CN107016182A - A kind of composite hatch door optimization method - Google Patents

A kind of composite hatch door optimization method Download PDF

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Publication number
CN107016182A
CN107016182A CN201710200416.1A CN201710200416A CN107016182A CN 107016182 A CN107016182 A CN 107016182A CN 201710200416 A CN201710200416 A CN 201710200416A CN 107016182 A CN107016182 A CN 107016182A
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hatch door
laying
composite
constraints
suboptimization
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李超
卫康斌
杨华伦
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Xian Aircraft Design and Research Institute of AVIC
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Xian Aircraft Design and Research Institute of AVIC
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    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/20Design optimisation, verification or simulation
    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
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    • G06F30/15Vehicle, aircraft or watercraft design

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Abstract

The present invention relates to a kind of composite hatch door optimization method, belong to aircraft structure strength design field.First according to the FEM model of composite hatch door, by basic laying form laying, using laying quantity as optimized variable, first suboptimization is most gently carried out for object function with cabin door structure weight, afterwards, ply sequence modification is carried out, whether there is a certain layer laying as optimized variable, it is same that second suboptimization, the final composite plys mode for obtaining the minimum weight hatch door for meeting the constraints are most gently carried out for object function with above-mentioned cabin door structure weight.By above-mentioned optimization design composite cabin door structure of the invention on the premise of the performance indications such as rigidity, intensity are met, relative to metal hatch door scheme, hatch door weight is considerably reduced, the requirement of hatch door light-weight design is met.

Description

A kind of composite hatch door optimization method
Technical field
The invention belongs to aircraft structure strength design field, more particularly to a kind of composite hatch door optimization method.
Background technology
It is also increasingly strict to lightweight requirements with the continuous development of airborne vehicle, and composite excellent is subtracted with its Weight feature is received much concern, and application percentage of the composite at home in military-civil aircraft is significantly lifted in recent years, nearly all All composite application percentage is regard as an important design objective grinding aircraft.At present, foreign countries have been related to composite The engineer applied of airtight hatch door, data shows composite hatch door than metal hatch door loss of weight about 30%, such as A350XWB landing gates. Domestic composite is mainly used in the non-hermetically sealed hatch door such as undercarriage door, has also carried out the airtight hatch door of composite successively in recent years Research work.
Civil aircraft is in flight course, in order to ensure a home from home in aircraft cockpit, it is necessary to aircraft is carried out airtight Supercharging, airtight cargo door will bear very big differential pressure loading as other airtight hatch doors.Therefore in cabin door structure design, Rigidity requirement must also be met in addition to intensity requirement is met.
Conventional hatch door analysis is all based on strength constraint condition and laying constraints greatly, to deflection constraint conditional definition Compare general, generally there was only this index of maximum deformation quantity.Therefore in the design of composite hatch door, a variety of rigidity are improved about Beam condition, and study its hatch door optimization in implementation have practical engineering application be worth and demand.
The content of the invention
The perfect hatch door deflection constraint condition of the present invention, on this basis according to the requirement such as intensity and laying ratio there is provided A kind of composite hatch door optimization method for considering a variety of deflection constraints such as maximum deformation quantity, percent ripple, jump, gap, is obtained The composite hatch door layering type for adapting to requirement of engineering is arrived.
Composite hatch door optimization method of the present invention, is mainly included the following steps that:
S1, the FEM model for setting up the composite hatch door, the composite that the FEM model includes are initial Laying attribute is, according to metal hatch door etc. rigidity principle design the initial overlay thickness of composite hatch door, and basic laying lattice Formula is [45N1/0N2/-45N3/90N4]S, wherein, N1, N2, N3 and N4 are corresponding angle laying quantity;
S2, using N1, N2, N3 and N4 as optimized variable, the first suboptimum is most gently set up for object function with cabin door structure weight Change model;
S3, the first suboptimization of progress, and optimum results are carried out with the accordance inspection of constraints, if being unsatisfactory for constraining bar Part, then return to step S2 changes optimized variable, or modification constraints, until meeting constraint bar under the basic laying form of acquisition The optimal laying quantity and laying ratio of part;
S4, according to step S3 laying optimum results change ply sequence, amended ply sequence include symmetric layups, Consecutive identical angle laying is no more than three layers and adjacent laying angle is no more than 60 °;
S5, the ply sequence according to step S4, whether there is a certain layer laying as optimized variable, with the cabin door structure Weight most gently sets up the second suboptimization model for object function;
S6, the second suboptimization of progress, obtain the composite plys side for the minimum weight hatch door for meeting the constraints Formula.
