CN111008499A - Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method - Google Patents

Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method Download PDF

Info

Publication number
CN111008499A
CN111008499A CN201911259078.4A CN201911259078A CN111008499A CN 111008499 A CN111008499 A CN 111008499A CN 201911259078 A CN201911259078 A CN 201911259078A CN 111008499 A CN111008499 A CN 111008499A
Authority
CN
China
Prior art keywords
macro
unit
multiphase
solid material
modulus
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201911259078.4A
Other languages
Chinese (zh)
Inventor
徐宇星
张俐
金聪
李嘉诚
王郑亚
李志奇
曹程宏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huazhong University of Science and Technology
Original Assignee
Huazhong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huazhong University of Science and Technology filed Critical Huazhong University of Science and Technology
Priority to CN201911259078.4A priority Critical patent/CN111008499A/en
Publication of CN111008499A publication Critical patent/CN111008499A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing

Abstract

The invention belongs to the field of material structure optimization design, and particularly discloses a multiphase material thermal coupling topology optimization design method for additive manufacturing. The method comprises the following steps: dispersing a multiphase material structure into a plurality of macro units, interpolating Young modulus and thermal coefficient of the multiphase material structure according to the material type and the existence of material filling of each macro unit, and establishing a multiphase material topological optimization model taking the minimization of the compliance of the multiphase material structure as a target function and taking the upper limit of the use amount of each solid material forming the multiphase material structure as design constraint; and then, carrying out sensitivity analysis on the design variables of the topological optimization model, and iteratively updating the design variables in the macro scale and the micro scale so as to obtain the optimal result with clear boundary. The invention ensures that different materials have clear boundaries, omits the use of a supporting structure in the additive manufacturing process, and improves the manufacturability of the optimized structure and the adaptability to thermal conditions.

