CN113239480A - Structural topology optimization method based on comparative analysis - Google Patents
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Abstract
The invention provides a structure topology optimization method based on contrastive analysis, which divides the path of a primary optimization structure, contrasts and analyzes the change of a target function, and performs pseudo-density assignment and selection on checkerboard units on each path to obtain a topology continuous structure meeting the requirements of dynamic and static characteristics. Dividing a reserved unit set A according to paths after structural topology optimization; dividing each unit path into a deletion unit set B according to a classification standardnAnd reserved cell set Cn(ii) a Calculating the value of the objective function XnAnd the original objective function value Xn‑1And making a comparison if XnIs significantly less than Xn‑1Then the cell set C is reservedn(ii) a If XnIs significantly greater than Xn‑1Then the unit set C is rejectedn(ii) a If XnAnd Xn‑1If the difference is not large, the unit set C is modifiednCell density value of (1) such that XnGreater than Xn‑1Until all paths have completed the computation. The invention can effectively inhibit the checkerboard, improve the numerical stability, shorten the design period of the product and improve the research and development efficiency and quality of the product.
Description
Technical Field
The invention belongs to the field of mechanical structure topology optimization design, and relates to a structure topology optimization method based on comparative analysis.
Background
When the variable density method is used for topology optimization of a continuum, researchers always expect that an optimization result with clear and smooth boundaries can be obtained, but a checkerboard phenomenon (checkerboard patterns) always occurs in the actual optimization process, namely, the optimized structural units are arranged in a checkerboard-like form, as shown in the attached figure 2 of the specification, namely, a phenomenon that the density of unit materials is periodically distributed in high and low in the topology optimization. The checkerboard is essentially caused by numerical errors, so that the occurrence of the numerical errors can be reduced by adopting the high-order units, the checkerboard phenomenon is well inhibited, and the checkerboard phenomenon in the optimized structure is successfully eliminated by adopting the high-order unit method in the topology optimization. However, the use of high-order cells greatly increases the computation cost, so that in the case of limited computation conditions, low-order cells which are prone to checkerboard phenomenon still have to be adopted to increase the computation efficiency. In order to achieve both the calculation efficiency and the suppression of the checkerboard phenomenon, it is necessary to use a certain checkerboard suppression method to suppress the checkerboard phenomenon while using low-order cells.
In topology optimization, the checkerboard pattern appears independent of the design variables of the adopted materials, namely, the checkerboard phenomenon appears no matter the homogenization design method or the variable density method is adopted. In the early topological optimization research, some scholars misunderstand that the structure is a better ideal structure, but from the production perspective, the processing is difficult, the cost is high, and the practical application is not met. The material itself does not conform to the optimal distribution principle of the material, the checkerboard makes the extraction and manufacturing of the structure shape difficult, and the designer must make trade-offs between elements and holes.
Disclosure of Invention
Aiming at the checkerboard phenomenon widely existing in structural topology optimization, the invention provides a structural topology optimization method based on contrastive analysis. Specifically, as follows, the following description will be given,
the structural topology optimization method based on the comparative analysis is characterized by comprising the following steps: dividing a reserved unit set A into a unit set [ A ] according to a unit path after the structure is subjected to primary topological optimization1，A2，…An]N is the number of paths, AnRepresenting a unit set on the nth path; classifying the unit paths according to classification criteria, i.e. AnCan be divided into a unit set with relative density of 0 and 1 and a certain specific assignment, and the unit with relative density of 0 is marked as a deleted unit set BnThe reserved cells are denoted as set Cn. Reserved set CnCalculating to obtain the target function value XnIs related to the original objective function value Xn-1By comparison, if XnIs significantly less than Xn-1Then the cell set C on the nth path is reservednContinuously carrying out comparative analysis on the (n + 1) th path; if XnIs significantly greater than Xn-1Then, the key unit on the nth path is reserved and C is eliminatednCells in a checkerboard area appear; if XnAnd Xn-1If the difference is not large, modifying CnThe cell density of the middle part of the cell is assigned so that XnGreater than Xn-1That is, the optimization objective function value becomes smaller until all paths are calculated.
