CN112784457B - Thin film structure reinforcing band layout optimization method and system based on genetic algorithm - Google Patents

Thin film structure reinforcing band layout optimization method and system based on genetic algorithm Download PDF

Info

Publication number
CN112784457B
CN112784457B CN202110070185.3A CN202110070185A CN112784457B CN 112784457 B CN112784457 B CN 112784457B CN 202110070185 A CN202110070185 A CN 202110070185A CN 112784457 B CN112784457 B CN 112784457B
Authority
CN
China
Prior art keywords
reinforcing
film structure
layout
tensor
genetic algorithm
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.)
Active
Application number
CN202110070185.3A
Other languages
Chinese (zh)
Other versions
CN112784457A (en
Inventor
聂云清
李东旭
王杰
罗青
邹杰
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.)
National University of Defense Technology
Original Assignee
National University of Defense Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by National University of Defense Technology filed Critical National University of Defense Technology
Priority to CN202110070185.3A priority Critical patent/CN112784457B/en
Publication of CN112784457A publication Critical patent/CN112784457A/en
Application granted granted Critical
Publication of CN112784457B publication Critical patent/CN112784457B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a layout optimization method and system for a thin film structure reinforcing band based on a genetic algorithm, and belongs to the technical field of thin film structures. The layout optimization method comprises the following steps: s1, setting the design parameters of the reinforcing belt and constructing layout optimization parameters; s2, setting genetic algorithm parameters and initializing the population; s3, decoding the population to obtain layout optimization parameters of the reinforcing strips, establishing a nonlinear finite element model, and solving; s4, calculating an objective function based on the solution result; s5, calculating the fitness by using the objective function and judging whether the fitness meets the stop criterion; s6, if the stop criterion is not met, selecting, crossing and mutating the population, and repeating the steps S3-S5; and S7, if the stop criterion is met, ending the loop and outputting the optimal individuals. The invention optimizes the layout of the film structure reinforcing band through a genetic algorithm, can effectively avoid the occurrence of film structure wrinkles and improve the performance of the film structure.