Description

Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method
Technical Field
The invention belongs to the field of material structure optimization design, and particularly relates to a multiphase material thermal coupling topology optimization design method for additive manufacturing.
Background
The topological optimization is to optimize the material distribution in a given design domain and certain boundary conditions through a mathematical modeling and optimization algorithm so as to realize the improvement of the structural performance, and the method can automatically generate the structural topological configuration (such as the number, the position and the connectivity of holes) through the algorithm, get rid of the defects of empirical design and fully exert the material and structural performance. The thermoelasticity problem is a thermal weak coupling problem, namely, a temperature field can affect a force field, but the force field can not affect the temperature field. The structural form of the multiphase material has a relatively high upper limit of performance. Wu et al established a multi-scale topological optimization method for optimally designing aperiodic honeycomb structures affected by thermal and mechanical loads and for use in injection mold design. In the practical use of thermal coupling topology optimization, Mao et al have studied the optimal design of the battery frame structure of AUV under thermal stress coupling, Long et al have artificially overcome the problem that the multi-phase material topology optimization by the conventional SIMP method is prone to fall into local optimization, and introduce the interconversion function into the topology optimization formula.
The existing multiphase material thermal coupling topological optimization method has the following problems: 1) in the thermoelasticity problem, the thermal load is different from the mechanical load, is influenced by the material distribution and belongs to the design-dependent load, so that the thermal load needs to be reasonably interpolated by the material. Meanwhile, the existing thermal coupling topological optimization method is less in structural optimization by taking temperature distribution in the additive manufacturing process as heat load. 2) The topological optimization result based on the variable density method is easy to have intermediate density units and checkerboard configuration, so that clear structure boundaries cannot be obtained or the interference phenomenon between any two materials is easy to occur, and the structure cannot be directly used for manufacturing. 3) The research of the self-supporting method for the additive manufacturing structure is limited to the adjustment of the inclination angle of the overhanging part, belongs to an empirical post-processing method, and needs to modify the optimal structure form after topological optimization, so that the structural performance is influenced. Therefore, the self-supporting problem needs to be considered in the structural topology optimization process to take structural self-supporting property and structural performance into consideration.
Therefore, the art needs to provide a multiphase material thermal coupling topology optimization design method for additive manufacturing to solve the problems of insufficient consideration of thermal load, interference phenomenon between two materials, and self-supporting limitation in the prior art.
Disclosure of Invention
Aiming at the defects of insufficient heat load consideration, interference phenomenon between two materials and self-supporting limitation in the multiphase material thermal coupling topological optimization method in the prior art, the invention designs a set of multiphase material thermal coupling lattice structure multi-scale topological optimization scheme, so that different materials have clear boundaries, a supporting structure is omitted in the additive manufacturing process, and the manufacturability of the optimized structure and the adaptability to thermal conditions are improved. And is thus particularly suitable for theoretical research and actual manufacturing for additive manufacturing lattice structure topology optimization design.
In order to achieve the purpose, the invention provides a multiphase material thermal coupling topological optimization design method oriented to additive manufacturing, which is characterized by comprising the following steps of:
s1, dispersing the multiphase material structure into a plurality of macro units, interpolating the Young modulus and the thermal coefficient of the multiphase material structure according to the material type and the existence of material filling of each macro unit, and constructing a Young modulus interpolation model and a thermal coupling finite element balance equation of the multiphase material structure;
s2, establishing a multiphase material topology optimization model which takes the minimization of the structural compliance of the multiphase material as a target function and takes the upper limit of the use amount of each solid material forming the multiphase material structure as a design constraint based on the Young modulus interpolation model and the thermodynamic coupling finite element balance equation established in the step S1;
s3, then, sensitivity analysis is carried out on the design variables of the multiphase material topology optimization model, and the design variables in the macro scale and the micro scale are updated in an iterative mode, so that the optimal result with clear boundaries is obtained.
More preferably, in step S1, the design variable (x) is usedi1,xi2) To describe each macro-unit, i is a positive integer greater than 0, which is the number of macro-units; x is the number ofi1The volume ratio of the total volume of the first solid material and the second solid material in the macro unit to the volume of the macro unit, xi2The second solid material is in a volume ratio of the total volume of the first solid material and the second solid material.
More preferably, in step S1, the young' S modulus interpolation model of the multiphase material structure is:
E(xi1,xi2)＝ηE,1(xi1){ηE，2（xi2)E(2)+[1-ηE,2(xi2)]E(1)}+[1-ηE,1(xi1)]E(0)
wherein the content of the first and second substances,
Figure BDA0002311110740000031
E(0)modulus of elasticity of the macro-units when they are filled without material, E(1)Modulus of elasticity of the macro-unit when the macro-unit is only the first solid material, E(2)Modulus of elasticity of the macro-unit when it is the second solid material only, β(0)Heat of macro-unit when it is not filled with materialForce coefficient β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient of the macro-unit being the second solid material only; rE，1Is the Young's modulus interpolation coefficient, R, of the first solid material in the RAMP modelE，2And (4) interpolating coefficients for the Young's modulus of the second solid material in the RAMP model.
As a further preferred, in step S1, the thermodynamic coupling finite element balance equation is:
β(xi1,xi2)＝ηβ,1(xi1){ηβ,2(xi2)β(2)+[1-ηβ,2(xi2)]β(1)}+[1-ηβ,1(xi1)]β(0)
wherein the content of the first and second substances,
Figure BDA0002311110740000032
β(0)thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient, R, of the macro-unit being the second solid material onlyβ，1Interpolating coefficients and R for thermal coupling of a first solid material in a RAMP modelβ，2And interpolating coefficients for the thermal coupling of the second solid material in the RAMP model.
Further preferably, in step S2, the multiphase material topology optimization model is:
find:{xi1,xi2}(i＝1,2,...,n)
min:
Figure BDA0002311110740000041
subject to:Fm+Fth＝KU
Figure BDA0002311110740000042
volume constraint:
Figure BDA0002311110740000043
Figure BDA0002311110740000044
wherein, FmExternal mechanical load vector, F, for multiphase material structuresthFor the equivalent temperature load vector of the multiphase material structure calculated from the temperature, n represents the number of macro-units in the design domain of the multiphase material structure, ViDenotes the volume, V, of each macro-unit0Denotes the total volume of the designed domains of the multiphase material, vf1、vf2The volume fraction upper limit, k, of the first solid material and the second solid material in each macro-unit01The value of Young's modulus of the macro unit is E1Stiffness matrix of time-macroscopic unit, k02The value of Young's modulus of the macro unit is E2Stiffness matrix of time-macroscopic unit, RE，1And RE，2For the Young's modulus interpolation coefficient of macro-unit in RAMP model, Rβ，1And Rβ，2Interpolation coefficient for thermodynamic coupling of macro-units in RAMP model, uiIs a displacement matrix of macro-units, ui TIs the transpose of the displacement matrix of the macro-unit,
Figure BDA0002311110740000045
as a transposed matrix of the macro-cell strain matrix, Δ TiRepresents the amount of change in temperature of the macro-unit, ΩiRepresenting the design domain of the first macro-unit,
Figure BDA0002311110740000046
is an elastic matrix with Young's modulus value of 1, U is an integral rigidity displacement matrix of a multi-phase material structure, K is an integral rigidity matrix of the multi-phase material structure, and xminThe minimum lower limit of the singular matrix is prevented in the matrix calculation.
As a further preferred method, in step S3, a boundary processing model based on sensitivity filtering is used to perform filtering processing on the partial derivative of the objective function to obtain an optimal result with clear boundary.
As a further preferred, the boundary processing model based on sensitivity filtering is:
Figure BDA0002311110740000051
wherein the content of the first and second substances,
Figure BDA0002311110740000057
objective function for x representing a model for topological optimization of a multiphase materialkjPartial derivative of, xkjIs a macro unit xijThe adjacent filter units are arranged in the filter unit,
Figure BDA0002311110740000052
for the correction function, N represents the macro-unit xijThe number of adjacent filter units, j, is 1 or 2, HkIn order to be a function of the weighting,
Figure BDA0002311110740000053
Figure BDA0002311110740000054
is a design variable of the filter unit.
As a further preference, the correction function
Figure BDA0002311110740000055
The calculation formula of (a) is as follows:
Figure BDA0002311110740000056
where γ is a conditional threshold.
Preferably, after the optimal result with clear boundary is output, a finite element method is adopted to perform simulation analysis on the optimal result, and design variable constraint parameters are further adjusted according to the simulation analysis result so as to meet the condition of additive manufacturing.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the method takes the material type and the material filling as the variables of the optimization design according to the structure, so that the structural material has continuity, simultaneously, a Young modulus interpolation model and a thermal coupling finite element balance equation of the multiphase material structure are constructed, a multiphase material topological optimization model taking the compliance minimization of the multiphase material structure as an objective function and taking the upper limit of the use amount of each solid material forming the multiphase material structure as the design constraint is established, and therefore, clear boundaries are formed among different optimized materials, the use of a supporting structure is omitted in the material increase manufacturing process, and the manufacturability of the optimized structure and the adaptability to thermal conditions are improved.
2. The multi-configuration multi-scale topological optimization design method realizes the manufacturability of multi-scale topological optimization design of the lattice structure, and compared with a single-configuration lattice structure, the multi-configuration lattice structure is more excellent in mechanical property.
3. The invention adopts a boundary processing model based on sensitivity filtering to filter the partial derivative of the objective function so as to obtain the optimal result with clear boundary.
