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

Additive manufacturing-oriented shell and filling structure collaborative optimization design method Download PDF

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CN112699511A
CN112699511A CN202110049456.7A CN202110049456A CN112699511A CN 112699511 A CN112699511 A CN 112699511A CN 202110049456 A CN202110049456 A CN 202110049456A CN 112699511 A CN112699511 A CN 112699511A
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周明东
陆宇帆
刘义畅
魏创
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Shanghai Jiaotong University
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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

Additive manufacturing-oriented shell and filling structure collaborative optimization design method
Technical Field
The invention relates to the field of structure optimization design, in particular to a shell and filling structure collaborative optimization design method for additive manufacturing.
Background
The additive manufacturing component is usually designed into a shell and a filling structure, so that the material consumption can be obviously saved, the manufacturing efficiency is improved, and the additive manufacturing component has excellent specific stiffness, specific strength and energy absorption performance and is widely applied to heavy combat gear equipment such as heavy-duty rockets, wide-body airliners and high-speed trains.
Compared with the traditional manufacturing method, although the additive manufacturing processed point by point layer by layer is not limited by the geometrical shape of the component, the suspension area of the component needs to be additionally provided with a supporting structure so as to avoid suspension collapse in the processing process and further cause manufacturing failure, and meanwhile, the manufacturing precision and the manufacturing quality of the component are ensured. The suspension area arranged outside the shell can be supported by an external support structure and is removed after printing is finished; however, the suspension area inside the housing is located inside the structure, and the support structure cannot be removed after printing is completed, and meanwhile, the filling structure also needs to have a self-supporting characteristic in the point-by-point layer-by-layer manufacturing process. Aiming at the design problems of the components, the traditional design surrounds a fixed-shape shell, the internal area of the shell is filled by utilizing a periodic regular-shape filling structure meeting the self-supporting characteristic, and the internal suspension area is perfectly supported through artificial post-processing. The traditional design mode depends on the experience of a designer, repeated trial and error iteration is needed, the design period is long, the material redundancy is high, and the consistency of the shapes of the structure before and after design and manufacture is difficult to grasp.
Aiming at the design problem of a support structure of an additive manufacturing component, Chinese patent CN 110502822A discloses a topological optimization design method of a self-supporting structure for additive manufacturing, which calculates and restricts an overhang angle through a four-unit method, and combines the overhang angle restriction with a punished solid isotropic material method (SIMP) to obtain the self-supporting structure for additive manufacturing, wherein the design method can effectively avoid the overhang characteristic of the optimized structure, effectively reduce the material consumption and the manufacturing cost, and improve the surface quality of the component; however, the method is only directed at the optimization design of the self-supporting structure, and cannot universally solve the topological optimization design of the shell filling structure which is common in the additive manufacturing, and especially considers the cooperative optimization of the shell and the filling structure to obtain the shell filling structure which has better mechanical performance and more consistent shape of the structure before and after the design and the manufacture.
Therefore, those skilled in the art are dedicated to developing a design method for additive manufacturing by cooperating with a filling structure to optimize, which not only can realize an integrated design of a shell and a filling structure, but also can obtain a structure with additive manufacturing suspension-free features, and can directly realize processing through additive manufacturing.
Disclosure of Invention
In view of the above defects in the prior art, the technical problems to be solved by the present invention are that the prior art has a long design period and a large redundancy, cannot meet the requirement of additive manufacturing processing, and cannot universally solve the problem of topology optimization design of a shell filling structure, which is common in additive manufacturing.
