CN109711093A - A kind of composite propeller predeformation optimization method peculiar to vessel - Google Patents
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Abstract
The present invention relates to a kind of composite propeller predeformation optimization methods peculiar to vessel, belong to turbomachine simulation technical field.The present invention is by establishing composite propeller finite element model, and it is subjected to two-way fluid and structural simulation with composite propeller luid mechanics computation model, the deformation values on each blade section of blade at characteristic point along coordinate direction are extracted based on result, then the deformation values are reversely added in propeller Formula of Coordinate System Transformation and carry out pre-treatment, finally obtain predeformation composite propeller.The present invention has comprehensively considered the variation of the geometric parameters such as airscrew pitch angle, skew back and rake caused by composite propeller deformable blade under fluid structure interaction, improves the accuracy of predeformation design；And versatility of the present invention is relatively strong, universality is higher；Compared to existing predeformation design method, have calculation amount small, calculates easy, it can be achieved that saving a large amount of computing resource and time the advantages of parametrization, Programmed Design.
Description
Technical field
The present invention relates to a kind of composite propeller predeformation optimization methods peculiar to vessel, belong to turbomachine emulation technology neck
Domain.
Background technique
Replace traditional metal materials manufacture propeller that can significantly improve its hydrodynamic performance and vibration spy using composite material
Property.By the improvement of design and paddle blade structure to composite fiber laying, what composite propeller can be born according to it
Hydrodynamic load is adaptively adjusted skew back, trim and screw pitch distribution to improve hydrodynamic performance.Current fiber composite material peculiar to vessel
Material propeller mostly uses the offset of metal airscrew, does not account for the influence of propeller blade Coupling effect of seepage rock deformation, and compound
Material propeller blade can be deformed when working and propulsive efficiency is caused to reduce, and not be able to satisfy full working scope Ship Propeling demand.
In order to improve propeller propulsive efficiency, a large amount of scholars study and propose to the two-way Coupling effect of seepage rock deformation of composite propeller
Composite propeller predeformation design method, method (CN101706832A) is mainly by composite propeller finite element
Deformation values at each node of model carry out reversed superposition to obtain predeformation compound propeller blade geometry.But it is existing pre-
Deformation design method calculation amount is too big, and excessively dependence finite element software is solid through flowing without careful consideration blade without having versatility
Oblique, trim and screw pitch variation on rear side of coupling.
Summary of the invention
The purpose of the present invention is to solve do not consider blade through the solid coupling of stream in existing composite propeller design process
It the problem of cooperation deforms after changes skew back, trim and screw pitch, and composite propeller propulsive efficiency is caused to decline, mentions
For a kind of composite propeller predeformation optimization method peculiar to vessel；This method makes the composite material spiral designed by predeformation
The propulsive efficiency of paddle is equal under design conditions with rigid paddle, and better than rigid paddle under off-design behaviour, and then widen compound
The high efficient district of material propeller works.
The present invention is adopted the technical scheme that reach above-mentioned technical goal:
A kind of composite propeller predeformation optimization method peculiar to vessel, is realized using following steps:
Step 1: pass through the transformation for mula of metal airscrew blade section local coordinate system to global coordinate system, i.e. formula
(1), each blade section offset of metal airscrew is converted into three-dimensional cartesian coordinate points.
Wherein, x, y, z are propeller three-dimensional cartesian coordinate value；LiFor guide margin parameter；RiFor the corresponding radius of each blade section
Value；(X, Y) is blade section data point；For the angle of pitch；β is Angle of Trim.
Step 2: the metal airscrew three-dimensional cartesian coordinate points found out in step 1 are imported and construct gold in modeling software
Belong to propeller geometrical model, and the pressure face of propeller blade, suction surface and three, middle face Plane Entity model are saved respectively.
Step 3: it using the ACP module in WorkBench platform, is carried out by the plane of symmetry of face in metal airscrew blade
Fibrous composite laying, the blade pressure face kept and suction surface model in steps for importing two, for constraining composite wood
Expect laying shape, realizes the foundation of composite propeller finite element model.
The fibrous composite laying method is unidirectional laying or braiding laying；
Step 4: the composite propeller finite element model guiding structure finite element analysis of completion will be established in step 3
Module adds revolution speed of propeller and fixed constraint as boundary condition to calculate paddle blade structure response, and by composite material spiral
Paddle blade is set as fluid structurecoupling interface.
