CN106202798B - A kind of constructive method of bionical spiral reticulated shell - Google Patents
A kind of constructive method of bionical spiral reticulated shell Download PDFInfo
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- CN106202798B CN106202798B CN201610581606.8A CN201610581606A CN106202798B CN 106202798 B CN106202798 B CN 106202798B CN 201610581606 A CN201610581606 A CN 201610581606A CN 106202798 B CN106202798 B CN 106202798B
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Abstract
The invention discloses a kind of constructive methods of bionical spiral reticulated shell, comprising the following steps: drafting sunflower seeds growth arrangement, No. II helix of building, the Kai Weite reticulated shell of drafting, generation plane roof system, generates No. I spatially spiral line and No. II spatially spiral line, No. I spatially spiral line of array, No. II spatially spiral line of array, forms single layer spiral reticulated shell No. I helix of building.The present invention uses Parametric Design Technology, and complicated constructionization processing and design can be carried out to " Spatial prototype " and is modified.Not only materials save, intensity is high, rigidity is big, stability is good for the building structure of the correct simulation organism construction of the present invention, and are rich in art of architecture beauty.The present invention follows and payes attention to nature rule, successfully applies bionic principle, creates construction style that is novel, adapting to local environment, safeguards regional view.The present invention has ensured the combination of environmental ecology, economic benefit and novel form.
Description
Technical field
The invention belongs to a kind of constructive methods of reticulated shell, and in particular to the constructive method of bionical spiral reticulated shell.
Background technique
Construction harmonious co-existence between man and nature, the development in energy-saving, sustainable, environmentally protective direction overall background under from
Bionical angle change Architecture Thought of Design becomes necessary.The social mentality that bionic shaping design reflects people's back to nature needs
It asks；Ecological technique is bionical, is the developing direction of current Bionic Design, is the new issue for realizing the sustainable development architecture demand, body
The spirit of the times is showed.
Helix is a kind of beautiful space form existing for nature, and distinctive attribute is: fixed around one
From coil to coil curls up and finally formed curve point (pole) outward.The life and growth of helical structure and nature have universal connection
System, while helical structure is also also generally existing in non-living world and the artificial world.Log spiral is most normal in nature
The helical structure seen intuitively embodies the extension of diffusion and the growth of energy.
In architectural design field, helical wire form is rich to its deduction as ideal Spatial prototype, architect
It is rich colorful.
California, USA designer has used for reference lighting principle to Asiatic plantain, devises the big of the helical arrangement of 13 layers of a building
Building, the results show that each room can obtain sufficient sunlight.
Swiss Re Headquarters is designed by the graceful Foster of Britain's famous architect promise.It is contrary by two groups
18 helixes constitute space double helix reticulated shell, and form space in the building without column with indoor horizontal primary structure member.
The design that " the growth sequence " of the Garden of Eden Education Center of Cornwall,British using plant is carried out as space prototype.
It is with the item number of two respectively contrary race's helixes of adjacent Fibonacci number 34 and 21;Helix is from central nucleus portion
It stretches to the periphery, like one plant of growing plants in nature (form exactly likes sunflower and pine nut).
Tianjin Yu Jiabao Roof of Beijing Southern Railway Station is shell-like single-layer latticed shell, and welding box-shaped rods are in space double helix interwoven
It sets, is the current maximum single-layer latticed shell of state's interior span.Its shape is the shell-like hyperbolic as made of the braiding of positive and negative helix
Face, reticulated shell rod piece are cross-woven by 36 groups of spatially spiral lines clockwise and anticlockwise, are just connect between rod piece.
But bionical roof system how is constructed, rarely has explanation, it is bionical to carry out parametrization building for present invention application logarithmic spiral curve
Roof system discloses the constructive method of a kind of bionical roof system.
Summary of the invention
The present invention proposes that the purpose is to provide a kind of structure of bionical spiral reticulated shell in order to solve the problems existing in the prior art
At method.
The technical scheme is that a kind of constructive method of bionical spiral reticulated shell, comprising the following steps:
(I) draws sunflower seeds growth arrangement
Using Vogel's formula equation, sunflower seeds growth arrangement is drawn by Maple.
(II) constructs No. I helix
No. I helix, the polar equation of log spiral are constructed based on logarithmic spiral family of curves equation are as follows:
R is polar diameter, i.e., a little to the distance the pole of center from helix；
The angle that θ is rotated by the point on helix around center pole；
A, e and k is constant, and e is the truth of a matter of logarithmic function, k=tan α；
To equation (1) proper transformation, clockwise direction helical curve race cartesian coordinate equation are as follows:
β is fixed value, changes the form of adjustable helix；
No. I helix is constructed by equation (2), equation (3).
(III) constructs No. II helix
Based on No. II helix is constructed to Bernoulli Jacob's curvilinear equation, using Bernoulli Jacob's helix equation, cartesian coordinate
Equation are as follows:
No. II helix is constructed by equation (4).
The Kai Weite reticulated shell that (IV) is drawn
To be connected with peripheral helicoid shell node, Kai Weite reticulated shell is drawn.