In order to achieve the above object, the present invention provides a method for collaborative optimization design of a shell and a filling structure for additive manufacturing, comprising the following steps:
step 1: initializing parameters;
defining a design domain and a non-design domain of a structure according to the shape of the structure;
determining load and boundary conditions based on the actual working condition of the structure, and establishing a finite element model;
initializing optimization parameters and design variables mu and upsilon;
step 2: constructing a parameterized model of the density and the rigidity of the shell filling structure;
based on a density filtering formula and a Heaviside projection format, the design variable mu is converted into a base region by using a two-step filtering method
Figure BDA0002898698090000021
And a housing τ; sequentially using a density filtering and projection method to convert the design variable upsilon into a filling structure psi; according to the base region
Figure BDA0002898698090000022
The shell body tau and the filling structure psi construct a unified expression rho (phi, tau, psi) of unit density; adopting SIMP method to establish parameterized model of unit density and rigidityThe unit density interpolation is integrated in finite element analysis;
and step 3: constructing an additive manufacturing suspension constraint model and a local volume constraint model;
constructing an auxiliary field χ configured to enable an exterior of the structure to be in an intact supported state; obtaining a self-supporting auxiliary field after applying an additive manufacturing filter AM filter to the auxiliary field x
Figure BDA0002898698090000023
The auxiliary field x and the self-supporting auxiliary field
Figure BDA0002898698090000024
Taking the difference as a suspension area, calculating to obtain a suspension volume fraction, and constructing a suspension volume constraint T according to the suspension area and the suspension volume fraction;
taking each unit of the structure as a center, calculating a local volume fraction in a circular neighborhood of each unit, and constructing a local volume constraint l based on a p-norm of the local volume fraction; the local volume fraction is configured as a ratio of a sum of all cell densities within each cell circular neighborhood to a number of cells;
and 4, step 4: constructing topological optimization modeling, and determining a target function and a constraint function;
establishing a shell and filling structure cooperative topology optimization model facing additive manufacturing by adopting a two-field format considering an intermediate design field and a corrosion design field;
controlling the base region by the two-field format
Figure BDA0002898698090000025
And the minimum size of the filling structure psi, avoiding the occurrence of characteristics with no practical manufacturing significance in the optimization result;
taking the weighted flexibility c of the minimized intermediate design and the corrosion design as an objective function to ensure that the structural integral volume constraint G, the suspension volume constraint T and the local volume constraint l meet the limiting conditions;
and 5: solving the finite element model to obtain a design response;
respectively solving finite element models of intermediate design and corrosion design based on structural density information under the current optimization iteration step to obtain structural deformation and rigidity information, further calculating the weighted flexibility c, and simultaneously calculating a constraint function response comprising the integral volume constraint G, the suspension volume constraint T and the local volume constraint l;
step 6: analyzing the sensitivity of the target function and the constraint function;
solving a differential sensitivity value of a target function and each constraint function to the design variable mu and the design variable upsilon under the current iteration step according to an analytic sensitivity formula of each design response to the design variable mu and the design variable upsilon;
and 7: optimizing and solving; solving a shell and filling structure cooperative topology optimization model facing additive manufacturing by using a moving asymptote algorithm MMA, and updating the design variable mu and the design variable upsilon;
and 8: if the change rate of the weighting compliance c is lower than 0.2% in the current 5 iteration steps and the base region
Figure BDA0002898698090000031
The projection sharpness β of the Heaviside function for the housing τ and the filling structure ψ reaches a preset maximum value β with optimization iterationmaxIf yes, ending; otherwise, turning to the step 3.
In the technical scheme, the optimization result with a small number of gray scale units is obtained through the steps, the suspension constraint function value is small, and the post-processing can be further carried out.
In one technical scheme of the invention, the method further comprises a post-processing method, wherein the post-processing method comprises the following steps:
converting the optimized result with the gray scale unit into a clear 0-1 result by adopting a projection mode with a threshold value of 0.5;
the remaining small amount of hanging elements is detected using an additive manufactured filter and removed from the structure.
