CN105404732A - Random normal distribution based composite laminate stacking layer optimization method - Google Patents

Random normal distribution based composite laminate stacking layer optimization method Download PDF

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CN105404732A
CN105404732A CN201510754004.3A CN201510754004A CN105404732A CN 105404732 A CN105404732 A CN 105404732A CN 201510754004 A CN201510754004 A CN 201510754004A CN 105404732 A CN105404732 A CN 105404732A
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laying
normal distribution
layer sequence
stacking layer
optimization method
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吕乐丰
吴文科
吴远飞
张桥
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China Helicopter Research and Development Institute
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China Helicopter Research and Development Institute
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    • 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
    • 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
    • G06F2113/00—Details relating to the application field
    • G06F2113/24—Sheet material

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  • Automation & Control Theory (AREA)
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Abstract

The invention discloses a random normal distribution based composite laminate stacking layer optimization method, and relates to the technical field of machinery. The random normal distribution based composite laminate stacking layer optimization method comprises the following steps of: step 1: according to a ratio requirement of each stacking layer angle, determining a basic stacking layer sequence; step 2: performing digital coding on each stacking layer sequence, and then performing random transformation and decoding on the basic stacking layer sequence by adopting a normal distribution function to obtain a new stacking layer sequence in a next round of iteration; step 3: according to a target function formula defined in the specification, determining an optimal solution of the basic stacking layer sequence; and step 4: comparing optimal solutions of basic stacking layer sequences, and selecting a maximum value as an optimal stacking layer. The method has the beneficial effects that the basic stacking layer sequence is reconstructed by utilizing the random normal distribution function, an optimal axial compression bearing capacity of a flange of a composite laminate can be obtained, a structural weight ratio is reduced, the confidence degree is high, and the convergence is quick.

