CN104376136B - Aircraft casing sandwich and its implementation - Google Patents
Aircraft casing sandwich and its implementation Download PDFInfo
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- CN104376136B CN104376136B CN201310354930.2A CN201310354930A CN104376136B CN 104376136 B CN104376136 B CN 104376136B CN 201310354930 A CN201310354930 A CN 201310354930A CN 104376136 B CN104376136 B CN 104376136B
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Abstract
The aircraft casing sandwich and its implementation in a kind of aircraft manufacturing and computer image processing technology field, available for aircraft, such as the housing of passenger plane, unmanned plane, rocket, guided missile etc., it can also be used to submersible, such as the housing of submarine.
Description
Technical field
The present invention relates to a kind of aircraft manufacturing and the method in computer image processing technology field, specifically one kind just
In the aircraft casing sandwich and its implementation realized in computer program.
Background technology
Many research shows that three-dimensional origami structure has good specific strength, energy absorption characteristics and sound damping.Based on three-dimensional
These characteristics of origami structure, they are applied in quick air-drop technology, as the buffering energy-absorbing knot for delivering thing bottom
Structure.Meanwhile these structures can be as a kind of excellent aircraft or the interlayer of the crustless sandwich structure of submersible, so as to take
It must compare extensive honeycomb sandwich construction for current use.General rounded (such as the fire of the housing section of aircraft or submersible
Arrow, guided missile) or the closed loop (such as passenger plane, submarine) that is made up of several sections of circular arcs.When origami structure is applied into these housings,
One important technical problem is in the case of the physical dimension of given housing section, to design what is with this section matched
Origami structure.
The content of the invention
The present invention is directed to deficiencies of the prior art, proposes a kind of aircraft casing sandwich and its realization side
Method, the crustless sandwich structure can be used for aircraft, such as the housing of passenger plane, unmanned plane, rocket, guided missile etc., it can also be used to dive under water
Device, such as the housing of submarine.
The present invention is achieved by the following technical solutions：
The present invention relates to a kind of implementation method of aircraft sandwich structures, the sandwich is by inner casing, shell and is clipped in
Multiple interlayer compositions with origami structure between inside and outside shell.
Described interlayer is accomplished by the following way：
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd section
Long lsegThe external diameter r of interlayer needed for calculating1, internal diameter r2And length l：r1=Rout-tex；r2=Rin+tin；L=lseg；
Step 2：Determine m input point of the x-z-plane of three-dimensional cartesian coordinate systemAnd n+2 of y-z plane are defeated
Access point
Step 3：M × n summit V of origami structure is obtained according to input pointi,jCoordinate, Wherein：
iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | | represent to
Measure mould.
Step 4：Define { Vi,jVi+1,jOr { Vi,jVi,j+1It is a pair of adjacent vertexs.By all adjacent vertex straight lines
Connect, the connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure, and further uses computer
Auxiliary realizes that interlayer manufactures.
Described adjacent vertex refers to：With Vi,jFor summit, then its consecutive points is { Vi,jVi+1,jOr { Vi,jVi,j+1}。
Described computer-aided manufacturing includes：Manufacture mould corresponding with origami structure, using mould to flat sheet
It is molded；Printed using three-dimensional printing technology；Using with the similar method of manufacture comb core, i.e., first with can conveniently roll over
Folded material carries out manual folding, then immerses again in glue and the structure that folds is shaped and reinforced.
Brief description of the drawings
Fig. 1 is crustless sandwich structural representation.
Fig. 2 is adjacent vertex schematic diagram.
Fig. 3 is the origami structure schematic three dimensional views of embodiment 1.
Fig. 4 is the summit V of embodiment 1i,jSubpoint and radius on the y-z plane is 19 and 21 circle.
Fig. 5 is the schematic three dimensional views of the origami structure of embodiment 2.
Fig. 6 be embodiment 3 obtained by origami structure schematic three dimensional views.
Fig. 7 is the partial enlarged drawing of Fig. 6 structures.
Fig. 8 is the origami structure partial enlarged view of embodiment 3.
Fig. 9 is the schematic three dimensional views of the origami structure of embodiment 4.
Figure 10 be embodiment 5 obtained by origami structure 3-D view.
Figure 11 is the origami structure 3-D view of embodiment 5.
Figure 12 is the summit V of embodiment 5i,jSubpoint and radius on the y-z plane is 19 and 21 circle schematic diagram.
Figure 13 is the schematic three dimensional views of the origami structure of embodiment 6.
Figure 14 be embodiment 7 obtained by origami structure 3-D view.
Figure 15 is the partial enlarged view of structure shown in Figure 14.
Figure 16 is the summit V of embodiment 7i,jSubpoint and radius on the y-z plane is 19 and 21 circle schematic diagram.
Figure 17 be embodiment 8 obtained by origami structure 3-D view.
Figure 18 is the partial enlarged view of structure shown in Figure 17.
Figure 19 is the summit V of embodiment 8i,jSubpoint and radius on the y-z plane is 19 and 21 circle schematic diagram.
Figure 20 be embodiment 8 obtained by origami structure 3-D view.
Figure 21 is the partial enlarged view of structure shown in Figure 20.
Figure 22 is the summit V of embodiment 8i,jSubpoint and radius on the y-z plane is the signal of 19 and 21 circle
Figure.
Figure 23 be embodiment 9 obtained by origami structure 3-D view.
Figure 24 is the partial enlarged view of structure shown in Figure 22.
Figure 25 is the schematic three dimensional views of the origami structure of embodiment 12.
Figure 26 is the 3-D view of resulting origami structure.
Figure 27 is the partial enlarged view of structure shown in Figure 26.
Figure 28 is all summit Vi,jSubpoint and radius on the y-z plane is the schematic diagram of 19 and 21 circle.
