CN110502822A - A kind of method of topological optimization design of the self supporting structure for increasing material manufacturing - Google Patents
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Abstract
The invention discloses a kind of method of topological optimization design of self supporting structure for increasing material manufacturing, belong to Optimal Structure Designing correlative technology field, it is calculated by " four cell cube methods " and constrains pendency angle [alpha], angle restriction will be dangled in conjunction with SIMP method, it obtains in increasing material manufacturing as the method for the overhung structure of self supporting structure, the present invention can effectively contain that the overhung structure that needs support occurs, avoid the addition of support construction, consumptive material usage amount and cost is effectively reduced, improves workpiece surface quality；Furthermore the calculation method is completely suitable for Continuum Structure, and flexibility is high, applied widely, is easily implanted into topological optimization frame as expansion module, simple and easy.
Description
Technical Field
The invention relates to a topological optimization design method of a self-supporting structure for additive manufacturing, and belongs to the technical field related to structural optimization design.
Background
Topological optimization is an effective means for realizing the lightweight design of a workpiece structure, but because the optimized workpiece is often complex in structure, most of the topological optimization is only used for the conceptual design of the structure, and the later processing stage is difficult to perform due to the limitation of the traditional processing technology. In recent years, with the rise and development of additive manufacturing technology, it is widely believed by domestic and foreign scholars and industrial designers that the additive manufacturing technology is not limited by a workpiece structure any more due to the obvious advantages of high capability of processing complex components, short processing period, no need of tooling and dies and the like, and the combination of the additive manufacturing technology and topology optimization is an optimal method for realizing the light weight of parts.
The molding principle of additive manufacturing technology is "additive manufacturing", i.e. molding a part by layers of materials. However, manufacturing constraints still exist in the additive manufacturing process, with the overhanging structure constraint affecting the most severely. In the vibration material disk, the model is sliced by software and then printed layer by layer, in order to avoid printing collapse, each part of each layer after slicing the model is required to be supported by enough materials, if the materials supported by the layers are insufficient, a suspension structure can be formed, auxiliary supports must be added manually to ensure successful printing, the supports are formed during processing and are removed during post-processing, so that the serious waste of raw materials and time cost is caused, and even the surface of a workpiece is damaged during removal. Scholars at home and abroad find that whether the overhanging structure needs auxiliary support can be judged through an overhanging angle, wherein the overhanging angle is an included angle between an overhanging surface of a workpiece and a horizontal plane and is found at an overhanging threshold angle. When the overhang angle is greater than or equal to the overhang threshold angle, the overhang structure can realize self-support, and higher printing quality can be achieved without adding auxiliary support; when the overhang angle is less than the overhang threshold angle, additional support may be required.
In view of the above problems, there is a strong need to develop a topology optimization design method for a self-supporting structure for additive manufacturing. In the topological optimization process, the calculated overhang angle is constrained to be larger than or equal to the overhang threshold angle all the time, namely the overhang structure is ensured to be a self-supporting structure all the time, a workpiece can be directly processed without being supported, the cost is greatly saved, and the time is saved.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a topological optimization design method of a self-supporting structure for additive manufacturing, which can calculate and restrict a suspension angle to obtain a suspension structure which is always the self-supporting structure, avoid the addition of a supporting structure, effectively reduce the consumption of consumables and cost, and improve the surface quality of a workpiece.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a topological optimization design method of a self-supporting structure for additive manufacturing is a method for calculating and constraining a suspension angle alpha through a four-unit body method, and combining the suspension angle constraint with a SIMP method to obtain the suspension structure of the self-supporting structure in the additive manufacturing.
