CN115809515B - Multi-layer heat insulation structure optimization design method for high-speed aircraft - Google Patents

Multi-layer heat insulation structure optimization design method for high-speed aircraft Download PDF

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CN115809515B
CN115809515B CN202310085526.3A CN202310085526A CN115809515B CN 115809515 B CN115809515 B CN 115809515B CN 202310085526 A CN202310085526 A CN 202310085526A CN 115809515 B CN115809515 B CN 115809515B
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insulation structure
heat
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CN115809515A (en
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郝东
王琪
苏杰
刘建霞
丁智坚
武龙
贺元元
王�锋
余婧
杨大伟
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Institute of Aerospace Technology of China Aerodynamics Research and Development Center
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Abstract

The invention discloses an optimal design method of a multi-layer heat insulation structure of a high-speed aircraft, which relates to the technical field of heat insulation, wherein the heat insulation structure of the high-speed aircraft is divided into a plurality of layers of materials, and design variables, namely a selectable material database and the geometric dimensions of the materials of each layer, are determined; determining the heat insulation effective mass ratio of the optimized objective function, and setting constraint conditions; integrating the optimization objective function and the constraint condition, and obtaining an optimization model according to the design variable; and solving an optimization model by adopting an intelligent optimization algorithm to obtain optimized heat insulation material selection and geometric dimensions of each layer of heat insulation material. According to the invention, the material selection, the geometric dimension and the material thermal conductivity temperature change characteristics are introduced into an optimal design model, so that the optimal material selection and material geometric dimension are obtained, and the requirements of practical application are met.

Description

Multi-layer heat insulation structure optimization design method for high-speed aircraft
Technical Field
The invention relates to the technical field of heat insulation, in particular to an optimal design method of a multilayer heat insulation structure of a high-speed aircraft.
Background
The heat insulation structure is a key factor for protecting the high-speed aircraft from working safely and completing various tasks, and the effective heat insulation structure can meet the basic requirements of heat prevention and heat insulation of the high-speed aircraft, so that the high-speed aircraft is prevented from being damaged by extreme aerodynamic heat environment. With the development and upgrade of the national high-speed aircraft technology, the traditional heat insulation structure is difficult to meet the requirements of low cost, light weight, integrated heat insulation and prevention, and the like, so the design of the multilayer heat insulation structure is widely focused by various countries. The schematic diagram of the multi-layer heat insulation structure of the high-speed aircraft is shown in fig. 1, the extremely high temperature environment born by the high-speed aircraft in flight heats the high temperature resistant layer of the multi-layer heat insulation structure in a forced convection heat exchange mode, and meanwhile, the burning resistant layer radiates heat to the external space to remove part of heat. The main heat in the rest heat is blocked by the heat insulating layer, and a small part of heat is absorbed and stored by the self material of the burning-resistant layer and is transferred to the base layer, so that the base layer structure and the internal air perform natural convection heat exchange. The heat insulation performance of the multi-layer heat insulation structure mainly depends on the material parameters of the heat insulation layer and the thickness dimension of each layer, and the equivalent mechanical property of the whole structure is mainly determined by the material parameters of the base layer, so that the base layer is sometimes called a bearing layer according to the function of the base layer.
In the multi-layer heat insulation structure of the high-speed aircraft, materials of each layer are often selected from a plurality of materials, at present, most of optimal design of the heat insulation structure of the high-speed aircraft is considered that the heat conductivity of the materials is constant, the heat conductivity of the materials is sensitive to temperature, the heat transfer performance is severe along with the change of temperature, the heat conductivity of the heat insulation material of the existing aircraft is not considered along with the change of temperature, the temperature change characteristic of the heat conductivity of the heat insulation material has an influence on the heat insulation effect, and the multi-layer heat insulation structure of the high-speed aircraft, which is designed without considering the influence of the temperature on the heat conductivity, is often greatly different from the actual heat insulation performance; in addition, in the process of optimizing the design of the heat insulation structure, the current material selection type is determined, the condition of material preference is not considered, and the material selection and the dimensional variable are not simultaneously included in the design variable of the optimization of the heat insulation structure.
The existing optimal design method can not simultaneously solve the problems of material optimization and structure optimization, and has larger limitation.