Preferably, cabin door structure weight is in the step S2Wherein, ρiThe material used in component i The density of material, LiFor component i board area, AiFor component i panel thickness, N is the number of components.
In such scheme preferably, the constraints in the step S3 includes deflection constraint condition, strength constraint bar Part and laying ratio constraints.
In such scheme preferably, the deflection constraint includes connecing the percent ripple of hatch door, jump, gap and stop Row constraint is entered in contact.
In such scheme preferably, the strength constraint includes the permissible, composite strain and individual layer to hatch door Fail into row constraint.
In such scheme preferably, the laying ratio is constrained to 0 ° of laying accounting 35%~55%, and ± 45 ° of layings are accounted for Than 35%~60%, remaining is 90 ° of layings.
Advantages of the present invention and effect include:
1) by optimization design composite cabin door structure on the premise of the performance indications such as rigidity, intensity are met, relatively In metal hatch door scheme, hatch door weight is considerably reduced, the requirement of hatch door light-weight design is met.
2) two suboptimization analysis has been carried out to composite hatch door, meet construction weight it is most light in the case of, maximum limit The laying advantage of composite has been played degree;
3) using the present invention optimization method, it is contemplated that multiple deflection constraint conditions, including maximum deformation quantity, percent ripple, The rigidity requirements such as jump, gap, change traditional hatch door analysis and only account for the single constraints of maximum deformation quantity, optimize Obtained ply sequence provides reference for practical engineering application.
Brief description of the drawings
Fig. 1 is the flow chart of a preferred embodiment of composite hatch door optimization method of the present invention.
Fig. 2 is the hatch door percent ripple schematic diagram of embodiment illustrated in fig. 1 of the present invention.
Fig. 3 is the hatch door jump schematic diagram of embodiment illustrated in fig. 1 of the present invention.
Fig. 4 is the stop contact point maximum distortion schematic diagram of embodiment illustrated in fig. 1 of the present invention.
Fig. 5 is two suboptimization weight iterative process figures of embodiment illustrated in fig. 1 of the present invention.
Embodiment
To make the purpose, technical scheme and advantage of the invention implemented clearer, below in conjunction with the embodiment of the present invention Accompanying drawing, the technical scheme in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class As label represent same or similar element or the element with same or like function.Described embodiment is the present invention A part of embodiment, rather than whole embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to uses It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiment in the present invention, ordinary skill people The every other embodiment that member is obtained under the premise of creative work is not made, belongs to the scope of protection of the invention.Under Embodiments of the invention are described in detail with reference to accompanying drawing for face.
In the description of the invention, it is to be understood that term " " center ", " longitudinal direction ", " transverse direction ", "front", "rear", The orientation or position relationship of the instruction such as "left", "right", " vertical ", " level ", " top ", " bottom ", " interior ", " outer " is based on accompanying drawing institutes The orientation or position relationship shown, is for only for ease of the description present invention and simplifies description, rather than indicate or imply signified dress Put or element there must be specific orientation, with specific azimuth configuration and operation, therefore it is not intended that to present invention protection The limitation of scope.
The present invention is described in further details below by embodiment.
The invention provides a kind of composite hatch door optimization method, perfect hatch door deflection constraint condition is basic herein On there is provided one kind consider that maximum deformation quantity, percent ripple, jump, gap etc. are a variety of just according to the requirement such as intensity and laying ratio The composite hatch door optimization method of constraint is spent, has obtained adapting to the composite hatch door layering type of requirement of engineering, has finally obtained The minimum weight hatch door and the composite plys mode of the hatch door being met under the constraintss such as intensity, rigidity.