The technical scheme of the invention is further improved as follows: the method comprises the following steps:
a, establishing a part geometric model, defining load and boundary conditions, defining design variables, a target function and a constraint function based on a SIMP density-rigidity interpolation model, and initializing unit body density, material attribute parameters, material volume fraction and optimization algorithm parameters;
b, taking the relative density of the unit body as a design variable, and acquiring the intermediate density of the unit body through a linear density filter
C pass through nonlinear Density Filter and intermediate Density of Unit cellsObtaining physical Density of Unit bodiesD, obtaining an overhang angle alpha through a four-unit body method, taking the overhang angle as an overhang angle constraint function, and applying an overhang angle constraint condition to obtain an overhang angle constraint equation, wherein the overhang angle constraint condition isOverhang angle greater than or equal to the overhang threshold angle: alpha is more than or equal to alpha0；
E, calculating the sensitivity of the target function and the constraint function to the design variable to obtain a sensitivity control equation;
f according to physical Density of Unit cellSolving a suspension angle constraint equation and a SIMP density-rigidity interpolation model mathematical expression to obtain a structural response, and calculating an objective function value, a constraint function value and a sensitivity value;
and G, judging whether the algorithm is converged or not by using the obtained sensitivity value, if not, returning to the step (2) for algorithm iteration, if so, ending the algorithm iteration, and outputting a final topology optimization result.
The technical scheme of the invention is further improved as follows: in the step A, based on a SIMP density-rigidity interpolation model, the relative density of each discrete unit body is used as a design variable, the overall rigidity of the macro structure is used as a target function, the target is optimized to maximize the overall rigidity of the macro structure, namely the flexibility of the macro structure is minimized, the volume fraction of the structure is used as a volume constraint function, and the mathematical expression of the model is as follows:
find：ρ＝(ρ1,ρ2,……,ρnele)T (1)
min∶C＝FTU (2)
s.t.:K(ρ)U＝F (3)
0≤ρi≤1 i＝1,2,…,nele (5)
where ρ ═ p (ρ)1,ρ2,……,ρnele)TIs the discretized relative density of each unit body, and rho is [0,1 ]]A continuous variable of (a);
c is the flexibility of the macrostructure;
f is a load vector;
u is a node displacement vector;
k is the integral rigidity of the macrostructure;
ρirelative density of the ith unit cell;
viis the volume fraction of the ith unit cell;
v is the structural volume fraction;
to set the structural volume fraction;
equation (2) is the objective equation, equation (3) is the governing equation, and equation (4) is the volume constraint equation.
The technical scheme of the invention is further improved as follows: the step B adopts a linear density filter, and specifically comprises the following steps:
Ne＝{m|‖xm-xe‖≤R} (7)
w(xm)＝R-‖xm-xe‖ (8)
wherein,is the median density of unit e, i.e. the relative density of unit e after linear filtering;
r is the linear density filter radius;
xmis the centroid coordinate of the unit cell m.
The technical scheme of the invention is further improved as follows: in the step C, a nonlinear density filter is adoptedFiltering to physical densityThe method comprises the following specific steps:
wherein, beta is the filtering degree of the filter,
eta is a threshold parameter and is obtained by a bisection method, and is used for keeping the use of materials before and after the nonlinear filter unchanged, and the formula is as follows:
the technical scheme of the invention is further improved as follows: the four-unit method in the step D comprises the following steps:
when the SIMP method is used for topology optimization, a density uniform transition region with the unit volume density of 0-1 exists at the boundary of the SIMP density-rigidity interpolation model, a density gradient exists in the density uniform transition region, and the density gradient is perpendicular to the boundary of the SIMP density-rigidity interpolation model, so that a density contour line perpendicular to the density gradient exists in the density uniform transition region, and the density contour line is parallel to the model boundary.
The technical scheme of the invention is further improved as follows: the specific steps of the four-unit body method are as follows:
selecting a certain unit body in a transition area with uniform density and three adjacent unit bodies to form a four-unit body in a shape of Chinese character tian, and sequentially recording the density of the central points of the four unit bodies as rho from the selected unit body1、ρ2、ρ3、ρ4And the density distribution in the density transition region is a linear function, a density contour line is calculated according to the densities of the four selected unit bodies, and the included angle between the density contour line and the horizontal direction is the overhang angle alpha.