Figure 29 is the schematic three dimensional views of the origami structure of embodiment 14.
Figure 30 is the 3-D view of resulting origami structure.
Figure 31 is the partial enlarged view of structure shown in Figure 30.
Figure 32 is all summit Vi,jSubpoint and radius on the y-z plane is the schematic diagram of 19 and 21 circle.
Figure 33 is the schematic three dimensional views of the origami structure of embodiment 16.
Figure 34 is the 3-D view of resulting origami structure.
Figure 35 is the partial enlarged view of structure shown in Figure 34.
Figure 36 is the summit V of embodiment 17i,jSubpoint and radius on the y-z plane is the signal of 19 and 21 circle
Figure.
Figure 37 is the schematic three dimensional views of the origami structure of embodiment 17.
Figure 38 is the housing section schematic diagram of embodiment 19.
Figure 39 is the schematic three dimensional views of the origami structure of embodiment 19.
Figure 40 is the sectional view of the origami structure of embodiment 19.
Figure 41 is to include middle shell surface schematic diagram.
Figure 42 is not comprising middle shell surface schematic diagram.
Embodiment
Embodiments of the invention are elaborated below, the present embodiment is carried out lower premised on technical solution of the present invention
Implement, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited to following implementation
Example.
Embodiment 1
Make the internal diameter R of sandwichin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness t of shellex=1,
Segment length lseg=11.By r1=Rout-tex, r2=Rin+tin, l=lsegObtain the external diameter r of interlayer1=21, internal diameter r2=19, length
L=11.
M=12, h=1, a=1 are taken, byUnderstand b=1.ByObtain 12 x-
The input point of z-plane：
N=30 is taken, byObtain β=π/
30。
According to
R=19.9470 and δ=1.0084 is calculated.
N=2N+1=61 is taken, byObtain the defeated of 63 y-z planes
Access point：By 12 × 61 summit V are calculatedi,jCoordinate.
Scrimp is finally defined according to step 7.Fig. 3 is the 3-D view of resulting origami structure, and it joins end to end, and is formed
1 closed loop configuration.Fig. 4 is all summit Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that all
Summit is all fallen within the circumference of the two circles.Origami structure shown in this explanation Fig. 3 has reached radial dimension design requirement.Figure
The axial length of structure shown in 3 is equal to 11, has reached axial dimension design requirement.
Embodiment 2
Change the parameter n in embodiment 1 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 21, resulting origami structure forms 1/3 annulus, as shown in Figure 5.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (13-15) calculating1And internal diameter r2And length l.
r1=Rout-tex(13)；r2=Rin+tin(14)；L=lseg(15)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (16a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (17)
βset；
Step 4：Selected parameter beta, β1And β2, it is met β+β1+β2=βset, and meet β>β1And β>β2.Step 5：
Parameter r and δ are calculated according to formula (18-19).
Step 6：Parameter δ is calculated according to formula (20-21)1And δ2。
Step 7：N+2 input point of the y-z plane of three-dimensional cartesian coordinate system is determined by formula (22-23), wherein n is less than
Or equal to 6N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (24) and (25).
U=[P6×1 P6×1 …]∞×1(24)；Ω=[Q6×1 Q6×1 …]∞×1(25)；That is 1 dimensional vector U by numerous 6 ×
1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 6 × 1 vectorial Q.6 × 1 vectorial P and Q are given by formula (26) and (27) respectively
Go out.
P=[r+ δ r- δ r- δ2 r-δ r+δ r+δ1](26)；Q=[β1 β β2 β2 β β1](27)；
Step 8：M × n summit V is calculated by formula (28)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (29).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.Step 9：Define { Vi,j Vi+1,jOr
Person { Vi,j Vi,j+1It is 1 pair of adjacent vertex.All adjacent vertexs are connected with straight line, as shown in Figure 2.These adjacent vertexs
Between connecting line segment be to constitute the scrimp of origami structure.It can prove, the origami structure obtained by step 1 to 9 designs
External diameter be equal to the internal diameter of shell in shell structure, the internal diameter of origami structure is equal to the external diameter of inner casing in shell structure, paper folding knot
The length of structure is equal to the length of shell structure.Therefore, the origami structure has geometry compatible with inside and outside shell.Above-mentioned shell-
Origami structure-inner casing combination just constitutes the 2nd kind of aircraft casing sandwich of the present invention.
Embodiment 3
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (13-15)1=21, internal diameter r2=19, length l=11.
M=12, h=1, a=1 are taken, b=1 is understood by formula (16b).
The input point of 12 x-z-planes is obtained by formula (16a)：
N=30 is taken, β is obtained by formula (17)set=π/30.
Take β1=β2=π/300, then β=βset-β1-β2=8 π/300.
R=19.9572 and δ=1.0051 are calculated according to formula (18-19).
δ is calculated according to formula (20-21)1=0.7227 and δ2=0.7824.
N=6N+1=181 is taken, the input point of 183 y-z planes is obtained by formula (22-23)：
Wherein, ujAnd ωkIt is respectively
Two endless 1 dimensional vector U and Ω jth and k-th of element.Endless 1 dimensional vector U and Ω are；U=[P6×1 P6×1
…]∞×1；Ω=[Q6×1 Q6×1 …]∞×1；Wherein：
P=[20.9623 18.9520 19.1748 18.9520 20.9623 20.6798]；Q=[π/300 of π/300 8
π/300 π/300 8π/300 π/300]；12 × 181 summit V are calculated by formula (28)i,jCoordinate.
Scrimp is finally defined according to step 7.
