CN112699511A - Additive manufacturing-oriented shell and filling structure collaborative optimization design method - Google Patents

Abstract

The invention discloses a collaborative optimization design method for a shell and a filling structure for additive manufacturing, which relates to the related field of structure optimization design and comprises the following steps: step 1: initializing parameters; step 2: constructing a parameterized model of the density and the rigidity of the shell filling structure; and step 3: constructing an additive manufacturing suspension constraint model and a local volume constraint model; and 4, step 4: constructing topological optimization modeling, and determining a target function and a constraint function; and 5: solving the finite element model to obtain a design response; step 6: analyzing the sensitivity of the target function and the constraint function; and 7: optimizing and solving; and 8: if the convergence condition is met, ending; otherwise, turning to the step 3. By implementing the invention, not only can the integrated design of the shell and the filler structure be realized, but also a structure with additive manufacturing and no suspension characteristics can be obtained, and the processing can be realized directly through additive manufacturing.

Description

A collaborative optimization design method of shell and filling structure for additive manufacturing

technical field

The invention relates to the related field of structure optimization design, in particular to a collaborative optimization design method for a shell and a filling structure for additive manufacturing.

Background technique

Additive manufacturing components are usually designed into two parts: shell and filling structure, which can not only significantly save material consumption and improve manufacturing efficiency, but also have excellent specific stiffness, specific strength, and energy absorption performance, and are widely used in heavy-duty rockets, Major strategic equipment such as wide-body passenger aircraft and high-speed trains.

Compared with traditional manufacturing methods, although point-by-layer additive manufacturing is not limited by the geometry of the component, additional support structures are required in the hanging area of the component to avoid hanging collapse during processing, which will lead to manufacturing failure. Ensure component manufacturing accuracy and manufacturing quality. The hanging area provided outside the housing can be supported by an external support structure and removed after printing; however, the hanging area provided inside the housing is inside the structure, and its support structure cannot be removed after printing, and at the same time, the filling structure Self-supporting properties are also required in the point-by-layer manufacturing process. Aiming at the design problems of this type of components, the traditional design revolves around the fixed-shaped shell, fills the inner area of the shell with periodic regular shapes that satisfy the self-supporting characteristics, and realizes that the internal suspension area is well supported by artificial post-processing. This traditional design method relies on the designer's experience and requires repeated trial and error iterations. The design cycle is long and the material redundancy is large. It is difficult to grasp the shape consistency of the structure before and after the design and manufacture.

Aiming at the design problem of the support structure of additive manufacturing components, Chinese patent CN 110502822 A discloses a topology optimization design method for self-supporting structures for additive manufacturing. Constraints are combined with solid isotropic microstructures with penalization (SIMP) to obtain a self-supporting structure for additive manufacturing. The above design method can effectively avoid overhanging features in the optimized structure, effectively reducing material consumption and manufacturing. cost, and improve the surface quality of components; but this method is only for the optimal design of self-supporting structures, and cannot universally solve the topology optimization design of shell-filled structures commonly used in additive manufacturing, especially considering the synergistic optimization of shells and filling structures. A shell-filled structure with better mechanical properties and more consistent shape before and after design and fabrication is obtained.

Therefore, those skilled in the art are committed to developing a collaborative optimization design method for the shell and the filler structure for additive manufacturing, which can not only realize the integrated design of the shell and the filler structure, but also can obtain the additive manufacturing without suspension. The structure of features can be processed directly through additive manufacturing.

SUMMARY OF THE INVENTION

In view of the above-mentioned defects of the prior art, the technical problems to be solved by the present invention are that the prior art has a long design cycle, large redundancy, cannot meet the processing requirements of additive manufacturing, and cannot universally solve the common shell filling structure in additive manufacturing. Topology optimization design problem.