Disclosure of Invention
The invention aims at: the multi-layer heat insulation structure optimization design method of the high-speed aircraft aims at the multi-layer heat insulation structure optimization design of the high-speed aircraft, introduces material selection design variables and material heat conductivity temperature change characteristics into an optimization design model, and solves the problem that the existing multi-layer heat insulation structure optimization design method of the high-speed aircraft does not consider material optimization and material heat conductivity temperature change influences.
The technical scheme adopted by the invention is as follows:
the invention relates to a method for optimally designing a multi-layer heat insulation structure of a high-speed aircraft, wherein the heat insulation structure of the high-speed aircraft is divided into multi-layer materials,
determining design variables of the heat insulation structure, namely a selectable material database and the geometric dimensions of each layer of material;
determining the heat insulation effective mass ratio of the optimized objective function, and setting constraint conditions;
integrating the optimization objective function and the constraint condition, and obtaining an optimization model according to the design variable;
and solving an optimization model by adopting an intelligent optimization algorithm to obtain optimized design variables, namely optimized material selection and geometric dimensions of each layer of heat insulation material.
Further, the multi-layer material specifically comprises an outer layer material, an intermediate layer material and an inner layer material, wherein the optional material data are respectively
Figure SMS_1
、/>
Figure SMS_2
And
Figure SMS_3
the database of selectable materials is +.>
Figure SMS_4
；
The geometric dimensions of the three layers of materials are respectively the thickness of the outer layer of material
Figure SMS_5
Thickness of the interlayer Material->
Figure SMS_6
Thickness of inner layer material->
Figure SMS_7
。
Further, the optimization objective function heat insulation effective mass ratio, namely the mass ratio of heat insulation efficiency and heat insulation structure, has the formula:
Figure SMS_8
，
the heat insulation efficiency is the effective working time length
Figure SMS_9
The heat insulation rate at the time is:
Figure SMS_10
，
wherein ,
Figure SMS_11
for the heat source temperature->
Figure SMS_12
The temperature response of the inner wall surface;
the mass of the heat insulation structure is as follows:
Figure SMS_13
，
wherein ,
Figure SMS_14
is the density of the outer layer material->
Figure SMS_15
For the density of the interlayer material>
Figure SMS_16
In order to achieve the density of the inner layer material,
according to the concept of the maximum heat insulation effective mass ratio, the optimized objective function is obtained as follows:
Figure SMS_17
。
further, the constraint condition specifically includes:
the inner layer of the heat insulation structure has an inner surface wall temperature facing the inner cavity
Figure SMS_18
Time temperature->
Figure SMS_19
Less than or equal to->
Figure SMS_20
；
The thickness of each layer of material is as follows
Figure SMS_22
、/>
Figure SMS_25
、/>
Figure SMS_27
, wherein ,
Figure SMS_23
、/>
Figure SMS_26
、/>
Figure SMS_28
upper limit of thickness dimension for each layer of material, +.>
Figure SMS_29
、/>
Figure SMS_21
、/>
Figure SMS_24
A lower limit of the thickness dimension of each layer of material;
equivalent modulus
Figure SMS_30
The equivalent modulus is defined as:
Figure SMS_31
，
wherein ,
Figure SMS_32
is the minimum allowed modulus body, +.>
Figure SMS_33
Modulus of the outer layer material>
Figure SMS_34
Modulus of the interlayer material, +.>
Figure SMS_35
Modulus for the inner layer material;
material selection belonging to a material dataset
Figure SMS_36
。
Further, the inner surface wall temperature of the inner layer of the heat insulation structure facing the inner cavity is as follows
Figure SMS_37
Time temperature->
Figure SMS_38
It is necessary to solve for the heat transfer equation,
the heat transfer equation:
Figure SMS_39
，
the boundary conditions are:
Figure SMS_40
and
Figure SMS_41
，
wherein ,
Figure SMS_43
for material thermal conductivity, +.>
Figure SMS_47
Is specific heat capacity->
Figure SMS_51
For temperature, < >>
Figure SMS_44
For time (I)>
Figure SMS_48
For space coordinates>
Figure SMS_52
Is the heat conductivity of the inner layer material->
Figure SMS_54
Is the heat exchange coefficient between the inner layer structure and the air>
Figure SMS_42
For the thermal conductivity of the outer layer material->
Figure SMS_46
Is the heat exchange coefficient between the outer layer structure and the air, +.>
Figure SMS_50
Is Stefin-Boltzmann constant, < ->
Figure SMS_53
For the internal air temperature>
Figure SMS_45
Is the temperature of the outer wall surface of the outer layer->
Figure SMS_49
Is the outside air temperature or the heat source temperature.