4. After the optimal result with clear boundary is output, the invention also needs to adopt a finite element method to carry out simulation analysis on the optimal result, and further adjusts the design variable constraint parameters according to the simulation analysis result so as to meet the condition of additive manufacturing.
Drawings
Fig. 1 is a flow chart of a multiphase material thermal coupling topology optimization design method for additive manufacturing according to a preferred embodiment of the present invention;
FIG. 2 is a schematic illustration of a plurality of material distributions according to an embodiment of the present invention;
fig. 3 is an analysis result diagram of a finite element simulation for simulating an optimization result obtained by the multiphase material thermal coupling topology optimization design method according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the invention relates to a multiphase material thermal coupling topology optimization design method for additive manufacturing, which is characterized by comprising the following steps:
s1, dispersing the multiphase material structure into a plurality of macro units, interpolating the Young modulus and the thermal coefficient of the multiphase material structure according to the material type and the existence of material filling of each macro unit, and constructing a Young modulus interpolation model and a thermal coupling finite element balance equation of the multiphase material structure;
s2, establishing a multiphase material topology optimization model which takes the minimization of the structural compliance of the multiphase material as a target function and takes the upper limit of the use amount of each solid material forming the multiphase material structure as a design constraint based on the Young modulus interpolation model and the thermodynamic coupling finite element balance equation established in the step S1;
s3, then, sensitivity analysis is carried out on the design variables of the multiphase material topology optimization model, and the design variables in the macro scale and the micro scale are updated in an iterative mode, so that the optimal result with clear boundaries is obtained.
More preferably, in step S1, the design variable (x) is usedi1,xi2) To describe each macro-unit, i is a positive integer greater than 0, which is the number of macro-units; x is the number ofi1The volume ratio of the total volume of the first solid material and the second solid material in the macro unit to the volume of the macro unit, xi2The second solid material is in a volume ratio of the total volume of the first solid material and the second solid material.
More preferably, in step S1, the young' S modulus interpolation model of the multiphase material structure is:
E(xi1,xi2)＝ηE,1(xi1){ηE,2(xi2)E(2)+[1-ηE,2(xi2)]E(1)}+[1-ηE,1(xi1)]E(0)
wherein the content of the first and second substances,
Figure BDA0002311110740000071
E(0)modulus of elasticity of the macro-units when they are filled without material, E(1)Modulus of elasticity of the macro-unit when the macro-unit is only the first solid material, E(2)Modulus of elasticity of the macro-unit when it is the second solid material only, β(0)Thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient of the macro-unit being the second solid material only; rE，1Is the Young's modulus interpolation coefficient, R, of the first solid material in the RAMP modelE，2And (4) interpolating coefficients for the Young's modulus of the second solid material in the RAMP model.
As a further preferred, in step S1, the thermodynamic coupling finite element balance equation is:
β(xi1,xi2)＝ηβ,1(xi1){ηβ,2(xi2)β(2)+[1-ηβ,2(xi2)]β(1)}+[1-ηβ,1(xi1)]β(0)
wherein the content of the first and second substances,
Figure BDA0002311110740000081
β(0)thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient, R, of the macro-unit being the second solid material onlyβ，1Is firstThermodynamic coupling interpolation coefficient and R of solid material in RAMP modelβ，2And interpolating coefficients for the thermal coupling of the second solid material in the RAMP model.
Further preferably, in step S2, the multiphase material topology optimization model is:
find:{xi1,xi2}(i＝1,2,...,n)
min:
Figure BDA0002311110740000082
subject to:Fm+Fth＝KU
Figure BDA0002311110740000083
volume constraint:
Figure BDA0002311110740000084
Figure BDA0002311110740000085
wherein, FmExternal mechanical load vector, F, for multiphase material structuresthFor the equivalent temperature load vector of the multiphase material structure calculated from the temperature, n represents the number of macro-units in the design domain of the multiphase material structure, ViDenotes the volume, V, of each macro-unit0Denotes the total volume of the designed domains of the multiphase material, vf1、vf2The volume fraction upper limit, k, of the first solid material and the second solid material in each macro-unit01The value of Young's modulus of the macro unit is E1Stiffness matrix of time-macroscopic unit, k02The value of Young's modulus of the macro unit is E2Stiffness matrix of time-macroscopic unit, RE，1And RE，2For the Young's modulus interpolation coefficient of macro-unit in RAMP model, Rβ，1And Rβ，2Interpolation coefficient for thermodynamic coupling of macro-units in RAMP model, uiIs a displacement matrix of macro-units, ui TIs the transpose of the displacement matrix of the macro-unit,
Figure BDA0002311110740000091
as a transposed matrix of the macro-cell strain matrix, Δ TiRepresents the amount of change in temperature of the macro-unit, ΩiRepresenting the design domain of the ith macro-cell,
Figure BDA0002311110740000092
is an elastic matrix with Young's modulus value of 1, U is an integral rigidity displacement matrix of a multi-phase material structure, K is an integral rigidity matrix of the multi-phase material structure, and xminThe minimum lower limit of the singular matrix is prevented in the matrix calculation.
As a further preferred method, in step S3, a boundary processing model based on sensitivity filtering is used to perform filtering processing on the partial derivative of the objective function to obtain an optimal result with clear boundary.
