step structure volume
Figure 621294DEST_PATH_IMAGE037
：
Figure 213949DEST_PATH_IMAGE038
。
3) From the next step structure volume
Figure 888513DEST_PATH_IMAGE008
Calculating sensitivity threshold
Figure 566619DEST_PATH_IMAGE009
Sensitivity of the if empty cell
Figure 860197DEST_PATH_IMAGE010
Greater than a sensitivity threshold
Figure 448305DEST_PATH_IMAGE009
The cell is converted to a physical cell (i.e., the cell state variable of the cell is changed to 1) if the physical cell sensitivity is high
Figure 903557DEST_PATH_IMAGE010
Less than a sensitivity threshold
Figure 68959DEST_PATH_IMAGE009
The element is converted to an empty element (i.e., the element state variable of the element is changed to 0), thereby updating the cantilever finite element model.
Wherein the sensitivity threshold value
Figure 900649DEST_PATH_IMAGE009
The calculation method specifically comprises the following steps: all units in the design domain are sorted according to the sensitivity level, and at the moment
Figure 863969DEST_PATH_IMAGE009
By
Figure 490122DEST_PATH_IMAGE008
It is decided, for example, that there are 1000 cells in the design domain,
Figure 814924DEST_PATH_IMAGE048
if, if
Figure 840518DEST_PATH_IMAGE037
Corresponding to a design with 700 physical units, then
Figure 527851DEST_PATH_IMAGE045
;
4) Repeating 2), 3) until the structure volume reaches the target volume, the target function satisfying the following convergence criterion:
Figure 246277DEST_PATH_IMAGE049
. Referring to fig. 3(a) and fig. 3(b), fig. 3(a) is a graph of a calculation result of a fixed erasure rate in an embodiment of the present invention, and fig. 3(b) is a graph of a calculation result of an improved dynamic erasure rate in an embodiment of the present invention.
It can be seen from fig. 3(a) and 3(b) that the final structures obtained by the two methods are similar, and only slight differences exist. In the optimization process of the cantilever beam model, the strain energy of the final structure obtained by the fixed deletion rate topological optimization method and the final structure obtained by the method is 2.3246N ∙ mm and 2.3170N ∙ mm respectively, and the strain energy of the final structure obtained by the method provided by the invention is smaller, which shows that the method provided by the invention has relatively better optimization quality.
Referring to fig. 4, fig. 4 is a graph comparing the structural strain energy change history of the topology optimization method with the fixed erasure rate and the topology optimization method with the improved dynamic erasure rate according to an embodiment of the present invention. The deleting rate of the fixed deleting rate topological optimization method is the average value of the upper limit and the lower limit of the deleting rate of the topological optimization method for improving the dynamic deleting rate, wherein the deleting rate of the fixed deleting rate topological optimization method is 0.03.
Referring to fig. 5, fig. 5 is a graph comparing the unit erasure count history of the topology optimization method with the fixed erasure rate and the topology optimization method with the improved dynamic erasure rate according to an embodiment of the present invention.
As can be seen from fig. 5, with the method provided by the present invention, when the structure at the early stage of optimization has more redundant materials and the stress distribution is very uneven, the number of single-step unit deletions is large, and as the structure is continuously close to the target volume and the stress distribution is relatively even, the number of single-step unit deletions gradually decreases. Compared with a fixed deletion rate topology optimization method which needs 65 steps to reach a convergence condition, the method provided by the invention can converge only in 47 steps to obtain an optimal structure, the efficiency is improved by 27.7%, and the method provided by the invention is more efficient and reasonable.