Further, the optimization objective function and the constraint condition are integrated to obtain an optimization design mathematical model:
Figure SMS_55
the design variables are defined as:
Figure SMS_56
，
the optimization model is defined as:
Figure SMS_57
。/>
furthermore, the design variable is a mixed type of coexistence of discrete variable and continuous variable, is a mixed design variable type optimization problem, and adopts an intelligent optimization algorithm to carry out optimization model solution to obtain an optimized design variable, namely a material selection variable M and the geometric dimensions of three layers of materials
Figure SMS_58
、/>
Figure SMS_59
and />
Figure SMS_60
The intelligent optimization algorithm is a genetic algorithm or a particle swarm algorithm.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
the invention discloses a multilayer heat insulation structure optimization design method of a high-speed aircraft, which aims at the multilayer heat insulation structure optimization design of the high-speed aircraft, introduces material selection, geometric dimension and material heat conductivity temperature change characteristics into an optimization design model, solves the problem that the existing multilayer heat insulation structure optimization design method of the high-speed aircraft does not consider the influence of material optimization and material heat conductivity temperature change, obtains optimized material selection and material geometric dimension, and meets the requirements of practical application.
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For a clearer description of the technical solutions of embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and should not be considered limiting in scope, and other related drawings can be obtained according to these drawings without inventive effort for a person skilled in the art, wherein:
FIG. 1 is a schematic view of a multi-layer insulation structure of a high speed aircraft;
FIG. 2 is a flow chart of an optimization method of the present invention;
FIG. 3 is a result of optimizing a solution using the Monte Carlo method;
fig. 4 is a result of optimizing a solution using PSO.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
It should be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 2, the present invention is a method for optimizing a multi-layered heat insulation structure of a high-speed aircraft, the heat insulation structure of the high-speed aircraft is divided into a plurality of layers of materials,
determining design variables of the heat insulation structure, namely a selectable material database and the geometric dimensions of each layer of material;
specifically, as shown in fig. 1, the multi-layer material specifically includes an outer layer material, an intermediate layer material, and an inner layer material, and the optional material data are respectively
Figure SMS_61
、/>
Figure SMS_62
And
Figure SMS_63
the database of selectable materials is +.>
Figure SMS_64
；
The geometric dimensions of the three layers of materials are respectively the thickness of the outer layer of material
Figure SMS_65
Thickness of the interlayer Material->
Figure SMS_66
Thickness of inner layer material->
Figure SMS_67
。
Determining the heat insulation effective mass ratio of the optimized objective function, and setting constraint conditions;
specifically, the optimization objective function heat insulation effective mass ratio, namely the mass ratio of heat insulation efficiency and heat insulation structure, has the formula:
Figure SMS_68
，
the heat insulation efficiency is the effective working time length
Figure SMS_69
The heat insulation rate at the time is:
Figure SMS_70
，
wherein ,
Figure SMS_71
for the heat source temperature->
Figure SMS_72
The temperature response of the inner wall surface;
the mass of the heat insulation structure is as follows:
Figure SMS_73
，
wherein ,
Figure SMS_74
is the density of the outer layer material->
Figure SMS_75
For the density of the interlayer material>
Figure SMS_76
In order to achieve the density of the inner layer material,
according to the concept of the maximum heat insulation effective mass ratio, the optimized objective function is obtained as follows:
Figure SMS_77
。
the optimization objective function is the ratio of quality to efficiency, so the smaller the optimization objective function, the better the optimization result.
