CN112784468A - Multi-scale topology optimization method for light heat-insulation-preventing bearing structure - Google Patents

Multi-scale topology optimization method for light heat-insulation-preventing bearing structure Download PDF

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CN112784468A
CN112784468A CN202110177692.7A CN202110177692A CN112784468A CN 112784468 A CN112784468 A CN 112784468A CN 202110177692 A CN202110177692 A CN 202110177692A CN 112784468 A CN112784468 A CN 112784468A
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周明东
耿达
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Abstract

The invention discloses a multi-scale topological optimization method for a light heat-insulation bearing structure, which relates to the field of multi-scale structural topological optimization design and comprises the steps of predicting the equivalent attribute of a composite lattice microstructure and constructing an explicit agent model of the equivalent attribute; establishing a thermal convection diffusion equation and a linear balance equation, and solving a temperature field and a displacement field; establishing a continuous interpolation format of the coolant attribute and the equivalent attribute of the composite lattice; establishing a multi-scale topological optimization model and a target function and a constraint function thereof; calculating an objective function and a constraint function of the optimization model based on the temperature field and the displacement field; carrying out sensitivity analysis; and iteratively updating each design variable until a convergence condition is met. The method realizes multi-scale collaborative optimization design of metal, heat insulation materials and coolants, and realizes optimization of structural rigidity, heat insulation resistance and light weight.

Description

Multi-scale topology optimization method for light heat-insulation-preventing bearing structure
Technical Field
The invention relates to the field of topological optimization design of a multi-scale structure, in particular to a multi-scale topological optimization method for a light heat-proof and heat-insulating bearing structure.
Background
The structural topology optimization method is a simulation-driven structural design method, can realize reasonable distribution of materials in a design domain under the condition of meeting design constraint conditions, and is widely applied to lightweight design of industrial structures. Compared with the traditional topological optimization method which only carries out design on the macroscopic scale of the structure, the multi-scale topological optimization can consider the scale coupling effect and realize the integrated design of the material structure. Under the promotion of application requirements of industrial equipment such as aerospace and the like, numerous scholars at home and abroad begin to actively explore new theories and new technologies of lightweight and multifunctional structural design from the aspects of multi-physical-field coupling, cross-scale calculation and the like.
The traditional design mode aiming at the heat-insulation-preventing bearing structure generally needs to obtain an acceptable design scheme through multiple trial and error, the involved multi-physics simulation solving efficiency is low, the design period is long, the design period depends on the experience and professional level of a designer, the design factors and the coupling effect among different subjects and different scales are often ignored, and the obtained optimized design can not meet multiple functional requirements.
Although the existing multi-scale structure topological optimization method can realize the optimal distribution of microstructures in different topological forms, the geometrical continuity of the boundary of adjacent microstructures is difficult to guarantee. In the service process of the structure, the geometric continuous transition of adjacent microstructures is an important prerequisite for ensuring the bearing and heat-proof and heat-insulating performance of the structure. Although continuity of microstructure boundaries can be guaranteed by shape mapping techniques or by adding geometric constraints, the design optimization space is often severely constrained by related constraints. Although the optimization idea of adopting the parameterized microstructure can solve the problem of geometric continuity of boundaries of adjacent microstructures, the microstructure adopted in the prior work has simpler form and fewer types, and the design advantage of material structure integration is not fully exerted. In addition, the integrated design of the current material structure mostly aims at improving the bearing performance of the structure, and multi-scale optimization research for improving the heat-insulating performance of the structure and improving the heat dissipation capacity of fluid does not exist.
At present, the light weight degree of a designed structure is low by considering a topological optimization method of structural bearing and runner heat dissipation, and a method for efficiently designing a light heat-proof bearing structure containing runners in an electromechanical coupling environment is lacked.
Therefore, those skilled in the art are dedicated to develop a multi-scale topological optimization method for a lightweight heat-insulation-proof load-bearing structure, so as to realize multi-scale collaborative optimization design of metal, heat-insulation materials and cooling agents, and realize structural rigidity, heat-insulation-proof performance optimization and light weight.
Disclosure of Invention
In view of the above defects in the prior art, the technical problem to be solved by the present invention is how to perform a multi-scale topology optimization design under the premise of simultaneously considering the structural load and the heat dissipation of the flow channel, and to ensure that the solution is fast and the design is light.