Composite hatch door optimization method of the present invention, as shown in figure 1, mainly including the following steps that:
S1, the FEM model for setting up the composite hatch door, the composite that the FEM model includes are initial Laying attribute is, according to metal hatch door etc. rigidity principle design the initial overlay thickness of composite hatch door, and basic laying lattice Formula is [45N1/0N2/-45N3/90N4]S, wherein, N1, N2, N3 and N4 are corresponding angle laying quantity;
S2, using N1, N2, N3 and N4 as optimized variable, the first suboptimum is most gently set up for object function with cabin door structure weight Change model;
S3, the first suboptimization of progress, and optimum results are carried out with the accordance inspection of constraints, if being unsatisfactory for constraining bar Part, then return to step S2 changes optimized variable, or modification constraints, until meeting constraint bar under the basic laying form of acquisition The optimal laying quantity and laying ratio of part;
S4, according to step S3 laying optimum results change ply sequence, amended ply sequence include symmetric layups, Consecutive identical angle laying is no more than three layers and adjacent laying angle is no more than 60 °;
S5, the ply sequence according to step S4, whether there is a certain layer laying as optimized variable, with the cabin door structure Weight most gently sets up the second suboptimization model for object function;
S6, the second suboptimization of progress, obtain the composite plys side for the minimum weight hatch door for meeting the constraints Formula.
Step S1 is the FEM model for setting up the composite hatch door, and unit simplifies and node grid division should be able to be true Real simulation cabin door structure rigidity, and at least in the midpoint of skin areas (covering between adjacent longeron, crossbeam), Liangping face With the intersection point placement model node of seal line, the following aspects is specifically included:
Unit simplifies:Covering is reduced to Shell Finite Element, and band blend stop is reduced to Shell Finite Element, and outer edge strip is reduced to bar list Member, interior edge strip is reduced to beam element, and web is reduced to Shell Finite Element, and detent joint is reduced to rigid unit, is connected and adopts with fuselage Use spring unit.
Node grid:Using the theoretical profile intersection point of longeron plane, crossbeam plane and hatch door as fundamental node.Each skin areas Interior size of mesh opening is about 30mm × 30mm, and hatch door periphery and corner's skinned mesh are coordinated to draw according to inner skins number of grid Point, the web size of mesh opening between interior edge strip and outer edge strip is about 30mm × 24mm.
The initial laying attribute of composite hatch door FEM model:According to metal hatch door by etc. rigidity principle design composite wood Expect the initial overlay thickness of hatch door, basic laying form is [45N1/0N2/-45N3/90N4]S, wherein, N1, N2, N3 and N4 are correspondence Angle laying quantity, S is one cycle.The present embodiment table 1 below gives certain specific initial ply parameter of composite hatch door.
Table 1, the initial ply stacking-sequence of composite hatch door
Structure position Laying
Covering [452/02/-452/902]S
Stiffened skin [452/04/-452/902]S
Crossbeam [452/02/-452/902]S
Common longeron [45/03/-45/90]S
Strengthen longeron [452/02/-452/902]S
Step S2 before this step, further comprises output model data to set up Optimized model.For example, completing Being submitted after laying assignment should be comprising node, unit, material category in NASTRAN output Data of Finite Element Model files, data file Property, cell attribute, load and model boundary constraint.
Composite hatch door Data of Finite Element Model file (BDF) is opened, sequence is solved and is changed to SOL200, it is complete in order Into the editor of Optimized model file:Optimized variable → objective function → definition constraints is defined, it is specific as follows:
Optimized variable is set:According to basic laying form [45N1/0N2/-45N3/90N4]S, with each angle laying quantity N1, N2, N3 and N4 are optimized variable, it is to be understood that N1, N2, N3 and N4 are corresponding angle laying quantity, therefore these variables Be defined as discrete variable, that is, be the positive integer (N1/N2/N3/N4=1,2,3 ... ...) more than or equal to 1, optimized variable by The locking justice of DESVAR, variable centrifugal pump is by DDVAL card controls.It is by the locking justice of DVPREL2, optimizing index variable and laying is thick Degree is connected, i.e. Tj=Njt0, wherein TjFor jth layer overlay thickness, t0For thickness in monolayer, NjFor jth laying target variable.
Objective function:Cabin door structure weight is most gently object function, and its weight is represented by Wherein, ρiFor the density of component i material therefors, LiFor component i board area, AiFor component i panel thickness, N is number of components Amount.