The technical scheme of the invention is further improved as follows: the specific calculation process of the four-unit body method is as follows:
a. the boundary structure of the SIMP density-rigidity interpolation model is divided into an upper boundary, a vertical boundary and a lower boundary, wherein the lower boundary is a suspension structure, and suspension constraint conditions need to be considered only when the suspension structure is processed, so that the boundary structure where the four-unit body is located is judged:
that is, the formula (12) is satisfied, that is, the selected four-unit body is located at the lower boundary:
b. calculating the overhang angle α:
the technical scheme of the invention is further improved as follows: the suspension angle constraint equation is:
the technical scheme of the invention is further improved as follows: the sensitivity control equation in the step E is:
due to the adoption of the technical scheme, the invention has the technical progress that:
according to the invention, by combining the overhang angle constraint with the traditional SIMP topological optimization method, the appearance of an overhang structure needing to be supported can be restrained, extra supports do not need to be added and removed manually in the additive manufacturing process, the manufacturing period is shortened, the material consumption is saved, the cost is reduced, and the surface quality of a workpiece is improved; meanwhile, the method is completely suitable for a continuum structure, high in flexibility, wide in application range, easy to implement and easy to implement, and can be easily used as an extension module to be implanted into a topology optimization framework.
The method is based on the SIMP density-rigidity interpolation model, the linear density filter is used for obtaining the intermediate density of the unit bodies, then the physical density of the unit bodies is obtained through the nonlinear density filter and the intermediate density of the unit bodies, and the checkerboard phenomenon in the optimization process and the grid dependency of the optimization result can be avoided.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic view of the overhang structure and support structure of the present invention;
FIG. 3 is a schematic diagram of the topology optimization structure without applying the dangling constraints of the present invention;
FIG. 4 is an enlarged fragmentary view taken at A2 of FIG. 3 in accordance with the present invention;
FIG. 5 is a diagram illustrating the "four-unit method" at B in FIG. 4 according to the present invention;
FIG. 6 is a schematic diagram of the topology optimization structure after the application of the dangling constraints according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples:
a topological optimization design method of a self-supporting structure for additive manufacturing is a method for calculating and constraining a suspension angle alpha through a four-unit body method, and combining the suspension angle constraint with a SIMP method to obtain the suspension structure of the self-supporting structure. As shown in FIG. 2, the overhang structure of the printed entity is overhung by a threshold angle α0Is divided into two parts. Wherein the thick solid portion is a overhang angle alpha equal to or greater than a overhang threshold angle alpha0The suspension structure does not need to be additionally provided with auxiliary support during printing, and self-support is realized; the dashed portion is where the overhang angle α is less than the overhang threshold angle α0The suspension structure of (2) needs to be added with auxiliary support during printing to ensure successful printing.
As shown in fig. 1, the method comprises the following steps:
a, establishing a part geometric model, defining load and boundary conditions, defining design variables, a target function and a constraint function based on a SIMP density-rigidity interpolation model, and initializing unit body density, material attribute parameters, material volume fraction and optimization algorithm parameters;
in the step A, based on a SIMP density-rigidity interpolation model, the relative density of each discrete unit body is used as a design variable, the overall rigidity of the macro structure is used as a target function, the target is optimized to maximize the overall rigidity of the macro structure, namely the flexibility of the macro structure is minimized, the volume fraction of the structure is used as a constraint function, and the mathematical expression of the model is as follows:
find：ρ＝(ρ1,ρ2,……,ρnele)T (1)
min∶C＝FTU (2)
s.t.:K(ρ)U＝F (3)
0≤ρi≤1 i＝1,2,…,nele (5)
where ρ ═ p (ρ)1,ρ2,……,ρnele)TIs the discretized relative density of each unit body, and rho is [0,1 ]]A continuous variable of (a);
c is the flexibility of the macrostructure;
f is a load vector;
u is a node displacement vector;
k is the integral rigidity of the macrostructure;
ρirelative density of the ith unit cell;
viis the volume fraction of the ith unit cell;
v is the structural volume fraction;
to set the structural volume fraction;
equation (2) is a target equation, equation (3) is a control equation, and equation (4) is a constraint equation.
B, taking the relative density of the unit body as a design variable, and acquiring the intermediate density of the unit body through a linear density filter
The step B adopts a linear density filter, and specifically comprises the following steps:
Ne＝{m|‖xm-xe‖≤R} (7)
w(xm)＝R-‖xm-xe‖ (8)
wherein,is the median density of unit e, i.e. the relative density of unit e after linear filtering;
r is the linear density filter radius;
xmis the centroid coordinate of the unit cell m.