In order to achieve the above object, the present invention provides a method for co-optimizing the design of a shell and a filling structure for additive manufacturing, comprising the following steps:

Step 1: parameter initialization;

According to the shape of the structure, define the design domain and the non-design domain of the structure;

Based on the actual working conditions of the structure, determine the load and boundary conditions, and establish a finite element model;

Initialize optimization parameters and design variables μ and υ;

Step 2: Build a parametric model of the density and stiffness of the shell-filled structure;

和壳体τ；依次使用密度过滤与投影法，将所述设计变量υ转化为填充结构ψ；根据所述基区

所述壳体τ和所述填充结构ψ，构建单元密度的统一表达式ρ(φ,τ,ψ)；采用SIMP方法，建立单元密度及刚度的参数化模型，将单元密度插值集成于有限元分析中；Based on the density filtering formula and Heaviside projection format, a two-step filtering method is used to convert the design variable μ into a base area

and shell τ; using density filtering and projection in turn, transform the design variable υ into the filling structure ψ; according to the base area

The shell τ and the filling structure ψ are used to construct a unified expression of element density ρ(φ,τ,ψ); the SIMP method is used to establish a parameterized model of element density and stiffness, and the element density interpolation is integrated into the finite element Analyzing;

Step 3: Build the additive manufacturing suspension constraint model and local volume constraint model;

将所述辅助场χ与自支撑辅助场

的差作为悬挂区域并计算获得悬挂体积分数，根据所述悬挂区域和所述悬挂体积分数构建悬挂体积约束T；constructing an auxiliary field x, the auxiliary field x being configured so that the outside of the structure is in a state of being well supported; applying an additive manufacturing filter AM filter to the auxiliary field x to obtain a self-supporting auxiliary field

Compare the auxiliary field χ with the self-supporting auxiliary field

The difference is taken as the suspension area and calculated to obtain the suspension volume fraction, and the suspension volume constraint T is constructed according to the suspension area and the suspension volume fraction;

Taking each unit of the structure as the center, calculate the local volume fraction in the circular neighborhood of each unit, and build the local volume constraint 1 based on the p-norm of the local volume fraction; the local volume fraction is configured as each unit The ratio of the sum of the density of all cells in the circular neighborhood to the number of cells;

Step 4: Build topology optimization modeling, determine objective function and constraint function;

Using the two-field format considering the intermediate design field and the corrosion design field, a collaborative topology optimization model of the shell and filling structure for additive manufacturing was established;

和所述填充结构ψ的最小尺寸，避免优化结果出现不具备实际制造意义的特征；Controlling the base by the two-field format

and the minimum size of the filling structure ψ, to avoid the characteristics of the optimization results that do not have practical manufacturing significance;

Taking the weighted compliance c that minimizes the intermediate design and the corrosion design as the objective function, it is ensured that the overall volume constraint G of the structure, the suspended volume constraint T, and the local volume constraint l satisfy the constraints;

Step 5: Solve the finite element model to obtain the design response;

Based on the structural density information in the current optimization iteration step, the finite element models of the intermediate design and the corrosion design are solved respectively, and the structural deformation and stiffness information are obtained, and then the weighted compliance c is calculated, and the constraint function response including the overall volume constraint G is calculated at the same time. , the suspension volume constraint T, the local volume constraint l;

Step 6: Sensitivity analysis of objective function and constraint function;

According to the analytical sensitivity formula of each design response to the design variable μ and the design variable υ, solve the differential sensitivity value of the objective function and each constraint function to the design variable μ and the design variable υ under the current iteration step;

Step 7: optimization solution; use the moving asymptote algorithm MMA to solve the additive manufacturing-oriented collaborative topology optimization model of the shell and the filling structure, and update the design variable μ and the design variable υ;

所述壳体τ和所述填充结构ψ所用Heaviside函数的投影锐度β随着优化迭代达到预设的最大值β_max，则结束；否则转所述步骤3。Step 8: If the rate of change of the weighted compliance c is lower than 0.2% in the current 5 iteration steps, and the base

When the projection sharpness β of the Heaviside function used by the shell τ and the filling structure ψ reaches the preset maximum value β _max along with the optimization iteration, the process ends; otherwise, go to step 3 .

In this technical solution, the optimization result with a small number of gray units is obtained through the above steps, and the value of the suspension constraint function is small, and further post-processing can be performed.