Constraints:It is locking by DCONSTR including the constraint of deflection constraint condition, strength constraint condition and laying ratio The above-mentioned constraint response of justice, it is specific as follows.
1) the deflection constraint condition of hatch door specifically includes a variety of rigidity such as maximum deformation quantity, percent ripple, jump, gap and wanted Ask, table 2 gives a variety of deflection constraint conditions of hatch door.
The a variety of deflection constraint conditions of table 2, hatch door
Maximum deformation quantity is expressed as cabin door structure any part maximum deformation quantity, and it is responded in NASTRAN softwares The locking justice of DRESP2.
Percent ripple is used for representing the unevenness of flat or continuous bend contoured surface even variation, by peak swing b with Wavelength L ratio is determined, is illustrated as shown in Fig. 2 giving hatch door with fuselage positions relation and corrugated cabin door structure, this reality Percent ripple in example is applied to respond by the locking justice of DRESP2 in NASTRAN softwares.
Jump is the difference in height between hatch door and fuselage skin, and hatch door is deformed inward to bear jump with respect to fuselage, otherwise is In positive jump, schematic diagram when Fig. 3 gives to form negative jump, the present embodiment, it is responded by the locking justice of DRESP1.
Gap is the distance between hatch door and fuselage skin, and it is responded by the locking justice of DRESP1.
Stop contact point deformation, is defined as the elastic deformation at stop contact point, such as Fig. 4 in the case where boost limit load is acted on Shown, stop contact point state before the change of left figure in Fig. 4 is deformed after ultimate load, and schematic diagram is Fig. 4 right figures after deformation, Wherein, outmost turns are fuselage load block, and its radius is Rp, and inner ring is hatch door latch, and its radius is Rs, before deformation, fuselage Load block and hatch door latch are coaxial, and the center of circle is latch initial contact point, and after deformation, the contact point changes, such as Fig. 4 The latch deforming contact point on right side, two contact point distance as maximum distortion radius Rm, the optimization border provided by upper table 2 Condition understands that maximum distortion radius Rm should be less than or equal to the 75% of fuselage load block radius Rp.In the present embodiment, it rings It should be defined by DRESP2.
Stop contact point deformation containing maximum alignment error, when being defined as existing maximum alignment error, is carried in supercharging limitation Elastic deformation at the lower stop contact point of lotus effect, it is responded by the locking justice of DRESP2.
2) strength constraint of hatch door mainly considers failure criteria and the permissible limitation of composite, before table 3 gives The strength constraint condition of cargo door.
The strength constraint condition of table 3, fore hold door
Composite permissible is limited by the locking justice of DRESP1, and expression formula is:εt≤[εt], εc≤[εc], γ≤ [γ];
The composite strain factor is calculated as follows:
Wherein, ε is worked asa>When 0, εat;Work as εa<When 0, εac
In the present embodiment, responded by the locking justice of DRESP2, calculation formula is realized by DEQATN cards.
Tsai-Wu failure criterias, Tsai-Wu Failure Factors are calculated as follows:
Wherein, F11=1/ (XtXc), F1=1/Xt-1/Xc, F22=1/ (YtYc), F2=1/Yt-1/Yc F66=1/S2, σ6= τ12,
In the present embodiment, responded by the locking justice failures of DRESP1, regard invalid principle as constraints less than 1.0.
3) laying ratio is constrained, 0 ° of laying 35%~55%, ± 45 ° of layings 35%~60%, and remaining is 90 ° of layings, by DRESP2 sets the response of laying ratio, and its proportionate relationship is defined by equation card DEQATN:
% ± 45 °=(N1+N3)/(N1+N2+N3+N4);
%0 °=N2/ (N1+N2+N3+N4);
%90 °=N4/ (N1+N2+N3+N4).
By above-mentioned optimized variable, object function to carry out after the first suboptimization, editor is completed after Optimized model file, is submitted NASTRAN is calculated.
Step S3 checks that control constraints carries out accordance inspection to optimization result of calculation for optimum results accordance, If result of calculation is unsatisfactory for constraints, reply design variable definition is modified, returns to second step and calculated;Such as Fruit meets constraints, then carries out next step.Analyzed by the first suboptimization, obtained meeting about under basic laying form The optimal laying quantity and laying ratio of beam condition.
