CN111339617B - Multi-material topology optimization design method for additive manufacturing - Google Patents
Multi-material topology optimization design method for additive manufacturing Download PDFInfo
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Abstract
The invention relates to a multi-material topology optimization design method for additive manufacturing, which specifically comprises the following steps: step 1, defining a topology optimization design domain by combining with an actual engineering problem, and carrying out continuum multi-material topology optimization; step 2, generating an initial truss layout for additive manufacturing according to a topological optimization design domain, and calculating a mapping matrix of a multi-material topological optimization result and the truss layout on the basis; step 3, evaluating the effectiveness of the cell element according to the multi-material topological optimization result and the mapping matrix, and further deleting invalid/inefficient cell elements without strain energy/low strain energy in the initial design domain; and 4, obtaining a truss structure design result in the effective cell area by using a continuous/discrete mapping method according to the topological optimization result and the mapping matrix. The method can effectively balance the design efficiency and quality in the design process of the multi-material truss structure, and ensures clear multi-material distribution and good manufacturability suitable for additive manufacturing.
Description
Technical Field
The invention belongs to the field of engineering structure design and analysis, and particularly relates to a multi-material topology optimization design method for additive manufacturing.
Background
The core idea of light weight design is to arrange appropriate materials at appropriate positions, and additive manufacturing provides an effective manufacturing means for preparation of light weight design, so that a multi-material topology optimization design method suitable for additive manufacturing characteristics is urgently needed to be developed for realizing light weight to the greatest extent.
The invention discloses a structural topology optimization design method considering load action times, and particularly discloses a structural topology optimization design method considering load action times. The invention applies the equivalent method of random load multiple action and the moving asymptote algorithm to the reliable topological optimization design of the structure, improves the safety and the reliability of the structure work compared with the deterministic topological optimization design, and overcomes the defect that the reliable topological optimization design only considering the static load action can not effectively express the reliability time attribute.
The invention discloses a topological optimization method for a shell-filling structure, belongs to the field related to structure optimization design, and particularly discloses a topological optimization method for a shell-filling structure. The invention adopts the super-unit technology to establish the connection between the macroscopic structure and the mesostructure, can obtain the optimal filling distribution through the optimization of the macroscopic scale, automatically obtain the shell with uniform thickness, and simultaneously can obtain the optimal topological configuration of the filling porous structure through the optimization of the mesoscale.
The invention discloses a topological optimization design method of a connected structure in additive manufacturing, which is used for solving the technical problem of poor practicability of the existing topological optimization method of the connected structure. The technical scheme is that a certain number of closed hole features are arranged in an entity design area, and the topological layout evolution of the structure is driven through the actions of hole movement, deformation, fusion, shrinkage, expansion and the like. In addition, the center point of each hole feature is controlled to be outside the design domain, so that the hole features cannot completely enter the design domain to form a closed hole, thereby achieving the purpose of structural communication.
The document "Alzahrani M, Choi S K, Rosen D W.design of truss-like structure using relative density mapping method [ J ]. Materials & Design,2015,85: 349-. However, the method disclosed in the literature can only effectively deal with the problem of single material topological configuration design, and cannot be applied to the design of a multi-material truss-like structure for additive manufacturing.
Disclosure of Invention
In order to realize the light weight to the maximum extent, the method aims to generate the multi-material truss structure design according to the mapping of the multi-material topological optimization result. The method constructs a mapping relation based on a distance relation between a topological optimization design domain and an additive manufacturing truss structure design domain. The continuous body multi-material topological optimization design result is mapped and converted into a truss structure design result, the material attributes of all rod pieces of the truss in the truss structure design are obtained through the continuous type/discrete type mapping method, and the section scales of all rod pieces of the truss are obtained according to the continuous body topological result mapping, so that the multi-material truss structure which is good in performance and clear in boundary and suitable for additive manufacturing can be provided.
The technical scheme of the invention is to provide a multi-material additive manufacturing structure design method, which is characterized by comprising the following steps: the method specifically comprises the following steps:
Step 2, mapping between a multi-material topological optimization result and truss design parameters according to a topological optimization design domain and an additive manufacturing initial truss layout;
and step 3: calculating the validity of the cells according to the design domain of the topological optimization and the initial truss layout of the additive manufacturing, and deleting the inefficient cells.
And 4, obtaining a truss structure design result in an effective cell range by using a continuous mapping method or a discrete mapping method according to the multi-material topological optimization result and the mapping matrix.