As a further preferred, the boundary processing model based on sensitivity filtering is:
Figure BDA0002311110740000093
wherein the content of the first and second substances,
Figure BDA0002311110740000097
objective function for x representing a model for topological optimization of a multiphase materialkjPartial derivative of, xkjIs a macro unit xijThe adjacent filter units are arranged in the filter unit,
Figure BDA0002311110740000094
for the correction function, N represents the macro-unit xijThe number of adjacent filter units, j, is 1 or 2, HkIn order to be a function of the weighting,
Hk＝rmin-dis(i，k)，{k∈n|dis(i，k)≤rmin}
rminthe radius of the filter representing the sensitivity analysis, dis (i, k) being between macro-unit i and filter unit kThe distance of (c).
Figure BDA0002311110740000095
Is a design variable of the filter unit.
As a further preference, the correction function
Figure BDA0002311110740000096
The calculation formula of (a) is as follows:
Figure BDA0002311110740000101
where γ is a conditional threshold.
Preferably, after the optimal result with clear boundary is output, a finite element method is adopted to perform simulation analysis on the optimal result, and design variable constraint parameters are further adjusted according to the simulation analysis result so as to meet the condition of additive manufacturing.
Example 1
First, two design variables x are introducedi1、xi2For describing the material distribution. A representative multiphase material distribution of the structure is shown in FIG. 2, the structure is composed of a first solid material, a second solid material and pores, wherein xi1For determining the presence, x, of local materiali2For determining whether the localized material is a first solid material or a second solid material.
Based on finite element thought, the structure is dispersed into a finite number of units, and two design variables x are set for each uniti1、xi2To determine the material used at the cell, according to the design variable (x)i1,xi2) The combination forms of the two design variable values are different, and the mode for judging the material type at a specific point is shown in the following table:
Figure BDA0002311110740000102
and interpolating the Young modulus and the thermal stress coefficient of the multiphase material structure by using a RAMP interpolation model. The Young modulus interpolation model of the multiphase material structure is as follows:
Figure BDA0002311110740000103
η thereinE,1(xi1)、ηE,2(xi2) The specific expression of (A) is as follows:
Figure BDA0002311110740000111
Figure BDA0002311110740000112
the thermodynamic coupling finite element balance equation is as follows:
Figure BDA0002311110740000113
wherein, ηβ,1(xi1)、ηβ,2(xi2) The specific expression of (A) is as follows:
Figure BDA0002311110740000114
Figure BDA0002311110740000115
E(0)modulus of elasticity of the macro-units when they are filled without material, E(1)Modulus of elasticity of the macro-unit when the macro-unit is only the first solid material, E(2)Modulus of elasticity of the macro-unit when it is the second solid material only, β(0)Thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient of the macro-unit being the second solid material only; rE，1Is a first solid material inYoung's modulus interpolation coefficient, R, in RAMP modelE，2Interpolating coefficients for Young's modulus of a second solid material in a RAMP model β(0)Thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient, R, of the macro-unit being the second solid material onlyβ，1Interpolation coefficient and R for thermal coupling of first solid materialβ，2And the thermodynamic coupling interpolation coefficient of the second solid material is obtained. RE,1、RE,2、Rβ,1、Rβ,1Is a RAMP interpolation coefficient set for different material properties and different design variables.
Based on the young modulus interpolation model constructed in the step S1 and the thermodynamic coupling finite element balance equation, a multiphase material topology optimization model is established, in which the compliance of the multiphase material structure is minimized as an objective function, and the upper limit of the usage amount of each solid material constituting the multiphase material structure is a design constraint. The optimization model is specifically represented as follows:
find:{xi1,xi2}(i＝1,2,...,n)
min:
Figure BDA0002311110740000121
subject to:Fm+Fth＝KU
Figure BDA0002311110740000122
volume constraint:
Figure BDA0002311110740000123
Figure BDA0002311110740000124
wherein, FmExternal mechanical load vector, F, for multiphase material structuresthFor multiphase material structure calculated from temperature, etcEffective temperature load vector, n represents the number of macro-units in the design domain of the multiphase material structure, ViDenotes the volume, V, of each macro-unit0Denotes the total volume of the designed domains of the multiphase material, vf1、vf2The volume fraction upper limit, k, of the first solid material and the second solid material in each macro-unit01The value of Young's modulus of the macro unit is E1Stiffness matrix of time-macroscopic unit, k02The value of Young's modulus of the macro unit is E2Stiffness matrix of time-macroscopic unit, RE，1And RE，2As the Young's modulus interpolation coefficient, Rβ，1And Rβ，2As a coefficient of thermodynamic coupling interpolation, uiIs a displacement matrix of macro-units, ui TIs the transpose of the displacement matrix of the macro-unit,
Figure BDA0002311110740000125
as a transposed matrix of the macro-cell strain matrix, Δ TiRepresents the amount of change in temperature of the macro-unit, ΩiRepresenting the design domain of the first macro-unit,
Figure BDA0002311110740000126
is an elastic matrix with Young's modulus value of 1, U is an integral rigidity displacement matrix of a multi-phase material structure, K is an integral rigidity matrix of the multi-phase material structure, and xminThe minimum lower limit of the singular matrix is prevented in the matrix calculation.