In order to better implement the topology optimization method for improving dynamic deletion rate in the embodiment of the present invention, on the basis of the topology optimization method for improving dynamic deletion rate, correspondingly, please refer to fig. 6, where fig. 6 is a schematic structural diagram of an embodiment of the topology optimization system for improving dynamic deletion rate provided by the present invention, and an embodiment of the present invention provides a topology optimization system 600 for improving dynamic deletion rate, including:
the establishing module 601 is used for establishing an initial structure finite element model and a structure topology optimization mathematical model based on an engineering structure, allocating an initial element state variable value to each element in the initial structure finite element model, and determining a topology optimization related parameter for improving a dynamic deletion rate;
a solving module 602, configured to perform finite element solution on the initial structure finite element model to obtain element sensitivity
Figure 510905DEST_PATH_IMAGE010
Degree of structural stress uniformity
Figure 74611DEST_PATH_IMAGE002
Structural volume fraction index
Figure 757396DEST_PATH_IMAGE003
And a first
Figure 990931DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 352642DEST_PATH_IMAGE005
And according to the first
Figure 329826DEST_PATH_IMAGE004
Step dynamic deletion rate
Figure 585226DEST_PATH_IMAGE005
Calculate the first
Figure 989663DEST_PATH_IMAGE007
Volume of step structure
Figure 104250DEST_PATH_IMAGE008
；
An update module 603 for
Figure 760490DEST_PATH_IMAGE007
Volume of step structure
Figure 667135DEST_PATH_IMAGE008
Solving for sensitivity threshold
Figure 508052DEST_PATH_IMAGE009
And according to cell sensitivity
Figure 782039DEST_PATH_IMAGE001
And sensitivity threshold
Figure 485378DEST_PATH_IMAGE009
Updating the initial structure finite element model according to the size of the initial structure;
and the output module 604 is configured to perform the solving and updating steps in a loop iteration manner until the updated finite element model of the structure reaches a preset constraint condition and a preset convergence condition, and output an optimized topological structure of the engineering structure.
Here, it should be noted that: the system 600 provided in the foregoing embodiment may implement the technical solutions described in the foregoing method embodiments, and the specific implementation principle of each module or unit may refer to the corresponding content in the foregoing method embodiments, which is not described herein again.
Based on the topology optimization method for improving the dynamic deletion rate, an embodiment of the present invention further provides an electronic device, including: a processor and a memory and a computer program stored in the memory and executable on the processor; the processor, when executing the computer program, implements the steps in the topology optimization method for improving dynamic deletion rate as described in the embodiments above.
A schematic structural diagram of an electronic device 700 suitable for implementing embodiments of the present invention is shown in fig. 7. The electronic devices in the embodiments of the present invention may include, but are not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), in-vehicle terminals (e.g., car navigation terminals), and the like, and fixed terminals such as digital TVs, desktop computers, and the like. The electronic device shown in fig. 7 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present invention.
The electronic device includes: a memory and a processor, wherein the processor may be referred to as the processing device 701 hereinafter, and the memory may include at least one of a Read Only Memory (ROM) 702, a Random Access Memory (RAM) 703 and a storage device 708 hereinafter, as shown in detail below:
as shown in fig. 7, electronic device 700 may include a processing means (e.g., central processing unit, graphics processor, etc.) 701 that may perform various appropriate actions and processes in accordance with a program stored in a Read Only Memory (ROM) 702 or a program loaded from storage 708 into a Random Access Memory (RAM) 703. In the RAM703, various programs and data necessary for the operation of the electronic apparatus 700 are also stored. The processing device 701, the ROM702, and the RAM703 are connected to each other by a bus 704. An input/output (I/O) interface 705 is also connected to bus 704.
Generally, the following devices may be connected to the I/O interface 705: input devices 706 including, for example, a touch screen, touch pad, keyboard, mouse, camera, microphone, accelerometer, gyroscope, etc.; an output device 707 including, for example, a Liquid Crystal Display (LCD), a speaker, a vibrator, and the like; storage 708 including, for example, magnetic tape, hard disk, etc.; and a communication device 709. The communication means 709 may allow the electronic device 700 to communicate with other devices, wireless or wired, to exchange data. While fig. 7 illustrates an electronic device 700 having various means, it is to be understood that not all illustrated means are required to be implemented or provided. More or fewer devices may be alternatively implemented or provided.
In particular, according to an embodiment of the present invention, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, an embodiment of the invention includes a computer program product comprising a computer program carried on a non-transitory computer readable medium, the computer program containing program code for performing the method illustrated by the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network via the communication means 709, or may be installed from the storage means 708, or may be installed from the ROM 702. The computer program, when executed by the processing device 701, performs the above-described functions defined in the methods of embodiments of the present invention.