Further, in step 2, the design variable field information rho of each material obtained in step 1 through the multi-material topology optimization is obtainedimThe mapping relationship between the design variable field information and the truss design parameters is represented by the following formula:
wherein, wjmRepresenting the weight of the m-numbered material mapping of the structure j in the additive manufacturing truss design domain, wherein the structure j can be a truss/face/body;
ρimrepresenting design variables corresponding to m-number materials of a unit i in the multi-material topological optimization design domain;
rijrepresents the distance between cell i and structure j;
l represents the size of structure j.
Further, in step 3, through the topology-optimized design domain and the initial truss layout of the additive manufacturing, the relative position relationship between the unit in the topology-optimized design domain and the cell in the initial truss layout of the additive manufacturing can be obtained.
Further, in step 3, the design variable field information ρ of each material obtained in step 1 is combinedimUnit displacement u of structureiAnd unit stiffness kiThe information can be used for calculating the effectiveness of each cell in the additive manufacturing truss layout, and the expression formula of the effectiveness of the cells in the truss structure is as follows:
wherein, EfcAs the validity of cell c, uiAnd kiUnit displacement and unit stiffness; r isicRepresents the distance between unit i and cell c; l represents the area, area of the body cell, or the length of the body diagonal.
Further, in step 4, the continuous mapping method includes the following steps:
step one, calculating the material attribute of the truss according to the truss structure design parameter after mapping obtained in the step 2 and the material attribute in the material library;
secondly, filtering the material properties of the trusses according to the position relationship among the trusses and the material property calculation result to ensure that a material distribution interface is clear;
step three, calculating the cross section size of the truss according to the punished material attribute of the truss and the multi-material topological optimization truss mapping result;
and fourthly, obtaining a multi-material truss design result according to the truss material attribute and the cross section size obtained by the multi-material relative density mapping method.
Further, in step 4, the discrete mapping method includes the following steps:
firstly, selecting cell material according to a multi-material topological optimization result and a mapping matrix;
selecting materials of the truss according to the multi-material topological optimization result, the mapping matrix and the materials of the truss-related cells;
step three, calculating the cross section size of the truss according to the material attribute selected by the truss and the multi-material topological optimization truss mapping result;
and fourthly, obtaining a multi-material truss design result according to the truss material attribute and the cross section size obtained by the multi-material relative density mapping method.
Compared with the prior art, the invention has the following advantages: the continuum multi-material topological optimization and the relative density mapping are successfully combined, and compared with the prior art, the optimization efficiency and the optimization effect are well balanced, and a good multi-material truss structure optimization result can be efficiently obtained. The continuous mapping method and the discrete mapping method provided by the invention can well solve the optimization problems of the material property of the truss and the section size of the truss in the optimization problem of the multi-material truss structure, and a clear material interface is formed.
Drawings
FIG. 1 is a schematic diagram of an embodiment based on an initial truss design;
FIG. 2 is a result of multi-material topology optimization;
FIG. 3 shows the result of the continuous mapping method;
FIG. 4 is a result of a discrete mapping method;
FIG. 5 shows the cell-structure distance rijA schematic diagram;
FIG. 6 shows the unit-cell distance ricA schematic diagram;
FIG. 7 is a schematic diagram of a material property penalty function;
fig. 8 is a flow chart of a multi-material additive manufacturing structure topology optimization design method.
Detailed Description
In order to more clearly illustrate the technical route of the method provided by the invention, the invention is further explained by a two-dimensional cantilever beam embodiment in combination with the attached drawings. It is to be noted that the scope of application of the present invention is not limited to the embodiment.
As shown in fig. 1, this embodiment provides a method for designing a multi-material additive manufacturing structure, which specifically includes the following steps:
step 1: according to the practical problem of the actual engineering, defining a topological optimization design domain, carrying out multi-material topological optimization, and obtaining the distribution of each material, namely the design variable field information rho of each materialim. Meanwhile, the unit displacement u is obtained by finite element analysis in the topological optimization processiAnd unit stiffness kiThe information may also be saved for later use.
In this embodiment, as shown in fig. 1(a), an Alternating Active-phase (aap) algorithm is used to perform multi-material topology optimization, the topology design domain is set as a two-dimensional design domain composed of 80 × 40 units, each unit has a length and width of 1mm, the stiffness of two materials in the material library is respectively set as material No. 1 (soft material) of 1N/mm and material No. 2 (hard material) of 3N/mm, the allowable material amount is 0.2 × total area, and the optimization result is shown in fig. 2, wherein the black part is a hard material structural part and the gray part is a soft material structural part.
And 2, mapping between the multi-material topological optimization result and truss design parameters according to the topological optimization design domain and the initial truss layout of additive manufacturing.