In one technical solution of the present invention, the step 2 includes the following steps:
step 2.1: the density filtering and Heaviside projections are as follows:
Figure BDA0002898698090000032
Figure BDA0002898698090000033
wherein the content of the first and second substances,
Figure BDA00028986980900000311
and
Figure BDA0002898698090000034
respectively the density field to be filtered or projected,
Be,R＝{i:||xi-xer is less than or equal to | l, i belongs to omega, is a set of all units in a neighborhood of a unit radius R away from e,
Hei＝max(r-||xi-xe0) is a weight function of density filtering,
beta and eta are respectively the sharpness and the threshold of the Heaviside function;
the threshold value eta of the intermediate design is 0.50, and the threshold value eta of the corrosion design is 0.70;
step 2.2: for smooth base region after density filtration
Figure BDA0002898698090000035
Performing normalized gradient mode calculation to obtain shell interface
Figure BDA0002898698090000036
The calculation formula is as follows:
Figure BDA0002898698090000037
wherein the content of the first and second substances,
Figure BDA0002898698090000038
is composed of
Figure BDA0002898698090000039
α is a normalization coefficient;
step 2.3:
Figure BDA00028986980900000310
performing Heaviside projection treatment once again to obtain the shell tau;
step 2.4: sequentially carrying out density filtering and Heaviside projection processing on the design variable upsilon to obtain the filling structure psi;
step 2.5: a unified expression ρ (Φ, τ, ψ) for cell density was constructed as follows:
Figure BDA0002898698090000041
step 2.6: establishing a parameterized model of the unit density and the rigidity by adopting an SIMP method, and integrating the unit density interpolation into finite element analysis;
Figure BDA0002898698090000042
wherein E ismin＝10-9The minimum value of the elastic modulus is used to avoid matrix singularity, and p is 3 as a penalty factor.
In one technical solution of the present invention, a construction formula of the auxiliary field χ in the step 3 is as follows:
Figure BDA0002898698090000043
in one technical solution of the present invention, a construction formula of the suspension volume constraint T in the step 3 is as follows:
Figure BDA0002898698090000044
wherein, VeIs a unit volume, I is an identity matrix, εrIs a tolerance.
In one embodiment of the present invention, the local volume constraint l in step 3 is constructed as follows:
step 3.1: calculating the circular neighborhood centered on each cell
Figure BDA0002898698090000045
Ratio of sum of all cell densities to number of cells:
Figure BDA0002898698090000046
step 3.2: the local volume constraint/, is as follows:
Figure BDA0002898698090000047
wherein N is the total unit number of the design domain,
Figure BDA0002898698090000048
is set to p norm parameterl＝8。
In one technical solution of the present invention, the unified expression formula of the density of each unit of the corrosion design in the step 4 is as follows:
Figure BDA0002898698090000049
wherein the content of the first and second substances,
Figure BDA00028986980900000410
and
Figure BDA00028986980900000411
can be obtained from the Heaviside function with η ═ 0.70.
In one embodiment of the present invention, the formula of the overall volume constraint G in step 4 is as follows:
Figure BDA00028986980900000412
wherein the content of the first and second substances,
Figure BDA00028986980900000413
is an approximate density.
In one technical solution of the present invention, the shell and filling structure collaborative topology optimization model in step 4 is constructed as follows:
Figure BDA0002898698090000051
where c is the weighted compliance of the integrated intermediate and corrosion designs, ω is the weighting factor, and the displacement response is obtained by solving for KU-F.
In one technical solution of the present invention, in the step 6, an analytical sensitivity formula of the objective function, the integral volume constraint G, the suspension volume constraint T, and the local volume constraint l to the design variable μ and the design variable υ is as follows:
Figure BDA0002898698090000052
Figure BDA0002898698090000053
Figure BDA0002898698090000054
Figure BDA0002898698090000055
Figure BDA0002898698090000056
Figure BDA0002898698090000057
Figure BDA0002898698090000058
Figure BDA0002898698090000059
compared with the prior art, the implementation of the invention has at least the following beneficial technical effects:
(1) according to the technical scheme disclosed by the invention, two design variables are constructed in the topological optimization model to respectively control the structure of the shell and the filler, so that the integrated design of the shell and the filler structure is realized, the thought of the shell and filler separation design in the traditional scheme is broken through, and the structure with better mechanical property is obtained;
(2) according to the technical scheme disclosed by the invention, suspension constraint is integrated in a topology optimization model, a structure with additive manufacturing non-suspension characteristics is obtained, and the structure can be directly processed in an additive manufacturing mode;
(3) according to the technical scheme disclosed by the invention, two field formats are introduced into the topological optimization model, the phenomenon that the optimization result has the characteristics without actual manufacturing significance is avoided, and the optimization result can be directly processed in an additive manufacturing mode.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a schematic flow chart of a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of the parametric modeling of the structure according to a preferred embodiment of the present invention;
FIG. 3 is a schematic view of the additive manufacturing suspension region field calculation process according to a preferred embodiment of the invention;
FIG. 4 is a schematic diagram of the cantilever beam structure design domain, loading and boundary conditions of a preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of the resulting cantilever beam structure incorporating suspension constraint of the embodiment of FIG. 4;
FIG. 6 is a schematic diagram of the resulting cantilever beam structure of the embodiment of FIG. 4 without the introduction of suspension constraints;
FIG. 7 is a printed result diagram of a cantilevered beam structure of the embodiment of FIG. 4 without the introduction of suspension constraints;
figure 8 is a printed result diagram of a cantilevered beam structure incorporating suspension constraint according to the embodiment of figure 4.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
In the drawings, structurally identical elements are represented by like reference numerals, and structurally or functionally similar elements are represented by like reference numerals throughout the several views. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. The thickness of the components may be exaggerated where appropriate in the figures to improve clarity.