Based on the topology optimization method for improving dynamic deletion rate, embodiments of the present invention also provide a computer-readable storage medium, where one or more programs are stored, and the one or more programs are executable by one or more processors to implement the steps in the topology optimization method for improving dynamic deletion rate according to the embodiments.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (9)

1. A topology optimization method for improving dynamic deletion rate is applied to a structure optimization design process, and is characterized by comprising the following steps:
establishing an initial structure finite element model and a structure topological optimization mathematical model based on an engineering structure, allocating initial unit state variable values to each unit in the initial structure finite element model, and determining topological optimization related parameters for improving dynamic deletion rate, wherein the topological optimization related parameters for improving dynamic deletion rate comprise minimum deletion rate
Figure 181027DEST_PATH_IMAGE001
And an upper limit of increase in deletion rate
Figure 911216DEST_PATH_IMAGE002
；
Carrying out finite element solution on the initial structure finite element model to obtain element sensitivity
Figure 753270DEST_PATH_IMAGE003
Degree of structural stress uniformity
Figure 991223DEST_PATH_IMAGE004
Structural volume fraction index
Figure 602333DEST_PATH_IMAGE005
And a first
Figure 237844DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 567195DEST_PATH_IMAGE007
According to said second
Figure 880276DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 362204DEST_PATH_IMAGE008
Calculate the first
Figure 621147DEST_PATH_IMAGE009
Volume of step structure
Figure 703373DEST_PATH_IMAGE010
；
According to the said first
Figure 486390DEST_PATH_IMAGE009
Volume of step structure
Figure 150721DEST_PATH_IMAGE010
Solving for sensitivity threshold
Figure 642882DEST_PATH_IMAGE011
And according to the cell sensitivity
Figure 196092DEST_PATH_IMAGE012
And the sensitivity threshold
Figure 549844DEST_PATH_IMAGE011
Updating the initial structure finite element model;
degree of uniformity of the structural stress
Figure 52369DEST_PATH_IMAGE004
The solving process comprises the following steps:
Figure 433541DEST_PATH_IMAGE013
wherein
Figure 490359DEST_PATH_IMAGE014
is a first
Figure 116643DEST_PATH_IMAGE015
The von Mises stress of the individual cells,
Figure 676938DEST_PATH_IMAGE016
the stress mean value of von Mises of all entity units in the current iteration step;
the structural volume fraction indicator
Figure 754310DEST_PATH_IMAGE005
The solving process comprises the following steps:
indexing the volume fraction of the structure by means of relative difference quotient
Figure 314735DEST_PATH_IMAGE005
And (3) solving:
Figure 259557DEST_PATH_IMAGE017
wherein
Figure 923626DEST_PATH_IMAGE006
for the current number of iteration steps,
Figure 662912DEST_PATH_IMAGE018
is as follows
Figure 913895DEST_PATH_IMAGE006
The volume of the step structure is increased,
Figure 396829DEST_PATH_IMAGE019
in order to optimize the target volume,
Figure 180983DEST_PATH_IMAGE020
to design domain volume;
the first mentioned
Figure 622329DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 95030DEST_PATH_IMAGE007
The solving process comprises the following steps:
based on the structural stress uniformity
Figure 381655DEST_PATH_IMAGE004
And structural volume fraction index
Figure 754736DEST_PATH_IMAGE005
For the second step, by means of a sine function
Figure 101404DEST_PATH_IMAGE006
Solving the step dynamic deletion rate:
Figure 123718DEST_PATH_IMAGE021
；
and circularly and iteratively executing the solving and updating steps until the updated structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure.
2. The method of claim 1, wherein the structural topology optimization mathematical model comprises:
Figure 948454DEST_PATH_IMAGE022
wherein
Figure 244218DEST_PATH_IMAGE023
in order to have an average flexibility of the structure,
Figure 246940DEST_PATH_IMAGE024
and
Figure 209080DEST_PATH_IMAGE025
respectively, the load and the unit displacement vector,
Figure 821196DEST_PATH_IMAGE026
in order to transpose the symbols,
Figure 981919DEST_PATH_IMAGE027
in order to be a constraint condition, the method comprises the following steps of,
Figure 889963DEST_PATH_IMAGE028
in order to optimize the target volume,
Figure 119825DEST_PATH_IMAGE029
is the total number of the entity units,
Figure 551944DEST_PATH_IMAGE030
is as follows
Figure 52326DEST_PATH_IMAGE015
The volume of each unit cell is equal to the volume of each unit cell,
Figure 692124DEST_PATH_IMAGE031
is as follows
Figure 894435DEST_PATH_IMAGE015
The state variable of each unit is changed into a state variable,
Figure 615397DEST_PATH_IMAGE032
represents
Figure 564479DEST_PATH_IMAGE015
The unit is a physical unit which is a unit,
Figure 798014DEST_PATH_IMAGE033
represents
Figure 238354DEST_PATH_IMAGE015
The unit is an empty unit;
the assigning of the initial element state variable value to each element in the initial structure finite element model includes the initial element of each element in the initial structure finite element model being a solid element.