Description

Thin film structure reinforcing band layout optimization method and system based on genetic algorithm
Technical Field
The invention relates to the technical field of film structures, in particular to a film structure reinforcing band layout optimization method and system based on a genetic algorithm.
Background
The film structure has the characteristics of light weight and easy folding and storage, and is widely applied to spacecraft structures, such as a solar sail surface, a film antenna array surface and the like. However, the membrane structure has small thickness and small bending rigidity, and is easy to generate wrinkle deformation under the action of pressure load, and the static and dynamic characteristics of the membrane structure may be influenced by the existence of wrinkles, so that the performance of the spacecraft is influenced. Usually, a certain number of reinforcing bands need to be arranged on a film structure in engineering design to improve the mechanical property of the film structure and achieve the purpose of reducing wrinkle deformation.
There are two main methods for analyzing the wrinkles of the film structure: one is an analysis method based on a tension field theory, and the method can acquire the area and the direction of the film wrinkle and the stress strain state after the wrinkle occurs, but cannot acquire the specific morphology and the structural characteristics of the wrinkle; the other method is an analysis method based on a post-buckling theory, the method firstly introduces an initial displacement defect, and then performs post-buckling analysis on the film structure, and has the characteristics of low calculation efficiency and difficult convergence. The wrinkle analysis method based on the tension field theory has small relative calculation amount and is suitable for the optimal design of the film structure.
In the current engineering design, the layout of the film structure reinforcing band is designed based on engineering experience mostly, mature theoretical guidance is lacked, and the fold deformation of the film structure is a key design index influencing the performance of the film. The existing design method generally does not consider the influence of the layout of the reinforcing band on the wrinkle deformation of the film structure, so that the layout of the reinforcing band of the film structure needs to be optimized to improve the performance of the film structure.
Disclosure of Invention
The invention provides a method and a system for optimizing the layout of a film structure reinforcing band based on a genetic algorithm, and aims to improve the wrinkle characteristic of the film structure by optimizing the layout of the reinforcing band.
The purpose of the invention is realized by the following technical scheme: a layout optimization method of a film structure reinforcing band based on a genetic algorithm comprises the following steps of S1-S7:
s1, determining design parameters of the reinforcing belt aiming at the film structure, and constructing layout optimization parameters of the reinforcing belt to be solved according to the design parameters of the reinforcing belt; the design parameters of the reinforcing belts comprise the number of transverse reinforcing belts, the number of longitudinal reinforcing belts, the thickness of the reinforcing belts and the width of the reinforcing belts;
s2, setting genetic algorithm parameters and initializing the population; the genetic algorithm parameters comprise population size, individual size, cross probability, variation probability and maximum iteration number;
s3, decoding the population to obtain a solving result of the layout optimization parameters of the reinforcing strip, establishing a nonlinear finite element model of the film structure based on the layout optimization parameters of the reinforcing strip, and solving by using a nonlinear finite element method;
s4, constructing an objective function based on the performance parameters of the film structure, and calculating the objective function based on the solving result of the nonlinear finite element method;
s5, calculating the fitness by using the solving result of the objective function, and judging whether the iteration times meet the preset stop criterion;
s6, if the stopping criterion is not met, selecting, crossing and mutating the population, and repeating the steps S3-S5;
and S7, if the stop criterion is met, ending the circulation, outputting the optimal individuals, decoding the optimal individuals to obtain the optimal layout optimization parameters of the reinforcing belts, and laying out the reinforcing belts of the film structure according to the optimal layout optimization parameters of the reinforcing belts.
Optionally, the expression of the enhancement band layout optimization parameter constructed in step S1 is:
b＝[(y11,y12),(y21,y22),...,(ym1,ym2),(x11,x12),(x21,x22),...,(xn1,xn2)]，
in the formula, m is the number of transverse reinforcing belts, n is the number of longitudinal reinforcing belts, b represents a set of layout optimization parameters of the reinforcing belts, and b contains 2(m + n) elements in total; (y)11,y12) The vertical coordinates of two intersection points of the 1 st transverse reinforcing belt and the film edge form a set; (y)21,y22) The set is formed by the vertical coordinates of two intersection points of the No. 2 transverse reinforcing belt and the film edge; (y)m1,ym2) The m-th transverse reinforcing belt is a set formed by the vertical coordinates of two intersection points of the m-th transverse reinforcing belt and the film edge; (x)12,x12) The transverse coordinates of two intersection points of the No. 1 longitudinal reinforcing belt and the film edge form a set; (x)21,x22) The transverse coordinates of two intersection points of the No. 2 longitudinal reinforcing belt and the film edge form a set; (x)n1,xn2) Is a set formed by the abscissa of the two intersection points of the nth longitudinal reinforcing band and the film edge.
Optionally, the population in step S2 Is a population composed of individuals whose number Is equal to Ps, and Is represented by a binary array whose number of rows Is equal to Ps, number of columns Is equal to Is, and a value of each cell Is 0 or 1, where Ps represents a population size and Is represents an individual size; the initialization method of the population comprises the following steps: and generating Ps multiplied by Is random numbers, and sequentially assigning values to each unit of the population.
Optionally, the step of decoding the population in step S3 is as follows:
(1) respectively extracting individuals with the size of Is in the population, splitting the individuals into 2(m + n) sub-individuals aiI is 1,2, …,2(m + n), m is the number of transverse reinforcing belts, and n is the number of longitudinal reinforcing belts;