Specifically, the constraint condition specifically includes:
the inner layer of the heat insulation structure has an inner surface wall temperature facing the inner cavity
Figure SMS_78
Time temperature->
Figure SMS_79
Less than or equal to->
Figure SMS_80
；
The thickness of each layer of material is as follows
Figure SMS_82
、/>
Figure SMS_86
、/>
Figure SMS_88
, wherein ,
Figure SMS_83
、/>
Figure SMS_85
、/>
Figure SMS_87
upper limit of thickness dimension for each layer of material, +.>
Figure SMS_89
、/>
Figure SMS_81
、/>
Figure SMS_84
A lower limit of the thickness dimension of each layer of material;
equivalent modulus
Figure SMS_90
The equivalent modulus is defined as:
Figure SMS_91
，
wherein ,
Figure SMS_92
is the minimum allowed modulus body, +.>
Figure SMS_93
Modulus of the outer layer material>
Figure SMS_94
Modulus of the interlayer material, +.>
Figure SMS_95
Modulus for the inner layer material;
material selection belonging to a material dataset
Figure SMS_96
。
Specifically, the inner surface wall temperature of the inner layer of the heat insulation structure facing the inner cavity is as follows
Figure SMS_97
Time temperature
Figure SMS_98
It is necessary to solve for the heat transfer equation,
the heat transfer equation:
Figure SMS_99
，
the boundary conditions are:
Figure SMS_100
and
Figure SMS_101
，
wherein ,
Figure SMS_104
for material thermal conductivity, +.>
Figure SMS_107
Is specific heat capacity->
Figure SMS_111
For temperature, < >>
Figure SMS_103
For time (I)>
Figure SMS_109
For space coordinates>
Figure SMS_112
Is the heat conductivity of the inner layer material->
Figure SMS_114
Is the heat exchange coefficient between the inner layer structure and the air>
Figure SMS_102
For the thermal conductivity of the outer layer material->
Figure SMS_106
Is the heat exchange coefficient between the outer layer structure and the air, +.>
Figure SMS_110
Is Stefin-Boltzmann constant, < ->
Figure SMS_113
As the internal air temperature (background temperature in figure 2),
Figure SMS_105
is the temperature of the outer wall surface of the outer layer->
Figure SMS_108
Is the outside air temperature or the heat source temperature.
The partial differential equation (heat transfer equation) is solved by adopting a finite difference implicit format, the space region sequence is represented by i, and the time sequence is represented by j. The spatial grid line and the temporal grid line (i, j) represent a node of the time-space, and the state at the moment j at the spatial position i, the differential equation is converted into a differential equation by replacing the differential quotient with the finite difference:
Figure SMS_115
with taylor expansion, the finite differential expression of its derivative is:
Figure SMS_116
Figure SMS_117
the following two formulas are known:
Figure SMS_118
the differential with respect to partial differentiation over time is:
Figure SMS_119
bringing the above results into a heat transfer differential equation, a discrete form of iterative recursion format is obtained:
Figure SMS_120
recursively 1 in time, i.e. j changes to j+1, there are
Figure SMS_121
Then there are:
Figure SMS_122
the above formula is a finite difference iteration recurrence formula.
Integrating the optimization objective function and the constraint condition, and obtaining an optimization model according to the design variable;
specifically, the optimization objective function and the constraint condition are integrated to obtain an optimization design mathematical model:
Figure SMS_123
the design variables are defined as:
Figure SMS_124
，
the optimization model is defined as:
Figure SMS_125
。
and solving an optimization model by adopting an intelligent optimization algorithm to obtain optimized design variables, namely optimized material selection and geometric dimensions of each layer of heat insulation material.
Specifically, the design variable is a mixed type of coexistence of discrete variable and continuous variable, is a mixed design variable type optimization problem, and adopts an intelligent optimization algorithm to carry out optimization model solution to obtain an optimized design variable, namely a material selection variable M and the geometric dimensions of three layers of materials
Figure SMS_126
、/>
Figure SMS_127
and />
Figure SMS_128
The intelligent optimization algorithm is a genetic algorithm or a particle swarm algorithm, but is not limited to such an optimization algorithm.