3. The method of claim 2, wherein the cell sensitivity is
Figure 12275DEST_PATH_IMAGE003
The solving process comprises the following steps:
Figure 454627DEST_PATH_IMAGE034
wherein
Figure 186959DEST_PATH_IMAGE035
is as follows
Figure 380174DEST_PATH_IMAGE015
The displacement vector of the node of each unit,
Figure 472633DEST_PATH_IMAGE036
is as follows
Figure 67693DEST_PATH_IMAGE015
A cell stiffness matrix of individual cells.
4. The method of claim 3, wherein said determining is based on said second
Figure 174190DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 556498DEST_PATH_IMAGE008
Calculate the first
Figure 219692DEST_PATH_IMAGE009
Volume of step structure
Figure 652947DEST_PATH_IMAGE010
The method comprises the following steps:
Figure 451051DEST_PATH_IMAGE037
。
5. the method of claim 4, wherein the cell sensitivity is based on the cell sensitivity
Figure 540230DEST_PATH_IMAGE012
And the sensitivity threshold
Figure 7114DEST_PATH_IMAGE011
Optimizing the initial structure finite element model in terms of size, comprising:
when the cell sensitivity of any cell
Figure 232559DEST_PATH_IMAGE003
Greater than the sensitivity threshold
Figure 398967DEST_PATH_IMAGE011
If so, converting the unit into an entity unit;
when the cell sensitivity of any cell
Figure 303338DEST_PATH_IMAGE003
Less than the sensitivity threshold
Figure 246018DEST_PATH_IMAGE011
Then the cell is converted to an empty cell.
6. The method according to claim 5, wherein the preset constraint condition comprises: the structure volume reaches the optimized target volume;
the preset convergence condition comprises the following steps:
Figure 857128DEST_PATH_IMAGE038
wherein
Figure 522333DEST_PATH_IMAGE023
the value of the objective function, i.e. the average compliance of the structure,
Figure 851683DEST_PATH_IMAGE006
for the current number of iteration steps,
Figure 863633DEST_PATH_IMAGE039
is the tolerance of the convergence of the signals,
Figure 329249DEST_PATH_IMAGE039
is an integer.
7. A topology optimization system for improving dynamic deletion rate is applied to a structure optimization design process, and is characterized by comprising the following steps:
the establishing module is used for establishing an initial structure finite element model and a structure topological optimization mathematical model based on an engineering structure, allocating initial unit state variable values to each unit in the initial structure finite element model and determining topological optimization related parameters for improving the dynamic deletion rate, wherein the topological optimization related parameters for improving the dynamic deletion rate comprise the minimum deletion rate
Figure 899777DEST_PATH_IMAGE001
And an upper limit of increase of deletion rate
Figure 185264DEST_PATH_IMAGE002
；
A solving module for carrying out finite element solution on the initial structure finite element model to obtain element sensitivity
Figure 735326DEST_PATH_IMAGE012
Structural stress uniformity
Figure 524290DEST_PATH_IMAGE004
Structural volume fraction index
Figure 56597DEST_PATH_IMAGE005
And a first step of
Figure 298223DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 416089DEST_PATH_IMAGE007
According to said second
Figure 872609DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 473355DEST_PATH_IMAGE007
Calculate the first
Figure 779440DEST_PATH_IMAGE009
Volume of step structure
Figure 920572DEST_PATH_IMAGE010
；
An update module for updating the first data according to the second data
Figure 231598DEST_PATH_IMAGE009
Volume of step structure
Figure 799983DEST_PATH_IMAGE010
Solving for sensitivity threshold
Figure 281780DEST_PATH_IMAGE011
And according to the cell sensitivity
Figure 475870DEST_PATH_IMAGE003
And the sensitivity threshold
Figure 890670DEST_PATH_IMAGE011
Updating the initial structure finite element model;
degree of structural stress uniformity
Figure 646268DEST_PATH_IMAGE004
The solving module of (2) is specifically configured to:
the degree of uniformity of the structural stress by using the coefficient of variation
Figure 146519DEST_PATH_IMAGE004
And (3) solving:
Figure 884580DEST_PATH_IMAGE040
wherein
Figure 701358DEST_PATH_IMAGE014
is as follows
Figure 877124DEST_PATH_IMAGE015
The von Mises stress of the individual cells,
Figure 67934DEST_PATH_IMAGE016
the stress mean value of von Mises of all entity units in the current iteration step;