(2) 2(m + n) sub-individuals aiRespectively solving by using the following formula to obtain the ith variable b in the corresponding reinforcing band layout optimization parameter set biComprises the following steps:
Figure BDA0002905524140000031
in the formula bminAnd bmaxAre respectively a variable biMaximum and minimum values of amax＝2Is/2(m+n)-1，
Figure BDA0002905524140000032
Figure BDA0002905524140000033
Is the size of the individual, m and n are the number of transverse reinforcing belts and the number of longitudinal reinforcing belts respectively,
Figure BDA0002905524140000034
is a sub-individual aiThe k-th digit.
Optionally, the solving process using the nonlinear finite element method in step S3 includes the following sub-steps S31 to S34:
s31, giving an initial strain tensor increment delta epsilon0Separately calculating the initial stress tensor increment delta sigma0Initial stress tensor σ0And the initial strain tensor ε0：
Δσ0＝DΔε0
σ0＝Δσ0
ε0＝Δε0
Wherein D is an elastic stiffness matrix having, under elastic stress conditions:
Figure BDA0002905524140000041
wherein E is the elastic modulus of the material and v is the Poisson's ratio;
s32, assigning values to a Jacobian matrix according to different stress states of the film structure, wherein the stress states comprise a tensioning state, a loosening state and a folding state;
the Jacobian matrix J is defined as:
Figure BDA0002905524140000042
in the formula, delta sigma is the increment of the stress tensor, and delta epsilon is the increment of the strain tensor;
s33, calculating the increment of the strain tensor as delta epsilon by using the Jacobian matrixiDelta sigma of stress tensor of timeiFold strain tensor increment Δ εwiStrain tensor ε, wrinkle strain tensor εwStress tensor σ:
Δσi＝JΔεi
Δεwi＝QΔεi
Figure BDA0002905524140000043
Figure BDA0002905524140000044
Figure BDA0002905524140000045
matrix in the formula
Figure BDA0002905524140000046
D is an elastic stiffness matrix, s2Is the minimum principal strain direction vector; delta epsiloniIncrement of strain tensor, Δ σ, representing step iiIncrement of stress tensor, Δ ε, representing step iwiDenotes the fold strain tensor increment for the ith step, the index i denotes the number of incremental steps, when i equals 0, Δ ε0Representing the increment of the initial strain tensor, Δ σ0Representing the initial stress tensor increment, σ0Representing the initial stress tensor,. epsilon0Representing an initial strain tensor; delta epsilonkIncrement of strain tensor, Δ σ, representing the kth stepkIncrement of stress tensor, Δ ε, representing the kth stepwkRepresenting the increment of the fold strain tensor of the kth step, wherein the value range of k is 0,1, 2, … …, i; symbol
Figure BDA0002905524140000047
Means for summing the initial value and the values from step 1 to step i;
s34, judging whether the termination condition is reached, if not, repeating the steps S32-S33; if the folding strain tensor epsilon of the last step is outputw(ii) a The termination condition being that the stress tensor σ of the film structure is equal to a given termination stress tensor σc。
Further, in step S32:
(1) when the film structure is in a tensioned state, the value of the Jacobian matrix J is as follows:
Figure BDA0002905524140000051
wherein D is an elastic stiffness matrix, E is an elastic modulus, and v is a Poisson's ratio;
(2) when the film structure is in a relaxed state, the value of the Jacobian matrix J is as follows:
Figure BDA0002905524140000052
(3) when the film structure is in a folded state, the value of the Jacobian matrix J is as follows:
Figure BDA0002905524140000053
where D is the elastic stiffness matrix and v is the Poisson's ratio, ε1And ε2Maximum principal strain and minimum principal strain, n, respectively1、n2Direction vectors of maximum principal stress and minimum principal stress, respectively, direction vector n3＝n1×n2Matrix of
Figure BDA0002905524140000054
Where I is the identity matrix, s2For the minimum principal strain direction vector, superscript T denotes the vector transpose.
Optionally, in step S4, an objective function is constructed based on a membrane structure wrinkle strength factor, where the expression of the membrane structure wrinkle strength factor is:
Figure BDA0002905524140000055
in the formulawDenotes the fold strength factor, εwIs the fold strain tensor, D is the elastic stiffness matrix;
the calculation process of the objective function in the step S4 includes the following sub-steps S41 to S43:
s41, extracting each film unit in the solving result of the nonlinear finite element method in the step S3Crease strain epsilon ofw；
S42, integrating each film unit based on the expression of the film structure fold strength factor to respectively obtain the unit fold strength factor of each film unit;
cell fold strength factor of the kth cell
Figure BDA0002905524140000061
Comprises the following steps:
Figure BDA0002905524140000062
wherein k represents a cell number, [ phi ]wIs a unit fold strength factor and has
Figure BDA0002905524140000063
εwIs the cell fold strain tensor, D is the elastic stiffness matrix, VeIs the unit area;
s43, summing the unit fold strength factors to obtain a fold strength factor U of the whole film structurew：
Figure BDA0002905524140000064
In the formula NeThe number of the total units is the number of the units,
Figure BDA0002905524140000065
the cell fold strength factor for the k-th cell is represented and the sign sigma represents the summation operation.
Optionally, the calculation formula of the fitness in step S5 is as follows:
Figure BDA0002905524140000066
wherein f represents the individual fitness, UwA fold strength factor for the overall film structure;
the stop criterion preset in step S5 is that the actual number of iterations is greater than the maximum number of iterations.
In addition, the present invention also provides a system for optimizing a layout of a film structure reinforced belt based on a genetic algorithm, which comprises a microprocessor and a memory, which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the method for optimizing the layout of the film structure reinforced belt based on the genetic algorithm, or the memory stores a computer program which is programmed or configured to execute the method for optimizing the layout of the film structure reinforced belt based on the genetic algorithm.
Furthermore, the present invention also proposes a computer-readable storage medium having stored therein a computer program programmed or configured to execute the method for optimizing a layout of a reinforced strip of a membrane structure based on a genetic algorithm.