In order to achieve the above object, the present invention provides a multi-scale topology optimization method for a light heat-proof and heat-insulation bearing structure, comprising the following steps:
step 1, predefining a plurality of topological gradient composite lattice microstructures, predicting equivalent attributes of the composite lattice microstructures, and constructing an explicit agent model of the equivalent attributes of the composite lattice microstructures; wherein the proxy model is an explicit function of the composite lattice microstructure geometric parameters and material volume fractions;
step 2, dividing a structure to be designed into a plurality of macro units, supposing that each macro unit is filled with a composite lattice microstructure, and endowing each macro unit with an initial relative density value; establishing a continuous interpolation format of the coolant attribute and the equivalent attribute of the composite lattice microstructure based on a variable density topological parameter model of 'design variable field-filter field-physical density field'; based on the physical density value of each macro unit, obtaining the equivalent attribute of each composite lattice microstructure according to the explicit proxy model mapping constructed in the step 1, establishing a thermal convection diffusion equation and a linear balance equation, and solving a temperature field and a displacement field of each macro unit;
step 3, establishing a multi-scale topological optimization model; the multi-scale topological optimization model takes the average temperature of a minimized designated area as an objective function, and the constraint functions of the multi-scale topological optimization model comprise a metal volume constraint function, a fluid volume constraint function, a structure maximum displacement constraint function and a phase interface constraint function; the multi-scale topological optimization model has a microscopic design variable and a macroscopic design variable; the microscopic design variables include the geometric parameter design variables and the material volume fraction design variables; the macro design variables include macro topology variables;
step 4, calculating the objective function, the metal volume constraint function, the fluid volume constraint function, the structure maximum displacement constraint function and the phase interface constraint function of the multi-scale topological optimization model based on the temperature field of the macro structure and the displacement field of the macro structure obtained by solving in the step 2; carrying out sensitivity analysis according to a chain type calculation rule in topology optimization; iteratively updating the macroscopic design variables and the microscopic design variables by adopting a moving asymptote algorithm;
and 5, repeating the steps 2-4 until the following conditions are simultaneously met, and finishing: the value of the metal volume constraint function is less than or equal to 0, the value of the fluid volume constraint function is less than or equal to 0, the value of the maximum displacement constraint function is less than or equal to 0, the value of the phase interface constraint function is less than or equal to 0, and the difference of the target functions of two adjacent optimization iteration steps is less than 0.005.
Further, the equivalent properties include an equivalent elastic matrix of the composite lattice microstructure, an equivalent heat conduction matrix of the composite lattice microstructure, and an equivalent thermal expansion vector of the composite lattice microstructure.
Further, in the step 1, a numerical homogenization method is adopted to predict the equivalent property of the composite lattice microstructure.
Further, in the step 1, an explicit proxy model of the equivalent property of the composite lattice microstructure is constructed by adopting a surface fitting method.
Further, the step 1 of predicting the equivalent properties of the composite lattice microstructure comprises:
calculating the equivalent elastic matrix D of the predefined composite lattice microstructure according to the following formulaH:
Figure BDA0002940519050000031
Wherein
Figure BDA0002940519050000032
Respectively shows the filling of the metal material and the heat insulation material in the composite lattice microstructureThe material domain, | omega | represents the volume of the composite lattice microstructure, DAL，DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieContaining displacement fields caused by six unit test strain fields, and N represents the number of finite units in the composite lattice structure.
Further, the step 1 of predicting the equivalent property of the composite lattice microstructure further comprises:
calculating the equivalent heat conduction matrix k of a predefined composite lattice microstructure according to the formulaH：
Figure BDA0002940519050000033
Wherein
Figure BDA0002940519050000034
Respectively representing the domains of the composite lattice microstructure filled with metal materials and heat insulating materials, | omega | represents the volume of the composite lattice microstructure, kAL，kARHeat conduction matrices representing the metallic material and the heat insulating material, respectively, ITIs an identity matrix, BeTGradient matrix representing a shape function, TeAnd (3) representing a characteristic temperature field, and N representing the number of finite units in the composite lattice microstructure.
Further, the step 1 of predicting the equivalent property of the composite lattice microstructure further comprises:
calculating the equivalent thermal expansion vector alpha of the predefined composite lattice microstructure according to the formulaH：
αH＝(DH)-1βH，
Wherein DHSaid equivalent elastic matrix, β, representing said composite lattice microstructureHExpressed as:
Figure BDA0002940519050000035
wherein
Figure BDA0002940519050000036
Respectively representing the domains of the composite lattice microstructure filled with metal materials and heat insulating materials, | omega | represents the volume of the composite lattice microstructure, and DAL，DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieContaining displacement fields caused by six unit test strain fields,
Figure BDA0002940519050000037
respectively representing the thermal expansion vectors, Γ, of the metallic material and of the insulating materialeAnd (3) representing a displacement field corresponding to a unit temperature field, wherein N represents the number of finite units in the composite lattice microstructure.