index of volume fraction of structure
Figure 603827DEST_PATH_IMAGE005
The solving module of (2) is specifically configured to:
indexing the volume fraction of the structure by means of relative difference quotient
Figure 993220DEST_PATH_IMAGE005
And (3) solving:
Figure 90620DEST_PATH_IMAGE017
wherein
Figure 565463DEST_PATH_IMAGE006
for the current number of iteration steps,
Figure 170626DEST_PATH_IMAGE018
is as follows
Figure 961996DEST_PATH_IMAGE006
The volume of the step structure is increased,
Figure 259991DEST_PATH_IMAGE019
in order to optimize the target volume,
Figure 956551DEST_PATH_IMAGE020
to design domain volume;
first, the
Figure 132449DEST_PATH_IMAGE006
Step dynamic deletion rate
Figure 965275DEST_PATH_IMAGE007
The solving module of (2) is specifically configured to:
based on the structural stress uniformity
Figure 982908DEST_PATH_IMAGE004
And structural volume fraction index
Figure 714235DEST_PATH_IMAGE005
For the second step, by means of a sine function
Figure 661200DEST_PATH_IMAGE006
Solving the step dynamic deletion rate:
Figure 427162DEST_PATH_IMAGE021
；
and the output module is used for circularly and iteratively executing the solving and updating steps until the updated structure finite element model reaches a preset constraint condition and a preset convergence condition, and outputting the optimized topological structure of the engineering structure.
8. An electronic device comprising a memory and a processor, wherein the memory is configured to store a program; the processor, coupled to the memory, is configured to execute the program stored in the memory to implement the steps in the topology optimization method for improving dynamic deletion rate of any of the above claims 1 to 6.
9. A computer-readable storage medium storing a computer-readable program or instructions, which when executed by a processor, implement the steps of the topology optimization method for improving dynamic deletion rate according to any of the claims 1 to 6.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109299519A (en) * 2018-08-29 2019-02-01 湖南科技大学 A kind of method of concrete component topology strut and tie adding window progressive structure optimization
CN110069800A (en) * 2018-11-17 2019-07-30 华中科技大学 Three-dimensional structure method of topological optimization design and equipment with smooth boundary expression
CN110348102A (en) * 2019-07-04 2019-10-18 广州大学 Dynamic evolution rate BESO Topology Optimization Method and its application based on arc tangent
CN111353246A (en) * 2020-02-28 2020-06-30 湖南科技大学 Static and dynamic force multi-target topology evolution method for concrete member design
CN111737839A (en) * 2020-05-19 2020-10-02 广州大学 BESO (beam-based event optimization) topology optimization method based on dynamic evolution rate and adaptive grid and application thereof

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
TWI519987B (en) * 2014-11-14 2016-02-01 財團法人工業技術研究院 Structural topology optimization design method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109299519A (en) * 2018-08-29 2019-02-01 湖南科技大学 A kind of method of concrete component topology strut and tie adding window progressive structure optimization
CN110069800A (en) * 2018-11-17 2019-07-30 华中科技大学 Three-dimensional structure method of topological optimization design and equipment with smooth boundary expression
CN110348102A (en) * 2019-07-04 2019-10-18 广州大学 Dynamic evolution rate BESO Topology Optimization Method and its application based on arc tangent
CN111353246A (en) * 2020-02-28 2020-06-30 湖南科技大学 Static and dynamic force multi-target topology evolution method for concrete member design
CN111737839A (en) * 2020-05-19 2020-10-02 广州大学 BESO (beam-based event optimization) topology optimization method based on dynamic evolution rate and adaptive grid and application thereof

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
creep model of high-strength high-performance concrete under cyclic loading;Li, Q., Liu, M., Lu, Z. et al.;《 Wuhan Univ. Technol.-Mat. Sci. Edit》;20191231;622–629 *
一种变删除率的渐进结构优化方法;李旭宇等;《长沙理工大学学报(自然科学版)》;20130628;第10卷(第02期);57-62、81 *
加窗渐进结构优化算法;王磊佳等;《应用力学学报》;20181015;第35卷(第05期);1037-1044 *
卢志芳 ; 黎子童 ; 刘沐宇 ; 刘齐民 ; 张强.基于正交试验新型钢－混组合板梁桥结构参数优化.《武汉理工大学学报》.2020, *
基于一种动态删除率的ESO方法;罗静等;《计算力学学报》;20150415;第32卷(第02期);274-279 *

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