In order to solve the minimization optimization problem, the variation of an objective function and a design constraint relative to a design variable needs to be deduced by a sensitivity analysis method. The derivative of the compliance objective function to the design variables is calculated as follows:
Figure BDA0002311110740000131
due to FmThere is no connection to design variables, so the sensitivity calculation can be simplified to:
Figure BDA0002311110740000132
it is clear that it is possible to use,
Figure BDA0002311110740000133
and
Figure BDA0002311110740000134
is the basic term of the calculation required in this formula. According to the RAMP interpolation model, the partial derivatives of the overall stiffness matrix K of the multiphase material structure with respect to two design variables are:
Figure BDA0002311110740000135
Figure BDA0002311110740000136
wherein the content of the first and second substances,
Figure BDA0002311110740000137
and
Figure BDA0002311110740000138
the specific form of (A) is as follows:
Figure BDA0002311110740000139
Figure BDA00023111107400001310
the partial derivative of the equivalent temperature load with respect to the design variable is:
Figure BDA0002311110740000141
the partial derivatives of the thermal stress coefficient with respect to two design variables are in the form:
Figure BDA0002311110740000142
Figure BDA0002311110740000143
Figure BDA0002311110740000144
and
Figure BDA0002311110740000145
the specific form of (A) is as follows:
Figure BDA0002311110740000146
Figure BDA0002311110740000147
through the formulas (8) to (17), a final objective function sensitivity calculation formula can be derived and expressed as follows:
Figure BDA0002311110740000148
Figure BDA0002311110740000149
due to the existence of the intermediate density macro-units, the boundaries between the materials of all phases are not clear, and the optimization result with clear boundaries is obtained by filtering the partial derivative of the objective function by adopting a boundary processing method based on sensitivity filtering. The sensitivity filtration format was as follows:
wherein the correction function is represented as follows:
Figure BDA0002311110740000151
wherein the correction function
Figure BDA0002311110740000152
The calculation formula of (a) is as follows:
Figure BDA0002311110740000153
wherein the content of the first and second substances,
Figure BDA0002311110740000159
objective function for x representing a model for topological optimization of a multiphase materialkjPartial derivative of, xkjIs a macro unit xijThe adjacent filter units are arranged in the filter unit,
Figure BDA0002311110740000158
for the correction function, N represents the macro-unit xijThe number of adjacent filter units, j, is 1 or 2, HkIn order to be a function of the weighting,
Figure BDA0002311110740000154
Figure BDA0002311110740000155
is a design variable of the filter unit. Subscript i denotes the number of a macro-cell, subscript j is used to distinguish design variables, subscript k denotes the number of a filter cell within the filter radius of the macro-cell, and subscript g denotes the number of four macro-cells adjacent to the macro-cell. Gamma is used as a condition threshold value to judge whether the filter unit is at the structure boundary, and when the difference value of the design variables of the filter unit in the filtering radius of the macro unit is larger than the condition threshold value, the filter unit can be judged to be positioned at the structure boundary. Then, pass the correction function
Figure BDA0002311110740000156
The sensitivity filtering of the filtering units at the structural boundary is weakened, and the filtering units at the non-boundary are processed in a traditional sensitivity filtering mode. Further, adopt
Figure BDA0002311110740000157
The design variables of the original filter unit are replaced, so that the sensitivity value of the filter unit at the non-boundary position is amplified,to process the checkerboard configuration problem of the optimization results and to apply MMA method to two design variables (x)i1,xi2) And respectively carrying out iterative updating.
Finally, a finite element method is used for carrying out simulation analysis on the design result, and as shown in fig. 3, the design variable constraint parameters are further adjusted according to the analysis result so as to meet the conditions of additive manufacturing.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A multiphase material thermal coupling topological optimization design method oriented to additive manufacturing is characterized by comprising the following steps:
s1, dispersing the multiphase material structure into a plurality of macro units, interpolating the Young modulus and the thermal coefficient of the multiphase material structure according to the material type and the existence of material filling of each macro unit, and constructing a Young modulus interpolation model and a thermal coupling finite element balance equation of the multiphase material structure;
s2, establishing a multiphase material topology optimization model which takes the minimization of the structural compliance of the multiphase material as a target function and takes the upper limit of the use amount of each solid material forming the multiphase material structure as a design constraint based on the Young modulus interpolation model and the thermodynamic coupling finite element balance equation established in the step S1;
s3, sensitivity analysis is carried out on the design variables of the multiphase material topological optimization model, and the design variables in the macro scale and the micro scale are updated in an iterative mode, so that the optimal result with clear boundaries is obtained.
2. The additive manufacturing-oriented multiphase material thermal coupling topology optimization design method according to claim 1, wherein in step S1, design variables (x) are adoptedi1,xi2) To describe each macro-unit, i is a positive integer greater than 0, is a macroThe number of view units; x is the number ofi1The volume ratio of the total volume of the first solid material and the second solid material in the macro unit to the volume of the macro unit, xi2The second solid material is in a volume ratio of the total volume of the first solid material and the second solid material.