Further, the specific method for establishing the continuous interpolation format in step 2 includes:
and adopting an improved porous anisotropic material penalty method and an improved solid isotropic material penalty method to establish a continuous interpolation format of the equivalent elastic matrix, the equivalent heat conduction matrix, the equivalent thermal expansion vector, a fluid penalty term and the fluid flow rate of the composite lattice microstructure.
Further, in the step 4, the macroscopic design variables and the microscopic design variables are iteratively updated using a moving asymptote algorithm.
Further, in the step 4, the sensitivity analysis includes sensitivity analysis on the macro design variables and sensitivity analysis on the micro design variables for the objective function and the constraint function in the multi-scale topological optimization model.
Compared with the prior art, the invention has the beneficial technical effects that:
(1) an explicit agent model of the equivalent attributes of the composite lattice microstructure with respect to the geometric parameters and the material volume fraction is constructed, a fussy homogenization iteration process is avoided, the calculation cost is low, and the connectivity among the microstructures can be ensured.
(2) An efficient multi-scale and hot fluid simulation model is provided, and the solving efficiency of the fluid-containing mechanical-thermal coupling simulation problem is greatly accelerated.
(3) The cooperative layout of the coolant, the metal and the heat insulation material in a macro structure domain is realized, compared with the traditional parameter and size optimization design, the calculation cost is obviously reduced, the multi-scale design space is greatly expanded, and the structural performance is greatly improved.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a flow chart of a design method of a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of a structure to be designed according to a preferred embodiment of the present invention;
FIG. 3 is a schematic diagram of the macro-structure topology of a preferred embodiment of the present invention;
FIG. 4 is a schematic diagram of the metal content distribution of the composite lattice microstructure in the optimized design according to a preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of the metal content of the frame of the composite lattice microstructure in the optimized design according to a preferred embodiment of the invention.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
The flow chart of the multi-scale topological optimization method for the light heat-insulation-preventing bearing structure is shown in figure 1.
As shown in fig. 1, the proposed optimization model contains two types of design variables, which are a macroscopic design variable x, y and a microscopic design variable v, z; e.g., unit i at the macro scale, as a macro design variablexi，yiPhysical density obtained after filtering and projection processing
Figure BDA0002940519050000041
When, unit i represents coolant; when physical density
Figure BDA0002940519050000042
Or 1 of the number of the groups in the group,
Figure BDA0002940519050000043
for each unit i, filling the unit i with a composite lattice microstructure; when physical density
Figure BDA0002940519050000051
When the unit i is a pore. When microscopic design variable vi，ziMicro-filtration density obtained after filtration
Figure BDA0002940519050000052
And when different values are taken, the unit i under the macro scale is filled by the composite lattice microstructure with different topology and metal content. Thus in the figure "macro scale: updating the distribution of the coolant and the microstructure "means that the distribution positions of the coolant and the composite lattice in the macro design domain are continuously updated in the optimization process; "microscopic Scale: updating the configuration of the composite lattice microstructure means that the topology and the metal content of the composite lattice microstructure filled in a certain position of the macroscopic structure are continuously updated in the optimization process. "all constraints are satisfied" means that the metal volume constraint function h in the optimization model in the optimization iteration process is optimized1Fluid volume constraint function h2Maximum displacement constraint function h3Boundary constraint function h4Meanwhile, the content is less than or equal to 0; "| Δ φ | < 0.005" means that the difference of the objective functions of two adjacent optimization iteration steps is less than 0.005.
The method mainly comprises the following steps:
step 1, predefining a plurality of composite lattice microstructures, wherein the composite lattice microstructures have different topologies, geometric dimensions and material volume fractions, and the composite lattice microstructures between different topologies can be mutually converted by changing the geometric dimensions and the material volume fractions; and predicting the equivalent property of the composite lattice microstructure by adopting a numerical homogenization method, and constructing an explicit proxy model of the equivalent property of the composite lattice microstructure by adopting a surface fitting method, wherein the proxy model is an explicit function of the geometric parameters and the material volume fraction of the composite lattice microstructure.
Specifically, step 1 comprises the following sub-steps:
step 1.1, calculating an equivalent elastic matrix D of a predefined composite lattice microstructure according to the following formulaH：
Figure BDA0002940519050000053
Wherein
Figure BDA0002940519050000054
Respectively representing the domains of the composite lattice microstructure filled with the metal material and the heat insulating material, | omega | represents the volume of the microstructure, and DAL，DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieContains displacement fields caused by six element test strain fields, and N represents the number of finite elements in the microstructure.