Compared with the prior art, the invention has the following effective gain effects: the method and the system for optimizing the layout of the reinforcing band of the film structure based on the genetic algorithm are adopted to optimize the layout of the reinforcing band of the film structure, so that the wrinkle characteristic of the film structure can be effectively improved, and the design level of the film structure is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic view of a transverse reinforcing band and a longitudinal reinforcing band of the film structure;
FIG. 3 is a schematic diagram of a finite element model of a thin film structure according to an embodiment of the present invention;
fig. 4 is a schematic diagram of the layout optimization result of the reinforcing band with the film structure in the embodiment of the invention.
Reference numerals: 1-transverse reinforcing band, 2-longitudinal reinforcing band, 3-film structure, 11-1 st transverse reinforcing band, 12-2 nd transverse reinforcing band, 13-mth transverse reinforcing band, 21-1 st longitudinal reinforcing band, 22-2 nd longitudinal reinforcing band, 23-nth longitudinal reinforcing band.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention designs a method and a system for optimizing the layout of a film structure reinforcing band based on a genetic algorithm, as shown in figure 1, the steps and the technical principle are as follows:
step S1: determining design parameters of a reinforcing band aiming at a thin film structure, and constructing layout optimization parameters of the reinforcing band to be solved according to the design parameters of the reinforcing band;
in the embodiment of the invention, for a trapezoidal solar sail film structure, a polyimide film is adopted as a material, the thickness of the polyimide film is 25 mu m, and the wrinkle characteristic of the film structure under load is improved through optimizing the layout of a reinforcing belt, so that the flatness of the film is improved.
The design parameters of the reinforcing belt comprise the number m of transverse reinforcing belts, the number n of longitudinal reinforcing belts, the thickness t of the reinforcing belt and the width l of the reinforcing belt. The schematic diagram of the trapezoidal solar sail film structure is shown in fig. 2, four vertexes of the film structure are A, B, C, D respectively, four sides of the film structure are AB, BC, CD and AD respectively, the film reinforcing bands are mainly divided into transverse reinforcing bands and longitudinal reinforcing bands, three transverse reinforcing bands 11, 12 and 13 and three longitudinal reinforcing bands 21, 22 and 23 are illustrated in fig. 2.
The reinforcing band layout optimization parameter b is constructed as follows:
b＝[(y11,y12),(y21,y22),...,(ym1,ym2),(x11,x12),(x21,x22),...,(xn1,xn2)]
wherein y is11,y12The ordinate of the intersection points of the 1 st transverse reinforcing band with the longitudinal edges AB and CD of the film respectively, (y)11,y12) Representing a set of these two ordinates; y is21,y22The vertical coordinates of two intersection points of the 2 nd transverse reinforcing belt and the film longitudinal edges AB and CD are respectively; y ism1,ym2The vertical coordinates of two intersection points of the mth transverse reinforcing strip and the longitudinal edges AB and CD of the film are respectively; x is a radical of a fluorine atom12,x12The abscissa of the intersection of the 1 st longitudinal reinforcing band with the transverse edges BC and AD of the film, respectively, is likewise (x)12,x12) A set of these two abscissas; x is the number of21,x22Respectively is the abscissa of two intersection points of the 2 nd longitudinal reinforcing band and the film transverse edges BC and AD; x is the number ofn1,xn2And respectively, the abscissa of two intersection points of the nth longitudinal reinforcing band and the transverse edges BC and AD of the film, so that the layout optimization parameter b of the reinforcing band has 2(m + n) variables. Since the film structure is known, the placement of the reinforcing strips on the film can be uniquely determined by b, as shown in FIG. 2.
Step S2: setting genetic algorithm parameters and initializing a population;
because the whole search strategy and the optimization strategy of the genetic algorithm do not depend on gradient information or other auxiliary knowledge during calculation, and only need to influence the target function of the search direction and the corresponding fitness function, the optimal layout of the film structure reinforcing band can be searched by adopting the genetic algorithm so as to reduce the wrinkles of the film structure.
The genetic algorithm parameters mainly comprise population size Ps, individual size Is and cross probability pcProbability of variation pmMaximum number of iterations Nmax. In the genetic algorithm, a population Is a population consisting of individuals of which the number Is equal to Ps, and binary arrays of which the number of rows Is equal to Ps, the number of columns Is equal to Is and the value of each unit Is 0 or 1 are adopted for representing, wherein Ps represent the size of the population, and Is represents the size of the individual; the initialization method of the population comprises the following steps: and generating Ps multiplied by Is random numbers, and sequentially assigning values to each unit of the population.
Step S3: decoding the population to obtain a solving result of the layout optimization parameters of the reinforcing strips, establishing a nonlinear finite element model of the thin film structure based on the layout optimization parameters of the reinforcing strips, and solving by using a nonlinear finite element method;
the population decoding step in step S3 is as follows:
(1) respectively extracting individuals with the size of Is in the population, splitting the individuals into 2(m + n) sub-individuals ai(i ═ 1,2, …,2(m + n), m is the number of transverse reinforcing strips and n is the number of longitudinal reinforcing strips), and the subelement aiIs/2(m + n) bit binary number;
(2) 2(m + n) sub-individuals aiRespectively solving by the following formula to obtain the ith variable b in the corresponding reinforcing band layout optimization parameter biComprises the following steps:
Figure BDA0002905524140000091
in the formula bminAnd bmaxAre respectively a variable biMaximum and minimum values of amax＝2Is/2(m+n)-1，
Figure BDA0002905524140000092
Figure BDA0002905524140000093
Is the size of the individual, m and n are the number of transverse reinforcing belts and the number of longitudinal reinforcing belts respectively,
Figure BDA0002905524140000094
is a sub-individual aiThe k-th digit.
The optimized b ═ b parameter of the layout of the reinforcing band can be obtained1,b2,…,b2(m+n)]。