In the description of the embodiments of the present application, it should be clear that the terms "center", "upper", "lower", "left", "right", "inner", "outer", "top", "bottom", "side", "vertical", "horizontal", etc. indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the embodiments of the present application and simplifying the description, but do not indicate or imply that the described devices or elements must have specific orientations or positional relationships, i.e., cannot be construed as limiting the embodiments of the present application; furthermore, the terms "first," "second," "third," "fourth," and the like are used merely to facilitate description or to simplify description, and do not indicate or imply importance.
The embodiment provides an additive manufacturing-oriented casing and filling structure collaborative optimization design method, which comprises the following steps:
the method comprises the following steps:
step 1: initializing parameters;
defining a design domain and a non-design domain of the structure according to the shape of the structure;
determining load and boundary conditions based on the actual working condition of the structure, and establishing a finite element model;
initializing optimization parameters and design variables mu and upsilon;
step 2: constructing a parameterized model of the density and the rigidity of the shell filling structure;
based on a density filtering formula and a Heaviside projection format, a two-step filtering method is applied to convert a design variable mu into a base region
Figure BDA0002898698090000071
And a housing τ; sequentially using a density filtering and projection method to convert a design variable upsilon into a filling structure psi; according to the base region
Figure BDA0002898698090000072
The shell tau and the filling structure psi construct a unified expression rho (phi, tau, psi) of the unit density; establishing a parameterized model of the unit density and the rigidity by adopting an SIMP method, and integrating the unit density interpolation into finite element analysis;
and step 3: constructing an additive manufacturing suspension constraint model and a local volume constraint model;
constructing an auxiliary field χ configured to enable an exterior of the structure to be in an intact supported state; obtaining a self-supporting auxiliary field after applying an additive manufacturing filter AM filter to the auxiliary field x
Figure BDA0002898698090000073
The auxiliary field x and the self-supporting auxiliary field
Figure BDA0002898698090000074
Taking the difference as a suspension area, calculating to obtain a suspension volume fraction, and constructing a suspension volume constraint T according to the suspension area and the suspension volume fraction;
calculating local volume fractions in circular neighborhoods of all units by taking all units of the structure as centers, and constructing local volume constraints l on the basis of p norms of the local volume fractions; the local volume fraction is configured as a ratio of the sum of all cell densities within each cell circular neighborhood to the number of cells;
and 4, step 4: constructing topological optimization modeling, and determining a target function and a constraint function;
establishing a shell and filling structure cooperative topology optimization model facing additive manufacturing by adopting a two-field format considering an intermediate design field and a corrosion design field;
controlling base regions by two-field format
Figure BDA0002898698090000075
And the minimum size of the filling structure psi, so as to avoid the characteristic that the optimization result has no practical manufacturing significance;
taking the weighted flexibility c of the minimized intermediate design and the corrosion design as an objective function to ensure that the whole volume constraint G, the suspension volume constraint T and the local volume constraint l of the structure meet the limiting conditions;
and 5: solving the finite element model to obtain a design response;
respectively solving finite element models of the intermediate design and the corrosion design based on structural density information under the current optimization iteration step to obtain structural deformation and rigidity information, further calculating weighted flexibility c, and simultaneously calculating constraint function response comprising integral volume constraint G, suspension volume constraint T and local volume constraint l;
step 6: analyzing the sensitivity of the target function and the constraint function;
solving a differential sensitivity value of the target function and each constraint function to the design variable mu and the design variable upsilon under the current iteration step according to an analytic sensitivity formula of each design response to the design variable mu and the design variable upsilon;
and 7: optimizing and solving; solving a shell and filling structure cooperative topology optimization model facing additive manufacturing by using a moving asymptote algorithm MMA, and updating a design variable mu and a design variable upsilon;
and 8: if the change rate of the weighting compliance c is lower than 0.2% in the current 5 iteration steps and the base region
Figure BDA0002898698090000081
The projection sharpness β of the Heaviside function for the housing τ and the filling structure ψ reaches a preset maximum value β with optimization iterationmaxTurning to step 9; otherwise, turning to the step 3;
and step 9: converting the optimized result with the gray scale unit into a clear 0-1 result by adopting a projection mode with a threshold value of 0.5; the remaining small amount of hanging elements is detected using an additive manufactured filter and removed from the structure.