In this example, an additive manufactured initial truss layout of 16 x 8 square cells, each 5mm long and wide, was selected, as shown in fig. 1 (b).
According to the topology optimization design domain and the initial truss layout of additive manufacturing, the relative position relation between the unit in the topology optimization design domain and the truss in the additive manufacturing design can be obtained, and the multi-material topology optimization variable field information rho obtained in the step 1 is combined withim. The mapping relationship between the design variable field information and the truss design parameters is represented by the following formula:
wherein, wjmRepresenting the weight of the m-numbered material mapping of the structure j in the additive manufacturing truss design domain, wherein the structure j can be a truss/face/body;
ρimrepresenting design variables corresponding to m-number materials of a unit i in the multi-material topological optimization design domain;
rijrepresents the distance between cell i and structure j;
Ljthe dimension of structure j, in this embodiment the length of the truss, is shown.
The designer can define the structure size by himself according to the set truss type, for example, the size of a planar rectangular structure can be defined as the area, and can also be defined as the diagonal length.
And step 3: and calculating the effectiveness of the cells according to the topological optimization design domain and the initial truss layout of the additive manufacturing, and deleting the low-efficiency cells.
Similar to step 2, as shown in fig. 1(a) (b), the relative position relationship between the unit in the topology optimization design domain and the cell in the initial truss layout of the additive manufacturing can be obtained by the topology optimization design domain and the initial truss layout of the additive manufacturing, and the design variable field information ρ of each material obtained in step 1 is combinedimUnit displacement u of structureiAnd unit stiffness kiThe information can be used for calculating the effectiveness of each cell in the additive manufacturing truss layout, and the expression formula of the effectiveness of the cells in the truss structure is as follows:
wherein, EfcAs the validity of cell c, uiAnd kiUnit node displacement and unit stiffness; r isicRepresents the distance between unit i and cell c; l represents the area/body diagonal length of the area/body cell.
When EfcWhen the values satisfy the following relationship, cell c and its corresponding truss are deleted from the truss design.
Efc＜thEf
Wherein thEfIs a preset validity threshold.
In this embodiment, thEfIs set as the maximum Ef in each cell of the trussc0.1 times of that of (A), FIGS. 3 andin comparison with fig. 4, the erased cell in fig. 1(b) is the erased cell due to the low availability of the cell.
And 4, obtaining a truss structure design result in the effective cell area by using a continuous mapping method or a discrete mapping method according to the topological optimization result and the mapping matrix. As shown in fig. 3 and 4, respectively.
In this step, the continuous mapping method and the discrete mapping method are also divided into a plurality of steps. As will be explained in detail below.
In the step (i) of the continuous type mapping method, calculating the material attribute of the truss according to the structural design parameters of the truss after mapping obtained in the step (2) and the material attribute in the material library, wherein the material attribute calculation formula of the truss is as follows:
wherein EjCalculating the material property of the truss j; emIs the material stiffness of material No. m.
In addition, wc can also be used in this stepjmIn this step w is replacedjm：
In this embodiment, we use wcjmIn place of wjm。
And secondly, performing truss material attribute filtering according to the position relation between trusses and the material attribute calculation result in the step II of a continuous mapping method so as to ensure that a material distribution interface is clear. The filtering formula for the material properties is as follows:
wherein
To passMaterial properties of the filtered truss j; ehIs the material property of truss h; r isminIs the filtration radius of the filter; r isjhThe center distance between a truss j and a truss h; the truss h needs to satisfy rjh＜rminThe conditions of (1).
Is obtained by
Then, to
Further processed to ensure
Approaching the material property of a certain material in the predetermined material library.
Wherein
The penalized material property of truss j;
Em-1and EmMaterial properties of No. m-1 and No. m materials in a preset material set are set;
pE is a material property penalty coefficient.
The influence of the penalty function on the material property is shown in fig. 7, and the material property of each truss after penalty is close to the specific material in the material library, and the distribution in this embodiment can be seen in the gray truss (truss with material property close to material No. 1) and black truss (truss with material property close to material No. 2) distribution in fig. 3.
And in the third step of the continuous type mapping method, calculating the cross section size of the truss according to the punished material attribute of the truss and the multi-material topological optimization truss mapping result.
The calculation formula of the cross section size of the truss is as follows:
in the formula ArjIs the cross-sectional area of truss j. In this embodiment, the area of each truss can be seen as the thickness of each truss in fig. 3.