In one of the technical solutions of the present invention, a post-processing method is also included, and the post-processing method comprises the following steps:

Using a projection method with a threshold of 0.5, the optimized results with grayscale units are converted into clear 0 to 1 results;

Using an additive manufacturing filter, the remaining few suspended elements are detected and removed from the structure.

In one of the technical solutions of the present invention, the step 2 includes the following steps:

Step 2.1: The density filtering and Heaviside projection are as follows:

in,

和

分别为需要过滤或投影处理的密度场，

and

are the density fields that need to be filtered or projected, respectively,

B _e,R ={i:||x _i -x _e ||≤R,i∈Ω} is the set of all units within the radius R neighborhood of unit e,

_{He ei} =max(r-||x _i -x _e ||,0) is the weight function of density filtering,

β and η are the sharpness and threshold of the Heaviside function, respectively;

The threshold value of the intermediate design is η=0.50, and the threshold value of the corrosion design is η=0.70;

进行归一梯度模计算，获得壳体界面

计算公式如下：Step 2.2: Density-filtered smooth base

Perform the normalized gradient norm calculation to obtain the shell interface

Calculated as follows:

为

的空间梯度，α为归一系数；in,

for

The spatial gradient of , α is the normalization coefficient;

再经一次Heaviside投影处理，获得所述壳体τ；Step 2.3:

After another Heaviside projection process, the shell τ is obtained;

Step 2.4: After the design variable υ is sequentially processed by density filtering and Heaviside projection, the filling structure ψ is obtained;

Step 2.5: Construct the unified expression ρ(φ,τ,ψ) of the cell density as follows:

Step 2.6: Use the SIMP method to establish a parametric model of element density and stiffness, and integrate element density interpolation into the finite element analysis;

Among them, E _min =10 ^-9 is the minimum value of the elastic modulus to avoid the singularity of the matrix, and p=3 is the penalty factor.

In one of the technical solutions of the present invention, the construction formula of the auxiliary field x in the step 3 is as follows:

In one of the technical solutions of the present invention, the construction formula of the suspension volume constraint T in the step 3 is as follows:

where V _e is the unit volume, I is the identity matrix, and ε _r is the tolerance.

In one of the technical solutions of the present invention, the local volume constraint 1 in the step 3 is constructed as follows:

所有单元密度之和与单元数目之比：Step 3.1: Calculate the circular neighborhood centered on each cell

The ratio of the sum of all cell densities to the number of cells:

Step 3.2: The local volume constraint l is as follows:

的p范数参数设置为p_l＝8。Among them, N is the total number of elements in the design domain,

The p-norm parameter of is set to p _l =8.

In one of the technical solutions of the present invention, the uniform expression formula of each cell density of the corrosion design in the step 4 is as follows:

与

可由η＝0.70的Heaviside函数获得。in,

and

It can be obtained from the Heaviside function with η=0.70.

In one of the technical solutions of the present invention, the formula of the overall volume constraint G in the step 4 is as follows:

为近似密度。in,

is the approximate density.

In one of the technical solutions of the present invention, the collaborative topology optimization model of the shell and the filling structure in the step 4 is constructed as follows:

Among them, c is the weighted compliance of the integrated intermediate design and corrosion design, ω is the weighting factor, and the displacement response is obtained by solving KU=F.

In one of the technical solutions of the present invention, in the step 6, the objective function, the overall volume constraint G, the suspension volume constraint T, and the local volume constraint 1 have an impact on the design variable μ and the design variable The analytical sensitivity formula for υ is as follows:

Compared with the prior art, through the implementation of the present invention, at least the following beneficial technical effects are obtained:

(1) The technical solution disclosed in the present invention realizes the integrated design of the shell and the filler structure by constructing two design variables in the topology optimization model to control the structure configuration of the shell and the filler respectively, breaking through the traditional The idea of separating the shell and the filler in the scheme to obtain a structural configuration with better mechanical properties;

(2) In the technical solution disclosed in the present invention, the suspension constraint is integrated into the topology optimization model, and a structure with the feature of additive manufacturing without suspension is obtained, which can be directly processed by the additive manufacturing method;

(3) In the technical solution disclosed in the present invention, a two-field format is introduced into the topology optimization model, so as to avoid the characteristics of the optimization results that do not have practical manufacturing significance, and the optimization results can be directly processed by the additive manufacturing method.