The present example further discloses a further implementation manner of the above scheme as follows:
fig. 1 is a schematic flow chart of this embodiment, which is specifically as follows:
step 1: as shown in fig. 4, a cantilever beam design domain with dimensions 500 × 300 is defined, and a non-design domain of 6 × 6 is arranged at the load and fixing boundary; establishing a finite element model, fixing all nodes on the left end surface of the model, and applying a point load F which is vertically downward to the midpoint of the right end surface of the model to be 100N;
the optimization parameters are initialized as follows: upper limit of volume fraction V*0.45, upper limit of local volume fraction alpha is 0.65, and the radius of constraint of density filter and local volume is R1＝20，R2＝6，R3＝2.5，R46, suspension constraint tolerance εr＝6×10-5(ii) a The material is titanium alloy with elastic modulus E0108GPa, poisson's ratio ν 0.33;
sharpness maximum β of the Heaviside functionmaxTwo design variables μ and ν are set to all cell densities V, respectively, 64*And a matrix of alpha.
Step 2: as shown in FIG. 2, a two-step filtering method is adopted for the first design variable mu to obtain a base region
Figure BDA0002898698090000082
And a shell τ, in this embodiment, the density filtering and the Heaviside projection of the two-step filtering method are respectively as follows:
Figure BDA0002898698090000083
Figure BDA0002898698090000084
wherein the content of the first and second substances,
Figure BDA0002898698090000085
and
Figure BDA0002898698090000086
density fields requiring filtering or projection processing, Be,R＝{i:||xi-xeR is less than or equal to | l, i belongs to omega } is a set of all units in the neighborhood of the unit radius R at the distance of e, Hei＝max(r-||xi-xe0) is the weight function of the density filtering. Beta and eta are respectively sharpness and threshold of the Heaviside function, wherein eta is 0.50 for the intermediate design, and eta is 0.70 for the corrosion design;
for smooth base region after density filtration
Figure BDA0002898698090000087
Performing normalized gradient mode calculation to obtain shell interface
Figure BDA0002898698090000088
The calculation formula is as follows:
Figure BDA0002898698090000089
wherein the content of the first and second substances,
Figure BDA00028986980900000810
is composed of
Figure BDA00028986980900000811
α is a normalization coefficient;
Figure BDA00028986980900000812
and finally obtaining the shell tau through once Heaviside projection treatment.
And sequentially carrying out density filtering and Heaviside projection processing on the second design variable upsilon to obtain a filling structure psi.
Accordingly, the uniform expression formula of the cell density is as follows:
Figure BDA0002898698090000091
adopting a Solid Isotropic Material Process (SIMP) with punishment to establish a parameterized model of unit density and rigidity, and integrating unit density interpolation into finite element analysis:
Figure BDA0002898698090000092
wherein E ismin＝10-9The minimum value of the elastic modulus is used to avoid matrix singularity, and p is 3 as a penalty factor.