The structure control equation of the composite propeller is
Wherein, [Ms] it is architecture quality matrix, [Cs] it is structural damping matrix, [Ks] it is structural stiffness matrix；{ X } i.e. displacement structure,I.e. structure speed,That is structure acceleration；{FCFDRepresent flow field forces suffered by fluid structure interaction flowering structure.
Step 5: using composite propeller Fluid Dynamical Analysis module, carries out thunder to composite propeller flow field
Equal N-S equation (RANS) solves when promise, obtains composite propeller flow field hydrodynamic load.
The composite propeller Fluid Dynamical Analysis is by the reality of Fluid Mechanics Computation (CFD) and metal airscrew
Operating condition combines to be calculated；
The RANS equation is closed using standard k- ω SST turbulence model；
The actual operating mode includes the speed of a ship or plane, revolving speed and corresponding hydrodynamic performance parameter；
The hydrodynamic performance parameter includes: thrust coefficientTorque coefficientAnd promote effect
RateWherein Q indicates the sum of the torque on all blades, i.e. total torque；ρ indicates that the density of water is 997kg/m3；
N is revolution speed of propeller；D is airscrew diameter；T indicates the sum of the thrust on all blades, i.e. gross thrust；J indicates advanced coefficient.
Step 6: by the System Coupling module in WorkBench platform, the paddle that step 4 is solved
The composite propeller flow field hydrodynamic load that impeller structure response is solved with step 5 is carried out two-way using substep algorithm
Fluid and structural simulation.
Step 7: according to fluid and structural simulation acquired results two-way in step 6, judge the hydrodynamic(al) of composite propeller
Whether power performance parameter is equal to metal airscrew under design conditions, and is better than metal airscrew under off-design behaviour；And
Whether judgement material fails.If meeting conditions above simultaneously, the Preliminary design of composite propeller is completed.
Step 8: it if being unsatisfactory for any judgment criteria in step 7, needs to become the composite propeller in advance
Shape design.Specific embodiment is as follows: first in each blade section table of offsets of propeller 0.2R-0.95R at same chord length
(0.1c-0.9c) determines two characteristic points (X, YO) and (X, YU), and two characteristic point is located at suction surface and pressure face
On, i.e., the X value of described two characteristic point is identical, and Y value is respectively YO、YU.According to the formula (1) in step 1, two feature is obtained
The three-dimensional cartesian coordinate of point is (xo, yo, zo)、(xu, yu, zu)。
Step 9: according to two-way fluid structurecoupling calculated result required in step 6, in structural finite element analysis module
Deformation values of two characteristic points described in step 8 on three directions of X, Y, Z axis, characteristic point (X, Y are extracted respectivelyO) deformation
Value is UX1, UY1, UZ1；Characteristic point (X, YU) deformation values be UX2, UY2, UZ2；Then on composite propeller in step 8
Two characteristic points carry out predeformation, i.e., the deformation values extracted are reversely added in the coordinate of two characteristic point, are somebody's turn to do
Two characteristic point predeformation coordinate (xo-UX1, yo-UY1, zo-UZ1)、(xu-UX2, yu-UY2, zu-UZ2).Note is by after predeformation
Two characteristic point coordinates are (xp1, yp1, zp1)、(xp2, yp2, zp2)；And coordinate (xp1, yp1, zp1) and (xp2, yp2, zp2) meet
Step 10: the ordinate of two characteristic points in step 9 is subtracted each otherIt can find out
The angle of pitch of predeformation composite propeller at the blade section of two characteristic points placeIt repeats Step 9: step 10 can be distinguished
Obtain the angle of pitch of each blade section predeformation composite propeller of 0.2R-0.95R
Step 11: the angle of pitch for each blade section of predeformation composite propeller 0.2R-0.95R that step 10 is obtainedIt substitutes into formula (1)In, it is pre- that each blade section of 0.2R-0.95R can be found out
The rake angle beta of deformation bonding material propellerpWith guide margin parameter Lpi.By the angle of pitch of obtained predeformation composite propellerRake angle betapWith guide margin parameter LpiFormula (1) in step 1 is substituted into respectively, so that it is determined that predeformation composite propeller
The three-dimensional cartesian coordinate of blade entirety.