The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings, so as to fully understand the purpose, characteristics and effects of the present invention.

Description of drawings

1 is a schematic flowchart of a preferred embodiment of the present invention;

2 is a schematic diagram of the structural parameterization modeling of a preferred embodiment of the present invention;

3 is a schematic diagram of the calculation process of the additive manufacturing suspension area field according to a preferred embodiment of the present invention;

4 is a schematic diagram of a cantilever beam structural design domain, loads and boundary conditions according to a preferred embodiment of the present invention;

Fig. 5 is the schematic diagram of the result of the cantilever beam structure introduced into the suspension constraint in the embodiment shown in Fig. 4;

6 is a schematic diagram of the result of the cantilever beam structure without introducing suspension constraints in the embodiment shown in FIG. 4;

7 is a schematic diagram of the printing result of the cantilever beam structure without introducing suspension constraints in the embodiment shown in FIG. 4;

FIG. 8 is a schematic diagram of the printing result of the cantilever beam structure with the suspension constraint introduced in the embodiment shown in FIG. 4 .

Detailed ways

The following describes several preferred embodiments of the present invention with reference to the accompanying drawings, so as to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned herein.

In the drawings, structurally identical components are denoted by the same numerals, and structurally or functionally similar components are denoted by like numerals throughout. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thicknesses of components are appropriately exaggerated in some places in the drawings.

In the description of the embodiments of the present application, it should be clear that the terms "center", "middle", "upper", "lower", "left", "right", "inner", "outer", "top", " The orientation or positional relationship indicated by "bottom", "side", "vertical", "horizontal", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the embodiments of the present application and simplifying the description, rather than indicating Or imply that the described device or element must have a specific direction or positional relationship, that is, it cannot be construed as a limitation on the embodiments of the present application; in addition, the terms "first", "second", "third", "fourth" etc. are only used to facilitate or simplify the description, not to indicate or imply their importance.

This embodiment provides a method for co-optimizing the design of a shell and a filling structure for additive manufacturing, including the following steps:

It includes the following steps:

Step 1: parameter initialization;

According to the shape of the structure, define the design domain and non-design domain of the structure;

Based on the actual working conditions of the structure, determine the load and boundary conditions, and establish a finite element model;

Initialize optimization parameters and design variables μ and υ;

Step 2: Build a parametric model of the density and stiffness of the shell-filled structure;

和壳体τ；依次使用密度过滤与投影法，将设计变量υ转化为填充结构ψ；根据基区

壳体τ和填充结构ψ，构建单元密度的统一表达式ρ(φ,τ,ψ)；采用SIMP方法，建立单元密度及刚度的参数化模型，将单元密度插值集成于有限元分析中；Based on the density filtering formula and Heaviside projection format, a two-step filtering method is used to convert the design variable μ into the base area

and shell τ; using density filtering and projection in turn, the design variable υ is transformed into the filling structure ψ; according to the base area

The shell τ and the filling structure ψ are used to construct a unified expression of element density ρ(φ,τ,ψ); the SIMP method is used to establish a parameterized model of element density and stiffness, and the element density interpolation is integrated into the finite element analysis;

Step 3: Build the additive manufacturing suspension constraint model and local volume constraint model;

将辅助场χ与自支撑辅助场

的差作为悬挂区域并计算获得悬挂体积分数，根据悬挂区域和悬挂体积分数构建悬挂体积约束T；An auxiliary field χ is constructed, and the auxiliary field χ is configured so that the outside of the structure is in a state of being well supported; the self-supporting auxiliary field is obtained by applying an additive manufacturing filter AM filter to the auxiliary field χ

Compare the auxiliary field χ with the self-supporting auxiliary field

The difference is used as the suspension area and calculated to obtain the suspension volume fraction, and the suspension volume constraint T is constructed according to the suspension area and the suspension volume fraction;