Description

A kind of composite material laminated board laying optimization method based on random normal distribution
Technical field
The present invention designs field of mechanical technique, is specifically related to a kind of composite material laminated board laying optimization method based on random normal distribution.
Background technology
As the basic structure form of helicopter, composite material laminated board, by suitable Lay up design, can improve its load-bearing capacity.Compound substance flanged structure can be used as the long laminate process of a long limit freedom, another long limit freely-supported.In actual applications, about the selection of laminate ply sequence, the factors such as wing flapping, laying ratio, ply stacking-sequence be considered.Consider from the restriction of process conditions and the angle of simplified design, ply stacking angle is selected usually in the angular range of π/4.Therefore, the design variable of the optimum design of laminate layup of composite material laminated board is ply stacking-sequence, belong to the optimization problem of discrete variable, relate to that discrete heat sources is many, constraint condition is many and complicated, there is the difficult points such as multiple extreme points, solve very difficult by traditional mathematic programming methods.At present, in the optimization of composite material laminated board laying, applying wider is take genetic algorithm as the modern intelligence optimization algorithm such as evolution algorithm and neural network of representative.Genetic algorithm and neural net method applicability and versatility stronger than mathematical programming approach, but calculated amount is but very large, convergence is slow, and counting yield is relatively low.
Summary of the invention
The invention provides a kind of composite material laminated board laying optimization method based on random normal distribution, with solve or at least to alleviate in background technology existing calculated amount large, restrain slow problem.
The technical solution adopted in the present invention is: provide a kind of composite material laminated board laying optimization method based on random normal distribution, comprise following steps: step one: according to the proportion requirement of each laying angle, determine basic layer sequence; Step 2: carry out numerical coding to each layer sequence, then adopts normal distyribution function to carry out stochastic transformation and decoding to basic layer sequence, obtains the new layer sequence of next round iteration; Step 3: according to objective function Equation max f ( x ) = m a x ( N c c , N c r , N c u ) = Δ N c s t g j ( x ) , j = 1 , 2 , ... , m , Determine basic layer sequence optimum solution; Wherein, f (x) is objective function, i.e. the axial load carrying capacity of composite material laminated board, N ccfor axial compression crushing load, N crfor buckling load, N cufor limited compression load, g j(x), j=1,2 ... m is constraint function, x ∈ { R nshu x 1, x 2..., x n, the vector that laying angle is formed }; Step 4: the optimum solution of more basic layer sequence, chooses maximal value as optimum laying.
Preferably, the proportion requirement of each laying angle that described step one is vertical is, each laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, wherein 0 ° of laying is between 25%-40%, ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%.
Preferably, in optimal design, first according to the proportion requirement of each laying angle, obtain laying number and the combined situation of 0 °, 45 ° ,-45 °, 90 ° laying, after laying combination is determined, carry out the setting of basic layer sequence; When the pawnshop number of plies is even number, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °; When the pawnshop number of plies is odd-level, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °, laying number is that the laying angle of odd number is placed on middle layer.
Preferably, should meet in described step 2: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
Preferably, the objective function in described step 3 comprises two types, and type one is axial compression cripling load, and computing formula is wherein, N crfor the axial compression buckling load on unit width, b is the width of flange, and L is the length of flange, D 11, D 66for the bending stiffness coefficient of laminate; Type two is crushing load, and computing formula is wherein, N cufor the limited compression load of laminate, N ccfor the axial compression crushing load on unit width.
Preferably, before step one, consider the symmetry of laying and the two-layer laying angle of outermost, solve number of times for reducing, in fact the number of design variable is wherein CELL (.) is the function that rounds up, and N is laying number.
Preferably, the constraint function in described step 3 should meet the following conditions: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Each laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, and wherein 0 ° of laying is between 25%-40%, and ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
Beneficial effect of the present invention is: the innovative point of this patent is to utilize random normal distribution function to reconstruct basic layer sequence, when meeting constraint condition, obtains optimum layer sequence fast.Can obtain the best axial load carrying capacity of composite material laminated board flange, reduce construction weight ratio, degree of confidence is high, convergence is rapid.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the composite material laminated board laying optimization method based on normal distribution of the present invention;
Fig. 2 is based on the iterations probability distribution graph obtained based on the composite material laminated board laying optimization method of normal distribution of the present invention.
Embodiment
For making object of the invention process, technical scheme and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is further described in more detail.In the accompanying drawings, same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Described embodiment is the present invention's part embodiment, instead of whole embodiments.Be exemplary below by the embodiment be described with reference to the drawings, be intended to for explaining the present invention, and can not limitation of the present invention be interpreted as.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.Below in conjunction with accompanying drawing, embodiments of the invention are described in detail.
