CN110751729A - Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator - Google Patents

Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator Download PDF

Info

Publication number
CN110751729A
CN110751729A CN201911005931.XA CN201911005931A CN110751729A CN 110751729 A CN110751729 A CN 110751729A CN 201911005931 A CN201911005931 A CN 201911005931A CN 110751729 A CN110751729 A CN 110751729A
Authority
CN
China
Prior art keywords
optimization
microstructure
model
microscopic
design
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
CN201911005931.XA
Other languages
Chinese (zh)
Inventor
李取浩
徐瑞
刘书田
吴强波
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.)
Shandong University
Original Assignee
Shandong University
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 Shandong University filed Critical Shandong University
Priority to CN201911005931.XA priority Critical patent/CN110751729A/en
Publication of CN110751729A publication Critical patent/CN110751729A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/10—Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/10—Processes of additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/30—Auxiliary operations or equipment
    • B29C64/386—Data acquisition or data processing for additive manufacturing
    • 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
    • B33Y10/00—Processes of additive manufacturing
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Chemical & Material Sciences (AREA)
  • Materials Engineering (AREA)
  • Manufacturing & Machinery (AREA)
  • Geometry (AREA)
  • Computer Graphics (AREA)
  • Software Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Optics & Photonics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a corrosion-diffusion operator-based quasi-periodic hierarchical structure topology optimization method, which comprises the following steps: building a structural model; carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library; predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method; based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model; calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model; iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the density of the micro-unit and the density of the macro-unit; and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.