Fig. 6 is the schematic three dimensional views of resulting origami structure.Fig. 7 is the partial enlarged drawing of Fig. 6 structures.It can be seen that
Compared to embodiment 1, the present embodiment is considered as every scrimp in embodiment 1 to be replaced with " v " type groove.Fig. 8 is all tops
Point Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that most of summit all falls within the circle of the two circles
Zhou Shang, remaining summit then fall in radius slightly larger than 19 or on the circumference of the radius circle that is slightly less than 21, behind this part summit pair
The bottom of Ying Yu " v " type groove.Origami structure shown in this explanation Fig. 6 has reached radial dimension design requirement.In addition, Fig. 6 institutes
The axial length for the structure shown is equal to 11, has also reached axial dimension design requirement.
Embodiment 4
Change the parameter n in embodiment 3 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 61, resulting origami structure forms 1/3 annulus, as shown in Figure 9.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (32-34) calculating1And internal diameter r2And length l.
r1=Rout-tex(32)；r2=Rin+tin(33)；L=lseg(34)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (35a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (36)
βset；
Step 4：Selected parameter beta and β1, it is met the β of β+21=βset.Step 5：Ginseng is calculated according to formula (37-39)
Number r and δ.
Step 6：N+2 input point of the y-z plane of three-dimensional cartesian coordinate system is determined by formula (40-41), wherein n is less than
Or equal to 3N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (42) and (43).
U=[P3×1 P3×1 …]∞×1(42)；Ω=[Q3×1 Q3×1 …]∞×1(43)；That is 1 dimensional vector U by numerous 3 ×
1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 3 × 1 vectorial Q.3 × 1 vectorial P and Q are given by formula (44) and (45) respectively
Go out.
P=[r+ δ r+ δ r- δ] (44)；Q=[β1 β β1](45)；
Step 7：M × n summit V is calculated by formula (46)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (47).
Wherein：
iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | | represent
To vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 8：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.It can prove,
The external diameter of the origami structure obtained by step 1 to 8 designs is equal to the internal diameter, the internal diameter of origami structure etc. of shell in shell structure
The external diameter of inner casing in shell structure, the length of origami structure are equal to the length of shell structure.Therefore, the origami structure with it is interior,
Shell has geometry compatible.Above-mentioned shell-origami structure-inner casing combination just constitutes the 3rd kind of aircraft shell of the present invention
Interlayer body structure.
Embodiment 5
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (32-34)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (35b).
The input point of 12 x-z-planes is obtained by formula (35a)： N=30 is taken, β is obtained by formula (36)set=π/15.
Take β1=π/75, then β=βset-2β1=3 π/75.
R=19.7573 and δ=0.7660 are calculated according to formula (37-39).
N=3N+1=91 is taken, the input point of 93 y-z planes is obtained by formula (40-41)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P3×1 P3×1 …]∞×1；Ω=[Q3×1 Q3×1 …]∞×1；Wherein：P=[20.5232 20.5232
18.9913]；Q=[π of π/75 3/75 π/75]；12 × 91 summit V are calculated by formula (46)i,jCoordinate.
Scrimp is finally defined according to step 7.
Figure 10 is the 3-D view of resulting origami structure.Figure 11 is the partial enlarged view of structure shown in Figure 10.Figure
12 be all summit Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that most of summit all falls within this
On two round circumference, remaining summit then falls between above-mentioned two circumference.This illustrates reaching for the origami structure shown in Figure 10
Radial dimension design requirement.In addition, the axial length of the structure shown in Figure 10 is equal to 11, also having reached axial dimension design will
Ask.
Embodiment 6
Change the parameter n in embodiment 5 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 31, resulting origami structure forms 1/3 annulus, as shown in figure 13.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (50-52) calculating1And internal diameter r2And length l.
r1=Rout-tex(50)；r2=Rin+tin(51)；L=lseg(52)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (53a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (54)
βset；
Step 4：Selected parameter beta and β1, it is met the β of β+21=βset。
Step 5：Parameter r and δ are calculated according to formula (55-57).
Step 6：N+2 input point of the y-z plane of three-dimensional cartesian coordinate system is determined by formula (58-59), wherein n is less than
Or equal to 3N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (60) and (61).
U=[P3×1 P3×1 …]∞×1(60)；Ω=[Q3×1 Q3×1 …]∞×1(61)；That is 1 dimensional vector U by numerous 3 ×
1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 3 × 1 vectorial Q.3 × 1 vectorial P and Q are given by formula (62) and (63) respectively
Go out.
P=[r- δ r- δ r+ δ] (62)；Q=[β1 β β1](63)；
Step 7：M × n summit V is calculated by formula (64)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (65).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 8：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.It can prove,
The external diameter of the origami structure obtained by step 1 to 8 designs is equal to the internal diameter, the internal diameter of origami structure etc. of shell in shell structure
The external diameter of inner casing in shell structure, the length of origami structure are equal to the length of shell structure.Therefore, the origami structure with it is interior,
Shell has geometry compatible.Above-mentioned shell-origami structure-inner casing combination just constitutes the 4th kind of aircraft shell of the present invention
Interlayer body structure.
Embodiment 7
Make the internal diameter R of fuselage sandwichin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness t of shellex
=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (50-52)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (53b).
The input point of 12 x-z-planes is obtained by formula (53a)： N=30 is taken, β is obtained by formula (54)set=π/15.
Take β1=π/75, then β=βset-2β1=3 π/75.
R=20.2617 and δ=0.7305 are calculated according to formula (55-57).
N=3N+1=91 is taken, the input point of 93 y-z planes is obtained by formula (58-59)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P3×1 P3×1 …]∞×1；Ω=[Q3×1 Q3×1 …]∞×1；Wherein：P=[19.5312 19.5312
20.9922]；Q=[π of π/75 3/75 π/75]；12 × 91 summit V are calculated by formula (64)i,jCoordinate.
Scrimp is finally defined according to step 7.