Constructing a finite element model based on the film structure parameters, the reinforcing band design parameters and the layout optimization parameters, wherein the film structure in the finite element model is modeled by adopting a plane stress unit; the reinforcing belt is modeled by a beam unit.
The solving of the nonlinear finite element method in the step S3 specifically includes the following sub-steps S31 to S34:
substep S31, giving an initial strain tensor increment Δ ε0Calculating the initial stress tensor increment delta sigma0Initial stress tensor σ0And the initial strain tensor ε0：
Δσ0＝DΔε0，σ0＝Δσ0，ε0＝Δε0，
Wherein D is an elastic stiffness matrix having
Figure BDA0002905524140000095
Wherein E is the elastic modulus of the material and v is the Poisson's ratio.
Substep S32, assigning values to the Jacobian matrix according to different stress states of the film structure, including a tensioning state, a relaxation state and a folding state;
the Jacobian matrix J is defined as:
Figure BDA0002905524140000101
in the formula, delta sigma is the increment of the stress tensor, and delta epsilon is the increment of the strain tensor;
the maximum principal stress sigma can be obtained according to the stress tensor sigma and the stress tensor epsilon1Minimum principal stress σ2Maximum principal strain ε1Minimum principal strain ε2Angle of direction theta, and sigma1、σ2、ε1、ε2Is directed to a direction vector n1、n2、s1、s2Respectively as follows:
Figure BDA0002905524140000102
Figure BDA0002905524140000103
Figure BDA0002905524140000104
Figure BDA0002905524140000105
Figure BDA0002905524140000106
n1＝[sin2θcos2θsinθcosθ]T
n2＝[sin2θcos2θ-sinθcosθ]T
s1＝[sin2θcos2θ2sinθcosθ]T
s2＝[sin2θcos2θ-2sinθcosθ]T
in the formula sigmaxIs positive stress in the x direction, σyIs positive stress in the y direction, τxyIs an in-plane shear stress,. epsilonxIs a positive strain in the x direction, epsilonyPositive strain in the y-direction, gammaxyIs in-plane shear strain and has [ sigma ]xσyτxy]T，ε＝[εxεyγxy]T；
According to the minimum principal stress σ2And maximum principal strain ε1Judging the stress state of the film, and assigning a Jacobian matrix:
(1) if σ2And if the value is more than or equal to 0, the film structure is in a tensioned state, and the value of the Jacobian matrix J is as follows:
Figure BDA0002905524140000111
wherein D is an elastic stiffness matrix, E is an elastic modulus, and v is a Poisson's ratio;
(2) if σ2＜0,ε1Less than or equal to 0, the film structure is in a relaxed state, and the JacobianThe matrix J takes the values:
Figure BDA0002905524140000112
(3) if σ2＜0,ε1If the value is more than 0, the film structure is in a folded state, and the value of the Jacobian matrix J is as follows:
Figure BDA0002905524140000113
where D is the elastic stiffness matrix and v is the Poisson's ratio, ε1And ε2Maximum principal strain and minimum principal strain, n, respectively1、n2Direction vectors of maximum principal stress and minimum principal stress, respectively, direction vector n3＝n1×n2Matrix of
Figure BDA0002905524140000114
Where I is the identity matrix, s2Is the minimum principal strain direction vector.
Substep S33, obtaining the increment of the strain tensor as delta epsilon by using the Jacobian matrixiDelta sigma of stress tensor of timeiFold strain tensor increment Δ εwiStrain tensor ε, wrinkle strain tensor εwStress tensor σ:
Δσi＝JΔεi
Δεwi＝QΔεi
Figure BDA0002905524140000115
Figure BDA0002905524140000116
Figure BDA0002905524140000117
matrix in the formula
Figure BDA0002905524140000118
D is an elastic stiffness matrix, s2Is the minimum principal strain direction vector; delta epsiloniIncrement of strain tensor, Δ σ, representing step iiIncrement of stress tensor, Δ ε, representing step iwiDenotes the fold strain tensor increment for the ith step, the index i denotes the number of incremental steps, when i equals 0, Δ ε0Representing the increment of the initial strain tensor, Δ σ0Representing the initial stress tensor increment, σ0Representing the initial stress tensor,. epsilon0Representing an initial strain tensor;
Δεkincrement of strain tensor, Δ σ, representing the kth stepkIncrement of stress tensor, Δ ε, representing the kth stepwkRepresenting the increment of the fold strain tensor of the kth step, wherein the value range of k is 0,1, 2, … …, i; symbol(s)
Figure BDA0002905524140000121
Means for summing the initial value and the values from step 1 to step i;
substep S34, determining whether the termination condition is reached, and if not, repeating substeps S32-S33; if the folding strain tensor epsilon of the last step is outputw(ii) a The termination condition being that the stress tensor σ of the film structure is equal to a given termination stress tensor σc。
Step S4: constructing an objective function based on the performance parameters of the thin film structure, and calculating the objective function based on the solving result of a nonlinear finite element method;
in this embodiment, the membrane structure wrinkle strength factor is used as a target function, the membrane structure wrinkle strength factor is a tensor reflecting the wrinkle strain magnitude of the whole membrane structure, the wrinkle deformation strength of the membrane structure can be effectively measured, the wrinkle deformation strength can be obtained by solving through a nonlinear finite element method based on a plane stress model, and compared with a post-buckling method, the method has the characteristics of small calculated amount and simple evaluation index.
The fold strength factor of the film structure in step S4 is defined as follows:
Figure BDA0002905524140000122
in the formulawDenotes the fold strength factor, εwAnd D is an elastic stiffness matrix.
Further, the calculation process in step S4 includes the following sub-steps S41 to S43:
substep S41, extracting the wrinkle strain epsilon of each film unit in the finite element analysis solution result of the step S3w；
A substep S42, integrating each film unit based on the expression of the film structure fold strength factor, and respectively obtaining the unit fold strength factor of each film unit;
wherein the cell fold strength factor of the k-th cell
Figure BDA0002905524140000123
Comprises the following steps:
Figure BDA0002905524140000124
wherein k represents a cell number, [ phi ]wIs a unit fold strength factor and has
Figure BDA0002905524140000125
εwIs the cell fold strain tensor, D is the elastic stiffness matrix, VeIs the unit area;
substep S43, folding the cell by the strength factor
Figure BDA0002905524140000131
Summing to obtain the fold strength factor U of the whole film structurew：
Figure BDA0002905524140000132
In the formula NeThe number of the total units is the number of the units,
Figure BDA0002905524140000133
the cell fold strength factor for the k-th cell is represented and the sign sigma represents the summation operation.