Description

Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator
Technical Field
The invention belongs to the technical field of structural topology optimization, and particularly relates to a quasi-periodic hierarchical structural topology optimization method based on a corrosion-diffusion operator.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Biological structures in nature, such as animal bones and plant stalks, are mostly hierarchical structures. The geometrical characteristics of the composite material are represented by a plurality of scale configurations such as macroscopic, sub-microscopic and microscopic configurations, and the composite material has the characteristics of higher specific stiffness, defect resistance, multiple functions and the like. Inspired by this, many artificial hierarchical structures, such as sandwich boards, lattice materials, etc., are widely used in the fields of aerospace, biomedical, etc. In recent years, the rapid development of advanced manufacturing technologies, especially additive manufacturing technologies, provides a powerful tool for the preparation of hierarchical structures with complex geometric features, and also puts higher demands on the design method of the hierarchical structures.
The topology optimization technology designs the optimal structure configuration meeting the specific performance/material constraint by searching the optimal distribution of the material, and is an advanced and intelligent structure design method. Designing a hierarchical structure through topology optimization techniques has become a research focus in the art. The earliest review can be traced to document 1 ("rodriges, h., guidelines, j.m., and Bendsoe, M.P. (2002). iterative Optimization of material and structure. structural and multiple Hierarchical Optimization 24, 1-10"), which discloses a nested heterogeneous Hierarchical topology Optimization solution strategy that can obtain optimal material property distributions and corresponding microstructure configurations by an inverse homogenization method. However, the method has huge calculation amount, is difficult to solve the multi-constraint and multi-physical-field optimization problem, and has a limited application range.
Document 2 ("Liu, l., Yan, j., and Cheng, G. (2008). optim structure with a homogenetic Optimum. computers & Structures86, 1417-. The method is a single-layer optimization model, has the advantages of less design variables, small calculated amount, good universality and the like, and the obtained periodic hierarchical structure does not have interface discontinuity among microstructures. However, since the periodic layered structure only contains one microstructure configuration on a macro scale, the design space is small, and the improvement of the structural performance is limited.
Document 3 ("Zhang, p.; Toman, j.; Yu, y.; Biyikli, e.; Kirca, m.; chimielus, m.; To, a.c. (2015) effective Design-Optimization of Variable-Density hexagonal cellular Structure by Additive Manufacturing: the invention and variation.journal Manufacturing Science & Engineering, 137") proposes an Optimization method of quasi-periodic hierarchy Structure, which can effectively improve structural performance by optimizing the macroscopic distribution of unit cell pore diameters and is prepared using Additive Manufacturing techniques. However, this approach does not optimize the microstructure topology.
Document 4 ("Wang, y.; Chen, f.; Wang, M.Y. (2017) current design with connected hierarchical microstructure. computer Methods in Applied Mechanics and engineering,317, 84-101.") discloses a quasi-periodic hierarchy topology optimization method based on a level set framework, but it cannot be directly Applied to the variable density method topology optimization framework which is the most widely used.
In summary, the hierarchical topology optimization method disclosed in the prior art has incompatible contradictions in terms of computational efficiency, application range and structural performance.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a quasi-periodic hierarchical structure topology optimization method based on a corrosion-diffusion operator, and the method improves the structure performance while reducing the calculated amount and widening the use range by optimally designing the topology configurations on a macroscopic scale and a microscopic scale.
In order to achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
the quasi-periodic hierarchical structure topology optimization method based on the erosion-diffusion operator comprises the following steps:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to a macroscopic design variable and a microscopic design variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the micro density and the macro density;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
According to the further technical scheme, a square or cubic structure is selected in the micro design domain and is divided into quadrilateral or hexahedral meshes.
According to the further technical scheme, a first type of design variable of the density of the micro-units is defined, and the density of the macro-units is a second type of design variable.
The method comprises the following steps of substituting the obtained elastic modulus of the microstructure into a finite element solution column, calculating to obtain a unit stiffness matrix, and performing finite element analysis to obtain a macroscopic displacement field; in the corresponding topological optimization problem, an objective function is defined as the minimum flexibility of the structure, and the constraint condition is that the usage of the microscopic material is less than the volumeAnd the amount of macroscopic material is less than the volume
Figure BDA0002242776750000032