Step 12: the three-dimensional cartesian seat based on the predeformation composite propeller blade entirety that step 11 obtains
Mark repeats step 2 to step 6, carries out predeformation to the composite material marine propeller blade geometrical model newly obtained, until
Meet the requirement of composite material marine Hydrodynamic Performance on Propeller and Structural strength calls described in step 7, obtains that full work can be achieved
The best geometric shape that composite material marine propeller efficiently navigates by water under condition completes final predeformation optimization.
The utility model has the advantages that
1. a kind of composite propeller predeformation optimization method peculiar to vessel of the invention, has comprehensively considered fluid structure interaction
The variation of the geometric parameters such as airscrew pitch angle, skew back and rake caused by lower composite propeller deformable blade, improves
The accuracy of predeformation optimization.
2. it is public that the conversion of propeller coordinate is utilized in a kind of composite propeller predeformation optimization method peculiar to vessel of the invention
Formula (formula 1) is a kind of versatility compared with strong, the higher composite propeller predeformation optimization method of universality, is applicable to
Such as pump, most of composite material impellers machinery such as hydraulic turbine.
3. a kind of composite propeller predeformation optimization method peculiar to vessel of the invention compares existing predeformation optimization side
Method has calculation amount small, calculates easy, it can be achieved that it is timely to save a large amount of computing resources the advantages of parametrization, Programmed Design
Between.
Detailed description of the invention
Fig. 1 is that composite propeller Fluid Dynamical Analysis calculates basin schematic diagram；
Fig. 2 is the two-way fluid structurecoupling calculation flow chart of composite propeller；
Fig. 3 is two characteristic point schematic diagrames determining on suction surface at each blade section of propeller and pressure face；
Fig. 4 is composite propeller predeformation optimisation technique flow chart of the present invention；
Fig. 5 is that the propulsive efficiency of metal airscrew, composite propeller and predeformation composite propeller compares.
Specific embodiment
In conjunction with attached drawing, with the big skew back marine propeller (HSP) of SEIUN-MARU for embodiment, the present invention is made furtherly
It is bright.
Embodiment 1
The fibrous composite marine propeller predeformation optimization method of present embodiment is realized by following steps:
Step 1: derive that HSP type metal airscrew blade section local coordinate system is sat to the overall situation based on principle of coordinate transformation
The transformation for mula for marking system, such as formula (1).It is programmed by Matlab by HSP type propeller 0.2R-0.95R (R is propeller radius)
Locate each blade section offset and is converted to three-dimensional cartesian coordinate points.
Wherein, x, y, z are HSP type propeller three-dimensional cartesian coordinate value, LiFor guide margin parameter；RiIt is corresponding for each blade section
Radius value；(X, Y) is blade section data point；For the angle of pitch；β is Angle of Trim.
Step 2: the HSP type metal airscrew three-dimensional coordinate point found out in step 1 is imported into 3 d modeling software
HSP type metal airscrew geometrical model is constructed in SolidWorks, and by propeller pressure side, suction surface and three, middle face plane
Physical model saves respectively.
Step 3: using the ACP module in WorkBench platform using face in HSP type metal airscrew blade as the plane of symmetry
It carries out the unidirectional 45 degree of layings of fibrous composite (being laid with 25 layers altogether), the blade pressure face kept and suction in steps for importing two
Power face constrains the shapes of composite plys.The final foundation for realizing HSP type composite propeller finite element model.
Step 4: the HSP type composite propeller finite element model guiding structure that completion is established in step 3 is limited
To calculate paddle blade structure response in meta analysis module (Workbench Static Structure), revolution speed of propeller is added
(90.7RPM), fixed constraint (propeller shank) are used as boundary condition, and set fluid structurecoupling for compound propeller blade
Interface.Wherein paddle blade structure governing equation isWherein, [Ms] it is knot
Structure mass matrix, [Cs] it is structural damping matrix, [Ks] it is structural stiffness matrix；{ X } i.e. displacement structure,I.e. structure speed,That is structure acceleration；{FCFDRepresent flow field forces suffered by paddle blade structure under the fluid structure interaction solved by CFD software.
Step 5: use composite propeller Fluid Dynamical Analysis module, i.e. Fluid Mechanics Computation (CFD) software CFX,
Equal N-S equation (RANS) solves when carrying out Reynolds to composite propeller flow field, obtains composite propeller flow field hydrodynamic(al)
Power load.