Preferably, the classification standard is to record the density of the solid cells with the density of 1 on the main path and the density of the partial checkerboard cells at the edges of the solid cells as 1 and a certain assignment, and record the density of the rest cells with the checkerboard phenomenon as 0; for the cells on the branch path, the direction of force transmission is relatively fuzzy due to the fact that the solid cells do not appear in a large area, the cells with the higher cell density are selected to form the direction of force transmission on the branch path, the cell density in the direction is recorded as 1 or a certain assigned value, and the rest cell densities are recorded as 0. After classification, the unit set with the density of 0 is recorded as BnThe set of cells with density 1 and a particular assignment is denoted as Cn。
Preferably, in said comparative analysis, when X isnIs significantly greater than Xn-1For C on the nth pathnThe unit set is divided again, only the original solid unit or repair unit is reservedChanging the density assignment of the unit with larger density and rejecting CnCells in which a checkerboard region appears; and X appears for the branch pathnIn larger cases, C may be repartitioned according to the number of cells on the branch pathnWhen there are fewer cells in a branch path, all cells in that path may be deleted.
Preferably, the calculation order is according to the order of the first main path and the second main path until all paths are completely calculated.
Preferably, the specific assignment is close to 1, and the values of the different paths can also be adjusted according to the contribution to the structure.
Advantageous effects
The invention provides a structure topology optimization method based on contrastive analysis, which divides the path of a primary optimization structure into a main path and a branch path, and carries out pseudo-density assignment and selection on checkerboard units on each force transmission path to inhibit checkerboards and improve the stability of topology optimization calculation, thereby greatly reducing the operation time of structure optimization design, ensuring that the force transmission paths are more reasonable, ensuring that the stress distribution of the optimized structure is more uniform, meeting the static and dynamic characteristic requirements of the structure, improving the manufacturability of a topology optimization result, shortening the design and manufacturing period of a product, and improving the research and development efficiency and quality of the product.
Drawings
FIG. 1 is a topology optimization contrastive analysis flow of the present invention.
Fig. 2 is a schematic diagram of a checkerboard phenomenon.
FIG. 3 is a cell range division for Path one.
Fig. 4 is a cell range division for path three.
Fig. 5 is a cell range division for path four.
Detailed Description
For a better understanding of the present invention, reference is made to the following description taken in conjunction with the accompanying drawings and examples. The present invention may be embodied in many different forms and is not limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
The invention discloses a structural topology optimization method based on comparative analysis, which is characterized by comprising the following steps: dividing the reserved unit set A into [ A ] according to the path after the structure topology optimization1，A2，…An]，AnRepresenting a unit set on the nth path; dividing each unit path into a deletion unit set B according to a classification standardnAnd reserved cell set Cn. Set CnCalculating to obtain the objective function value XnIs related to the original objective function value Xn-1By comparison, if XnIs significantly less than Xn-1Then the cell set C on the nth path is reservednContinuously carrying out comparative analysis on the (n + 1) th path; if XnIs significantly greater than Xn-1Then, the key units on the nth path are reserved and subjected to density assignment modification, and C is eliminatednCells in a checkerboard area appear; if XnAnd Xn-1If the difference is not large, modifying CnThe cell density of the middle part of the cell is assigned so that XnGreater than Xn-1Until all paths have completed the computation. The topology optimization steps are as follows:
(1) and establishing a structural topological optimization mathematical model, determining a design variable as unit density by adopting a variable density method, and determining a constraint condition and an objective function.
(2) And establishing a structural topological optimization finite element model.
(3) And determining a topological optimization iteration control process.
(4) And finishing the primary calculation of topology optimization to obtain a primary optimization structure.
(5) And re-optimizing the structure by adopting a comparative analysis method to inhibit the checkerboard phenomenon.
(6) And designing a new structure according to the re-optimization result.
The present invention will be explained in detail with reference to the preliminary optimization block diagrams shown in fig. 2, 3, 4 and 5.
a) As shown in FIG. 2, all the cells remaining in the structure diagram from step (4) above are referred to as a set [ A ]1，A2，…A7]Also included are hollow elements in the structure, according to solid elementsAnd is divided into 7 paths from high to low.
b) As shown in FIG. 3, the route 1 is divided into three regions according to the classification criteria, and the cells to be deleted in the regions one and three are recorded as a cell set B1The value of the density value of other cells on the path 1 assigned to 1 or close to 1 is recorded as a cell set C1(ii) a FIG. 4 shows the division of the path 3, i.e. the first and second areas are the sets of cells to be deleted and are denoted as B3The value of the density of other cells on the path 3 assigned to 1 or close to 1 is denoted as C3Assigning a cell density closer to 1 to the hollow cells in the third area; FIG. 5 shows the division of the area of the path 4, since the path has fewer elements, the element assignment density of area one is 1 or a value close to 1 is marked as C after the force transmission direction is determined4Here, there is no cell to be written as density 0.