Taking each unit of the structure as the center, calculate the local volume fraction in the circular neighborhood of each unit, and build the local volume constraint l based on the p-norm of the local volume fraction; the local volume fraction is configured as all units in the circular neighborhood of each unit The ratio of the sum of the densities to the number of cells;

Step 4: Build topology optimization modeling, determine objective function and constraint function;

Using the two-field format considering the intermediate design field and the corrosion design field, a collaborative topology optimization model of the shell and filling structure for additive manufacturing was established;

和填充结构ψ的最小尺寸，避免优化结果出现不具备实际制造意义的特征；Base control via two-field format

and the minimum size of the filling structure ψ to avoid features that are not meaningful for practical manufacturing in the optimization results;

The objective function is to minimize the weighted compliance c of the intermediate design and the corrosion design to ensure that the overall volume constraint G, the suspension volume constraint T, and the local volume constraint l of the structure meet the constraints;

Step 5: Solve the finite element model to obtain the design response;

Based on the structural density information in the current optimization iteration step, the finite element models of the intermediate design and the corrosion design are solved respectively, and the structural deformation and stiffness information are obtained, and then the weighted compliance c is calculated. At the same time, the constraint function responses including the overall volume constraint G and the suspension volume constraint are calculated. T, the local volume constraint l;

Step 6: Sensitivity analysis of objective function and constraint function;

According to the analytical sensitivity formula of each design response to the design variable μ and the design variable υ, solve the differential sensitivity value of the objective function and each constraint function to the design variable μ and the design variable υ under the current iteration step;

Step 7: Optimization solution; use the moving asymptote algorithm MMA to solve the additive manufacturing-oriented collaborative topology optimization model of the shell and the filling structure, and update the design variable μ and the design variable υ;

壳体τ和填充结构ψ所用Heaviside函数的投影锐度β随着优化迭代达到预设的最大值β_max，则转步骤9；否则转步骤3；Step 8: If the rate of change of the weighted compliance c is less than 0.2% in the current 5 iteration steps, and the base

The projection sharpness β of the Heaviside function used by the shell τ and the filling structure ψ reaches the preset maximum value β _max along with the optimization iteration, then go to step 9; otherwise, go to step 3;

Step 9: Use a projection method with a threshold of 0.5 to convert the optimized result with grayscale cells into a clear 0-1 result; apply an additive manufacturing filter to detect the small amount of residual hanging cells and remove them from the structure .

The present embodiment further discloses the further implementation of the above scheme as follows:

As shown in Figure 1, the flow chart of the present embodiment is as follows:

Step 1: As shown in Figure 4, define a cantilever beam design domain with a size of 500 × 300, and a 6 × 6 non-design domain is arranged at the load and fixed boundary; establish a finite element model, all nodes on the left end of the model are fixed, and the model Apply a vertical downward point load F=100N at the midpoint of the right end face;

The optimization parameters are initialized as follows: the upper limit of the overall volume fraction V ^* = 0.45, the upper limit of the local volume fraction α = 0.65, the density filter and the local volume constraint radius are R ₁ =20, R ₂ =6, R ₃ =2.5, R ₄ = 6. Suspension constraint tolerance ε _r =6×10 ^-5 ; material is titanium alloy, elastic modulus E ₀ =108GPa, Poisson's ratio ν = 0.33;

The maximum sharpness of the Heaviside function β _max =64, and the two design variables μ and υ are set to all matrices with cell densities V ^* and α, respectively.

及壳体τ，本实施例中两步过滤法的密度过滤及Heaviside投影分别如下所述：Step 2: As shown in Figure 2, for the first design variable μ, a two-step filtering method is used to obtain the base area

and shell τ, the density filtering and Heaviside projection of the two-step filtering method in this embodiment are as follows:

和

分别为需要过滤或投影处理的密度场，B_e,R＝{i:||x_i-x_e||≤R,i∈Ω}为距离e单元半径R邻域内所有单元的集合，H_ei＝max(r-||x_i-x_e||,0)为密度过滤的权重函数。β与η分别为Heaviside函数的锐度及阈值，其中，中间设计的阈值取η＝0.50，腐蚀设计的阈值取η＝0.70；in,

and

are the density fields that need to be filtered or projected, respectively, Be _,R ={i:||x _i -x _e ||≤R,i∈Ω} is the set of all units within the radius R of the distance e unit, He _ei =max(r-||x _i -x _e ||,0) is the weight function of density filtering. β and η are the sharpness and threshold of the Heaviside function, respectively, where the threshold of the intermediate design is η=0.50, and the threshold of the corrosion design is η=0.70;