The Fluid Dynamical Analysis of the composite propeller is based on Fluid Mechanics Computation (CFD) and to combine HSP type spiral shell
Revolve the actual operating mode of paddle: i.e. speed of a ship or plane 9knots, revolving speed 90.7RPM, thrust coefficient KT=0.1012, torque coefficient KQ=
0.01863, propulsive efficiency η=0.736.Equal N-S equation (RANS) is asked when carrying out Reynolds to the type composite propeller flow field HSP
It is as shown in Figure 1 to solve domain for solution.Equation is closed using standard k- ω SST turbulence model, and HSP type composite material spiral shell is calculated
Revolve paddle flow field hydrodynamic load.
Step 6: by business software System Coupling, the HSP type composite propeller that step 4 is obtained
The composite propeller hydrodynamic load that paddle blade structure response is obtained with step 5 carries out bidirectional flow using substep algorithm and consolidates coupling
It is total to calculate, calculation process such as Fig. 2.
Step 7: according to fluid and structural simulation acquired results two-way in step 6, judge to find that obtained HSP type is compound
Material propeller (J=0.851) propulsive efficiency η=0.7183 under design conditions is lower than HSP type metal airscrew η=0.736；
Fibre reinforced composites do not fail.
Step 8: it because the HSP type composite propeller is unsatisfactory for hydrodynamic performance judgment criteria, needs compound to this
Material propeller carries out predeformation design.Specific embodiment is as follows: as shown in figure 3, each in propeller 0.2R-0.95R first
(0.6c) determines two characteristic points (X, Y at same chord length in blade section table of offsetsO) and (X, YU), and two characteristic point is distinguished
On suction surface and pressure face.By taking 0.9R blade section as an example, the three-dimensional cartesian coordinate of selected two characteristic point be (613.58,
71.716,1499.306), (608.4078,91.95995,1501.413).
Step 9: according to the two-way fluid structurecoupling calculated result in step 6, in structural finite element analysis module respectively
Extract deformation values of two characteristic points described in step 8 on three directions of X, Y, Z axis, characteristic point (X, YO) deformation values be
UX1, UY1, UZ1；Characteristic point (X, YU) deformation values be UX2, UY2, UZ2；Then to two on composite propeller in step 8
Characteristic point carries out predeformation, and the deformation values that will also extract reversely are added in the coordinate of two characteristic point, obtains two spy
Sign point predeformation coordinate (xo-UX1, yo-UY1, zo-UZ1)、(xu-UX2, yu-UY2, zu-UZ2).Two features after predeformation
Point coordinate is (613.2863,72.03,1499.12), (608.1047,92.273,1501.32).
Step 10: two characteristic point ordinates in step 9 are subtracted each otherI.e.The angle of pitch of predeformation composite propeller at the blade section can be found outIt repeats Step 9: ten can be obtained the spiral shell of each blade section predeformation composite propeller of 0.2R-0.95R
Elongation
Step 11: the angle of pitch for each blade section of predeformation composite propeller 0.2R-0.95R that step 10 is obtainedIt substitutes into step 1 in formula (1)0.2R-0.95R can be found out
The rake angle beta of each blade section predeformation composite propellerpWith guide margin parameter Lpi.The predeformation composite material spiral that will be obtained
The angle of pitch of paddleRake angle betapWith guide margin parameter LpiFormula (1) in step 1 is substituted into, so that it is determined that predeformation composite material
The three-dimensional cartesian coordinate of propeller blade entirety.
Step 12: the three-dimensional cartesian coordinate based on the predeformation composite propeller that step 11 obtains repeats
Step 2 is to step 6, as shown in Figure 4.The HSP type composite material marine propeller blade geometric shape newly obtained is carried out pre-
Deformation, until the hydrodynamic performance for meeting composite material marine propeller described in step 7 in summary of the invention requires and structural strength
It is required that obtaining that the optimal geometric shape that HSP type composite material marine propeller efficiently navigates by water under full working scope can be achieved, complete most
Whole predeformation optimization.
A kind of exemplary application fibre enhanced composite material marine propeller predeformation optimization method of the present invention, it is right
HSP type composite propeller peculiar to vessel carries out pre-treatment.As shown in figure 5, the predeformation optimization method makes by predeformation
The propulsive efficiency of HSP type composite propeller later is equal at design conditions (J=0.851) with rigid rotor, and
It is better than rigid rotor under off-design behaviour, has widened the high efficient district of HSP type composite propeller work peculiar to vessel.Thus table
Bright, a kind of fibre enhanced composite material marine propeller predeformation optimization method has practical application value.