The preceding 6 step iteration of first suboptimization analysis as shown in Figure 5 (shorter line), starts to receive after the iterative calculation of 6 steps Hold back, with the increase of iterations, the quality of hatch door is continuously increased, and increased amplitude is less and less, because composite wood Expect that initial laying is unsatisfactory for constraints, so architecture quality first increased;Meeting after Prescribed Properties, then in progressively The trend of reduction, this is the result being improved to design variable.Iteration final step hatch door quality has a mutation, this be because Discrete variable is defined as optimized variable, when completing optimization design, optimized variable will carry out rounding.Optimization terminates rear door matter Amount adds 17.33% than initial laying model.
According to previous step laying optimum results, laying is carried out by following laying criterions:Composite element is as far as possible symmetrical paving Layer, superficial layer is ± 45 °, and consecutive identical angle laying is no more than three layers, and adjacent laying differential seat angle is no more than 60 °.
The second suboptimization model is built on the basis of the first suboptimization model, the ply sequence of composite is have changed, Table 4 is listed after the first suboptimization, the composite hatch door ply stacking-sequence provided by laying criterion.
Table 4, the composite hatch door ply stacking-sequence provided by laying criterion
Part Ply stacking-sequence
Covering [45/02/-45/902/45/02/-452/90]S
Stiffened skin [45/02/-45/902/452/03/-452/90]S
Cantilever diaphragm [45/02/45/90/-452/0_]S
Common longitudinal-beam web plate [45/03/-45/90/4_5_]S
Strengthen longitudinal-beam web plate [45/02/-45/90/45/02/-452/9_0_]S
Afterwards, the second suboptimization model file is set up, its optimized variable and object function are as follows:
Optimized variable is set:One discrete optimization variables L is defined to each layer of layingj(j=1,2), when j=1 represents this Layer is deleted, and j=2 represents that this layer retains;Optimized variable is by the locking justice of DESVAR, and variable centrifugal pump is by DDVAL card controls.Pass through The locking justice of DVPREL2, optimized variable is connected with overlay thickness, i.e. Tj=(Lj-1)t0, wherein TjIt is thick for jth layer laying Degree, t0For thickness in monolayer, NjFor jth laying target variable.
Objective function:Cabin door structure weight is most gently object function, consistent with the object function of the first suboptimization, no Repeat again.
Constraints:Compared with the first suboptimization model, rigidity, intensity and the laying ratio constraint bar of composite hatch door Part keeps constant.
Editor is completed after Optimized model file, submits NASTRAN to calculate.The second suboptimization analysis is carried out, has been obtained to full " losing layer " design of the ply sequence of sufficient laying criterion calls, can obtain a minimum weight cabin for meeting above-mentioned constraints Door, optimization design terminates.
By Fig. 5, the second suboptimization analysis restrains after the iterative calculation of 13 steps, with the increase of iterations, hatch door Quality progressively reduces, and each design variable also tends to stabilization, and iteration final step quality has a mutation, because optimized variable Discrete variable is defined as, when completing optimization design, optimized variable will carry out rounding.Second optimization terminates rear door mass ratio the One optimum results reduce 6.75%, illustrate that it is very significant to carry out the second suboptimization.Table 5 is listed by the second suboptimum The composite hatch door ply stacking-sequence obtained after change.
Composite hatch door ply stacking-sequence after table 5, the second suboptimization
Part Ply stacking-sequence
Covering [45/0/-45/902/45/02/-452/90]S
Stiffened skin [45/0/-45/902/452/03/-452/90]S
Cantilever diaphragm [45/02/45/90/-452/0_]S
Common longitudinal-beam web plate [45/0/-45/90/4_5_]S
Strengthen longitudinal-beam web plate [45/0/-45/90/45/0/-45/9_0_]S
To embody effect of the present invention, after optimization finishes beam, as shown in figure 1, also including following two steps:
Composite hatch door after terminating to optimization carries out static analysis, has obtained stress after the completion of optimization design, should The result of calculation for becoming and deforming.