进行归一梯度模计算，获得壳体界面

计算公式如下：For density filtered smooth bases

Perform the normalized gradient norm calculation to obtain the shell interface

Calculated as follows:

为

的空间梯度，α为归一系数；in,

for

The spatial gradient of , α is the normalization coefficient;

再经一次Heaviside投影处理，最终获得壳体τ。

After another Heaviside projection process, the shell τ is finally obtained.

After the second design variable υ is processed by density filtering and Heaviside projection in turn, the filling structure ψ is obtained.

Accordingly, the unified expression formula of cell density is as follows:

Using the Solid Isotropic Material Method with Penalty (SIMP), a parametric model of element density and stiffness is established, and element density interpolation is integrated into the finite element analysis:

Among them, E _min =10 ^-9 is the minimum value of the elastic modulus to avoid the singularity of the matrix, and p=3 is the penalty factor.

壳体τ及填充结构ψ的基础上，构建辅助场χ使结构外部区域被材料完全填充，如下所示：Step 3: In the base area

On the basis of shell τ and filling structure ψ, an auxiliary field χ is constructed so that the outer area of the structure is completely filled with material, as follows:

通过计算辅助场χ及自支撑辅助场

的密度差，获得悬挂区域场。Using the auxiliary field χ, the outer suspension areas of the shell are considered to be well supported, while the outer suspension areas are actually boosted in manufacturing by outer support structures that can be removed after printing. After that, the AM filter was used to remove the suspended area inside the shell and the area where the filling structure could not be self-supporting to obtain a self-supporting auxiliary field.

By calculating the auxiliary field χ and the self-supporting auxiliary field

The density difference of , obtains the hanging area field.

Build the additive manufacturing suspension constraint T:

where V _e is the unit volume and I is the identity matrix. The tolerance _εr determines the tightness of the suspension constraints. If _εr is too small, it will lead to difficulty in the convergence of topology optimization; if _εr is too large, a large number of suspension areas cannot guarantee self-support.

Local volume constraints are used to prevent bulk material build-up in infill structures to form infill structures with porous features.

所有单元密度和与单元数目之比：First, calculate the circular neighborhood centered on each cell

The ratio of the sum of all cell densities to the number of cells:

的p范数构成：The local volume constraint obtains a porous filling structure by constraining the element with the maximum local volume fraction, and the local volume constraint function l can be given by

The p-norm of :

Among them, N is the total number of units in the design domain, and the p-norm parameter is set to p _l =8.

Step 4: Build a collaborative topology optimization model of the shell and infill structure for additive manufacturing. The two-field format considering the intermediate design field and the corrosion design field is adopted to control the minimum size of the base area and the filler to avoid the appearance of features similar to the size of the filler in the intermediate design base area.

The uniform expression formula for the density of each element in the corrosion design:

与

可由η＝0.70的Heaviside函数求得。Among them, the corrosion design in

and

It can be obtained by Heaviside function with η=0.70.

A collaborative topology optimization model of shell and infill structures for additive manufacturing:

where c is the weighted compliance of the combined intermediate design and corrosion design, ω is the weighting factor, G is the overall volume constraint, T is the suspended volume constraint, and l is the local volume constraint. The displacement response is obtained by solving KU=F.