Above-described specific descriptions have carried out further specifically the purpose of invention, technical scheme and beneficial effects
It is bright, it should be understood that the above is only a specific embodiment of the present invention, the protection model being not intended to limit the present invention
It encloses, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in the present invention
Protection scope within.
Claims (5)
1. a kind of composite propeller predeformation optimization method peculiar to vessel, it is characterised in that: realized using following steps:
Step 1:, will by the transformation for mula of metal airscrew blade section local coordinate system to global coordinate system, i.e. formula (1)
Each blade section offset of metal airscrew is converted to three-dimensional cartesian coordinate points；
Wherein, x, y, z are propeller three-dimensional cartesian coordinate value；LiFor guide margin parameter；RiFor the corresponding radius value of each blade section；
(X, Y) is blade section data point；For the angle of pitch；β is Angle of Trim；
Step 2: the metal airscrew three-dimensional cartesian coordinate points found out in step 1 are imported and construct metal spiral shell in modeling software
Paddle geometrical model is revolved, and the pressure face of propeller blade, suction surface and three, middle face Plane Entity model are saved respectively；
Step 3: using the ACP module in WorkBench platform, fiber is carried out by the plane of symmetry of face in metal airscrew blade
Composite plys, the blade pressure face kept and suction surface model in steps for importing two, for constraining composite material paving
Layer shape, realizes the foundation of composite propeller finite element model；
The fibrous composite laying method is unidirectional laying or braiding laying；
Step 4: the composite propeller finite element model guiding structure finite element analysis module of completion will be established in step 3
To calculate paddle blade structure response, revolution speed of propeller and fixed constraint are added as boundary condition, and by composite propeller paddle
Leaf is set as fluid structurecoupling interface；
The structure control equation of the composite propeller isIts
In, [Ms] it is architecture quality matrix, [Cs] it is structural damping matrix, [Ks] it is structural stiffness matrix；{ X } be displacement structure,
For structure speed,For structure acceleration；{FCFDRepresent flow field forces suffered by fluid structure interaction flowering structure；
Step 5: using composite propeller Fluid Dynamical Analysis module, when carrying out Reynolds to composite propeller flow field
Equal N-S equation solution, obtains composite propeller flow field hydrodynamic load；
Step 6: by the System Coupling module in WorkBench platform, the blade knot that step 4 is solved
It is solid to carry out bidirectional flow using substep algorithm for the composite propeller flow field hydrodynamic load that structure response is solved with step 5
Coupling calculates；
Step 7: according to fluid and structural simulation acquired results two-way in step 6, judge the hydrodynamic force of composite propeller
Whether energy parameter is equal to metal airscrew under design conditions, and is better than metal airscrew under off-design behaviour；And judge
Whether material fails；If meeting conditions above simultaneously, the Preliminary design of composite propeller is completed；
Step 8: it if being unsatisfactory for any judgment criteria in step 7, needs to carry out predeformation to the composite propeller to set
Meter；
(0.1c-0.9c) determines two characteristic points at same chord length in each blade section table of offsets of propeller 0.2R-0.95R first
(X, YO) and (X, YU), and two characteristic point is located on suction surface and pressure face, i.e., the X value of described two characteristic point is identical,
Y value is respectively YO、YU；According to the formula (1) in step 1, the three-dimensional cartesian coordinate for obtaining two characteristic point is (xo, yo,
zo)、(xu, yu, zu)；
Step 9: according to two-way fluid structurecoupling calculated result required in step 6, in structural finite element analysis module respectively
Extract deformation values of two characteristic points described in step 8 on three directions of X, Y, Z axis, characteristic point (X, YO) deformation values be
UX1, UY1, UZ1；Characteristic point (X, YU) deformation values be UX2, UY2, UZ2；Then to two on composite propeller in step 8
Characteristic point carries out predeformation, i.e., the deformation values extracted is reversely added in the coordinate of two characteristic point, obtains two spy