c) Comparative analysis was performed with route 1: reserved set C1Calculating to obtain the target function value X1And the objective function value X obtained by the preliminary optimization structure0By comparison, if X1Is significantly less than X0Then the cell set C on the 1 st path is reserved1Continuing to perform comparative analysis on the 2 nd path; if X1Is significantly greater than X0If yes, the solid cells in the third area in the 1 st path are reserved, the density assignment of the cells in the third area with checkerboards is modified or deleted, and the set C is determined again1Range and unit density of (1) up to X1Greater than X0Then, the next path analysis is carried out; if X1And X0If the difference is not large, modifying C1The cell density of the middle part of the cell is assigned so that XnGreater than Xn-1That is, the optimization objective function value becomes smaller until all paths are calculated.
d) Comparing and analyzing the subsequent 6 paths until obtaining the structure with less checkerboard phenomena, and notably, if X is the resultnIs significantly greater than Xn-1In the case of a path structure such as path 4, all cells in the path can be deleted and calculated. Finally, the obtained structure is taken as a reference, and a new structure is redesigned.
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.
Claims (7)
1. A structural topology optimization method based on comparative analysis is characterized in that: dividing the reserved unit set A into [ A ] according to unit path after the structure topology optimization1，A2，…An]N is the number of paths, AnRepresenting a unit set on the nth path; classifying the unit paths according to classification criteria, i.e. AnCan be divided into a unit set with relative density of 0 and 1 and a certain specific assignment, and the unit with relative density of 0 is marked as a deleted unit set BnThe reserved set of cells is denoted as set Cn. Reserved Unit set CnCalculating to obtain the target function value XnIs related to the original objective function value Xn-1By comparison, if XnIs significantly less than Xn-1Then the cell set C on the nth path is reservednContinuously carrying out comparative analysis on the (n + 1) th path; if XnIs significantly greater than Xn-1Then, the key unit on the nth path is reserved and C is eliminatednCells appearing in checkerboard regions or modifying cell density assignments so that XnGreater than Xn-1(ii) a If XnAnd Xn-1If the difference is not large, modifying CnThe cell density of the middle part of the cell is assigned so that XnGreater than Xn-1That is, the optimization objective function value becomes smaller until all paths are calculated.
2. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: the unit set A is divided into n paths, namely a main path and branch paths according to a primarily optimized structure, the number of the branch paths is larger than that of the main path, the checkerboard phenomenon of the main path is relatively unobvious, namely the relative density of most units is 1, the checkerboard phenomenon on the branch paths is relatively common, and hollow units and solid units appear alternately.
3. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: the classification standard is to record the density of the solid units with the density of 1 on the main path and the density of partial checkerboard units at the edge of the solid units as 1 and a certain specific assignment value, and record the density of the rest units with the checkerboard phenomenon as 0; for the cells on the branch path, the direction of force transmission is relatively fuzzy due to the fact that the solid cells do not appear in a large area, the cells with the higher cell density are selected to form the direction of force transmission on the branch path, the cell density in the direction is recorded as 1 or a certain assigned value, and the rest cell densities are recorded as 0. After classification, the unit set with the density of 0 is recorded as BnThe set of cells with density 1 and a particular assignment is denoted as Cn。
4. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: in the comparative analysis, when X isnIs significantly greater than Xn-1For C on the nth pathnThe unit set is divided again, only the original solid units and the units with larger density are reserved, and C is removednCells in which a checkerboard region appears; and X appears for the branch pathnIn larger cases, C may be repartitioned according to the number of cells on the branch pathnWhen there are fewer cells in a branch path, all cells in that path may be deleted.
5. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: the calculation sequence is according to the sequence of the first main path and the second path until all paths are calculated.
6. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: the specific assignment is close to 1 and the values of the different paths can be adjusted.
7. The structural topology optimization method based on the comparative analysis according to claim 1, wherein: the topology optimization steps are as follows:
(1) establishing a structural topological optimization mathematical model, determining a design variable as unit density by adopting a variable density method, and determining a constraint condition and a target function;
(2) establishing a structural topological optimization finite element model;
(3) determining a topological optimization iteration control process;
(4) completing the primary calculation of topology optimization to obtain a primary optimization structure;
(5) re-optimizing the structure by adopting a comparative analysis method to inhibit the checkerboard phenomenon;
(6) and designing a new structure according to the re-optimization result.
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| CN103020361A (en) * | 2012-12-17 | 2013-04-03 | 华南理工大学 | Method for extracting no-checkerboard topological diagram from compliant mechanism |
| CN110555263A (en) * | 2019-08-30 | 2019-12-10 | 华南理工大学 | level set topology optimization method for curved shell structure optimization design |
| CN111339616A (en) * | 2020-03-06 | 2020-06-26 | 北京理工大学 | Topology optimization method for maximizing fundamental frequency of mechanical structure |
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