Step 1.2, calculating an equivalent heat conduction matrix k of a predefined composite lattice microstructure according to the following formulaH：
Figure BDA0002940519050000055
Wherein
Figure BDA0002940519050000056
Respectively representing the domains of the composite lattice microstructure filled with the metal material and the heat insulating material, | omega | represents the volume of the microstructure, kAL，kARHeat conduction matrices representing the metallic material and the heat insulating material, respectively, ITIs an identity matrix, BeTGradient matrix representing a shape function, TeRepresenting a characteristic temperature field and N representing the number of finite elements within the microstructure.
Step 1.3, calculating the equivalent thermal expansion vector alpha of the predefined composite lattice microstructure according to the following formulaH，
αH＝(DH)-1βH，
Wherein DHEquivalent elastic matrix, beta, representing a composite lattice microstructureHCan be expressed as:
Figure BDA0002940519050000061
wherein
Figure BDA0002940519050000062
Respectively representing the domains of the composite lattice microstructure filled with the metal material and the heat insulating material, | omega | represents the volume of the microstructure, and DAL，DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieContaining the displacement field caused by the six-element test strain field.
Figure BDA0002940519050000063
Respectively representing the thermal expansion vectors, Γ, of the metallic material and of the insulating materialeAnd the displacement field corresponding to a unit temperature field is expressed, and N represents the number of finite units in the microstructure.
Step 1.4, establishing equivalent attributes of the composite lattice microstructure and geometric parameters of the composite lattice microstructure
Figure BDA00029405190500000611
And volume fraction of material
Figure BDA00029405190500000612
As shown in the following three formulas,
equivalent elastic matrix of composite lattice microstructure with respect to its geometrical parameters
Figure BDA0002940519050000064
And volume fraction of material
Figure BDA0002940519050000065
Explicit proxy model of (2):
Figure BDA0002940519050000066
where a, b, c, d, w, f, g, h, i, j, k, l, m, n, o are the coefficients of the fitted quadratic polynomial. It should be noted that, for the same composite lattice microstructure, D11＝D22＝D33，D12＝D13＝D21＝D23＝D31＝D32，D44＝D55＝D66。
Equivalent heat conduction matrix of composite lattice microstructure with respect to material volume fraction thereof
Figure BDA0002940519050000067
Explicit proxy model of (2):
Figure BDA0002940519050000068
where p, q, r, s are the coefficients of the fitted cubic polynomial. It should be noted that, for the same composite lattice microstructure, k is11＝k22＝k33。
Equivalent thermal expansion vector of composite lattice microstructure with respect to its material volume fraction
Figure BDA0002940519050000069
Explicit proxy model of (2):
Figure BDA00029405190500000610
wherein beta' is the natural index of the fitted nonlinear functione power exponent. It should be noted that, for the same composite lattice microstructure, α1＝α2＝α3。
Step 2, dividing the structure to be designed shown in fig. 2 into a plurality of macro units, supposing that each macro unit is filled with a composite lattice microstructure, and endowing each macro unit with an initial relative density value; establishing a continuous interpolation format of the coolant attribute and the equivalent attribute of the composite lattice microstructure based on a variable density topological parameter model of 'design variable field-filter field-physical density field'; based on the physical density value of each macro unit, obtaining the equivalent attribute of each composite lattice microstructure according to the explicit proxy model mapping constructed in the step 1, establishing a thermal convection diffusion equation and a linear balance equation, and solving a temperature field and a displacement field of each macro unit.
The step 2 specifically comprises the following substeps:
step 2.1, using macro topological variables x and y as macro variables, using micro geometric parameters z and material volume fraction v as micro variables, giving initial relative density values x, y, v and z to each macro unit, and obtaining the physical density of each macro unit based on a variable density topological parameter model of' design variable field-filter field-physical density field
Figure BDA0002940519050000071
Step 2.2, adopting an improved porous anisotropic material penalty method (PAMP) and an improved solid isotropic material penalty method (SIMP) to establish an equivalent elastic matrix D, an equivalent heat conduction matrix k, an equivalent thermal expansion vector alpha of the microstructure, a fluid penalty term gamma and a fluid flow velocity u according to the following formulazContinuous interpolation format of (2):
Figure BDA0002940519050000072
Figure BDA0002940519050000073
Figure BDA0002940519050000074
Figure BDA0002940519050000075
Figure BDA0002940519050000076
where p is a penalty index, kwIs the thermal conductivity of the coolant, alphawIs the coefficient of thermal expansion of the coolant, IU，ITIs two identity matrices, LT＝[1 1 1 0 0 0]T，D0，k0，α0Is a small value, gamma, set to avoid numerical singularities0Is a maximum, here 1000000, u0Is the fluid flow rate.