Figure 14 is the 3-D view of resulting origami structure.Figure 15 is the partial enlarged view of structure shown in Figure 14.Figure
16 be all summit Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that most of summit all falls within this
On two round circumference, remaining summit then falls between above-mentioned two circumference.This illustrates reaching for the origami structure shown in Figure 14
Radial dimension design requirement.In addition, the axial length of the structure shown in Figure 14 is equal to 11, also having reached axial dimension design will
Ask.
Embodiment 8
Change the parameter n in embodiment 7 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 31, resulting origami structure forms 1/3 annulus, as shown in figure 17.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (68-70) calculating1And internal diameter r2And length l.
r1=Rout-tex(68)；r2=Rin+tin(69)；L=lseg(70)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (71a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (72)
βset；
Step 4：Selected parameter beta, β1And β2, it is met 2 β+β1+β2=βset。
Step 5：Parameter r and δ are calculated according to formula (73-76).
Step 6：N+2 input point of the y-z plane of three-dimensional cartesian coordinate system is determined by formula (77-78), wherein n is less than
Or equal to 4N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (79) and (80).
U=[P4×1 P4×1 …]∞×1(79)；Q=[Q4×1 Q4×1 …]∞×1(80)；I.e. 1 dimensional vector U is by numerous 4 × 1
Vectorial P compositions, 1 dimensional vector Ω are made up of numerous 4 × 1 vectorial Q.4 × 1 vectorial P and Q are given by formula (81) and (82) respectively
Go out.
P=[r+ δ r+ δ r- δ r- δ] (81)；Q=[β β1 β β2](82)；
Step 7：M × n summit V is calculated by formula (83)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (84).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 8：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.
It can prove, the external diameter of the origami structure obtained by step 1 to 8 designs is equal in shell structure in shell
Footpath, the internal diameter of origami structure are equal to the external diameter of inner casing in shell structure, and the length of origami structure is equal to the length of shell structure.Cause
This, the origami structure has geometry compatible with inside and outside shell.Above-mentioned shell-origami structure-inner casing combination just constitutes this hair
The 5th kind of bright aircraft casing sandwich.
Embodiment 9
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (68-70)1=21, internal diameter r2=19, length l=11.
M=12, h=0.2, a=1 are taken, b=1 is understood by formula (71b).
The input point of 12 x-z-planes is obtained by formula (71a)：
Take N=30,
β is obtained by formula (72)set=π/15.
Take β1=β2=π/45, then β=(βset-β1-β1)/2=π/90.
R=20.0053 and δ=0.7994 are calculated according to formula (73-76).
N=4N+1=121 is taken, the input point of 123 y-z planes is obtained by formula (77-78)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P4×1 P4×1 …]∞×1；Ω=[Q4×1 Q4×1 …]∞×1；Wherein：
P=[20.8048 20.8048 19.2059 19.2059]；Q=[π of the π of π/90/45/90 π/45]；By formula
(83) 12 × 121 summit V are calculatedi,jCoordinate.
Scrimp is finally defined according to step 8.
Figure 18 is the 3-D view of resulting origami structure.Figure 19 is the partial enlarged view of structure shown in Figure 18.Figure
20 be all summit Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that most of summit all falls within this
On two round circumference, remaining summit then falls between above-mentioned two circumference.This illustrates reaching for the origami structure shown in Figure 18
Radial dimension design requirement.In addition, the axial length of the structure shown in Figure 18 is equal to 11, also having reached axial dimension design will
Ask.
Embodiment 10
Change the parameter n in embodiment 9 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 41, resulting origami structure forms 1/3 annulus, as shown in figure 21.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (87-89) calculating1And internal diameter r2And length l.
r1=Rout-tex(87)；r2=Rin+tin(88)；L=lseg(89)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (90a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (91)
βset；
Step 4：Selected parameter beta, β1And β2, it is met the β of β+21+2β2=βset, and meet β1>β2.Step 5：According to public affairs
Parameter r and δ is calculated in formula (92-94).
Step 6：Parameter δ is calculated according to formula (95)2。
Step 7：N+2 input point of the y-z plane of three-dimensional cartesian coordinate system is determined by formula (96-97), wherein n is less than
Or equal to 5N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (98) and (99).
U=[P5×1 P5×1 …]∞×1(98)；Ω=[Q5×1 Q5×1 …]∞×1(99)；That is 1 dimensional vector U by numerous 5 ×
1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 5 × 1 vectorial Q.5 × 1 vectorial P and Q are respectively by formula (100) and (101)
Provide.
P=[r- δ r+ δ r+ δ r- δ r- δ2](100)；Q=[β2 β1 β β1 β2](101)；
Step 8：M × n summit V is calculated by formula (102)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (103).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 9：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.It can prove,
The external diameter of the origami structure obtained by step 1 to 9 designs is equal to the internal diameter, the internal diameter of origami structure etc. of shell in shell structure
The external diameter of inner casing in shell structure, the length of origami structure are equal to the length of shell structure.Therefore, the origami structure with it is interior,
Shell has geometry compatible.Above-mentioned shell-origami structure-inner casing combination just constitutes the 6th kind of aircraft shell of the present invention
Interlayer body structure.
Embodiment 11
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (87-89)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (90b).
The input point of 12 x-z-planes is obtained by formula (90a)： N=30 is taken, β is obtained by formula (91)set=π/15.
Take β2=π/300, β1=π/75, then β=βset-2β1-2β2=π/30.
R=19.7551 and δ=0.7638 are calculated according to formula (92-94).
Parameter δ is calculated according to formula (95)2=0.4068.
N=5N+1=151 is taken, the input point of 153 y-z planes is obtained by formula (96-97)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P5×1 P5×1 …]∞×1；Ω=[Q5×1 Q5×1 …]∞×1；Wherein：P=[18.9913 20.5189 20.5189
18.9913 19.3483]；Q=[π of the π of the π of π/300/75/30/75 π/300]；12 × 151 are calculated by formula (102)
Summit Vi,jCoordinate.