3. The additive manufacturing-oriented multiphase material thermal coupling topology optimization design method according to claim 2, wherein in step S1, the young' S modulus interpolation model of the multiphase material structure is:
E(xi1,xi2)＝ηE,1(xi1){ηE,2(xi2)E(2)+[1-ηE,2(xi2)]E(1)}+[1-ηE,1(xi1)]E(0)
wherein the content of the first and second substances,
Figure FDA0002311110730000011
E(0)modulus of elasticity of the macro-units when they are filled without material, E(1)Modulus of elasticity of the macro-unit when the macro-unit is only the first solid material, E(2)Modulus of elasticity of the macro-unit when it is the second solid material only, β(0)Thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient of the macro-unit being the second solid material only; rE，1Is the Young's modulus interpolation coefficient, R, of the first solid material in the RAMP modelE，2And (4) interpolating coefficients for the Young's modulus of the second solid material in the RAMP model.
4. The additive manufacturing oriented multiphase material thermal coupling topological optimization design method according to claim 2, wherein in step S1, the thermal coupling finite element balance equation is:
β(xi1,xi2)＝ηβ,1(xi1){ηβ,2(xi2)β(2)+[1-ηβ,2(xi2)]β(1)}+[1-ηβ,1(xi1)]β(0)
wherein the content of the first and second substances,
Figure FDA0002311110730000021
β(0)thermal coefficient of macro-unit without material filling β(1)Thermal coefficient of macro-unit when it is only the first solid material, β(2)The thermal coefficient, R, of the macro-unit being the second solid material onlyβ，1Interpolating coefficients and R for thermal coupling of a first solid material in a RAMP modelβ，2And interpolating coefficients for the thermal coupling of the second solid material in the RAMP model.
5. The additive manufacturing-oriented multiphase material thermal coupling topological optimization design method according to claim 2, wherein in step S2, the multiphase material topological optimization model is:
find:{xi1,xi2}(i＝1,2,...,n)
min:
Figure FDA0002311110730000031
subject to:Fm+Fth＝KU
Figure FDA0002311110730000032
volume constra int:
Figure FDA0002311110730000033
Figure FDA0002311110730000034
wherein the content of the first and second substances,Fmexternal mechanical load vector, F, for multiphase material structuresthFor the equivalent temperature load vector of the multiphase material structure calculated from the temperature, n represents the number of macro-units in the design domain of the multiphase material structure, ViDenotes the volume, V, of each macro-unit0Denotes the total volume of the designed domains of the multiphase material, vf1、vf2The volume fraction upper limit, k, of the first solid material and the second solid material in each macro-unit01The value of Young's modulus of the macro unit is E1Stiffness matrix of time-macroscopic unit, k02The value of Young's modulus of the macro unit is E2Stiffness matrix of time-macroscopic unit, RE，1And RE，2For the Young's modulus interpolation coefficient of macro-unit in RAMP model, Rβ，1And Rβ，2Interpolation coefficient for thermodynamic coupling of macro-units in RAMP model, uiIs a displacement matrix of macro-units, ui TIs the transpose of the displacement matrix of the macro-unit,
Figure FDA0002311110730000035
as a transposed matrix of the macro-cell strain matrix, Δ TiRepresents the amount of change in temperature of the macro-unit, ΩiRepresenting the design domain of the ith macro-cell,
Figure FDA0002311110730000036
is an elastic matrix with Young's modulus value of 1, U is an integral rigidity displacement matrix of a multi-phase material structure, K is an integral rigidity matrix of the multi-phase material structure, and xminThe minimum lower limit of the singular matrix is prevented in the matrix calculation.
6. The additive manufacturing oriented multiphase material thermal coupling topology optimization design method according to claim 2, wherein in step S3, a boundary processing model based on sensitivity filtering is adopted to perform filtering processing on the partial derivative of the objective function to obtain an optimal result with clear boundaries.
7. The additive manufacturing-oriented multiphase material thermal coupling topology optimization design method according to claim 6, wherein the sensitivity filtering-based boundary processing model is as follows:
Figure FDA0002311110730000041
wherein the content of the first and second substances,
Figure FDA0002311110730000042
objective function for x representing a model for topological optimization of a multiphase materialkjPartial derivative of, xkjIs a macro unit xijThe adjacent filter units are arranged in the filter unit,
Figure FDA0002311110730000043
for the correction function, N represents the macro-unit xijThe number of adjacent filter units, j, is 1 or 2, HkIn order to be a function of the weighting,
Figure FDA0002311110730000044
Figure FDA0002311110730000045
is a design variable of the filter unit.
8. Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method according to claim 7, wherein the correction function
Figure FDA0002311110730000046
The calculation formula of (a) is as follows:
Figure FDA0002311110730000047
where γ is a conditional threshold.
9. The additive manufacturing-oriented multiphase material thermal power coupling topology optimization design method according to claim 1, wherein after the optimal result with clear boundaries is output, a finite element method is adopted to perform simulation analysis on the optimal result, and design variable constraint parameters are further adjusted according to the simulation analysis result so as to meet the conditions of additive manufacturing.
CN201911259078.4A 2019-12-10 2019-12-10 Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method Pending CN111008499A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911259078.4A CN111008499A (en) 2019-12-10 2019-12-10 Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911259078.4A CN111008499A (en) 2019-12-10 2019-12-10 Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method