Step S5: calculating the fitness by using the solving result of the objective function, and judging whether the iteration times meet a preset stopping criterion; the stopping criterion is that the actual iteration number is greater than the maximum iteration number.
The calculation formula of the fitness is as follows:
Figure BDA0002905524140000134
wherein f is the individual fitness, UwThe fold strength factor of the overall film structure.
Step S6: and if the stopping criterion is not met, performing selection, crossing and mutation operations on the population, and repeating the steps S3-S5.
In the embodiment of the invention, a roulette selection method is adopted to select individuals in a population, and the selection operation comprises the following specific steps:
1.1) probability p of the ith individual being selected in a population of size PsiIs composed of
Figure BDA0002905524140000135
In the formula fiIs the fitness of the ith individual,
Figure BDA0002905524140000136
sigma is a summation symbol;
1.2) production of [0,1]S ═ rand (·) xf is obtainedsum；
1.3) to satisfy
Figure BDA0002905524140000137
K, then the kth individual is selected;
1.4) carrying out Ps times of the operations of the steps 1.2) and 1.3) to obtain Ps individuals, and forming a new population after selection.
The specific steps of performing the crossover operation on the individuals in the population in the embodiment of the invention are as follows:
2.1) production of [0,1]And judging rand (-) and cross probability pcThe relationship of (1);
2.2) if rand (·)<pcThen [1, Is ] Is generated]The random integer round (-) of (a), the character strings of the ith individual and the (i + 1) th individual are exchanged with each other from the round (-) position;
2.3) if rand (·)>pcIf so, keeping the ith individual and the (i + 1) th individual as the same, and not exchanging;
2.4) repeating steps 2.1) to 2.3) until i ═ Ps-1.
The specific steps of performing the mutation operation on the individuals in the population in the embodiment of the invention are as follows:
3.1) production of [0,1]And judging rand (-) and the variation probability pmThe relationship of (1);
3.2) if rand (.)<pmThen [1, Is ] Is generated]The random integer round (-) of (a), changing the character of the round (-) bit on the ith individual from 0 to 1, or from 1 to 0;
3.3) repeat steps 3.1), 3.2) until i ═ Ps.
Step S7: if the stop criterion is met, ending the circulation, outputting the optimal individuals, decoding the optimal individuals to obtain the optimal layout optimization parameters of the reinforcing belts, and laying out the reinforcing belts with the film structures according to the optimal layout optimization parameters of the reinforcing belts.
The optimal individuals are individuals whose objective function obtained by the genetic algorithm can take the minimum value, and the population decoding step of step S3 can decode the optimal individuals to obtain the layout optimization parameters of the reinforcement band with the film structure, so that the layout scheme of the reinforcement band with the minimum wrinkle deformation of the film structure can be obtained.
The layout optimization method of the present invention is verified by performing a reinforced band layout optimization in conjunction with a typical trapezoidal solar sail membrane structure.
(1) The film structure dimensional parameters are as follows: the design parameters of the film thickness h-25 um reinforcing belt mainly comprise the number m-1 of transverse reinforcing belts, the number n-1 of longitudinal reinforcing belts and the thickness t-50 um width l-15 mm of the reinforcing belts; the enhancement band layout optimization parameters are defined as follows:
b＝[(y11,y12),(x11,x12)]
in the formula y11,y12The ordinate, x, of the intersection of the transverse reinforcing strip with the film edge AB and the edge CD, respectively11,x12The vertical coordinates of the two intersection points of the longitudinal reinforcing belt and the film side BC and AD are respectively.
(2) Setting genetic algorithm parameters, wherein the population size is 100, the chromosome length is 40, the cross probability is 0.6, the mutation probability is 0.01, and the maximum iteration number is 100, and then initializing the population.
(3) And (3) decoding the population to obtain a layout optimization parameter b of the reinforcing band, establishing a nonlinear finite element model based on the film structure parameter, the reinforcing band design parameter and the layout optimization parameter, and solving by using a nonlinear finite element method, wherein a typical film structure finite element model schematic diagram is shown in the figure, and the result is subjected to post-processing to obtain an objective function and fitness.
(4) And carrying out selection, crossing and mutation operations on the population to obtain a final optimization result. Fig. 4 is a schematic diagram of a layout optimization result of a reinforcing band of a film structure, wherein the ordinate of the diagram is the optimal fitness of each generation of population, which reflects the strength of wrinkle deformation, the abscissa of the diagram is the number of population iterations, the optimal fitness of the population is gradually reduced with the increase of the number of population iterations, the wrinkle deformation of the film structure is gradually reduced, the optimal parameters are finally reached, and the fitness value tends to be stable.
The method for optimizing the layout of the reinforcing band of the film structure based on the genetic algorithm can avoid the adoption of a film structure wrinkle analysis method with large calculation amount and long consumed time, quickly evaluates the wrinkle strength of the film structure by using a nonlinear finite element method, and optimizes the layout of the reinforcing band by using an evaluation result, thereby effectively improving the wrinkle characteristic of the film structure and improving the design level of the film structure.
In addition, the invention also provides a genetic algorithm-based film structure reinforced belt layout optimization system, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the genetic algorithm-based film structure reinforced belt layout optimization method, or the memory stores a computer program which is programmed or configured to execute the genetic algorithm-based film structure reinforced belt layout optimization method.
Furthermore, the present invention also proposes a computer-readable storage medium having stored therein a computer program programmed or configured to execute the method for optimizing a layout of a reinforced strip of a membrane structure based on a genetic algorithm.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (10)