(V) generates plane roof system
By No. I helix in step (II), No. II helix rotation in step (III) generates plane roof system.
(VI) generates No. I spatially spiral line and No. II spatially spiral line
Vertically asessory shaft stretches No. I helix forming face, and with curved surface intersecting shape where roof system at No. I spatially spiral
Line；
Vertically asessory shaft stretches No. II helix forming face, and with curved surface intersecting shape where roof system at No. II spatially spiral
Line.
No. I spatially spiral line of (VII) array
To No. I spatially spiral line along polar axis array n times.
No. II spatially spiral line of (VIII) array
To No. II spatially spiral line along polar axis array n times.
(IV) forms single layer spiral reticulated shell
Using spherical crown vertex as reference point, the array of figure of laminating step (VII) and step (VIII), and trim in above-mentioned array of figure
Between the excessively small part of grid, transition is given with Kai Weite reticulated shell, forms single layer spiral reticulated shell.
Six ring of Kai Weite reticulated shell broadwise in step (IV), outermost totally 36 nodes.
No. I spatially spiral line, No. II spatially spiral linear array are 36 times in step (VII), step (VIII).
Rod piece in the single layer spiral reticulated shell uses welding box-shaped rod piece, and the welding box-shaped rod piece passes through cross partition
Weld No. I gusset plate, No. II gusset plate is connected.
The present invention uses Parametric Design Technology, and complicated construction processing and design can be carried out to " Spatial prototype " and is repaired
Change.
The present invention allows " human civilization " and " law of nature " to talk, dialogue by reconstruct helix.
A kind of popular bionic design method of having deduced of the present invention --- it is closed from the mechanical characteristic of nature image, structure
The draw inspirations such as system, material property realize the functional requirement that traditional structure cannot achieve applied in the structure design of building.
Not only materials save, intensity is high, rigidity is big, stability for the building structure of the correct simulation organism construction of the present invention
It is good, and it is rich in art of architecture beauty.
The present invention follows and payes attention to nature rule, successfully applies bionic principle, creates novel, the local ecology of adaptation
The construction style of environment safeguards regional view.
The present invention has ensured the combination of environmental ecology, economic benefit and novel form.
Detailed description of the invention
Fig. 1 is the sunflower seeds arrangement simulation schematic diagram based on " growth sequence "；
Fig. 2 is No. I helix in the present invention；
Fig. 3 is No. II helix in the present invention；
Fig. 4 is the Kai Weite reticulated shell top view in the present invention among roof system.
Fig. 5 is the plane roof system that No. I helix and No. II helix rotation generate in the present invention；
Fig. 6 be in the present invention No. I helix and No. II helix to the schematic three dimensional views of curved surface projection where roof system；
Fig. 7 be in the present invention No. I helix to the curve formed after curved surface projection where roof system along polar axis array 36 times
Schematic three dimensional views；
Fig. 8 be in the present invention No. II helix to the curve formed after curved surface projection where roof system along polar axis array 36 times
Schematic three dimensional views；
Fig. 9 is the shaft side figure of bionical reticulated shell in the present invention；
Figure 10 is bionical reticulated shell top view in the present invention；
Figure 11 is interior joint structural map of the present invention；
Wherein:
1 No. I helixes, 2 No. II helixes
34 No. I spatially spiral lines of triumphant Witter reticulated shell
5 No. II vertical asessory shafts of spatially spiral line 6
7 No. I gusset plates, 8 No. II gusset plates
9 welding box-shaped rod pieces.
Specific embodiment
Hereinafter, referring to drawings and examples, the present invention is described in detail:
As shown in Fig. 1 ~ 11, a kind of constructive method of bionical spiral reticulated shell, comprising the following steps:
(I) draws sunflower seeds growth arrangement
Using Vogel's formula equation, sunflower seeds growth arrangement is drawn by Maple.
(II) constructs No. I helix
No. I helix 1, the polar equation of log spiral are constructed based on logarithmic spiral family of curves equation are as follows:
R is polar diameter, i.e., a little to the distance the pole of center from helix；
The angle that θ is rotated by the point on helix around center pole；
A, e and k is constant, and e is the truth of a matter of logarithmic function, k=tan α；
The form of logarithmic function and parameter k are closely related, and which control the elasticity of helix and directions.Work as k > 0 and not
When disconnected increase, helix will be far from focus and infinitely stretch to the periphery；As k=0, it will obtain one using a as radius
Circle；When k < 0 and when being continuously increased, helix internally unlimited by the attraction of focus will be shunk.The numerical value of k more approaches
In infinity, helix is more intended to stretch in alignment；The numerical value of k more levels off to 0, and helix then more tightens at one
Group.
To equation (1) proper transformation, clockwise direction helical curve race cartesian coordinate equation are as follows:
β is fixed value, changes the form of adjustable helix；
No. I helix 1 is constructed by equation (2), equation (3).