C pass through nonlinear Density Filter and intermediate Density of Unit cellsObtaining physical Density of Unit bodies
The traditional SIMP only adopts a linear density filter, and in order to avoid the checkerboard phenomenon in the optimization process and the grid dependency of the optimization result, the invention further adopts a nonlinear density filterFurther filtering to physical densityThe method comprises the following specific steps:
wherein, beta is the filtering degree of the filter,
eta is a threshold parameter and is obtained by a bisection method, and is used for keeping the use of materials before and after the nonlinear filter unchanged, and the formula is as follows:
d, obtaining an overhang angle alpha through a four-unit body method, taking the overhang angle as an overhang angle constraint function, and applying an overhang angle constraint condition to obtain an overhang angle constraint equation, wherein the overhang angle constraint condition is that the overhang angle is greater than or equal to an overhang threshold angle: alpha is more than or equal to alpha0；
As shown in fig. 3 to 5, when the SIMP method is used for topology optimization, a density uniform transition region with a unit volume density of 0-1 exists at the boundary of the SIMP density-stiffness interpolation model, and the density uniform transition region has a density gradient which is perpendicular to the boundary of the SIMP density-stiffness interpolation model, so that a density contour line which is perpendicular to the density gradient exists in the density uniform transition region and is parallel to the model boundary.
The four-unit-body method is characterized in that a certain unit body in a transition area with uniform density and three adjacent unit bodies are selected to form a four-unit body in a shape of Chinese character tian by utilizing the principle, and the density of the central points of the four unit bodies is recorded as rho from the selected unit body1、ρ2、ρ3、ρ4And the density distribution in the density transition region is a linear function, a density contour line is calculated according to the densities of the four selected unit bodies, and the included angle between the density contour line and the horizontal direction is the overhang angle alpha.
The specific calculation process is as follows:
a. the boundary structure of the SIMP density-rigidity interpolation model is divided into an upper boundary, a vertical boundary and a lower boundary, wherein the lower boundary is a suspension structure, and suspension constraint conditions need to be considered only when the suspension structure is processed, so that the boundary structure where the four-unit body is located is judged:
that is, the formula (12) is satisfied, that is, the selected four-unit body is located at the lower boundary:
b. calculating the overhang angle α:
applying a suspension angle constraint condition to obtain a suspension angle constraint equation as follows:
TABLE 1 center density table of a certain four-unit body
The suspension angles at points A1, A2 and A3 can be estimated to be about 30 degrees according to FIG. 3, and the suspension angles at points A1, A2 and A3 are calculated to be 31.4 degrees, 31.8 degrees and 32.6 degrees respectively according to the center density data of the four-unit body given in Table 1 and combined with the formula (13), thereby proving that the proposed suspension angle calculation method is accurate and effective.
E, calculating the sensitivity of the objective function and the constraint function to the design variable to obtain a sensitivity control equation (15):
f according to physical Density of Unit cellSolving a suspension angle constraint equation and a SIMP density-rigidity interpolation model mathematical expression to obtain a structural response, and calculating an objective function value, a constraint function value and a sensitivity value;
and G, judging whether the algorithm is converged or not by using the obtained sensitivity value, if not, returning to the step (2) for algorithm iteration, if so, ending the algorithm iteration, and outputting a final topology optimization result.
The result of the topology optimization with the added droop constraint is shown in fig. 5.
The specific embodiments described in this specification are merely illustrative of the invention. Various modifications and additions can be made to the described embodiments by those skilled in the art without departing from the spirit of the invention or exceeding the scope as defined in the appended claims.
Claims (10)
1. A method of topologically optimal design of a self-supporting structure for additive manufacturing, characterized by: the method for calculating and constraining the overhang angle alpha through a four-unit body method, and combining the overhang angle constraint with a SIMP method to obtain the overhang structure which is a self-supporting structure in the additive manufacturing.