1. A layout optimization method of a film structure reinforcing band based on a genetic algorithm is characterized by comprising the following steps of S1-S7:
s1, determining design parameters of the reinforcing belt aiming at the film structure, and constructing layout optimization parameters of the reinforcing belt to be solved according to the design parameters of the reinforcing belt; the design parameters of the reinforcing belts comprise the number of transverse reinforcing belts, the number of longitudinal reinforcing belts, the thickness of the reinforcing belts and the width of the reinforcing belts;
s2, setting genetic algorithm parameters and initializing the population; the genetic algorithm parameters comprise population size, individual size, cross probability, variation probability and maximum iteration number;
s3, decoding the population to obtain a solving result of the layout optimization parameters of the reinforcing strip, establishing a nonlinear finite element model of the film structure based on the layout optimization parameters of the reinforcing strip, and solving by using a nonlinear finite element method;
s4, constructing an objective function based on the performance parameters of the film structure, and calculating the objective function based on the solving result of the nonlinear finite element method;
s5, calculating the fitness by using the solving result of the objective function, and judging whether the iteration times meet the preset stop criterion;
s6, if the stopping criterion is not met, selecting, crossing and mutating the population, and repeating the steps S3-S5;
and S7, if the stop criterion is met, ending the circulation, outputting the optimal individuals, decoding the optimal individuals to obtain the optimal layout optimization parameters of the reinforcing belts, and laying out the reinforcing belts of the film structure according to the optimal layout optimization parameters of the reinforcing belts.
2. The method for optimizing layout of a reinforced plastic film strip based on genetic algorithm according to claim 1, wherein the expression of the optimized parameters for layout of the reinforced plastic strip constructed in step S1 is:
b＝[(y11,y12),(y21,y22),...,(ym1,ym2),(x11,x12),(x21,x22),...,(xn1,xn2)]，
in the formula, m is the number of transverse reinforcing belts, n is the number of longitudinal reinforcing belts, b represents a set of layout optimization parameters of the reinforcing belts, and b contains 2(m + n) elements in total; (y)11,y12) The vertical coordinates of two intersection points of the 1 st transverse reinforcing belt and the film edge form a set; (y)21,y22) The set is formed by the vertical coordinates of two intersection points of the No. 2 transverse reinforcing belt and the film edge; (y)m1,ym2) The m-th transverse reinforcing belt is a set formed by the vertical coordinates of two intersection points of the m-th transverse reinforcing belt and the film edge; (x)12,x12) The transverse coordinates of two intersection points of the No. 1 longitudinal reinforcing belt and the film edge form a set; (x)21,x22) At the intersection of the 2 nd longitudinal reinforcing strip and the film edgeA set of abscissas; (x)n1,xn2) Is a set formed by the abscissa of the two intersection points of the nth longitudinal reinforcing band and the film edge.
3. The method for optimizing the layout of the film structural reinforcing band based on the genetic algorithm according to claim 1, wherein the population in the step S2 Is a population consisting of individuals with the number equal to Ps, and Is represented by a binary array with the number equal to Ps, the number of columns equal to Is, and the value of each unit being 0 or 1, wherein Ps represents the size of the population and Is represents the size of the individual; the initialization method of the population comprises the following steps: and generating Ps multiplied by Is random numbers, and sequentially assigning values to each unit of the population.
4. The method for optimizing a layout of a film structure reinforcing band based on a genetic algorithm according to claim 1, wherein the step of decoding the population in the step S3 is as follows:
(1) respectively extracting individuals with the size of Is in the population, splitting the individuals into 2(m + n) sub-individuals aiI is 1,2, …,2(m + n), m is the number of transverse reinforcing belts, and n is the number of longitudinal reinforcing belts;
(2) 2(m + n) sub-individuals aiRespectively solving by using the following formula to obtain the ith variable b in the corresponding reinforcing band layout optimization parameter set biComprises the following steps:
Figure FDA0003572866120000021
in the formula bminAnd bmaxAre respectively a variable biMaximum and minimum values of amax＝2Is/2(m+n)-1，
Figure FDA0003572866120000022
Is the size of the individual, m and n are the number of transverse reinforcing belts and the number of longitudinal reinforcing belts respectively,
Figure FDA0003572866120000023
is a sub-individual aiThe k-th digit.
5. The method for optimizing layout of film structural reinforcing tape based on genetic algorithm as claimed in claim 1, wherein the solving process using the nonlinear finite element method in the step S3 comprises the following sub-steps S31-S34:
s31, giving an initial strain tensor increment delta epsilon0Separately calculating the initial stress tensor increment delta sigma0Initial stress tensor σ0And an initial strain tensor ε0：
Δσ0＝DΔε0
σ0＝Δσ0
ε0＝Δε0
Wherein D is an elastic stiffness matrix having, under elastic stress conditions:
Figure FDA0003572866120000024
wherein E is the elastic modulus of the material and v is the Poisson's ratio;
s32, assigning values to a Jacobian matrix according to different stress states of the film structure, wherein the stress states comprise a tensioning state, a loosening state and a folding state;
the Jacobian matrix J is defined as:
Figure FDA0003572866120000025
in the formula, delta sigma is the increment of the stress tensor, and delta epsilon is the increment of the strain tensor;
s33, calculating the increment of the strain tensor as delta epsilon by using the Jacobian matrixiDelta sigma of stress tensor of timeiFold strain tensor increment Δ εwiStrain tensor ε, wrinkle strain tensor εwStress tensor σ:
Δσi＝JΔεi
Δεwi＝QΔεi
Figure FDA0003572866120000031
Figure FDA0003572866120000032
Figure FDA0003572866120000033
matrix in the formula
Figure FDA0003572866120000034
D is an elastic stiffness matrix, s2Is the minimum principal strain direction vector; delta epsiloniIncrement of strain tensor, Δ σ, representing step iiIncrement of stress tensor, Δ ε, representing step iwiDenotes the fold strain tensor increment for the ith step, subscript i denotes the order of the incremental step, Δ ε when i equals 00Representing the increment of the initial strain tensor, Δ σ0Representing the initial stress tensor increment, σ0Representing the initial stress tensor,. epsilon0Representing an initial strain tensor; delta epsilonkIncrement of strain tensor, Δ σ, representing the kth stepkIncrement of stress tensor, Δ ε, representing the kth stepwkRepresenting the increment of the fold strain tensor of the kth step, wherein the value range of k is 0,1, 2, … …, i; symbol
Figure FDA0003572866120000035
Means for summing the initial value and the values from step 1 to step i;
s34, judging whether the termination condition is reached, if not, repeating the steps S32-S33; if the folding strain tensor epsilon of the last step is outputw(ii) a The termination condition being that the stress tensor σ of the film structure is equal to a given discontinuityStress tensor σc。
6. The method for optimizing layout of film structure reinforcing band based on genetic algorithm according to claim 5, wherein in the step S32:
(1) when the film structure is in a tensioned state, the value of the Jacobian matrix J is as follows:
Figure FDA0003572866120000036
wherein D is an elastic stiffness matrix, E is an elastic modulus, and v is a Poisson's ratio;
(2) when the film structure is in a relaxed state, the value of the Jacobian matrix J is as follows:
Figure FDA0003572866120000041
(3) when the film structure is in a folded state, the value of the Jacobian matrix J is as follows:
Figure FDA0003572866120000042
where D is the elastic stiffness matrix and v is the Poisson's ratio, ε1And ε2Maximum principal strain and minimum principal strain, n, respectively1、n2Direction vectors of maximum principal stress and minimum principal stress, respectively, direction vector n3＝n1×n2Matrix of
Figure FDA0003572866120000043
Where I is the identity matrix, s2For the minimum principal strain direction vector, superscript T denotes the vector transpose.
7. The method for optimizing layout of membrane structure reinforcing band based on genetic algorithm according to claim 1, wherein the step S4 is implemented by constructing an objective function based on a membrane structure wrinkle strength factor expressed by:
Figure FDA0003572866120000044
in the formulawDenotes the fold strength factor, εwIs the fold strain tensor, D is the elastic stiffness matrix;
the calculation process of the objective function in the step S4 includes the following sub-steps S41 to S43:
s41, extracting the wrinkle strain epsilon of each film unit in the solving result of the nonlinear finite element method in the step S3w；
S42, integrating each film unit based on the expression of the film structure fold strength factor to respectively obtain the unit fold strength factor of each film unit;
cell fold strength factor of the kth cell
Figure FDA0003572866120000045
Comprises the following steps:
Figure FDA0003572866120000046
wherein k represents a cell number, [ phi ]wIs a unit fold strength factor and has
Figure FDA0003572866120000047
εwIs the cell fold strain tensor, D is the elastic stiffness matrix, VeIs the unit area;
s43, summing the unit fold strength factors to obtain a fold strength factor U of the whole film structurew：
Figure FDA0003572866120000048
In the formula NeThe number of the total units is the number of the units,
Figure FDA0003572866120000049
the cell fold strength factor for the kth cell is represented and the sign sigma represents the summation operation.
8. The method for optimizing layout of film structural reinforcing band based on genetic algorithm according to claim 1, wherein the calculation formula of fitness in step S5 is:
Figure FDA0003572866120000051
wherein f represents the individual fitness, UwA fold strength factor for the overall film structure;
the stop criterion preset in step S5 is that the actual number of iterations is greater than the maximum number of iterations.
9. A system for optimizing layout of a membrane structure-based reinforced band layout based on genetic algorithm, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to perform the steps of the method for optimizing layout of a membrane structure-based reinforced band layout based on genetic algorithm according to any one of claims 1 to 8, or the memory stores therein a computer program programmed or configured to perform the method for optimizing layout of a membrane structure-based reinforced band layout based on genetic algorithm according to any one of claims 1 to 8.
10. A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, which is programmed or configured to perform the method for optimizing a layout of a film structure reinforced with a genetic algorithm according to any one of claims 1 to 8.
CN202110070185.3A 2021-01-19 2021-01-19 Thin film structure reinforcing band layout optimization method and system based on genetic algorithm Active CN112784457B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110070185.3A CN112784457B (en) 2021-01-19 2021-01-19 Thin film structure reinforcing band layout optimization method and system based on genetic algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110070185.3A CN112784457B (en) 2021-01-19 2021-01-19 Thin film structure reinforcing band layout optimization method and system based on genetic algorithm