In describing the invention; it will be appreciated that; term " " center ", " longitudinal direction ", " transverse direction ", "front", "rear", "left", "right", " vertically ", " level ", " top ", " end " " interior ", " outward " etc. instruction orientation or position relationship be based on orientation shown in the drawings or position relationship; be only the present invention for convenience of description and simplified characterization; instead of instruction or imply indication device or element must have specific orientation, with specific azimuth configuration and operation, therefore can not be interpreted as limiting the scope of the invention.
As described in Figure 1, a kind of composite material laminated board laying optimization method based on random normal distribution, comprises following steps: step one: according to the proportion requirement of each laying angle, determines basic layer sequence; Step 2: carry out numerical coding to each layer sequence, then adopts normal distyribution function to carry out stochastic transformation and decoding to basic layer sequence, obtains the new layer sequence of next round iteration; Step 3: according to objective function Equation max f ( x ) = m a x ( N c c , N c r , N c u ) = Δ N c s t g j ( x ) , j = 1 , 2 , ... , m , Determine basic layer sequence optimum solution; Wherein, f (x) is objective function, i.e. the axial load carrying capacity of composite material laminated board, N ccfor axial compression crushing load, N crfor buckling load, N cufor limited compression load, g j(x), j=1,2 ... m is constraint function, x ∈ { R nshu x 1, x 2..., x n, the vector that laying angle is formed }; Step 4: the optimum solution of more basic layer sequence, chooses maximal value as optimum laying.
The proportion requirement of each laying angle that step one is vertical is: each the laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, wherein 0 ° of laying is between 25%-40%, ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%.
Be understandable that, the ratio of often kind of laying angle can set according to actual needs.Such as, in an alternative embodiment, the ratio of the ratio of 0 ° of laying to be the ratio of 25%, ± 45 ° of layings be 65%, 90 ° of layings is 10%; In another alternative, the ratio of the ratio of 0 ° of laying to be the ratio of 40%, ± 45 ° of layings be 40%, 90 ° of layings is 20%; The ratio that can also be set as the ratio of 0 ° of laying to be the ratio of 30%, ± 45 ° of layings be 45%, 90 ° of layings is 25%.
In optimal design, first according to the proportion requirement of each laying angle, obtain laying number and the combined situation of 0 °, 45 ° ,-45 °, 90 ° laying, after laying combination is determined, carry out the setting of basic layer sequence; When the pawnshop number of plies is even number, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °; When the pawnshop number of plies is odd-level, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °, laying number is that the laying angle of odd number is placed on middle layer.
Should meet in step 2: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
Be understandable that, in an alternative embodiment, the ratio of zero degree laying is 25%, and the ratio of positive and negative 45 degree of layings is the ratio of 50%, 90 degree of layings is 25%.
Determine that basic layer sequence is: 45 ° ,-45 °, 45 ° ,-45 °, 0 °, 0 °, 90 °, 90 °;
The sequence number arranging basic laying is: 1,2,3,4,5,6,7,8;
Utilize random function between 0 to 1, arbitrarily get the numerical value of 8 different sizes:
0.5533、0.16696、0.096765、0.72381、0.49182、0.58178、0.94642、0.37737；
These group data are encoded to by size: 5,2,1,7,4,6,8,3;
According to the order of these group data to basic laying rearrangement be:
0°、-45°、45°、90°、-45°、0°、90°、45°。
Objective function in step 3 comprises two types, and type one is axial compression cripling load, and computing formula is wherein, N crfor the axial compression buckling load on unit width, b is the width of flange, and L is the length of flange, D 11, D 66for the bending stiffness coefficient of laminate; Type two is crushing load, and computing formula is wherein, N cufor the limited compression load of laminate, N ccfor the axial compression crushing load on unit width.
Before step one, consider the symmetry of laying and the two-layer laying angle of outermost, solve number of times for reducing, in fact the number of design variable is wherein CELL (.) is the function that rounds up, and N is laying number.
Constraint function in step 3 should meet the following conditions: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Each laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, and wherein 0 ° of laying is between 25%-40%, and ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
During laying sum N=32, the best laying number after compound substance flange final optimization pass, optimum ply stacking-sequence, optimal objective value N cmaxthe poorest desired value N cmincontrast as shown in table 1.Can see, after optimizing, the axial compression load-carrying properties of compound substance flange are greatly improved, and when the pawnshop number of plies is 32 layers, axial compression load ratio that is optimum and the poorest laying reaches 1.401.
Compound substance flange optimum results during table 1 laying sum N=32
Accompanying drawing 2 is based on the composite material laminated board laying optimization method based on random normal distribution of the present invention, the probability distribution graph of the compound substance flange laying Optimized Iterative number of times as N=32 obtained.Fig. 2 gives the probability distribution graph of the compound substance flange laying Optimized Iterative number of times of the laying sum N=32 of double counting 20 times.Can find out, this convergence time numerical example meets average μ=310.6, the normal distribution of standard deviation sigma=352.8, and convergence number of times M great majority are secondary lower than 664 (i.e. μ+σ), and when iterations M gets 1370 (i.e. μ+3 σ), convergent probability can reach 99.7%.This shows, the degree of confidence based on the composite plys optimized algorithm of random normal distribution is high, and convergence is rapid, engineer applied of being more convenient for compared with traditional optimization method.
Finally it is to be noted: above embodiment only in order to technical scheme of the present invention to be described, is not intended to limit.Although with reference to previous embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that: it still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature; And these amendments or replacement, do not make the essence of appropriate technical solution depart from the spirit and scope of various embodiments of the present invention technical scheme.