In the step of the discrete mapping method, the cell material is selected according to the multi-material topology optimization result and the mapping matrix. Obtaining the mapping weight w of each material in the cell c in the additive manufacturing truss design domain through comparison calculationcm. Selection weight wcmThe largest material is the material of the cell.
And in the second step of the discrete mapping method, selecting the material of the truss according to the topological optimization result of the multiple materials, the mapping matrix and the material selection of the truss-related cells.
In the selection process of the truss material, the post-mapping weight w of the material of each cell element to which the truss j belongs in the design domain of the additive manufacturing truss is obtained by comparison calculationjmOr wcjmThe material with the highest weight is selected as the material of the truss, and the distribution in this embodiment can be seen in the distribution of the gray truss (material selection truss of material No. 1) and the black truss (material selection truss of material No. 2) in fig. 4.
And in the step III of the discrete type mapping method, the cross section size of the truss is calculated according to the material property selected by the truss and the multi-material topological optimization truss mapping result. The calculation formula of the cross section size of the truss is as follows:
in the formula EjThe material properties selected for truss j. In this embodiment, the area of each truss can be seen as the thickness of each truss in fig. 4.
And in the step (IV) of the continuous mapping method and the step (IV) of the discrete mapping method, the material property and the section size of the truss are obtained according to the multi-material relative density mapping method, and the multi-material truss design result is obtained.
The result of the continuous mapping method is shown in fig. 3, and the force point displacement is 80.1. The result of the discrete mapping is shown in fig. 4, and the force point displacement is 75.0. It can be seen that the result of the discrete mapping method is generally better than that of the continuous mapping method, but the continuous mapping method is an effective method in consideration of the usability when the truss structure is complex.
Claims (4)
1. A multi-material additive manufacturing structure design method is characterized in that: the method specifically comprises the following steps:
step 1, defining a topological optimization design domain according to actual engineering problems, and carrying out multi-material topological optimization to obtain distribution of each material, namely design variable field information rho of each materialim(ii) a i is a unit number in the multi-material topology optimization design domain, and m is a material number;
step 2, mapping between a multi-material topological optimization result and truss design parameters according to a topological optimization design domain and an initial truss layout of additive manufacturing; wherein:
design variable field information ρ of each materialimAnd truss design parameters are expressed as follows:
wherein, wjmRepresenting the weight of the m-numbered material mapping of a structure j in the design domain of the additive manufacturing truss, wherein the structure j is a truss or a surface or a body;
rijrepresents the distance between cell i and structure j;
Ljrepresents the size of structure j;
and step 3: calculating the effectiveness of the cells according to the topology optimization design domain and the initial truss layout of additive manufacturing, and deleting invalid or inefficient cells;
design variable field information rho from each materialimDisplacement u of unit i of structureiAnd the stiffness k of the cell iiThe information calculates the effectiveness of the cells in the additive manufacturing truss layout, and the expression formula of the effectiveness of the cells is as follows:
wherein, EfcIs the validity of cell c; r isicRepresents the distance between unit i and cell c; l represents the face diagonal length of the face cell or the body diagonal length of the body cell; n represents the number of cells;
and 4, obtaining a truss structure design result in the effective cell area by using a continuous mapping method or a discrete mapping method according to the multi-material topological optimization result and the mapping matrix.
2. The method of claim 1, wherein the method further comprises: in step 3, the relative position relationship between the unit in the topological optimization design domain and the cell in the initial truss layout of the additive manufacturing is obtained through the topological optimization design domain and the initial truss layout of the additive manufacturing.
3. The method of claim 1, wherein the method further comprises: in step 4, the continuous mapping method comprises the following steps:
step one, calculating the material attribute of the truss according to the truss structure design parameter after mapping obtained in the step 2 and the material attribute in the material library;
secondly, filtering the material properties of the trusses according to the position relationship among the trusses and the material property calculation result to ensure that a material distribution interface is clear;
step three, calculating the cross section size of the truss according to the punished material attribute of the truss and the multi-material topological optimization truss mapping result;
and fourthly, obtaining a multi-material truss design result according to the truss material attribute and the cross section size obtained by the multi-material relative density mapping method.
4. The method of claim 1, wherein the method further comprises: in step 4, the discrete mapping method comprises the following steps:
firstly, selecting cell material according to a multi-material topological optimization result and a mapping matrix;
selecting materials of the truss according to the multi-material topological optimization result, the mapping matrix and the materials of the truss-related cells;
step three, calculating the cross section size of the truss according to the material attribute selected by the truss and the multi-material topological optimization truss mapping result;
and fourthly, obtaining a multi-material truss design result according to the truss material attribute and the cross section size obtained by the multi-material relative density mapping method.
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