Publications (2)

Publication Number Publication Date
CN112784457A CN112784457A (en) 2021-05-11
CN112784457B true CN112784457B (en) 2022-05-20

Family

ID=75757665

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110070185.3A Active CN112784457B (en) 2021-01-19 2021-01-19 Thin film structure reinforcing band layout optimization method and system based on genetic algorithm

Country Status (1)

Country Link
CN (1) CN112784457B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113779842A (en) * 2021-09-15 2021-12-10 哈尔滨理工大学 Reinforcing rib structure layout optimization design method based on genetic algorithm

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6781682B1 (en) * 2000-01-17 2004-08-24 Agency Of Industrial Science And Technology, Ministry Of International Trade & Industry Optical apparatus, optical apparatus adjustment method, and storage medium recorded with a processing program that executes said adjustment method
CN101508768A (en) * 2009-03-20 2009-08-19 华东理工大学 Intelligent modeling method in industrial polyester production process
CN102932422A (en) * 2012-09-29 2013-02-13 南京邮电大学 Cloud environment task scheduling method based on improved ant colony algorithm
CN106777768A (en) * 2017-01-09 2017-05-31 大连理工大学 A kind of Optimization Design that fold is stretched for eliminating membrane structure
CN111336935A (en) * 2020-03-31 2020-06-26 上海市计量测试技术研究院 Nano-film parameter inversion calculation method based on improved hybrid optimization algorithm

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR101289041B1 (en) * 2010-03-25 2013-07-23 엘지디스플레이 주식회사 High Light Transmittance In-Plan Switchin Liquid Crystal Display Device and Method For Manufacturing The Same
US20180342030A1 (en) * 2017-05-24 2018-11-29 The Research Foundation For The State University Of New York Neutral radistricting using a multi-level weighted graph partitioning algorithm
CN208548350U (en) * 2018-08-06 2019-02-26 京东方科技集团股份有限公司 A kind of film layer structure, array substrate and display device

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6781682B1 (en) * 2000-01-17 2004-08-24 Agency Of Industrial Science And Technology, Ministry Of International Trade & Industry Optical apparatus, optical apparatus adjustment method, and storage medium recorded with a processing program that executes said adjustment method
CN101508768A (en) * 2009-03-20 2009-08-19 华东理工大学 Intelligent modeling method in industrial polyester production process
CN102932422A (en) * 2012-09-29 2013-02-13 南京邮电大学 Cloud environment task scheduling method based on improved ant colony algorithm
CN106777768A (en) * 2017-01-09 2017-05-31 大连理工大学 A kind of Optimization Design that fold is stretched for eliminating membrane structure
CN111336935A (en) * 2020-03-31 2020-06-26 上海市计量测试技术研究院 Nano-film parameter inversion calculation method based on improved hybrid optimization algorithm

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
基于有限元分析的重型装备空投系统匹配和评估;王红岩等;《计算机辅助工程》;20120630(第03期);全文 *
柔性自回弹天线反射器结构厚度的优化;柏宏武等;《空间电子技术》;20050630(第02期);全文 *

Also Published As

Publication number Publication date
CN112784457A (en) 2021-05-11

Similar Documents

Publication Publication Date Title
Gao et al. Topology optimization for multiscale design of porous composites with multi-domain microstructures
Im et al. Surrogate modeling of elasto-plastic problems via long short-term memory neural networks and proper orthogonal decomposition
Demir et al. Design of variable stiffness composite structures using lamination parameters with fiber steering constraint
CN112784457B (en) Thin film structure reinforcing band layout optimization method and system based on genetic algorithm
Steven et al. Multicriteria optimization that minimizes maximum stress and maximizes stiffness
CN111353246B (en) Static and dynamic force multi-target topology evolution method for concrete member design
Li et al. Reanalysis assisted metaheuristic optimization for free vibration problems of composite laminates
CN106055791A (en) Prediction-correction algorithm-based aircraft global pneumatic optimization method
Chu et al. Explicit topology optimization of novel polyline-based core sandwich structures using surrogate-assisted evolutionary algorithm
US20200065447A1 (en) Method for fixture shape optimization design of space membrane structure for inhibiting wrinkling
CN114912578A (en) Training method and device of structure response prediction model and computer equipment
Nejat et al. Topology optimization of lightweight periodic lattices under stiffness and stability constraints
Hui et al. A data-driven CUF-based beam model based on the tree-search algorithm
Liu et al. LatLRR for subspace clustering via reweighted Frobenius norm minimization
CN112381591A (en) Sales prediction optimization method based on LSTM deep learning model
CN114970366B (en) Functional gradient metamaterial structure optimization design method and system
Yang et al. Skeleton Neural Networks via Low-rank Guided Filter Pruning
US20220207374A1 (en) Mixed-granularity-based joint sparse method for neural network
Eidelman et al. Efficient eigenvalue computation for quasiseparable Hermitian matrices under low rank perturbations
CN110889259B (en) Sparse matrix vector multiplication calculation unit for arranged block diagonal weight matrix
CN115587510A (en) Design method of stiffened plate structure
Zhao et al. Initial prestress design and optimization of cable-stiffened latticed shells
Stone et al. Ship hull structural scantling optimization
CN116401913B (en) Design and optimization method of hydrogel-based negative hydration swelling metamaterial
Li et al. Fast contact force calculation method for a wire mesh based on support vector machine

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
GR01 Patent grant
GR01 Patent grant