Scrimp is finally defined according to step 9.
Figure 22 is the 3-D view of resulting origami structure.Figure 23 is the partial enlarged view of structure shown in Figure 22.Can
To see, compared to embodiment 5, the present embodiment is considered as the inner side scrimp in embodiment 5 to be replaced with " v " type groove.Figure 24
For all summit Vi,jSubpoint and radius on the y-z plane be 19 and 21 circle, it is seen that most of summit all fall within this two
On the circumference of individual circle, remaining summit then falls between above-mentioned two circumference.Origami structure shown in this explanation Figure 22 has reached footpath
To Sizing requirements.In addition, the axial length of the structure shown in Figure 22 is equal to 11, axial dimension design requirement is also reached.
Embodiment 12
Change the parameter n in embodiment 11 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 51, resulting origami structure forms 1/3 annulus, as shown in figure 25.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (106-108) calculating1And internal diameter r2And length l.
r1=Rout-tex(106)；r2=Rin+tin(107)；L=lseg(108)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (109a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (110)
βset；
Step 4：Selected parameter beta, β1And β2, it is met the β of β+21+2β2=βset, and meet β1>β2。
Step 5：Parameter r and δ are calculated according to formula (111-113).
Step 6：Parameter δ is calculated according to formula (114)1。
Step 7：Determine n+2 input point of the y-z plane of three-dimensional cartesian coordinate system by formula (115-116), wherein n is small
In or equal to 5N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (117) and (118).
U=[P5×1 P5×1 …]∞×1(117)；Ω=[Q5×1 Q5×1 …]∞×1(118)；I.e. 1 dimensional vector U is by numerous 5
× 1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 5 × 1 vectorial Q.5 × 1 vectorial P and Q respectively by formula (119) and
(120) provide.
P=[r+ δ r- δ r- δ r+ δ r+ δ1](119)；Q=[β2 β1 β β1 β2](120)；
Step 8：M × n summit V is calculated by formula (121)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (122).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 9：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.
It can prove, the external diameter of the origami structure obtained by step 1 to 9 designs is equal in shell structure in shell
Footpath, the internal diameter of origami structure are equal to the external diameter of inner casing in shell structure, and the length of origami structure is equal to the length of shell structure.Cause
This, the origami structure has geometry compatible with inside and outside shell.Above-mentioned shell-origami structure-inner casing combination just constitutes this hair
The 7th kind of bright aircraft casing sandwich.
Embodiment 13
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (106-108)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (109b).
The input point of 12 x-z-planes is obtained by formula (109a)： N=30 is taken, β is obtained by formula (110)set=π/15.
Take β2=π/300, β1=π/75, then β=βset-2β1-2β2=π/30.
R=20.2580 and δ=0.7343 are calculated according to formula (111-113).
Parameter δ is calculated according to formula (114)1=0.3434.
N=5N+1=151 is taken, the input point of 153 y-z planes is obtained by formula (115-116)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P5×1 P5×1 …]∞×1；Ω=[Q5×1 Q5×1 …]∞×1；Wherein：P=[20.9922 19.5237 19.5237
20.9922 20.6013]；Q=[π of the π of the π of π/300/75/30/75 π/300]；7 × 151 are calculated by formula (121)
Summit Vi,jCoordinate.
Scrimp is finally defined according to step 9.
Figure 26 is the 3-D view of resulting origami structure.Figure 27 is the partial enlarged view of structure shown in Figure 26.Can
To see, compared to embodiment 7, the present embodiment is considered as the outside scrimp in embodiment 7 to be replaced with " v " type groove.Figure 28
For all summit Vi,jSubpoint and radius on the y-z plane be 19 and 21 circle, it is seen that most of summit all fall within this two
On the circumference of individual circle, remaining summit then falls between above-mentioned two circumference.Origami structure shown in this explanation Figure 26 has reached footpath
To Sizing requirements.In addition, the axial length of the structure shown in Figure 26 is equal to 11, axial dimension design requirement is also reached.
Embodiment 14
Change the parameter n in embodiment 13 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 51, resulting origami structure forms 1/3 annulus, as shown in figure 29.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (125-127) calculating1And internal diameter r2And length l.
r1=Rout-tex(125)；r2=Rin+tin(126)；L=lseg(127)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (128a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (129)
βset；
Step 4：Selected parameter beta, β1And β2, it is met the β of 2 β+21+2β2=βset。
Step 5：Parameter r and δ are calculated according to formula (130-131).
Step 6：Determine n+2 input point of the y-z plane of three-dimensional cartesian coordinate system by formula (132-133), wherein n is small
In or equal to 6N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (134) and (135).
U=[P6×1 P6×1 …]∞×1(134)；Ω=[Q6×1 Q6×1 …]∞×1(135)；I.e. 1 dimensional vector U is by numerous 6
× 1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 6 × 1 vectorial Q.6 × 1 vectorial P and Q respectively by formula (136) and
(137) provide.
P=[r r r+ δ r r r- δ] (136)；Q=[β2 β β1 β1 β β2](137)；
Step 7：M × n summit V is calculated by formula (138)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (139).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 8：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.
It can prove, the external diameter of the origami structure obtained by step 1 to 8 designs is equal in shell structure in shell
Footpath, the internal diameter of origami structure are equal to the external diameter of inner casing in shell structure, and the length of origami structure is equal to the length of shell structure.Cause
This, the origami structure has geometry compatible with inside and outside shell.Above-mentioned shell-origami structure-inner casing combination just constitutes this hair
The 8th kind of bright aircraft casing sandwich.
Embodiment 15
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (125-127)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (128b).
The input point of 12 x-z-planes is obtained by formula (128a)： N=30 is taken, β is obtained by formula (129)set=π/15.