2. The method of topologically optimized design of a self-supporting structure for additive manufacturing of claim 1, wherein: the method comprises the following steps:
a, establishing a part geometric model, defining load and boundary conditions, defining design variables, a target function and a constraint function based on a SIMP density-rigidity interpolation model, and initializing unit body density, material attribute parameters, material volume fraction and optimization algorithm parameters;
b, taking the relative density of the unit body as a design variable, and acquiring the intermediate density of the unit body through a linear density filter
C pass through nonlinear Density Filter and intermediate Density of Unit cellsObtaining physical Density of Unit bodies
D, obtaining an overhang angle alpha through a four-unit body method, taking the overhang angle as an overhang angle constraint function, and applying an overhang angle constraint condition to obtain an overhang angle constraint equation, wherein the overhang angle constraint condition is that the overhang angle is greater than or equal to an overhang threshold angle: alpha is more than or equal to alpha0；
E, calculating the sensitivity of the target function and the constraint function to the design variable to obtain a sensitivity control equation;
f according to physical Density of Unit cellSolving a suspension angle constraint equation and a SIMP density-rigidity interpolation model mathematical expression to obtain a structural response, and calculating an objective function value, a constraint function value and a sensitivity value;
and G, judging whether the algorithm is converged or not by using the obtained sensitivity value, if not, returning to the step (2) for algorithm iteration, if so, ending the algorithm iteration, and outputting a final topology optimization result.
3. The method of claim 2, wherein the method comprises: in the step A, based on a SIMP density-rigidity interpolation model, the relative density of each discrete unit body is used as a design variable, the overall rigidity of the macro structure is used as a target function, the target is optimized to maximize the overall rigidity of the macro structure, namely the flexibility of the macro structure is minimized, the volume fraction of the structure is used as a volume constraint function, and the mathematical expression of the model is as follows:
find：ρ＝(ρ1,ρ2,……,ρnele)T (1)
min∶C＝FTU (2)
s.t.:K(ρ)U＝F (3)
0≤ρi≤1 i＝1,2,…,nele (5)
where ρ ═ p (ρ)1,ρ2,……,ρnele)TIs the discretized relative density of each unit body, and rho is [0,1 ]]A continuous variable of (a);
c is the flexibility of the macrostructure;
f is a load vector;
u is a node displacement vector;
k is the integral rigidity of the macrostructure;
ρirelative density of the ith unit cell;
viis the volume fraction of the ith unit cell;
v is the structural volume fraction;
to set the structural volume fraction;
equation (2) is the objective equation, equation (3) is the governing equation, and equation (4) is the volume constraint equation.
4. The method of claim 2, wherein the method comprises: the step B adopts a linear density filter, and specifically comprises the following steps:
Ne＝{m|‖xm-xe‖≤R} (7)
w(xm)＝R-‖xm-xe‖ (8)
wherein,is the median density of unit e, i.e. the relative density of unit e after linear filtering;
r is the linear density filter radius;
xmis the centroid coordinate of the unit cell m.
5. The method of claim 2, wherein the method comprises: in the step C, a nonlinear density filter is adoptedFiltering to physical densityThe method comprises the following specific steps:
wherein, beta is the filtering degree of the filter,
eta is a threshold parameter and is obtained by a bisection method, and is used for keeping the use of materials before and after the nonlinear filter unchanged, and the formula is as follows:
6. the method of claim 2, wherein the method comprises: the four-unit method in the step D comprises the following steps:
when the SIMP method is used for topology optimization, a density uniform transition region with the unit volume density of 0-1 exists at the boundary of the SIMP density-rigidity interpolation model, a density gradient exists in the density uniform transition region, and the density gradient is perpendicular to the boundary of the SIMP density-rigidity interpolation model, so that a density contour line perpendicular to the density gradient exists in the density uniform transition region, and the density contour line is parallel to the model boundary.
7. The method of claim 6, wherein the method comprises: the specific steps of the four-unit body method are as follows:
selecting a certain unit body in a transition area with uniform density and three adjacent unit bodies to form a four-unit body in a shape of Chinese character tian, and sequentially recording the density of the central points of the four unit bodies as rho from the selected unit body1、ρ2、ρ3、ρ4And the density distribution in the density transition region is a linear function, a density contour line is calculated according to the densities of the four selected unit bodies, and the included angle between the density contour line and the horizontal direction is the overhang angle alpha.