Step 2.3, obtaining the equivalent attribute of the composite lattice microstructure by adopting the explicit agent model mapping constructed in the step 1, and establishing a heat convection diffusion equation according to the equivalent attribute as follows:
(k+ku+kγ)T＝fq+fγ，
wherein the heat conduction matrix k is in the form of uniteThermal convection matrix
Figure BDA0002940519050000077
Penalty matrix
Figure BDA0002940519050000078
Heat flow load vector
Figure BDA0002940519050000079
Penalty load vector
Figure BDA00029405190500000710
Can be respectively expressed as:
Figure BDA00029405190500000711
Figure BDA00029405190500000712
Figure BDA00029405190500000713
Figure BDA00029405190500000714
Figure BDA00029405190500000715
where ρ, cp，uzRespectively, coolant density, specific heat, and flow rate, q represents thermal load, and TARepresenting the ambient temperature, gamma represents a penalty term,
Figure BDA00029405190500000716
a gradient matrix representing a shape function.
Step 2.4, on the basis of obtaining the temperature field of the macro unit, considering structural thermodynamic coupling, establishing a linear balance equation, and solving the displacement field of the macro structure:
KU＝f+fte，
in which the stiffness matrix K is in the form of cellseExternal load vector feAnd the vector of thermal expansion
Figure BDA00029405190500000717
Can be respectively expressed as:
Ke＝∫Ω(LNs)TD(LNs)dΩ，
Figure BDA0002940519050000081
Figure BDA0002940519050000082
wherein N issRepresenting a shape function, L representing a gradient operator, D representing an elastic matrix of the material, f0Representing the mechanical load acting on the structure and alpha representing the coefficient of thermal expansion of the material.
And 3, establishing a multi-scale topological optimization model. The optimization model takes macroscopic topological variables x and y as macroscopic design variables, takes microscopic geometric parameters z and material volume fraction v as microscopic design variables, takes the minimum specified region average temperature phi as an objective function, and the constraint function of the multi-scale topological optimization model comprises a metal volume constraint function h1Coolant volume constraint function h2Constraint function h of maximum displacement of structure3Boundary constraint function h4The mathematical expression of the established multi-scale topological optimization model is as follows:
find：{x；y；v；z}
min：φ
s.t.hj≤0，j＝1，2，…，M
Figure BDA0002940519050000083
Figure BDA0002940519050000084
0≤xi，yi，vi，zi，≤1，i＝1，2，…，Ne
where M represents the number of constraints, NeRepresenting the number of cells in the macrostructure, the objective function phi is expressed as:
Figure BDA0002940519050000085
wherein
Figure BDA0002940519050000086
To specify the area of the region, L1Is the indication vector of the designated area, T is the structure temperature field, N1The number of nodes in the area.
Metal volume constraint function h1Expressed as:
Figure BDA0002940519050000087
wherein VsUpper limit of metal volume constraint, NeIndicating the number of units in the macrostructures.
Fluid volume constraint function h2Expressed as:
Figure BDA0002940519050000088
wherein VlUpper limit of fluid volume constraint, NeIndicating the number of units in the macrostructures.
Constraint function h of maximum displacement of structure3Can be expressed as:
Figure BDA0002940519050000089
wherein
Figure BDA00029405190500000810
U0Denotes the upper limit of structural displacement, N2Indicating the number of nodes in the macrostructure,
Figure BDA00029405190500000811
represents the node i to the power of t of the displacement magnitude, where t is 16.
Characterizing structural inflowPhase boundary constraint function h of contact degree of body and pore4Can be expressed as:
Figure BDA0002940519050000091
wherein
Figure BDA0002940519050000092
εpRepresents a small value, NeIndicating the number of units in the macrostructures.
Step 4, calculating an objective function phi and each constraint function h in the multi-scale topological optimization model based on the temperature field T and the displacement field U of the macro unit solved in the step 2j(i.e., metal volume constraint function h1Fluid volume constraint function h2Constraint function h of maximum displacement of structure3Boundary constraint function h4) According to the chain calculation rule in the topology optimization, the objective function phi and each constraint function h in the optimization model are subjected tojThe sensitivity analysis was performed for each of the design variables referred to in (1). Wherein the sensitivity of the objective function with respect to macroscopic design variables is:
Figure BDA0002940519050000093
where theta represents the sum of the macroscopic design variables x, y,
Figure BDA0002940519050000094
the sensitivity of the objective function with respect to microscopic design variables is
Figure BDA0002940519050000095
Where ψ denotes the microscopic design variables z, v.