And establishing an optimization model.
In a further technical scheme, the method for reconstructing the geometric model comprises the following steps: and identifying the geometric boundary of the microstructure obtained by optimizing the model by using a boundary identification program.
In a further technical scheme, the boundary is led into geometric software to reconstruct a unit cell geometric model: and reconstructing the optimized whole heterogeneous double-layer model by utilizing the optimization result information and the created single-cell geometric model.
The invention discloses an application of the quasi-periodic hierarchical structure topology optimization method based on the corrosion-diffusion operator in the fields of 3D printing, aeronautical structures and biomedicine.
A quasi-periodic hierarchical topology optimization system based on corrosion-diffusion operators comprises:
the structure model building module is used for building a structure model and subdividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
the optimization model establishing module is used for carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
the geometric model reconstruction module is used for calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic design variable and a microcell size variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the collaborative optimization design of the micro density, the macro density and the size variables;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic design variable and a microcell size variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the collaborative optimization design of the micro density, the macro density and the size variables;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
A computer-readable storage medium, on which a computer program is stored, which program, when executed by a processor, carries out the steps of:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic design variable and a microcell size variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the collaborative optimization design of the micro density, the macro density and the size variables;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
The above one or more technical solutions have the following beneficial effects:
(1) the method establishes the quasiperiodic hierarchy structure topology description method under the variable density method framework through the corrosion-diffusion operator, is suitable for any microstructure topology configuration, has the characteristics of wide application range, simple mathematical listing and the like, can well solve the problems of single unit cell singleness and limitation of the performance potential of the microstructure in the prior art, and can realize the spatial transformation of material attributes by adjusting the distribution of quasiperiodic unit cells on the space.
(2) Compared with the traditional topological optimization design of the periodic macro microstructure, the optimization method provided by the invention can improve the rigidity of the 3D printing structure by more than 200%, further exerts the performance potential of the microstructure and greatly improves the performance of the 3D printing structure; meanwhile, the optimization model in the optimization method provided by the invention is simple in format, and the problems of multiple constraints and multiple physical fields are conveniently considered.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a schematic representation of two types of design variables (micro-cell density, macro-cell density) in example 1;
FIG. 2 is a diagram showing the boundary conditions, dimensions and loads of the design domain model in example 1;
FIG. 3 is a quasi-periodic cell library generated based on the corrosion-diffusion operator in example 1;
FIG. 4 is an equivalent elastic matrix fitting curve of the quasi-periodic unit cell library in example 1;
FIGS. 5(a) -5 (b) are design diagrams for topology optimization in example 1 and comparative example 1; wherein, fig. 5(a) is comparative example 1, and fig. 5(b) is example 1;
6(a) -6 (b) are graphs of the effects of 3D prints of the topology optimization design results in example 1 and comparative example 1; fig. 6(a) shows comparative example 1, and fig. 6(b) shows example 1.
Detailed Description
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
The general idea provided by the invention is as follows:
quasi-periodic unit cell topology description under a variable density method framework is realized through a corrosion-diffusion operator, and the bottleneck that any unit cell can not be subjected to quasi-periodic transformation in the prior art can be well solved; and the spatial distribution optimization of material attributes can be realized by synergistically optimizing the single cell topology and the spatial distribution thereof, and the structural performance is further improved.
Example of implementation 1
The application discloses a corrosion-diffusion operator-based quasi-periodic hierarchical structure topology optimization method, which comprises the following steps of 1: establishing a structural model aiming at the design case, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
preferably, the micro-design domain usually selects a square or cubic structure and is divided into quadrilateral or hexahedral meshes;
dividing a finite element mesh: facilitating the finite element analysis and defining the design variables in step 2.
Step 2: defining cell density in a micro design domain
Figure BDA0002242776750000071
Cell density in the macroscopic design Domain for the first class of design variables
Figure BDA0002242776750000072
Designing variables for the second class, where NmiDesigning the number of meshes of a domain for a micro-scale, NmaDesigning the number of grids of the domain for the macro;