Take β2=β1=π/90, then β=(βset-2β1-2β2)/2=π/90.
R=19.9907 and δ=1.0005 are calculated according to formula (130-131).
N=6N+1=181 is taken, the input point of 183 y-z planes is obtained by formula (132-133)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；U=[P6×1 P6×1 …]∞×1；Ω=[Q6×1 Q6×1 …]∞×1；Wherein：
P=[19.9907 19.9907 20.9912 19.9907 19.9907 18.9901]；Q=[π of the π of π/90/90/
90 π/90 π/90 π/90]；12 × 181 summit V are calculated by formula (138)i,jCoordinate.
Scrimp is finally defined according to step 8.
Figure 30 is the 3-D view of resulting origami structure.Figure 31 is the partial enlarged view of structure shown in Figure 30.Figure
32 be all summit Vi,jSubpoint and radius on the y-z plane be 19 and 21 circle, it is seen that all summits all fall within this two
On the circumference of individual circle or fall between above-mentioned two circumference.The radial dimension that reached of origami structure shown in this explanation Figure 30 is set
Meter requires.In addition, the axial length of the structure shown in Figure 30 is equal to 11, axial dimension design requirement is also reached.
Embodiment 16
Change the parameter n in embodiment 15 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 61, resulting origami structure forms 1/3 annulus, as shown in figure 33.
Step 1：According to the internal diameter R of sandwichin, external diameter Rout, the thickness t of inner casingin, shell thickness texAnd segment length
lseg, utilize the external diameter r of interlayer needed for formula (142-144) calculating1And internal diameter r2And length l.
r1=Rout-tex(142)；r2=Rin+tin(143)；L=lseg(144)；
Step 2：M input point of the x-z-plane of three-dimensional cartesian coordinate system is determined by formula (145a), wherein, m is nature
Number.
Wherein, parameter a and b meets：
Step 3：Selected parameter N, wherein N are the natural number more than or equal to 3.Parameter is calculated according to formula (146)
βset；
Step 4：Selected parameter beta, β1, β2, β3And β4, it is met the β of 2 β+21+2β2+2β3+2β4=βset, and meet β1>β3
And β2>β4.Step 5：Parameter r and δ are calculated according to formula (147-148).
Step 6：Parameter δ is calculated according to formula (149-150)1And δ2。
Step 7：Determine n+2 input point of the y-z plane of three-dimensional cartesian coordinate system by formula (151-152), wherein n is small
In or equal to 10N+1.
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω definition is provided by formula (153) and (154).
U=[P10×1 P10×1 …]∞×1(153)；Ω=[Q10×1 Q10×1 …]∞×1(154)；I.e. 1 dimensional vector U is by countless
Individual 10 × 1 vectorial P compositions, 1 dimensional vector Ω are made up of numerous 10 × 1 vectorial Q.10 × 1 vectorial P and Q are respectively by formula (155)
(156) provide.
P=[r- δ r r r+ δ r+ δ1 r+δ r r r-δ r-δ2](155)；
Q=[β4 β2 β β1 β3 β3 β1 β β2 β4](156)；
Step 8：M × n summit V is calculated by formula (157)i,jCoordinate.
Wherein, 3 × 3 matrix [Aj] provided by formula (158).
Wherein：
Wherein, iy=[0 1 0]TFor the unit vector of y-coordinate axle, iz=[0 0 1]TFor the unit vector of z coordinate axle, | | | |
Represent to vectorial modulus.
M × n summit V obtained abovei,jConstitute the summit of origami structure.
Step 9：Define { Vi,j Vi+1,jOr { Vi,j Vi,j+1It is 1 pair of adjacent vertex.By all adjacent vertex straight lines
Connect, as shown in Figure 2.Connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure.It can prove,
The external diameter of the origami structure obtained by step 1 to 9 designs is equal to the internal diameter, the internal diameter of origami structure etc. of shell in shell structure
The external diameter of inner casing in shell structure, the length of origami structure are equal to the length of shell structure.Therefore, the origami structure with it is interior,
Shell has geometry compatible.Above-mentioned shell-origami structure-inner casing combination just constitutes the 9th kind of aircraft shell of the present invention
Interlayer body structure.
Embodiment 17
Make the internal diameter R of aircraft sandwich structuresin=18, external diameter Rout=22, the thickness t of inner casingin=1, the thickness of shell
tex=1, segment length lseg=11.The external diameter r of interlayer is obtained by formula (142-144)1=21, internal diameter r2=19, length l=11.
M=12, h=0.5, a=1 are taken, b=1 is understood by formula (145b).
The input point of 12 x-z-planes is obtained by formula (145a)： N=30 is taken, β is obtained by formula (146)set=π/15.
Take β3=β4=π/420, β1=β2=π/105, then β=(βset-2β1-2β2-2β3-2β4)/2=π/105.
R=19.9915 and δ=1.0005 are calculated according to formula (147-148).
Parameter δ is calculated according to formula (149-150)1=0.7393 and δ2=0.7615.
N=10N+1=301 is taken, the input point of 303 y-z planes is obtained by formula (151-152)：
Wherein, ujAnd ωkIt is two endless 1 dimensional vector U and Ω jth and k-th of element respectively.The dimensional vector U of endless 1 and
Ω is；
U=[P10×1 P10×1 …]∞×1；Ω=[Q10×1 Q10×1 …]∞×1；Wherein；
P=[18.9910 19.9915 19.9915 20.9920 20.7308 20.9920 19.9915 19.9915
18.9910 19.2300]；
Q=[π of the π of the π of the π of the π of the π of the π of the π of π/420/105/105/105/420/420/105/105/105 π/420]；By public affairs
12 × 301 summit V are calculated in formula (157)i,jCoordinate.
Scrimp is finally defined according to step 9.