Static Calculation result is exported, the weight that table 6 lists present example metal hatch door and composite hatch door is contrasted The result of calculation that analysis result, wherein rate of change are expressed as composite hatch door final mask and metal hatch door model is contrasted.
The weight of table 6, metal hatch door and composite hatch door compares analysis result
It can be seen from Table 6 that, advantages of the present invention and effect include:
1) by optimization design composite cabin door structure on the premise of the performance indications such as rigidity, intensity are met, relatively In metal hatch door scheme, hatch door weight is considerably reduced, the requirement of hatch door light-weight design is met.
2) two suboptimization analysis has been carried out to composite hatch door, meet construction weight it is most light in the case of, maximum limit The laying advantage of composite has been played degree;
3) using the present invention optimization method, it is contemplated that multiple deflection constraint conditions, including maximum deformation quantity, percent ripple, The rigidity requirements such as jump, gap, change traditional hatch door analysis and only account for the single constraints of maximum deformation quantity, optimize Obtained ply sequence provides reference for practical engineering application.
It is last it is to be noted that:The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.To the greatest extent The present invention is described in detail with reference to the foregoing embodiments for pipe, it will be understood by those within the art that:It is still Technical scheme described in foregoing embodiments can be modified, or which part technical characteristic is equally replaced Change;And these modifications or replacement, the essence of appropriate technical solution is departed from the essence of various embodiments of the present invention technical scheme God and scope.

Claims (6)

1. a kind of composite hatch door optimization method, it is characterised in that including:
S1, the FEM model for setting up the composite hatch door, the initial laying of composite that the FEM model includes Attribute is, according to metal hatch door etc. rigidity principle design the initial overlay thickness of composite hatch door, and basic laying form is [45N1/0N2/-45N3/90N4]S, wherein, N1, N2, N3 and N4 are corresponding angle laying quantity;
S2, using N1, N2, N3 and N4 as optimized variable, the first suboptimization mould is most gently set up for object function with cabin door structure weight Type;
S3, the first suboptimization of progress, and optimum results are carried out with the accordance inspection of constraints, if being unsatisfactory for constraints, Then return to step S2 changes optimized variable, or modification constraints, and constraints is met under basic laying form until obtaining Optimal laying quantity and laying ratio;
S4, change ply sequence according to step S3 laying optimum results, amended ply sequence includes symmetric layups, continuous Equal angular laying is no more than three layers and adjacent laying angle is no more than 60 °;
S5, the ply sequence according to step S4, whether there is a certain layer laying as optimized variable, with the cabin door structure weight Most gently set up the second suboptimization model for object function;
S6, the second suboptimization of progress, obtain the composite plys mode for the minimum weight hatch door for meeting the constraints.
2. composite hatch door optimization method as claimed in claim 1, it is characterised in that:Cabin door structure weight in the step S2 Measure and beWherein, ρiFor the density of component i material therefors, LiFor component i board area, AiFor component i Panel thickness, N is the number of components.
3. composite hatch door optimization method as claimed in claim 1, it is characterised in that:Constraints in the step S3 Including deflection constraint condition, strength constraint condition and laying ratio constraints.
4. composite hatch door optimization method as claimed in claim 3, it is characterised in that:The deflection constraint is included to hatch door Percent ripple, jump, gap and stop contact click through row constraint.
5. composite hatch door optimization method as claimed in claim 3, it is characterised in that:The strength constraint is included to hatch door Permissible, composite strain and individual layer fail into row constraint.
6. composite hatch door optimization method as claimed in claim 3, it is characterised in that:The laying ratio is constrained to 0 ° of paving Layer accounting 35%~55%, ± 45 ° of laying accountings 35%~60%, remaining is 90 ° of layings.
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CN109726437A (en) * 2018-12-04 2019-05-07 中国航空工业集团公司西安飞机设计研究所 A kind of hatch door aerodynamic loading equivalent nodal force processing method
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CN110727998A (en) * 2019-09-27 2020-01-24 中国人民解放军国防科技大学 Optimized design method and system for composite material X-shaped support structure for connecting fuel storage tank
CN112380624A (en) * 2020-11-20 2021-02-19 中国直升机设计研究所 Helicopter cabin skeleton rigidity optimization method

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