Sign point predeformation coordinate (xo-UX1, yo-UY1, zo-UZ1)、(xu-UX2, yu-UY2, zu-UZ2)；Note is special by two after predeformation
Sign point coordinate is (xp1, yp1, zp1)、(xp2, yp2, zp2)；And coordinate (xp1, yp1, zp1) and (xp2, yp2, zp2) meet
Step 10: the ordinate of two characteristic points in step 9 is subtracted each otherTwo spies can be found out
The angle of pitch of predeformation composite propeller at the blade section of sign point placeIt repeats Step 9: step 10 can respectively obtain
The angle of pitch of each blade section predeformation composite propeller of 0.2R-0.95R
Step 11: the angle of pitch for each blade section of predeformation composite propeller 0.2R-0.95R that step 10 is obtainedGeneration
Enter in formula (1)In, it is known that each blade section predeformation of 0.2R-0.95R is compound
The rake angle beta of material propellerpWith guide margin parameter Lpi；By the angle of pitch of obtained predeformation composite propellerRake
Angle betapWith guide margin parameter LpiFormula (1) in step 1 is substituted into respectively, so that it is determined that predeformation composite propeller blade is whole
Three-dimensional cartesian coordinate；
Step 12: the three-dimensional cartesian coordinate based on the predeformation composite propeller blade entirety that step 11 obtains,
Step 2 is repeated to step 6, predeformation is carried out to the composite material marine propeller blade geometrical model newly obtained, until full
Composite material marine Hydrodynamic Performance on Propeller described in sufficient step 7 requires and Structural strength calls, obtains that full working scope can be achieved
The best geometric shape that lower composite material marine propeller efficiently navigates by water completes final predeformation optimization.
2. a kind of composite propeller predeformation optimization method peculiar to vessel as described in claim 1, it is characterised in that: step 5
The composite propeller Fluid Dynamical Analysis is by the actual operating mode phase of Fluid Mechanics Computation and metal airscrew
In conjunction with being calculated.
3. a kind of composite propeller predeformation optimization method peculiar to vessel as described in claim 1, it is characterised in that: step 5
The RANS equation is closed using standard k- ω SST turbulence model.
4. a kind of composite propeller predeformation optimization method peculiar to vessel as described in claim 1, it is characterised in that: step 5
The actual operating mode includes the speed of a ship or plane, revolving speed and corresponding hydrodynamic performance parameter.
5. a kind of composite propeller predeformation optimization method peculiar to vessel as claimed in claim 4, it is characterised in that: the water
Power property arguments include: thrust coefficientTorque coefficientAnd propulsive efficiency
Wherein Q indicates the sum of the torque on all blades, i.e. total torque；ρ indicates that the density of water is 997kg/m3；N is revolution speed of propeller；
D is airscrew diameter；T indicates the sum of the thrust on all blades, i.e. gross thrust；J indicates advanced coefficient.
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| CN111444643A (en) * | 2020-03-02 | 2020-07-24 | 北京理工大学 | Neural network-based composite material propeller layering angle optimization method |
| CN111563320A (en) * | 2020-04-18 | 2020-08-21 | 西北工业大学 | Design method of structure and water elasticity integrated propeller |
| CN112464530A (en) * | 2020-11-22 | 2021-03-09 | 西北工业大学 | Sandwich structure composite material propeller finite element modeling method |
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| CN111159950A (en) * | 2019-12-30 | 2020-05-15 | 北京理工大学 | Acoustic-solid coupling-based composite propeller prestress wet mode prediction method |
| CN111159950B (en) * | 2019-12-30 | 2021-06-01 | 北京理工大学 | Acoustic-solid coupling-based composite propeller prestress wet mode prediction method |
| CN111444643A (en) * | 2020-03-02 | 2020-07-24 | 北京理工大学 | Neural network-based composite material propeller layering angle optimization method |
| CN111444643B (en) * | 2020-03-02 | 2022-04-19 | 北京理工大学 | Neural network-based composite material propeller layering angle optimization method |
| CN111563320A (en) * | 2020-04-18 | 2020-08-21 | 西北工业大学 | Design method of structure and water elasticity integrated propeller |
| CN112464530A (en) * | 2020-11-22 | 2021-03-09 | 西北工业大学 | Sandwich structure composite material propeller finite element modeling method |
| CN112464530B (en) * | 2020-11-22 | 2024-03-01 | 西北工业大学 | Sandwich structure composite material propeller finite element modeling method |
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