And step 3: at the base region
Figure BDA0002898698090000093
On the basis of the shell tau and the filling structure psi, an auxiliary field chi is constructed to completely fill the outer region of the structure with the material, as shown below:
Figure BDA0002898698090000094
application of auxiliary fieldsχ, the outer hanging region of the housing is considered to be well supported, while the outer hanging region is in actual manufacture supported by the outer support structures, which can be removed after printing is complete. After that, the AM filter of the additive manufacturing filter is adopted to remove the suspended area in the shell and the area where the filling structure can not be self-supported, and a self-supporting auxiliary field is obtained
Figure BDA0002898698090000095
By calculating the auxiliary field χ and the self-supporting auxiliary field
Figure BDA0002898698090000096
To obtain a suspended area field.
Constructing an additive manufacturing suspension constraint T:
Figure BDA0002898698090000097
wherein, VeIs the unit volume, and I is the identity matrix. Tolerance epsilonrDetermining the degree of tightness of the suspension constraint if erToo small, leading to difficulties in topology optimization convergence; if epsilonrToo large, resulting in a large number of suspension areas that are not guaranteed to be self-supporting.
The local volume constraint is used to prevent bulk material buildup in the fill structure to form a fill structure with porous characteristics.
First, a circular neighborhood centered on each cell is calculated
Figure BDA0002898698090000098
All cell densities and ratio to number of cells:
Figure BDA0002898698090000099
local volume constraint by limiting the maximum local volume fraction unit, a porous filling structure is obtained, the local volume constraint function l can be defined by
Figure BDA00028986980900000910
The p-norm of (d) constitutes:
Figure BDA00028986980900000911
wherein N is the total unit number of the design domain, and the p-norm parameter is set as pl＝8。
And 4, step 4: and establishing a collaborative topological optimization model of the shell and the filling structure facing the additive manufacturing. And the minimum sizes of the base region and the filler are controlled by adopting a two-field format considering the intermediate design field and the corrosion design field, so that the characteristic similar to the size of the filler in the intermediate design base region is avoided.
The density of each unit of the corrosion design is uniformly expressed by a formula:
Figure BDA0002898698090000101
wherein in the design of corrosion
Figure BDA0002898698090000102
And
Figure BDA0002898698090000103
it can be obtained from the Heaviside function where η is 0.70.
Additive manufacturing oriented collaborative topology optimization model of shell and filling structure:
Figure BDA0002898698090000104
wherein c is the weighted compliance of the integrated intermediate design and the corrosion design, ω is a weight factor, G is the integral volume constraint, T is the suspension volume constraint, and l is the local volume constraint. The displacement response is obtained by solving for KU — F.
And 5: respectively solving finite element of middle design and corrosion design of shell filling structure based on density information of currently optimized iteration step lower shell filling structureModel, obtaining two designed displacement responses U and UeroFurther, the weighted compliance c is calculated, and the following constraint function is calculated
(1) Overall volume constraint G:
Figure BDA0002898698090000105
wherein the content of the first and second substances,
Figure BDA0002898698090000106
for approximate density, the integral volume constraint of approximate density is used, so as to avoid the occurrence of a large pore area without a filling structure inside the structure;
(2) local volume constraint l:
Figure BDA0002898698090000107
(3) suspension volume constraint T:
Figure BDA0002898698090000108
step 6: the analytical sensitivity formula of the objective function c and the constraint function G, T, l on the design variables mu and upsilon is derived as follows:
Figure BDA0002898698090000109
Figure BDA00028986980900001010
Figure BDA0002898698090000111
Figure BDA0002898698090000112
Figure BDA0002898698090000113
Figure BDA0002898698090000114
Figure BDA0002898698090000115
Figure BDA0002898698090000116
step 7 to step: adopting a mobile moving asymptote algorithm MMA to solve a topological optimization model of the structure in the printing direction from south to north, and obtaining a topological optimization result meeting the suspension characteristics without additive manufacturing, as shown in FIG. 5, for comparison, as shown in FIG. 6, the topological optimization result without considering suspension constraint comprises 52544 suspension units, and the structure cannot be completely processed by additive manufacturing;
fig. 7 is an actual print of the structure of fig. 6, fig. 7 shows that the topological optimization without considering the suspension constraint has poor print quality and large areas of collapse, crack, and out-of-line, and fig. 8 shows good geometric integrity of the topological optimization with considering the suspension constraint of the structure of fig. 5. The effectiveness of the method disclosed by the technical scheme is fully demonstrated by the embodiment.