Step 5: Based on the density information of the shell-filled structure under the current optimization iteration step, solve the finite element model of the intermediate design and the corrosion design of the shell-filled structure respectively, obtain the displacement responses U and ^Uero of the two designs, and then calculate the weighted compliance c, And calculate the following constraint function

(1) The overall volume constraint G:

为近似密度，使用近似密度的整体体积约束，是为了避免结构内部出现无填充结构的大块孔隙区域；in,

In order to approximate the density, the overall volume constraint of the approximate density is used to avoid large pore regions with no filling structure inside the structure;

(2) Local volume constraint l:

(3) The suspension volume constraint T:

Step 6: The analytical sensitivity formulas of objective function c and constraint functions G, T, and l to design variables μ and υ are deduced as follows:

Step 7 to Step: Use the moving moving asymptote algorithm MMA to solve the topology optimization model of the structure in the "south to north" printing direction, and obtain the topology optimization results that meet the hanging characteristics of no additive manufacturing, as shown in Figure 5, as a comparison , as shown in Figure 6, the topology optimization result without considering the suspension constraints, which contains 52544 suspension elements, the structure will not be fully processed by additive manufacturing;

Figure 7 is the actual printing result of the structure in Figure 6. Figure 7 shows that the topology optimization results without considering the suspension constraints have poor printing quality, with large areas of collapse, cracks, and off-line areas, while Figure 8 is the result of Figure 5. The actual printed results of the structure, whose topology optimization results taking into account the suspension constraints show good geometric integrity. The above examples fully prove the effectiveness of the method disclosed in this technical solution.

This technical solution also discloses another embodiment. On the basis of the above embodiment, the shell and the filling structure are designed separately, that is, the shell is designed first, then the filling structure is designed, and the shell and the filling structure are eliminated through manual post-processing. Suspension elements at structural junctions to obtain structures without AM suspension features.

The preferred embodiments of the present invention have been described above in detail. It should be understood that many modifications and changes can be made according to the concept of the present invention by those skilled in the art without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (10)

1. A shell and filling structure collaborative optimization design method for additive manufacturing, characterized in that, comprising the steps: Step 1: parameter initialization; According to the shape of the structure, define the design domain and the non-design domain of the structure; Based on the actual working conditions of the structure, determine the load and boundary conditions, and establish a finite element model; Initialize optimization parameters and design variables μ and υ; Step 2: Build a parametric model of the density and stiffness of the shell-filled structure; Based on the density filtering formula and Heaviside projection format, a two-step filtering method is used to convert the design variable μ into a base area

and shell τ; using density filtering and projection in turn, transform the design variable υ into the filling structure ψ; according to the base area

The shell τ and the filling structure ψ are used to construct a unified expression of element density ρ(φ,τ,ψ); the SIMP method is used to establish a parameterized model of element density and stiffness, and the element density interpolation is integrated into the finite element Analyzing; Step 3: Build the additive manufacturing suspension constraint model and local volume constraint model; constructing an auxiliary field x, the auxiliary field x being configured so that the outside of the structure is in a state of being well supported; applying an additive manufacturing filter AM filter to the auxiliary field x to obtain a self-supporting auxiliary field

Compare the auxiliary field χ with the self-supporting auxiliary field

The difference is taken as the suspension area and calculated to obtain the suspension volume fraction, and the suspension volume constraint T is constructed according to the suspension area and the suspension volume fraction; Taking each unit of the structure as the center, calculate the local volume fraction in the circular neighborhood of each unit, and build the local volume constraint 1 based on the p-norm of the local volume fraction; the local volume fraction is configured as each unit The ratio of the sum of the density of all cells in the circular neighborhood to the number of cells; Step 4: Build topology optimization modeling, determine objective function and constraint function; Using the two-field format considering the intermediate design field and the corrosion design field, a collaborative topology optimization model of the shell and filling structure for additive manufacturing was established; Controlling the base by the two-field format

and the minimum size of the filling structure ψ, to avoid the characteristics of the optimization results that do not have practical manufacturing significance; Taking the weighted compliance c that minimizes the intermediate design and the corrosion design as the objective function, it is ensured that the overall volume constraint G of the structure, the suspended volume constraint T, and the local volume constraint l satisfy the constraints; Step 5: Solve the finite element model to obtain the design response; Based on the structural density information in the current optimization iteration step, the finite element models of the intermediate design and the corrosion design are solved respectively, and the structural deformation and stiffness information are obtained, and then the weighted compliance c is calculated, and the constraint function response including the overall volume constraint G is calculated at the same time. , the suspension volume constraint T, the local volume constraint l; Step 6: Sensitivity analysis of objective function and constraint function; According to the analytical sensitivity formula of each design response to the design variable μ and the design variable υ, solve the differential sensitivity value of the objective function and each constraint function to the design variable μ and the design variable υ under the current iteration step; Step 7: optimization solution; use the moving asymptote algorithm MMA to solve the additive manufacturing-oriented collaborative topology optimization model of the shell and the filling structure, and update the design variable μ and the design variable υ; Step 8: If the rate of change of the weighted compliance c is lower than 0.2% in the current 5 iteration steps, and the base