the two types of design variables are updated in step 9, and then the final design result is generated in step 10;
and step 3: the convergence criterion is set as: max | | | xi+1-xi||>ΔxmaxAnd i is less than or equal to imaxWherein i is an iterative step, imaxIs the maximum number of iteration steps, xiDesigning variable values (including) for the ith step
Figure BDA0002242776750000073
And
Figure BDA0002242776750000074
two types), Δ xmaxThe maximum variation value of the allowed variable;
and 4, step 4: each microscopic grid is provided with a unit density, the microstructure is described through the unit densities, and the microscopic design domain is subjected to corrosion-diffusion operation to obtain a quasi-periodic microstructure library. The calculation formula of the corrosion-diffusion operator is as follows:
Figure BDA0002242776750000081
wherein the content of the first and second substances,
Figure BDA0002242776750000082
and viCell density and cell volume in the micro design domain, w (x), respectivelyi)＝rmin-||xi-xe| | is a weight function, xiIs the cell center point coordinate. N is a radical ofe＝{i|||xi-xe||≤rminIs the filter design field, rminIs the filtration radius.
Wherein β and η are calculation parameters.
And 5: predicting equivalent elastic tensor D of microstructure in alignment period microstructure library by utilizing asymptotic homogenization methodHSaid D isHThe calculation formula of (a) is as follows:
Figure BDA0002242776750000084
wherein y represents the position coordinates of any point in the microscopic domain, D (y) is the elastic matrix of the material, εyFor the strain vector, phi is a characteristic displacement vector, and the calculation formula is as follows:
Figure BDA0002242776750000085
where v is the virtual displacement.
Step 6: based on the elasticity tensor of the microstructure database obtained by the previous step, B spline function fitting is adopted to establish the elastic modulus and the volume ratio of the microstructure
Figure BDA0002242776750000086
Explicit functional relationships between;
the effect of obtaining an explicit functional relationship is: reduces the amount of calculation and facilitates the sensitivity analysis in step 8.
And 7: the elasticity tensor obtained in the step 6
Figure BDA0002242776750000088
Carrying out finite element solution column, and calculating to obtain a unit stiffness matrix KeCarrying out finite element analysis to obtain a macroscopic displacement field U, wherein the macroscopic displacement field is used when calculating the structural rigidity (namely the flexibility of the target function); in the corresponding topological optimization problem, an objective function is defined as the minimum flexibility of the structure, and the constraint condition is that the usage amount of the microscopic material is less than the usage lower limit of the volume material
Figure BDA0002242776750000091
And the amount of the macroscopic material is less than the upper limit of the volume material
Figure BDA0002242776750000092
Establishing an optimization model shown as the following formula:
Figure BDA0002242776750000093
min c＝FTU＝UTKU
Figure BDA0002242776750000094
Figure BDA0002242776750000095
Figure BDA0002242776750000096
wherein N ismi＝2500，Nma＝300，
Figure BDA0002242776750000098
And 8: according to the finite element analysis result and the established optimization model in the step 7; calculating the compliance function (objective function) of the structure for macroscopic design variables
Figure BDA0002242776750000099
And microscopic design variables
Figure BDA00022427767500000910
Sensitivity of these two types of design variables:
Figure BDA00022427767500000911
Figure BDA00022427767500000912
and step 9: according to the sensitivity information obtained in the step 8, iteration updating is carried out on the two types of design variables by using an MMA algorithm, and collaborative optimization design of the micro density and the macro density is completed;
step 10: and (4) reconstructing the macroscopic and microscopic optimization results obtained by solving the optimization model in the step (7) to obtain a geometric model of the whole heterogeneous structure.
In step 3, imaxIs chosen to be 160, Δ xmaxSelecting the content as 0.001; the penalty coefficient is 2-5;
the selection of parameter β in step 4 is as follows:
Figure BDA00022427767500000913
Figure BDA0002242776750000101
in step 6, the punishment coefficient takes the values as follows:
in step 7, the finite element solution equation is: and KU is F, wherein K is an overall rigidity matrix, F is a load vector, and U is a structure displacement vector.
In step 10, the method for reconstructing the geometric model comprises the following steps: and (5) identifying the geometric boundary of the microstructure obtained by the optimized model in the step (5) by using a boundary identification program, and importing the boundary into geometric software to reconstruct the unit cell geometric model.
The geometric software comprises Hypermesh and the like, in the Hypermesh software, a program is written by utilizing a tcl script language, and the optimized result information obtained in the step 7 is utilized to quickly and accurately reconstruct the whole heterogeneous double-layer model obtained through optimization.
The invention further discloses application of the corrosion-diffusion operator-based quasi-periodic hierarchical structure topology optimization method in the fields of 3D printing, aeronautical structures, biomedicine and the like.
Example two
The present embodiment is directed to a computing device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the specific steps of the first embodiment.
EXAMPLE III