Publications (1)

Publication Number Publication Date
CN111008499A true CN111008499A (en) 2020-04-14

Family

ID=70115103

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911259078.4A Pending CN111008499A (en) 2019-12-10 2019-12-10 Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method

Country Status (1)

Country Link
CN (1) CN111008499A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112214917A (en) * 2020-10-13 2021-01-12 武汉大学 Method for manufacturing substrate through multi-scale optimized additive manufacturing and substrate
CN112685945A (en) * 2021-01-11 2021-04-20 北京理工大学 Magnetic-structure multi-physical-field topological optimization design method for additive manufacturing

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107025340A (en) * 2017-03-30 2017-08-08 华中科技大学 A kind of self-supporting network structure method of topological optimization design suitable for increasing material manufacturing
CN107491599A (en) * 2017-08-03 2017-12-19 华中科技大学 Heterogeneous material compliant mechanism Topology Optimization Method under a kind of stress constraint
US20190325098A1 (en) * 2018-04-23 2019-10-24 Honeywell Federal Manufacturing & Technologies, Llc System, method, and computer program for part model generation and analysis and part production and validation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107025340A (en) * 2017-03-30 2017-08-08 华中科技大学 A kind of self-supporting network structure method of topological optimization design suitable for increasing material manufacturing
CN107491599A (en) * 2017-08-03 2017-12-19 华中科技大学 Heterogeneous material compliant mechanism Topology Optimization Method under a kind of stress constraint
US20190325098A1 (en) * 2018-04-23 2019-10-24 Honeywell Federal Manufacturing & Technologies, Llc System, method, and computer program for part model generation and analysis and part production and validation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
徐宇星: "面向增材制造的热力耦合拓扑优化方法研究", 《万方数据》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112214917A (en) * 2020-10-13 2021-01-12 武汉大学 Method for manufacturing substrate through multi-scale optimized additive manufacturing and substrate
CN112214917B (en) * 2020-10-13 2022-07-15 武汉大学 Method for manufacturing substrate through multi-scale optimized additive manufacturing and substrate
CN112685945A (en) * 2021-01-11 2021-04-20 北京理工大学 Magnetic-structure multi-physical-field topological optimization design method for additive manufacturing
CN112685945B (en) * 2021-01-11 2021-08-13 北京理工大学 Magnetic-structure multi-physical-field topological optimization design method for additive manufacturing

Similar Documents

Publication Publication Date Title
CN110110413B (en) Structural topology optimization method based on material field reduction progression expansion
Jameson A proof of the stability of the spectral difference method for all orders of accuracy
Yan et al. A new optimal reactive power flow model in rectangular form and its solution by predictor corrector primal dual interior point method
McBane et al. Component-wise reduced order model lattice-type structure design
CN110069800B (en) Three-dimensional structure topology optimization design method and equipment with smooth boundary expression
CN111008499A (en) Additive manufacturing-oriented multiphase material thermal coupling topology optimization design method
CN109670200A (en) A kind of equal geometry density of material field structure Topology Optimization Method
CN109543207B (en) Method for realizing double-mold casting component multi-component design by considering variable parting line
CN111737835A (en) Three-period minimum curved surface-based three-dimensional porous heat dissipation structure design and optimization method
CN113094944A (en) Micro-channel radiator and microscopic scale topology optimization design method thereof
CN107563097B (en) Stress-based heuristic structure discrete topology optimization design method
CN112966420B (en) Heat sink structure design method combining topology optimization and shape optimization
CN112966419B (en) Multi-field coupling effect structure design method combining topology optimization and shape optimization
CN111539138B (en) Method for solving time domain response sensitivity of structural dynamics peak based on step function
CN108984914B (en) Rapid multi-scale calculation method for solving complex time domain electromagnetic problem
CN109145495B (en) The Topology Optimization Method of fixed parting line bimodulus cast member multicomponent
Cui et al. A parameterized level set method for structural topology optimization based on reaction diffusion equation and fuzzy PID control algorithm
CN113691993A (en) Method and system for predicting 5G connected cluster base station group flow based on graph neural network
CN110245410B (en) Multi-parametric variable-based topological optimization design method for thermoelastic structure of multiphase material
CN109502017B (en) Topology optimization bionic unmanned aerial vehicle and design method thereof
CN108897956B (en) Optimization design method for porous mechanical parts
CN113139313B (en) Equivalent lightweight structure analysis method based on finite element theory
CN112989661B (en) Underwater structure design method combining topology optimization and shape optimization
CN108134392B (en) Single-phase and three-phase hybrid power flow calculation method based on node current injection
CN209209024U (en) A kind of bionical unmanned plane of topological optimization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20200414