Figure 34 is the 3-D view of resulting origami structure.Figure 35 is the partial enlarged view of structure shown in Figure 34.Can
To see, compared to embodiment 15, the present embodiment is considered as the medial and lateral scrimp in embodiment 15 to be replaced with " v " type groove.
Figure 36 is all summit Vi,jSubpoint and radius on the y-z plane is 19 and 21 circle, it is seen that all summits all fall within this
On two round circumference or fall between above-mentioned two circumference.Origami structure shown in this explanation Figure 34 has reached radial dimension
Design requirement.In addition, the axial length of the structure shown in Figure 34 is equal to 11, axial dimension design requirement is also reached.
Embodiment 18
Change the parameter n in embodiment 17 and keep other specification constant, the origami structure of non-closed loop can be obtained.
Such as when n takes 101, resulting origami structure forms 1/3 annulus, as shown in figure 37.
Above-described embodiment is given suitable for aircraft casing sandwich and its implementation with circular cross-section.On
The method of stating can be readily applied in the housing of noncircular cross section.
When applied to aircraft casing with noncircular cross section, first by the housing section similar to by some sections of circles
Arc housing forms.For every 1 section of arc section, it may be determined that the external diameter r of interlayer needed for going out1With internal diameter r2, recycle above-described embodiment
Described in method design the interlayer based on origami structure suitable for the arc section.
Embodiment 19
Consider aircraft casing section as shown in figure 38, the housing is made up of 4 parts, is respectively：Top is with O1For circle
The arc section of the heart, the outer of its interlayer, internal diameter are respectively r '1With r '2；Left side is with O2For the arc section in the center of circle, its interlayer it is outer, interior
Footpath is respectively r "1With r "2；Bottom is with O3For the arc section in the center of circle, the outer of its interlayer, internal diameter are respectively r " '1With r " '2；Right side with
O4For the arc section in the center of circle, the outer of its interlayer, internal diameter are respectively r " "1With r " "2。
Make r '1=21, r '2=19, r "1=51, r "2=49, r " '1=29.786, r " '2=27.786, r " "1=51,
r″″2=49.Shell length l=11.Using the method for embodiment 1, the interlayer in top, right side, bottom, left side is separately designed.Tool
Body is as follows：
(i) top interlayer：M=12, h=1, a=1 are taken, b=1 is understood by formula (16b).12 are obtained by formula (16a)
The input point of x-z-plane： N=40 is taken, β=π/40 are obtained by formula (5).
R=19.9593 and δ=1.0045 are calculated according to formula (6-7).
N=21 is taken, the input point of 23 y-z planes is obtained by formula (8)：
12 × 21 summit V are calculated by formula (9)i,J coordinate.
(ii) left and right side interlayer：Because left and right side interlayer has identical physical dimension, therefore only need to design the folder of 1 side
Layer.
M=12, h=1, a=1 are taken, b=1 is understood by formula (16b).The defeated of 12 x-z-planes is obtained by formula (16a)
Access point：
N=80 is taken, by formula
(5) β=π/80 are obtained.
R=49.9803 and δ=1.0011 are calculated according to formula (6-7).
N=21 is taken, the input point of 23 y-z planes is obtained by formula (8)：
12 × 21 summit V are calculated by formula (9)i,jCoordinate.
(iii) bottom interlayer：M=12, h=1, a=1 are taken, b=1 is understood by formula (16b).12 are obtained by formula (16a)
The input point of individual x-z-plane： N=40 is taken, by
Formula (5) obtains β=π/40.
R=28.7462 and δ=1.0049 are calculated according to formula (6-7).
N=41 is taken, the input point of 43 y-z planes is obtained by formula (8)：
12 × 41 summit V are calculated by formula (9)i,jCoordinate.
Four part obtained above interlayer is joined end to end in order, that is, obtains origami structure as shown in figures 39 and 40,
It has the interlayer identical physical dimension with housing shown in Figure 38.
Above-mentioned aircraft casing is only made up of a layer interlayer.However, the method provided using above-described embodiment, can be held very much
Easily design with two layers or two layers aircraft casing with upper interlayer.It can be separated between interlayer by middle shell surface, such as Figure 41 institutes
Show, can also be separated without middle shell surface, as shown in figure 42.
For each layer interlayer, determine needed for interlayer external diameter r1With internal diameter r2, recycle described in above-described embodiment
Either method designs the interlayer based on origami structure accordingly.
Crustless sandwich structure with two layers or two layers with upper interlayer, it can be separated by middle shell surface between interlayer；With two
Layer or two layers of crustless sandwich structure with upper interlayer, separated without middle shell surface between interlayer；Above-mentioned design obtain based on paper folding
The interlayer of structure can be made by various suitable materials, be included but is not limited to：Metal, synthetic material, carbon fibre material, paper.
Manufacture method includes but is not limited to：Design mould corresponding with origami structure, flat sheet is carried out using mould
Shaping；Printed using three-dimensional printing technology；Using with the similar method of manufacture comb core, i.e., first with can conveniently fold
Material (such as paper) carries out manual folding, then immerses again in glue and the structure that folds is shaped and reinforced.
After interlayer is made, among interlayer is placed in into housing, it is connected using glue or welding with shell surface, you can produce
Aircraft casing sandwich of the present invention.