Description of the preferred embodiments
And (3) verifying and analyzing the optimization method by adopting an example. The values of parameters in the optimization model are as follows:
Figure SMS_129
=0.5mm、/>
Figure SMS_134
=3mm、/>
Figure SMS_138
=5mm、/>
Figure SMS_130
=50mm、/>
Figure SMS_133
=2mm、/>
Figure SMS_137
=5mm，/>
Figure SMS_140
=10Gpa，/>
Figure SMS_131
=1200℃，/>
Figure SMS_135
=20℃，/>
Figure SMS_139
heat exchange coefficient of outer layer structure and air =100℃>
Figure SMS_141
=230W/(m2· ℃) inner layer structure and air heat exchange coefficient +.>
Figure SMS_132
=10 W/（m2·℃），/>
Figure SMS_136
=300s。
The outer layer material dataset is as in table 1:
TABLE 1 ablation resistant layer (outer layer) Material parameters (outer layer)
Material name Density (kg, m-3) Specific heat capacity (J. Kg. K) -1) Thermal conductivity (W.m.K) -1) Young's modulus (GPa)
C/C composite material 1600 713 1.6 22.32
C/SiC composite material 2100 1420 5 49.8
ZrB 2-based composite material 6300 430 53 490
Inner material dataset:
TABLE 2 Material parameters of force bearing layer (inner layer)
Material name Density (kg, m-3) Specific heat capacity (J. Kg. K) -1) Thermal conductivity (W.m.K) -1) Young's modulus (GPa)
Aluminum alloy 7075 2800 962 129.4 71
GH4099 8470 624 18.9 175
Titanium alloy TC4 4440 659 9.13 115.85
Interlayer material dataset:
TABLE 3 parameters of insulating layer (middle layer) materials
Material name Density (kg, m-3) Specific heat capacity (J. Kg. K) -1) Thermal conductivity (W.m.K) -1) Young's modulus (GPa)
Carbon aerogel (carbon aerogels) 811 870 3.521505E-7T2+7.847416E-4T+1.104313 2.84
SiO2 aerogel 140 1050 1.135885E-10T3-2.256084E-8T2+1.640566E-5T+1.481429E-2 0.010
SiC aerogel 9.7 579 5.269242E-11T3-2.221319E-8T2+1.622211E-5T+2.377993E-2 0.013
And optimizing and solving by adopting a Monte Carlo method to obtain 200 feasible solution optimizing results, wherein the optimizing results are shown in figure 3.
PSO optimization is adopted, the population number is 50, the iteration number is 200, and the optimization result is shown in FIG. 4.
The PSO optimization method has better effect than the Monte Carlo method, and the PSO optimization method is adopted in the invention.
According to the PSO optimization result, the optimal value of the optimization objective function is 10.9167, and the corresponding design variables are: x= (2, 1,5.4070e-04,0.0120,0.0020), namely, the outer layer material is C/SiC composite material, the middle layer material is carbon aerogel, the inner layer material is GH4099, the outer layer thickness is 5.4070e-01mm, the middle layer thickness is 12mm, and the inner layer thickness is 2mm.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are not creatively contemplated by those skilled in the art within the technical scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope defined by the claims.