The technical scheme also discloses another embodiment, and on the basis of the embodiment, the shell and the filling structure are separately designed, namely the shell is firstly designed, then the filling structure is designed, and the suspension unit at the junction of the shell and the filling structure is eliminated through manual post-processing, so that the structure without additive manufacturing suspension characteristics is obtained.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A casing and filling structure collaborative optimization design method for additive manufacturing is characterized by comprising the following steps:
step 1: initializing parameters;
defining a design domain and a non-design domain of a structure according to the shape of the structure;
determining load and boundary conditions based on the actual working condition of the structure, and establishing a finite element model;
initializing optimization parameters and design variables mu and upsilon;
step 2: constructing a parameterized model of the density and the rigidity of the shell filling structure;
based on a density filtering formula and a Heaviside projection format, the design variable mu is converted into a base region by using a two-step filtering method
Figure FDA0002898698080000011
And a housing τ; sequentially using a density filtering and projection method to convert the design variable upsilon into a filling structure psi; according to the base region
Figure FDA0002898698080000012
The shell body tau and the filling structure psi construct a unified expression rho (phi, tau, psi) of unit density; establishing a parameterized model of the unit density and the rigidity by adopting an SIMP method, and integrating the unit density interpolation into finite element analysis;
and step 3: constructing an additive manufacturing suspension constraint model and a local volume constraint model;
constructing an auxiliary field χ configured to enable an exterior of the structure to be in an intact supported state; to the aboveObtaining a self-supporting auxiliary field after applying an additive manufacturing filter AM filter to the auxiliary field
Figure FDA0002898698080000014
The auxiliary field x and the self-supporting auxiliary field
Figure FDA0002898698080000015
The difference of (1) is used as a suspension area, a suspension volume fraction is obtained through calculation, and a suspension volume constraint T is constructed according to the suspension area and the suspension volume fraction;
taking each unit of the structure as a center, calculating a local volume fraction in a circular neighborhood of each unit, and constructing a local volume constraint l based on a p-norm of the local volume fraction; the local volume fraction is configured as a ratio of a sum of all cell densities within each cell circular neighborhood to a number of cells;
and 4, step 4: constructing topological optimization modeling, and determining a target function and a constraint function;
establishing a shell and filling structure cooperative topology optimization model facing additive manufacturing by adopting a two-field format considering an intermediate design field and a corrosion design field;
controlling the base region by the two-field format
Figure FDA0002898698080000013
And the minimum size of the filling structure psi, avoiding the occurrence of characteristics with no practical manufacturing significance in the optimization result;
taking the weighted flexibility c of the minimized intermediate design and the corrosion design as an objective function to ensure that the structural integral volume constraint G, the suspension volume constraint T and the local volume constraint l meet the limiting conditions;
and 5: solving the finite element model to obtain a design response;
respectively solving finite element models of intermediate design and corrosion design based on structural density information under the current optimization iteration step to obtain structural deformation and rigidity information, further calculating the weighted flexibility c, and simultaneously calculating a constraint function response comprising the integral volume constraint G, the suspension volume constraint T and the local volume constraint l;
step 6: analyzing the sensitivity of the target function and the constraint function;
solving a differential sensitivity value of a target function and each constraint function to the design variable mu and the design variable upsilon under the current iteration step according to an analytic sensitivity formula of each design response to the design variable mu and the design variable upsilon;
and 7: optimizing and solving; solving a shell and filling structure cooperative topology optimization model facing additive manufacturing by using a moving asymptote algorithm MMA, and updating the design variable mu and the design variable upsilon;
and 8: if the change rate of the weighting compliance c is lower than 0.2% in the current 5 iteration steps and the base region
Figure FDA0002898698080000021
The projection sharpness β of the Heaviside function for the housing τ and the filling structure ψ reaches a preset maximum value β with optimization iterationmaxIf yes, ending; otherwise, turning to the step 3.
2. The collaborative optimization design method according to claim 1, further comprising a post-processing method, the post-processing method comprising the steps of:
converting the optimized result with the gray scale unit into a clear 0-1 result by adopting a projection mode with a threshold value of 0.5;
the remaining small amount of hanging elements is detected using an additive manufactured filter and removed from the structure.