When the projection sharpness β of the Heaviside function used by the shell τ and the filling structure ψ reaches the preset maximum value β _max along with the optimization iteration, the process ends; otherwise, go to step 3 . 2. collaborative optimization design method as claimed in claim 1, is characterized in that, also comprises post-processing method, and described post-processing method comprises the steps: Using a projection method with a threshold of 0.5, the optimized results with grayscale units are converted into clear 0 to 1 results; Using an additive manufacturing filter, the remaining few suspended elements are detected and removed from the structure. 3. collaborative optimization design method as claimed in claim 1, is characterized in that, described step 2 comprises the steps: Step 2.1: The density filtering and Heaviside projection are as follows:

in,

and

are the density fields that need to be filtered or projected, respectively, B _e,R ={i:||x _i -x _e ||≤R,i∈Ω} is the set of all units within the radius R neighborhood of unit e, _{He ei} =max(r-||x _i -x _e ||,0) is the weight function of density filtering, β and η are the sharpness and threshold of the Heaviside function, respectively; The threshold value of the intermediate design is η=0.50, and the threshold value of the corrosion design is η=0.70; Step 2.2: Density-filtered smooth base

Perform the normalized gradient norm calculation to obtain the shell interface

Calculated as follows:

in,

for

The spatial gradient of , α is the normalization coefficient; Step 2.3:

After another Heaviside projection process, the shell τ is obtained; Step 2.4: After the design variable υ is sequentially processed by density filtering and Heaviside projection, the filling structure ψ is obtained; Step 2.5: Construct a unified expression for cell density

as follows:

Step 2.6: Use the SIMP method to establish a parametric model of element density and stiffness, and integrate element density interpolation into the finite element analysis;

Among them, E _min =10 ^-9 is the minimum value of the elastic modulus to avoid the singularity of the matrix, and p=3 is the penalty factor. 4. collaborative optimization design method as claimed in claim 3, is characterized in that, the construction formula of auxiliary field χ described in described step 3 is as follows:

5. The collaborative optimization design method according to claim 4, wherein the construction formula of the suspension volume constraint T described in the step 3 is as follows:

where V _e is the unit volume, I is the identity matrix, and ε _r is the tolerance. 6. The collaborative optimization design method according to claim 5, wherein the local volume constraint 1 described in the step 3 is constructed as follows: Step 3.1: Calculate the circular neighborhood centered on each cell

The ratio of the sum of all cell densities to the number of cells:

Step 3.2: The local volume constraint l is as follows:

Among them, N is the total number of elements in the design domain,

The p-norm parameter of is set to p _l =8. 7. The collaborative optimization design method according to claim 6, wherein the uniform expression formula of each cell density of the corrosion design described in the step 4 is as follows:

in,

and

It can be obtained from the Heaviside function with η=0.70. 8. The collaborative optimization design method according to claim 7, wherein the formula of the overall volume constraint G in the step 4 is as follows:

in,

is the approximate density. 9. The collaborative optimization design method according to claim 8, wherein the collaborative topology optimization model of the shell and the filling structure described in the step 4 is constructed as follows:

Among them, c is the weighted compliance of the integrated intermediate design and corrosion design, ω is the weighting factor, and the displacement response is obtained by solving KU=F. 10. The collaborative optimization design method according to claim 9, wherein in the step 6, the objective function, the overall volume constraint G, the suspended volume constraint T, and the local volume constraint 1 have a The analytical sensitivity formulas of the design variable μ and the design variable υ are as follows:

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