8. The method of claim 7, wherein the method comprises: the specific calculation process of the four-unit body method is as follows:
a. the boundary structure of the SIMP density-rigidity interpolation model is divided into an upper boundary, a vertical boundary and a lower boundary, wherein the lower boundary is a suspension structure, and suspension constraint conditions need to be considered only when the suspension structure is processed, so that the boundary structure where the four-unit body is located is judged:
that is, the formula (12) is satisfied, that is, the selected four-unit body is located at the lower boundary:
b. calculating the overhang angle α:
9. the method of claim 8, wherein the method comprises: the suspension angle constraint equation is:
10. a method of topologically optimised design of a self-supporting structure for additive manufacturing according to claim 3, characterised in that: the sensitivity control equation in the step E is:
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Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111319268A (en) * | 2020-02-20 | 2020-06-23 | 西北工业大学 | Self-supporting structure optimization design method considering additive manufacturing printing direction |
| CN111428397A (en) * | 2020-02-28 | 2020-07-17 | 中国民航大学 | Topological optimization design method considering additive manufacturing structure self-supporting constraint |
| CN111859671A (en) * | 2020-07-21 | 2020-10-30 | 南京理工大学 | Shape-preserving topology optimization method considering suspension characteristic constraint |
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| CN112699511A (en) * | 2021-01-14 | 2021-04-23 | 上海交通大学 | Additive manufacturing-oriented shell and filling structure collaborative optimization design method |
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| CN116522562A (en) * | 2023-05-22 | 2023-08-01 | 上海祉元社企业管理合伙企业(有限合伙) | Supporting structure construction method, system, electronic equipment and storage medium |
| JP7566290B2 (en) | 2022-10-25 | 2024-10-15 | 浙大城市学院 | Optimized design and manufacturing method for self-supporting structures based on multi-axis 3D printing |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106650026A (en) * | 2016-11-24 | 2017-05-10 | 浙江大学 | Self-supporting structure design method oriented to three-dimensional printing |
| US20170312986A1 (en) * | 2016-04-28 | 2017-11-02 | Wisconsin Alumni Research Foundation | Systems and methods for controlling support structures in manufacturing |
| CN107391824A (en) * | 2017-07-11 | 2017-11-24 | 西北工业大学 | The method of topological optimization design of self supporting structure in increasing material manufacturing |
| CN109002598A (en) * | 2018-06-29 | 2018-12-14 | 华中科技大学 | Consider the self-supporting micro-structure Topology Optimization Method at overhanging angle and minimum dimension constraint |
-
2019
- 2019-08-15 CN CN201910751448.XA patent/CN110502822B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170312986A1 (en) * | 2016-04-28 | 2017-11-02 | Wisconsin Alumni Research Foundation | Systems and methods for controlling support structures in manufacturing |
| CN106650026A (en) * | 2016-11-24 | 2017-05-10 | 浙江大学 | Self-supporting structure design method oriented to three-dimensional printing |
| CN107391824A (en) * | 2017-07-11 | 2017-11-24 | 西北工业大学 | The method of topological optimization design of self supporting structure in increasing material manufacturing |
| CN109002598A (en) * | 2018-06-29 | 2018-12-14 | 华中科技大学 | Consider the self-supporting micro-structure Topology Optimization Method at overhanging angle and minimum dimension constraint |
Non-Patent Citations (4)
| Title |
|---|
| ALAIN GARAIGORDOBIL等: ""Overhang constraint for topology optimization of self-supported compliant mechanisms considering additive manufacturing"", 《COMPUTER-AIDED DESIGN》 * |
| KAIQING ZHANG等: ""Topology optimization considering overhang constraint in additive manufacturing"", 《COMPUTERS AND STRUCTURES》 * |
| 刘书田 等: ""拓扑优化与增材制造结合:一种设计与制造一体化方法"", 《航空制造技术》 * |
| 王心怡: "《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅱ辑》", 15 January 2019 * |
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