Claims (3)

1. A method for optimizing the design of a multi-layer heat insulation structure of a high-speed aircraft is characterized in that the heat insulation structure of the high-speed aircraft is divided into a plurality of layers of materials,
determining design variables of the heat insulation structure, namely a selectable material database and the geometric dimensions of each layer of material;
the multi-layer material comprises an outer layer material, an intermediate layer material and an inner layer material, wherein the optional material data are respectively
Figure QLYQS_1
、/>
Figure QLYQS_2
And
Figure QLYQS_3
the database of selectable materials is +.>
Figure QLYQS_4
；
The geometric dimensions of the three layers of materials are respectively the thickness of the outer layer of material
Figure QLYQS_5
Thickness of the interlayer Material->
Figure QLYQS_6
Thickness of inner layer material->
Figure QLYQS_7
；
Determining the heat insulation effective mass ratio of the optimized objective function, and setting constraint conditions;
the optimized objective function heat insulation effective mass ratio, namely the mass ratio of heat insulation efficiency and heat insulation structure, has the formula:
Figure QLYQS_8
，
the heat insulation efficiency is the effective working time length
Figure QLYQS_9
The heat insulation rate at the time is:
Figure QLYQS_10
，
wherein ,
Figure QLYQS_11
for the heat source temperature->
Figure QLYQS_12
The temperature response of the inner wall surface;
the mass of the heat insulation structure is as follows:
Figure QLYQS_13
，
wherein ,
Figure QLYQS_14
is the density of the outer layer material->
Figure QLYQS_15
For the density of the interlayer material>
Figure QLYQS_16
In order to achieve the density of the inner layer material,
according to the concept of the maximum heat insulation effective mass ratio, the optimized objective function is obtained as follows:
Figure QLYQS_17
；
the constraint conditions are specifically as follows:
the inner layer of the heat insulation structure has an inner surface wall temperature facing the inner cavity
Figure QLYQS_18
Time temperature->
Figure QLYQS_19
Less than or equal to
Figure QLYQS_20
；
The thickness of each layer of material is as follows
Figure QLYQS_22
、/>
Figure QLYQS_26
、/>
Figure QLYQS_28
, wherein ,/>
Figure QLYQS_23
、
Figure QLYQS_25
、/>
Figure QLYQS_27
Upper limit of thickness dimension for each layer of material, +.>
Figure QLYQS_29
、/>
Figure QLYQS_21
、/>
Figure QLYQS_24
Thickness dimension of each layer of materialA lower limit;
equivalent modulus
Figure QLYQS_30
The equivalent modulus is defined as:
Figure QLYQS_31
，
wherein ,
Figure QLYQS_32
is the minimum allowed modulus body, +.>
Figure QLYQS_33
Modulus of the outer layer material>
Figure QLYQS_34
Modulus of the interlayer material, +.>
Figure QLYQS_35
Modulus for the inner layer material; />
Material selection belonging to a material dataset
Figure QLYQS_36
；
The inner surface wall temperature of the inner layer of the heat insulation structure facing one side of the inner cavity is as follows
Figure QLYQS_37
Time temperature->
Figure QLYQS_38
It is necessary to solve for the heat transfer equation,
the heat transfer equation:
Figure QLYQS_39
，
the boundary conditions are:
Figure QLYQS_40
and
Figure QLYQS_41
，
wherein ,
Figure QLYQS_45
for material thermal conductivity, +.>
Figure QLYQS_49
Is specific heat capacity->
Figure QLYQS_53
For temperature, < >>
Figure QLYQS_44
For time (I)>
Figure QLYQS_48
For space coordinates>
Figure QLYQS_51
Is the heat conductivity of the inner layer material->
Figure QLYQS_54
Is the heat exchange coefficient between the inner layer structure and the air>
Figure QLYQS_42
For the thermal conductivity of the outer layer material->
Figure QLYQS_46
Is the heat exchange coefficient between the outer layer structure and the air, +.>
Figure QLYQS_50
Is Stefin-Boltzmann constant, < ->
Figure QLYQS_52
For the internal air temperature>
Figure QLYQS_43
Is the temperature of the outer wall surface of the outer layer->
Figure QLYQS_47
Is the outside air temperature or the heat source temperature;
integrating the optimization objective function and the constraint condition, and obtaining an optimization model according to the design variable;
and solving an optimization model by adopting an intelligent optimization algorithm to obtain optimized design variables, namely optimized material selection and geometric dimensions of each layer of heat insulation material.
2. The method for optimizing the design of the multi-layer heat insulation structure of the high-speed aircraft according to claim 1, wherein the optimization objective function and the constraint condition are integrated to obtain an optimized design mathematical model:
Figure QLYQS_55
the design variables are defined as:
Figure QLYQS_56
，
the optimization model is defined as:
Figure QLYQS_57
。
3. the method for optimizing the design of the multi-layer heat insulation structure of the high-speed aircraft according to claim 2, wherein the method comprises the following steps: the design variable is a mixed type of discrete variable and continuous variable, is a mixed design variable type optimization problem, and adopts an intelligent optimization algorithm to carry out optimization model solution to obtain an optimized design variable, namely a materialSelecting the variable M and the geometry of the three-layer material
Figure QLYQS_58
、/>
Figure QLYQS_59
and />
Figure QLYQS_60
The intelligent optimization algorithm is a genetic algorithm or a particle swarm algorithm. />
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