Constraint function h of maximum displacement of structure3The sensitivity with respect to macroscopic design variables θ is:
Figure BDA0002940519050000096
constraint function h of maximum displacement of structure3The sensitivity for the microscopic design variable ψ is:
Figure BDA0002940519050000097
in the above-mentioned two formulas, the first and second groups,
Figure BDA0002940519050000098
Figure BDA0002940519050000099
Figure BDA00029405190500000910
Figure BDA00029405190500000911
k, f in the sensitivity formatte，k，ku，kγ，fγThe first derivatives for the macroscopic and microscopic design variables may be obtained based on a continuous interpolation format of the material and an explicit proxy model. Metal volume constraint function h1Fluid volume constraint function h2Boundary constraint function h4The sensitivity with respect to macroscopic design variables, respectively, can be obtained by taking the partial derivative. Metal volume constraint function h1Fluid volume constraint function h2Boundary constraint function h4The sensitivity with respect to the microscopic design variables, respectively, was 0.
The macroscopic design variables x and y, and the microscopic design variables z and v, i.e., the coolant and microstructure distributions and the composite lattice microstructure configuration, are iteratively updated using a moving asymptote algorithm (MMA).
Step 5, repeating the steps 2-4 until the metal volume constraint function h1Fluid volume constraint function h2Maximum displacement constraint function h3Phase boundary constraint function h4Meanwhile, the difference is less than or equal to 0, and the target function difference | delta phi | of two adjacent optimization iteration steps is less than 0.005, and the optimization design is finished.
According to the steps, a composite lattice structure with excellent heat dissipation performance and good bearing performance can be designed according to the optimization strategy shown in the figure 1.
In another embodiment of the present invention, the structure to be designed, which is shown in fig. 2 and has a height of 0.2m and a width of 1.0m, is divided into 40 × 200 macro cells, the metal material used is aluminum alloy, the heat insulating material is aerogel, the coolant is water, and the flow velocity perpendicular to the paper surface is uz1.0m/s at room temperature 293.15K. To distinguish from the optimized design of fig. 3, fig. 2 shows gray, representing the original design, gray representing the composite lattice microstructure and white representing the coolant. As shown in fig. 2, the bottom surface of the structure to be designed is fixed, and the top surface is subjected to a mechanical load of f 100MPa and q 50000W/m2The heat flow of (a); the upper limit of the volume fraction of the metal and the coolant is Vs＝0.5，Vl0.04; the maximum displacement upper limit of the structure is U01.0mm, phase boundary function tolerance εp＝2.5×10-7(ii) a The objective function is to minimize the average temperature of the bottom surface of the structure.
And (3) performing multi-scale topological optimization design on the structure to be designed by adopting the method to obtain a macroscopic structure topology shown in figure 3, wherein white represents a coolant, and black represents a composite dot matrix microstructure. FIG. 4 shows the metal content of the composite lattice microstructure in the design domain
Figure BDA0002940519050000101
The darker the color of the distribution diagram, the more metal content in the microstructure is shown, and the lighter the color is, the heat insulating material in the microstructure is shownThe more the content is, the main force transmission path is formed by the composite lattice microstructure with high metal content, and the surface heat can be quickly transmitted to the coolant enveloped by the composite lattice microstructure, so that the composite lattice microstructure is prevented from being transmitted to the bottom surface; the composite lattice microstructure with high heat insulating material content is distributed in a position far away from the coolant to play a heat insulating role. FIG. 5 shows the metal ratio of the composite lattice microstructure frame
Figure BDA0002940519050000102
Distribution diagram, it can be seen that the metal within the microstructure is distributed mainly to the structural border. In addition, under the working conditions, the average temperature of the bottom surface of the structure is 294.06K, which is close to room temperature, and the heat-proof performance of the optimized design is good; the maximum displacement of the optimized design is 1.0mm, and the design requirement is met. It should be noted that FIGS. 4 and 5 also show the continuously varying micro-filtration density in the optimization results, respectively
Figure BDA0002940519050000103
Distribution within the optimized structure, corresponding to any unit i within the macro-design domain
Figure BDA0002940519050000104
Can be any value of more than or equal to 0 and less than or equal to 1, and the black, white and different gray colors in the lower color bands of the figures 4 and 5 respectively represent different metal contents of the composite lattice microstructure
Figure BDA0002940519050000109
And the metal proportion of the composite lattice microstructure frame
Figure BDA0002940519050000106
Any two different
Figure BDA0002940519050000107
And
Figure BDA0002940519050000108
in combination, both represent a composite lattice microstructure. Therefore, the macro-micro information represented by fig. 3, 4 and 5 can be used for reconstructing the designed light heat-proof and heat-insulation bearingAnd a carrying structure.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A multi-scale topological optimization method for a light heat-insulation-preventing bearing structure is characterized by comprising the following steps:
step 1, predefining a plurality of topological gradient composite lattice microstructures, predicting equivalent attributes of the composite lattice microstructures, and constructing an explicit agent model of the equivalent attributes of the composite lattice microstructures; wherein the proxy model is an explicit function of the composite lattice microstructure geometric parameters and material volume fractions;
step 2, dividing a structure to be designed into a plurality of macro units, supposing that each macro unit is filled with a composite lattice microstructure, and endowing each macro unit with an initial relative density value; establishing a continuous interpolation format of the coolant attribute and the equivalent attribute of the composite lattice microstructure based on a variable density topological parameter model of 'design variable field-filter field-physical density field'; based on the physical density value of each macro unit, obtaining the equivalent attribute of each composite lattice microstructure according to the explicit proxy model mapping constructed in the step 1, establishing a thermal convection diffusion equation and a linear balance equation, and solving a temperature field and a displacement field of each macro unit;
step 3, establishing a multi-scale topological optimization model; the multi-scale topological optimization model takes the average temperature of a minimized designated area as an objective function, and the constraint functions of the multi-scale topological optimization model comprise a metal volume constraint function, a fluid volume constraint function, a structure maximum displacement constraint function and a phase interface constraint function; the multi-scale topological optimization model has a microscopic design variable and a macroscopic design variable; the microscopic design variables include the geometric parameter design variables and the material volume fraction design variables; the macro design variables include macro topology variables;
step 4, calculating the objective function, the metal volume constraint function, the fluid volume constraint function, the structure maximum displacement constraint function and the phase interface constraint function of the multi-scale topological optimization model based on the temperature field of the macro structure and the displacement field of the macro structure obtained by solving in the step 2; carrying out sensitivity analysis according to a chain type calculation rule in topology optimization; iteratively updating the macroscopic design variables and the microscopic design variables by adopting a moving asymptote algorithm;
and 5, repeating the steps 2-4 until the following conditions are simultaneously met, and finishing: the value of the metal volume constraint function is less than or equal to 0, the value of the fluid volume constraint function is less than or equal to 0, the value of the maximum displacement constraint function is less than or equal to 0, the value of the phase interface constraint function is less than or equal to 0, and the difference of the target functions of two adjacent optimization iteration steps is less than 0.005.
2. The multi-scale topological optimization method for a light heat-proof and insulating bearing structure according to claim 1, wherein the equivalent properties comprise an equivalent elastic matrix of the composite lattice microstructure, an equivalent heat conduction matrix of the composite lattice microstructure, and an equivalent thermal expansion vector of the composite lattice microstructure.
3. The multi-scale topological optimization method for the light heat-insulation load-bearing structure is characterized in that in the step 1, the equivalent property of the composite lattice microstructure is predicted by adopting a numerical homogenization method.
4. The multi-scale topological optimization method for the light heat-insulation load-bearing structure is characterized in that in the step 1, an explicit proxy model of the equivalent property of the composite lattice microstructure is constructed by adopting a surface fitting method.
5. The multi-scale topological optimization method for a light heat-proof and insulating bearing structure according to claim 4, wherein the predicting the equivalent properties of the composite lattice microstructure in the step 1 comprises:
calculating the equivalent elastic matrix D of the predefined composite lattice microstructure according to the following formulaH:
Figure FDA0002940519040000021
Wherein
Figure FDA0002940519040000022
Respectively representing the domains of the composite lattice microstructure filled with metal materials and heat insulating materials, | omega | represents the volume of the composite lattice microstructure, and DAL,DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieThe displacement field caused by the six-unit test strain field is contained, and N represents the number of finite units in the composite lattice microstructure.
6. The multi-scale topological optimization method for a light heat insulating bearing structure according to claim 5, wherein the predicting the equivalent properties of the composite lattice microstructure in step 1 further comprises:
calculating the equivalent heat conduction matrix k of a predefined composite lattice microstructure according to the formulaH:
Figure FDA0002940519040000023
Wherein
Figure FDA0002940519040000024
Respectively represent the compositionFilling the metal material and the heat insulating material in the lattice microstructure, | omega | represents the volume of the composite lattice microstructure, kAL,kARHeat conduction matrices representing the metallic material and the heat insulating material, respectively, ITIs an identity matrix, BeTGradient matrix representing a shape function, TeAnd (3) representing a characteristic temperature field, and N representing the number of finite units in the composite lattice microstructure.