Claims (7)

1., based on a composite material laminated board laying optimization method for random normal distribution, it is characterized in that, comprise following steps:
Step one: according to the proportion requirement of each laying angle, determines basic layer sequence;
Step 2: carry out numerical coding to each layer sequence, then adopts normal distyribution function to carry out stochastic transformation and decoding to basic layer sequence, obtains the new layer sequence of next round iteration;
Step 3: according to objective function Equation m a x f ( x ) = m a x ( N c c , N c r , N c u ) = Δ N c s t g j ( x ) , j = 1 , 2 , ... , m , Determine basic layer sequence optimum solution; Wherein, f (x) is objective function, i.e. the axial load carrying capacity of composite material laminated board, N ccfor axial compression crushing load, N crfor buckling load, N cufor limited compression load, g j(x), j=1,2 ... m is constraint function, x ∈ { R nshu x 1, x 2..., x n, the vector that laying angle is formed };
Step 4: the optimum solution of more basic layer sequence, chooses maximal value as optimum laying.
2. the composite material laminated board laying optimization method based on random normal distribution according to claim 1, it is characterized in that: the proportion requirement of each laying angle that described step one is vertical is, each laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, wherein 0 ° of laying is between 25%-40%, ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%.
3. the composite material laminated board laying optimization method based on random normal distribution according to claim 2, it is characterized in that: in optimal design, first according to the proportion requirement of each laying angle, obtain laying number and the combined situation of 0 °, 45 ° ,-45 °, 90 ° laying, after laying combination is determined, carry out the setting of basic layer sequence; When the pawnshop number of plies is even number, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °; When the pawnshop number of plies is odd-level, certainly lay outside to inside according to ± 45 °, 0 ° and 90 °, laying number is that the laying angle of odd number is placed on middle layer.
4. the composite material laminated board laying optimization method based on random normal distribution according to claim 1, is characterized in that: should meet in described step 2: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
5. the composite material laminated board laying optimization method based on random normal distribution according to claim 1, is characterized in that: the objective function in described step 3 comprises two types, and type one is axial compression cripling load, and computing formula is wherein, N crfor the axial compression buckling load on unit width, b is the width of flange, and L is the length of flange, D 11, D 66for the bending stiffness coefficient of laminate; Type two is crushing load, and computing formula is wherein, N cufor the limited compression load of laminate, N ccfor the axial compression crushing load on unit width.
6. the composite material laminated board laying optimization method based on random normal distribution according to claim 1, it is characterized in that: before step one, consider the symmetry of laying and the two-layer laying angle of outermost, solve number of times for reducing, in fact the number of design variable is wherein CELL (.) is the function that rounds up, and N is laying number.
7. the composite material laminated board laying optimization method based on random normal distribution according to claim 1, is characterized in that: the constraint function in described step 3 should meet the following conditions: the standard laying adopting 0 °, 45 ° ,-45 °, 90 °; Avoid using unidirectional laying group; For 0 °, ± laying of 45 °, laying number is less than or equal to 4 layers in the same way, and for the laying of 90 °, laying number is less than or equal to 2 layers in the same way; Each laying ratio in 0 °, 45 ° ,-45 °, 90 ° four kinds of layings at least will account for 10%, and wherein 0 ° of laying is between 25%-40%, and ± 45 ° of layings are between 40%-70%, and 90 ° of layings are between 10%-25%; Consider from stability and impact-resistant angle, outermost layer adopts ± 45 °; Laying should be symmetrically distributed.
CN201510754004.3A 2015-11-04 2015-11-04 Random normal distribution based composite laminate stacking layer optimization method Pending CN105404732A (en)

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CN107526898A (en) * 2017-09-13 2017-12-29 大连理工大学 A kind of variation rigidity composite panel shell structure Accurate Model analysis and reliability-based optimization integrated design method
US11400685B2 (en) * 2017-12-15 2022-08-02 Unm Rainforest Innovations Gradually recruited fiber reinforced polymer (FRP) composite

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CN106909706A (en) * 2016-12-30 2017-06-30 中国科学院长春光学精密机械与物理研究所 A kind of composite plys Compensation Design method
CN107526898A (en) * 2017-09-13 2017-12-29 大连理工大学 A kind of variation rigidity composite panel shell structure Accurate Model analysis and reliability-based optimization integrated design method
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