An object of the present embodiment is to provide a computer-readable storage medium.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the first embodiment.
Example four
The present embodiment aims to provide a quasi-periodic hierarchical topology optimization system based on erosion-diffusion operator, which includes:
the structure model building module is used for building a structure model and subdividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
the optimization model establishing module is used for carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
the geometric model reconstruction module is used for calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the micro density and the macro density;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
The steps involved in the apparatuses of the above second, third and fourth embodiments correspond to the first embodiment of the method, and the detailed description thereof can be found in the relevant description of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media containing one or more sets of instructions; it should also be understood to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any of the methods of the present invention.
Test example 1
Step 1: the topologically optimized micro design domain is defined as squares of size 1 x 1, the number of grids is 50 x 50, the macro design domain is defined as rectangles of 20 x 15, and the number of grids is 20 x 15 (see fig. 2).
Step 2: definition of microscopic Unit Density
Figure BDA0002242776750000111
Designing variables for the microcosmic view; density of macro unit
Figure BDA0002242776750000112
For macroscopic design variables, as shown in FIG. 1;
and step 3: the convergence criterion is set as: max | | | xi+1-xi||>ΔxmaxAnd i is less than or equal to imax，imaxIs 160, Δ xmaxIs 0.001;
and 4, step 4: the microstructure was subjected to an etch-diffusion operation to obtain a quasi-periodic microstructure library (shown in figure 3). The calculation formula of the corrosion-diffusion operator is as follows:
Figure BDA0002242776750000121
wherein N ise＝{i|||xi-xe||≤rminFor the filter design field, parameters β were selected as follows:
and 5: predicting equivalent elastic tensor D of microstructure in alignment period microstructure library by utilizing asymptotic homogenization methodHSaid D isHThe calculation formula of (a) is as follows:
Figure BDA0002242776750000124
wherein, phi is a characteristic displacement vector, and the calculation formula is as follows:
Figure BDA0002242776750000125
through the steps 4 and 5, the method can realize the spatial transformation of the material property by adjusting the distribution of the quasi-periodic unit cells on the space.
Step 6: based on the elastic modulus of the microstructure database obtained by the previous step, the elastic modulus and the volume ratio of the microstructure are established by adopting B spline function fitting
Figure BDA0002242776750000126
The fitted curve is shown in FIG. 4;
Figure BDA0002242776750000127
and 7: the elasticity tensor obtained in the step 6
Figure BDA0002242776750000128
Carrying out finite element solution column, and calculating to obtain a unit stiffness matrix KeCarrying out finite element analysis to obtain a macroscopic displacement field U; in the corresponding topological optimization problem, an objective function is defined as the minimum flexibility of the structure, and the constraint condition is that the usage of the microscopic material is less than the volume
Figure BDA0002242776750000131
And the amount of macroscopic material is less than the volume
Figure BDA0002242776750000132
Establishing an optimization model shown as the following formula:
Figure BDA0002242776750000133
min c＝FTU＝UTKU
Figure BDA0002242776750000134
Figure BDA0002242776750000135
Figure BDA0002242776750000136
Figure BDA0002242776750000137
wherein N ismi＝2500，Nma＝300，
Figure BDA0002242776750000138
And 8: according to the finite element analysis result and the established optimization model in the step 7; calculating the compliance function of the structure relative to the macro topological variables
Figure BDA0002242776750000139
And microscopic topological variables
Figure BDA00022427767500001310
The sensitivity of these two types of design variables:
Figure BDA00022427767500001311
Figure BDA00022427767500001312
and step 9: according to the sensitivity information obtained in the step 8, iteration updating is carried out on the two types of design variables by using an MMA algorithm, and collaborative optimization design of the density of the micro-units and the density of the macro-units is completed;
step 10: and (4) importing the macro and micro optimization results obtained by the optimization model in the step (7) into Hypermesh software, writing a program by utilizing a tcl script language, and reconstructing the obtained geometric model of the whole heterogeneous structure. The performance test is performed by using a fine finite element grid, the minimum size of the grid is 0.02, and the equivalent stiffness of the embodiment and the comparative example 1 is as follows: 39.48 and 18.93, the performance is improved by more than one time.
Step 11: and preparing a design result by adopting a photo-curing machine 3d printer technology, wherein the material is photosensitive resin, the elastic modulus is 181MPa, the Poisson ratio is 0.44, and the manufacturing precision is 0.01 mm. Fig. 6(a) and 6(b) are graphs of the effects of 3D prints of the topology optimization design results in this embodiment and comparative example 1, respectively.
Comparative example 1
The results are shown in fig. 5(a) -5 (b) as a comparison of the optimization methods proposed by the present invention, which are performed by using the topology optimization design method of periodic hierarchical structure (periodic arrangement of single microstructure) proposed in document 2 ("Liu, l., Yan, j., and Cheng, G. (2008). Optimumstructure with a homeogenetic optimal time rows computer & structures86, 1417-1425") in the background of the present invention.
Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using general purpose computer means, or alternatively, they can be implemented using program code that is executable by computing means, such that they are stored in memory means for execution by the computing means, or they are separately fabricated into individual integrated circuit modules, or multiple modules or steps of them are fabricated into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. The quasi-periodic hierarchical structure topology optimization method based on the corrosion-diffusion operator is characterized by comprising the following steps:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the density of the micro-unit and the density of the macro-unit;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
2. The method for optimizing the topology of the quasi-periodic hierarchical structure based on the erosion-diffusion operator as claimed in claim 1, wherein the micro-design domain selects a square or cubic structure and is subdivided into a quadrilateral or hexahedral mesh.
3. The method of claim 1, wherein a first type of design variable for the density of microscopic cells and a second type of design variable for the density of macroscopic cells are defined.
4. The corrosion-diffusion operator-based quasi-periodic hierarchical structure topology optimization method as claimed in claim 1, wherein the obtained elastic modulus is substituted into a finite element solution column, a unit stiffness matrix is obtained by calculation, and a macroscopic displacement field is obtained by finite element analysis; in the corresponding topological optimization problem, an objective function is defined as the minimum flexibility of the structure, and the constraint condition is that the usage of the microscopic material is less than the volume
Figure FDA0002242776740000021
And the amount of macroscopic material is less than the volume
Figure FDA0002242776740000022
And establishing an optimization model.
5. The method for optimizing the topology of the quasiperiodic hierarchical structure based on the erosion-diffusion operator as claimed in claim 1, wherein the method for reconstructing the geometric model comprises the following steps: and identifying the geometric boundary of the microstructure obtained by the optimization model by using a boundary identification program, and importing the boundary into geometric software to reconstruct the unit cell geometric model.
6. The method for optimizing the topology of the quasiperiodic hierarchical structure based on the erosion-diffusion operator as claimed in claim 5, wherein the boundary is introduced into geometric software to reconstruct the geometric model of the unit cell: and reconstructing the optimized whole heterogeneous double-layer model by utilizing the optimization result information and the created single-cell geometric model.
7. Use of the method for the topological optimization of a quasiperiodic hierarchical structure based on a corrosion-diffusion operator according to any one of claims 1 to 6 in the fields of 3D printing, aeronautical construction and biomedicine.
8. A quasi-periodic hierarchical structure topology optimization system based on corrosion-diffusion operators is characterized by comprising the following steps:
the structure model building module is used for building a structure model and subdividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
the optimization model establishing module is used for carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
the geometric model reconstruction module is used for calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the density of the micro-unit and the density of the macro-unit;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the density of the micro-unit and the density of the macro-unit;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
10. A computer-readable storage medium, on which a computer program is stored, which program, when executed by a processor, carries out the steps of:
establishing a structural model, and dividing a finite element grid; defining a topological optimization microscopic design domain and dividing a microscopic grid;
carrying out corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library;
predicting the equivalent elasticity tensor of the microstructures in the alignment period microstructure library by using an asymptotic homogenization method;
based on the elastic modulus of the obtained microstructure database, adopting a B spline function to fit and establish an explicit functional relation between the elastic modulus and the volume ratio of the microstructure, and establishing an optimization model;
calculating the sensitivity of a compliance function of the structure relative to two design variables, namely a macroscopic topological variable and a microscopic topological variable respectively according to the optimization model;
iteratively updating the design variables according to the obtained sensitivity information to complete the cooperative optimization design of the density of the micro-unit and the density of the macro-unit;
and reconstructing the macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.
CN201911005931.XA 2019-10-22 2019-10-22 Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator Pending CN110751729A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911005931.XA CN110751729A (en) 2019-10-22 2019-10-22 Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911005931.XA CN110751729A (en) 2019-10-22 2019-10-22 Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator

Publications (1)

Publication Number Publication Date
CN110751729A true CN110751729A (en) 2020-02-04

Family

ID=69279301

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911005931.XA Pending CN110751729A (en) 2019-10-22 2019-10-22 Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator

Country Status (1)

Country Link
CN (1) CN110751729A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112132968A (en) * 2020-08-25 2020-12-25 山东大学 Two-scale periodic lattice self-adaptive filling and modeling method
CN112182929A (en) * 2020-09-18 2021-01-05 北京航空航天大学 Size control-considered cross-scale reliability topological optimization method for porous material
CN116738571A (en) * 2023-06-12 2023-09-12 盛年科技有限公司 Method for analyzing equivalent medium parameters of chiral lattice structure material

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110166833A1 (en) * 2005-12-19 2011-07-07 The Board Of Governors For Higher Education, State Of Rhode Island And Providence Plantations Systems and methods for finite element based topology optimization
CN109657378A (en) * 2018-12-25 2019-04-19 山东大学 A kind of heterosphere level structure Topology Optimization Method of the size unit cell containing change

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110166833A1 (en) * 2005-12-19 2011-07-07 The Board Of Governors For Higher Education, State Of Rhode Island And Providence Plantations Systems and methods for finite element based topology optimization
CN109657378A (en) * 2018-12-25 2019-04-19 山东大学 A kind of heterosphere level structure Topology Optimization Method of the size unit cell containing change

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
CHEN WENJIONG等: "《Design of periodic unit cell in cellular materials with extreme properties using topology optimization》", 《PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART L-JOURNAL OF MATERIALS-DESIGN AND APPLICATIONS》 *
李取浩等: "《基于微结构映射的非均质结构拓扑优化方法》", 《2018年全国固体力学学术会议》 *
贾海朋: "《结构与柔性机构拓扑优化》", 《中国优秀博硕士学位论文全文数据库(博士) 工程科技Ⅱ辑》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112132968A (en) * 2020-08-25 2020-12-25 山东大学 Two-scale periodic lattice self-adaptive filling and modeling method
CN112132968B (en) * 2020-08-25 2023-08-08 山东大学 Two-scale periodic lattice self-adaptive filling and modeling method
CN112182929A (en) * 2020-09-18 2021-01-05 北京航空航天大学 Size control-considered cross-scale reliability topological optimization method for porous material
CN116738571A (en) * 2023-06-12 2023-09-12 盛年科技有限公司 Method for analyzing equivalent medium parameters of chiral lattice structure material
CN116738571B (en) * 2023-06-12 2024-02-09 盛年科技有限公司 Method for analyzing equivalent medium parameters of chiral lattice structure material

Similar Documents

Publication Publication Date Title
CN110110413B (en) Structural topology optimization method based on material field reduction progression expansion
CN109657378B (en) Heterogeneous hierarchical structure topology optimization method containing variable-size unit cells
CN110751729A (en) Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator
CN111597698B (en) Method for realizing pneumatic optimization design based on deep learning multi-precision optimization algorithm
Wang et al. Adaptive topology optimization with independent error control for separated displacement and density fields
CN109344524B (en) Method for optimizing distribution of reinforcing ribs of thin plate structure
Schury et al. Efficient two-scale optimization of manufacturable graded structures
CN110069800B (en) Three-dimensional structure topology optimization design method and equipment with smooth boundary expression
Acharya et al. A parallel and memory efficient algorithm for constructing the contour tree
CN104750780B (en) A kind of Hadoop configuration parameter optimization methods based on statistical analysis
CN108647405A (en) The minor structure interpolation model modeling method of multi-layer lattice structure topology optimization design
Wang et al. From computer-aided design (CAD) toward human-aided design (HAD): an isogeometric topology optimization approach
CN114254408A (en) Gradient lattice isogeometric topology optimization method based on proxy model
Liu et al. Intelligent optimization of stiffener unit cell via variational autoencoder-based feature extraction
Wang et al. An adaptive method for high-resolution topology design
CN108491654A (en) A kind of 3D solid structural topological optimization method and system
Pandian et al. Synthesis of tensegrity structures of desired shape using constrained minimization
CN111079279A (en) Multi-scale topological optimization design method for multi-configuration lattice structure
CN108897956B (en) Optimization design method for porous mechanical parts
CN113505929B (en) Topological optimal structure prediction method based on embedded physical constraint deep learning technology
CN100578538C (en) Virtual surroundings population objects behaviors evolvement method based on gradation picture organization and transformation
CN115859717A (en) Topological optimization design method of latticed shell structure assembled node
CN115659619A (en) Geometric topological optimization and additive manufacturing based integrated method
CN106202667A (en) Constrained domain optimizes Latin hypercube method for designing
CN114239363A (en) Variable density topology optimization method based on ABAQUS secondary development Python language

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