7. The multi-scale topological optimization method for a lightweight thermal insulating load-bearing structure according to claim 6, wherein said predicting said equivalent properties of said composite lattice microstructure in step 1 further comprises:
calculating the equivalent thermal expansion vector alpha of the predefined composite lattice microstructure according to the formulaH:
αH＝(DH)-1βH,
Wherein DHSaid equivalent elastic matrix, β, representing said composite lattice microstructureHExpressed as:
Figure FDA0002940519040000031
wherein
Figure FDA0002940519040000032
Respectively representing the domains of the composite lattice microstructure filled with metal materials and heat insulating materials, | omega | represents the volume of the composite lattice microstructure, and DAL,DARRespectively representing the elastic matrices of the metallic material and of the insulating material, IUIs an identity matrix, BeURepresenting the strain displacement matrix,. chieContaining displacement fields caused by six unit test strain fields,
Figure FDA0002940519040000033
respectively representing the thermal expansion vectors, Γ, of the metallic material and of the insulating materialeRepresenting the displacement field corresponding to a unit temperature field, N representing the complexCombining the number of the limited units in the point array microstructure.
8. The multi-scale topological optimization method for the lightweight thermal insulation load-bearing structure according to claim 7, wherein the specific method for establishing the continuous interpolation format in the step 2 comprises:
and adopting an improved porous anisotropic material penalty method and an improved solid isotropic material penalty method to establish a continuous interpolation format of the equivalent elastic matrix, the equivalent heat conduction matrix, the equivalent thermal expansion vector, a fluid penalty term and the fluid flow rate of the composite lattice microstructure.
9. The multi-scale topological optimization method for a light insulating load-bearing structure according to claim 1, wherein in said step 4, said macroscopic design variables and said microscopic design variables are iteratively updated using a moving asymptote algorithm.
10. The multi-scale topological optimization method for a light heat insulating load-bearing structure according to claim 1, wherein in said step 4, said sensitivity analysis comprises sensitivity analysis on said macro design variables and sensitivity analysis on said micro design variables for said objective function, constraint function in said multi-scale topological optimization model.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113744818A (en) * 2021-09-03 2021-12-03 上海大学 Method for predicting defects of ternary rare earth oxide composite points
CN115408914A (en) * 2022-09-02 2022-11-29 大连理工大学宁波研究院 Problem-independent machine learning topology optimization method, medium, and product of two-dimensional structure
CN117473836A (en) * 2023-11-16 2024-01-30 北京理工大学 Integrated design method for thin-wall-multi-class lattice filling structure
WO2024050982A1 (en) * 2022-09-05 2024-03-14 中车长春轨道客车股份有限公司 Method and apparatus for designing cold conduction structure on basis of topology optimization

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109871574A (en) * 2018-12-28 2019-06-11 华中科技大学 A kind of multiple dimensioned Topology Optimization Method based on agent model
CN110341178A (en) * 2018-04-02 2019-10-18 深圳前海赛恩科三维科技有限公司 A kind of composite fibre prepares dot matrix core material member forming process and device
CN110941924A (en) * 2019-11-25 2020-03-31 华中科技大学 Multi-component system integration integrated multi-scale topology optimization design method
CN112287491A (en) * 2020-12-28 2021-01-29 中国人民解放军国防科技大学 Composite lattice material and design method thereof

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110341178A (en) * 2018-04-02 2019-10-18 深圳前海赛恩科三维科技有限公司 A kind of composite fibre prepares dot matrix core material member forming process and device
CN109871574A (en) * 2018-12-28 2019-06-11 华中科技大学 A kind of multiple dimensioned Topology Optimization Method based on agent model
CN110941924A (en) * 2019-11-25 2020-03-31 华中科技大学 Multi-component system integration integrated multi-scale topology optimization design method
CN112287491A (en) * 2020-12-28 2021-01-29 中国人民解放军国防科技大学 Composite lattice material and design method thereof

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
DONGJIN KIM 等: "Topology optimization of functionally graded anisotropic composite structures using homogenization design method", 《COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING》 *
YICHANG LIU 等: "Topology optimization of self-supporting infill structures", 《STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION》 *
周涵 等: "基于参数化微结构的多尺度点阵结构拓扑优化设计", 《2018 年全国固体力学学术会议》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113744818A (en) * 2021-09-03 2021-12-03 上海大学 Method for predicting defects of ternary rare earth oxide composite points
CN113744818B (en) * 2021-09-03 2023-09-15 上海大学 Prediction method for ternary rare earth oxide composite point defects
CN115408914A (en) * 2022-09-02 2022-11-29 大连理工大学宁波研究院 Problem-independent machine learning topology optimization method, medium, and product of two-dimensional structure
CN115408914B (en) * 2022-09-02 2023-07-04 大连理工大学宁波研究院 Two-dimensional structure problem-free machine learning topology optimization method, medium and product
WO2024050982A1 (en) * 2022-09-05 2024-03-14 中车长春轨道客车股份有限公司 Method and apparatus for designing cold conduction structure on basis of topology optimization
CN117473836A (en) * 2023-11-16 2024-01-30 北京理工大学 Integrated design method for thin-wall-multi-class lattice filling structure

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