Claims (7)
1. a kind of implementation method of aircraft sandwich structures, the structure is by inner casing, shell and is clipped in multiple between inside and outside shell
Interlayer composition with origami structure, described interlayer are accomplished by the following way：
Step 1：According to the internal diameter of sandwich, external diameter, the thickness of inner casing, shell thicknessAnd segment lengthThe external diameter of interlayer needed for calculating, internal diameterAnd lengthl：；；；
Step 2：Determine three-dimensional cartesian coordinate systemx-zPlanemIndividual input point, andy-zPlanen+2 input points, wherein：,
Wherein：ParameterWithMeet；
Specifically realized using following either type：
2.1）, wherein：,NFor the natural number more than or equal to 3；
2.2),, wherein：nLess than or equal to 6N+ 1,NTo be more than or
Natural number equal to 3,, ；, ,,, and meetAnd；With
It is two endless one-dimensional vectors respectivelyWith jWithkIndividual element；
,；VectorWithFor
,；
2.3),, wherein：nLess than or equal to 3N+ 1,NTo be big
In or equal to 3 natural number,；；,,；WithIt is two endless one-dimensional vectors respectivelyWith jWithkIndividual element,,,VectorWithRespectively,；
2.4）,, wherein：nLess than or equal to 3N+ 1,NFor
Natural number more than or equal to 3,,；,,,WithIt is two endless one-dimensional vectors respectivelyWith jWithkIndividual element,,,VectorWithRespectively,；
2.5）,, wherein：nLess than or equal to 4N+ 1,NFor more than
Or the natural number equal to 3,,；,,,,WithIt is two endless one-dimensional vectors respectivelyWith jWithkIndividual element,,,VectorWith
Respectively,；
2.6),, wherein：nLess than or equal to 5N+1,NFor more than or equal to
3 natural number,,, and meet；,,,WithIt is two endless one respectively
Dimensional vectorWith jWithkIndividual element,；,
VectorWithRespectively,；
2.7）,, wherein：nLess than or equal to 5N+1,NTo be big
In or equal to 3 natural number,,And meet；
,,, ；WithIt is two endless one-dimensional vectors respectivelyWith jWithkIndividual element,；,VectorWithRespectively；；
2.8）,, wherein：nLess than or equal to 6N+1,NTo be big
In or equal to 3 natural number,, 2；,；WithIt is two endless one-dimensional vectors respectivelyWith jWith
ThekIndividual element,；,VectorWithRespectively；；
2.9）,, wherein：nLess than or equal to 10N+1,NFor the natural number more than or equal to 3,, 2, and meetWith
And；,,,；WithIt is two endless one-dimensional vectors respectivelyWith jWithkIndividual element,；,VectorWithRespectively,；
Step 3：Origami structure is obtained according to input pointIndividual summitCoordinate, , wherein：,,,ForyThe unit vector of reference axis,ForzThe unit vector of reference axis,Represent to vector
Modulus；
Step 4：DefinitionOrFor a pair of adjacent vertexs；All adjacent vertexs are connected with straight line
Come, the connecting line segment between these adjacent vertexs is the scrimp for constituting origami structure, and further real using area of computer aided
Existing interlayer manufacture.
2. according to the method for claim 1, it is characterized in that, described adjacent vertex refers to：WithFor summit, then its is adjacent
Put and beOr。
3. according to the method for claim 1, it is characterized in that, described inside and outside shell is made up of four parts, it is respectively：Top withO 1For the arc section in the center of circle, the outer of its interlayer, internal diameter are respectivelyWith；Left side withO 2For the arc section in the center of circle, its interlayer it is outer,
Internal diameter is respectivelyWith；Bottom withO 3For the arc section in the center of circle, the outer of its interlayer, internal diameter are respectivelyWith；Right side withO 4
For the arc section in the center of circle, the outer of its interlayer, internal diameter are respectivelyWith；
Order,,,,,,,；Shell
Body lengthl=11, using step 2.1）Mode separately design the interlayer in top, right side, bottom, left side；It is specific as follows：
（i）Top interlayer：Take,,, it is known that；Obtain 12x-zThe input point of plane：,,,,,,；
TakeN=40, obtain；It is calculatedWith；Taken=21, obtain 23y-zPlane
Input point：, it is calculatedIndividual summit's
Coordinate；
（ii）Left and right side interlayer：Because left and right side interlayer has identical physical dimension, therefore only need to design the interlayer of side；
Take,,, it is known that, obtain 12x-zThe input point of plane：,,；
TakeN=80, obtain；It is calculatedWith；Taken=21, obtain 23y-zThe input of plane
Point：, it is calculatedIndividual summitCoordinate；
（iii）Bottom interlayer：Take,,, it is known that, obtain 12x-zThe input point of plane：,,,,,,,,,,；TakeN=40, obtain；It is calculatedWith；Taken=41, obtain 43y-zThe input point of plane：,
It is calculatedIndividual summitCoordinate；Four part obtained above interlayer is joined end to end in order, that is, obtained described
Inside and outside shell.
4. according to the method for claim 1, it is characterized in that, described computer-aided manufacturing includes：Manufacture and paper folding knot
Mould corresponding to structure, flat sheet is molded using mould；Printed using three-dimensional printing technology；Rolled over first with that can facilitate
Folded material carries out manual folding, then immerses again in glue and the structure that folds is shaped and reinforced.
5. a kind of aircraft casing sandwich, it is characterised in that including being prepared according to any of the above-described claim methods described
Obtain.
6. sandwich according to claim 5, it is characterized in that, separated between the interlayer by middle shell surface.
7. sandwich according to claim 5, it is characterized in that, the interlayer is using metal, synthetic material, carbon fiber material
Material or paper are made.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101708772A (en) * | 2009-11-24 | 2010-05-19 | 南京航空航天大学 | Skin of morphing wing and drive method thereof |
| CN102756531A (en) * | 2012-05-07 | 2012-10-31 | 中国航空工业集团公司北京航空材料研究院 | Composite material plate with folding sandwich structure and forming method thereof |
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2013
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101708772A (en) * | 2009-11-24 | 2010-05-19 | 南京航空航天大学 | Skin of morphing wing and drive method thereof |
| CN102756531A (en) * | 2012-05-07 | 2012-10-31 | 中国航空工业集团公司北京航空材料研究院 | Composite material plate with folding sandwich structure and forming method thereof |
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