3. The collaborative optimization design method according to claim 1, wherein the step 2 includes the steps of:
step 2.1: the density filtering and Heaviside projections are as follows:
Figure FDA0002898698080000022
Figure FDA0002898698080000023
wherein the content of the first and second substances,
Figure FDA0002898698080000024
and
Figure FDA0002898698080000025
respectively the density field to be filtered or projected,
Be,R＝{i:||xi-xer is less than or equal to | l, i belongs to omega, is a set of all units in a neighborhood of a unit radius R away from e,
Hei＝max(r-||xi-xe0) is a weight function of density filtering,
beta and eta are respectively the sharpness and the threshold of the Heaviside function;
the threshold value eta of the intermediate design is 0.50, and the threshold value eta of the corrosion design is 0.70;
step 2.2: for smooth base region after density filtration
Figure FDA0002898698080000026
Performing normalized gradient mode calculation to obtain shell interface
Figure FDA0002898698080000027
The calculation formula is as follows:
Figure FDA0002898698080000028
wherein the content of the first and second substances,
Figure FDA0002898698080000029
is composed of
Figure FDA00028986980800000210
α is a normalization coefficient;
step 2.3:
Figure FDA00028986980800000211
performing Heaviside projection treatment once again to obtain the shell tau;
step 2.4: sequentially carrying out density filtering and Heaviside projection processing on the design variable upsilon to obtain the filling structure psi;
step 2.5: building unified expressions of cell density
Figure FDA0002898698080000031
The following were used:
Figure FDA0002898698080000032
step 2.6: establishing a parameterized model of the unit density and the rigidity by adopting an SIMP method, and integrating the unit density interpolation into finite element analysis;
Figure FDA0002898698080000033
wherein E ismin＝10-9The minimum value of the elastic modulus is used to avoid matrix singularity, and p is 3 as a penalty factor.
4. The collaborative optimal design method according to claim 3, wherein the construction formula of the auxiliary field χ in the step 3 is as follows:
Figure FDA0002898698080000034
5. the collaborative optimization design method according to claim 4, wherein the suspension volume constraint T in the step 3 is constructed according to the following formula:
Figure FDA0002898698080000035
wherein, VeIs a unit volume, I is an identity matrix, εrIs a tolerance.
6. The collaborative optimization design method according to claim 5, wherein the local volume constraint/' in step 3 is constructed as follows:
step 3.1: calculating the circular neighborhood centered on each cell
Figure FDA0002898698080000036
Ratio of sum of all cell densities to number of cells:
Figure FDA0002898698080000037
step 3.2: the local volume constraint/, is as follows:
Figure FDA0002898698080000038
wherein N is the total unit number of the design domain,
Figure FDA0002898698080000039
is set to p norm parameterl＝8。
7. The collaborative optimization design method according to claim 6, wherein the cell densities of the corrosion design in the step 4 are uniformly expressed by the following formula:
Figure FDA0002898698080000041
wherein the content of the first and second substances,
Figure FDA0002898698080000042
and
Figure FDA0002898698080000043
can be obtained from the Heaviside function with η ═ 0.70.
8. The collaborative optimization design method according to claim 7, wherein the overall volume constraint G in step 4 is formulated as follows:
Figure FDA0002898698080000044
wherein the content of the first and second substances,
Figure FDA0002898698080000045
is an approximate density.
9. The collaborative optimal design method according to claim 8, wherein the housing and filling structure collaborative topology optimization model in the step 4 is constructed as follows:
Figure FDA0002898698080000046
where c is the weighted compliance of the integrated intermediate and corrosion designs, ω is the weighting factor, and the displacement response is obtained by solving for KU-F.
10. The collaborative optimization design method according to claim 9, wherein in the step 6, analytical sensitivity formulas of the objective function, the global volume constraint G, the suspended volume constraint T, and the local volume constraint l on the design variable μ and the design variable ν are as follows:
Figure FDA0002898698080000047
Figure FDA0002898698080000048
Figure FDA0002898698080000049
Figure FDA0002898698080000051
Figure FDA0002898698080000052
Figure FDA0002898698080000053
Figure FDA0002898698080000054
Figure FDA0002898698080000055
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