(III) constructs No. II helix
Based on No. II helix 2 is constructed to Bernoulli Jacob's curvilinear equation, using Bernoulli Jacob's helix equation, cartesian coordinate
Equation are as follows:
No. II helix 2 is constructed by equation (4).
The Kai Weite reticulated shell that (IV) is drawn
To be connected with peripheral helicoid shell node, Kai Weite reticulated shell 3 is drawn.
(V) generates plane roof system
By No. I helix 1 in step (II), No. II helix 2 rotation in step (III) generates plane roof system.
(VI) generates No. I spatially spiral line and No. II spatially spiral line
Vertically asessory shaft 6 stretches No. I 1 forming face of helix, and with curved surface intersecting shape where roof system at No. I spatially spiral
Line 4；
Vertically asessory shaft 6 stretches No. II 2 forming face of helix, and with curved surface intersecting shape where roof system at No. II space spiral shell
Spin line 5.
No. I spatially spiral line of (VII) array
To No. I spatially spiral line 4 along polar axis array n times.
No. II spatially spiral line of (VIII) array
To No. II spatially spiral line 5 along polar axis array n times.
(IV) forms single layer spiral reticulated shell
Using spherical crown vertex as reference point, the array of figure of laminating step (VII) and step (VIII), and trim in above-mentioned array of figure
Between the excessively small part of grid, transition is given with Kai Weite reticulated shell 3, forms single layer spiral reticulated shell.
3 broadwise of Kai Weite reticulated shell, six ring in step (IV), outermost totally 36 nodes.
4, No. II 5 arrays of spatially spiral line of No. I spatially spiral line are 36 times in step (VII), step (VIII).
Step (II), step (III) can be, but not limited to be drawn by Maple mathematical tool.
Step (VI) can be, but not limited to be drawn by AutoCAD mapping software.
Rod piece in the single layer spiral reticulated shell uses welding box-shaped rod piece 9, the welding box-shaped rod piece 9 by cross every
Plate welds 7, No. II gusset plates 8 of No. I gusset plate and is connected.
The present invention uses Parametric Design Technology, and complicated construction processing and design can be carried out to " Spatial prototype " and is repaired
Change.
The present invention allows " human civilization " and " law of nature " to talk, dialogue by reconstruct helix.
A kind of popular bionic design method of having deduced of the present invention --- it is closed from the mechanical characteristic of nature image, structure
The draw inspirations such as system, material property realize the functional requirement that traditional structure cannot achieve applied in the structure design of building.
Not only materials save, intensity is high, rigidity is big, stability for the building structure of the correct simulation organism construction of the present invention
It is good, and it is rich in art of architecture beauty.
The present invention follows and payes attention to nature rule, successfully applies bionic principle, creates novel, the local ecology of adaptation
The construction style of environment safeguards regional view.
The present invention has ensured the combination of environmental ecology, economic benefit and novel form.
Claims (4)
1. a kind of constructive method of bionical spiral reticulated shell, it is characterised in that: the following steps are included:
(I) draws sunflower seeds growth arrangement
Using Vogel's formula equation, sunflower seeds growth arrangement is drawn by Maple；
(II) constructs No. I helix
No. I helix (1), the polar equation of log spiral are constructed based on logarithmic spiral family of curves equation are as follows:
R (θ)=aekθ (1)
R is polar diameter, i.e., a little to the distance the pole of center from helix；
The angle that θ is rotated by the point on helix around center pole；
A, e and k is constant, and e is the truth of a matter of logarithmic function, k=tan α；
To equation (1) proper transformation, clockwise direction helical curve race cartesian coordinate equation are as follows:
X=Re2β-θcosθ (2)
Y=Re2β-θsinθ (3)
β is fixed value, changes the form of adjustable helix；
No. I helix (1) is constructed by equation (2), equation (3)；
(III) constructs No. II helix
Based on No. II helix (2) is constructed to Bernoulli Jacob's curvilinear equation, using Bernoulli Jacob's helix equation, cartesian coordinate side
Journey are as follows:
R (t)={ etcos4t,etsin4t} (4)
No. II helix (2) is constructed by equation (4)；
The Kai Weite reticulated shell that (IV) is drawn
To be connected with peripheral helicoid shell node, draw Kai Weite reticulated shell (3)；
(V) generates plane roof system
By No. I helix (1) in step (II), No. II helix (2) rotation in step (III) generates plane roof system；
(VI) generates No. I spatially spiral line and No. II spatially spiral line
Vertically asessory shaft (6) stretches No. I helix (1) forming face, and with curved surface intersecting shape where roof system at No. I spatially spiral
Line (4)；
Vertically asessory shaft (6) stretches No. II helix (2) forming face, and with curved surface intersecting shape where roof system at No. II space spiral shell
Spin line (5)；
No. I spatially spiral line of (VII) array
To No. I spatially spiral line (4) along polar axis array n times；
No. II spatially spiral line of (VIII) array
To No. II spatially spiral line (5) along polar axis array n times；
(IV) forms single layer spiral reticulated shell
Using spherical crown vertex as reference point, the array of figure of laminating step (VII) and step (VIII), and trim above-mentioned array of figure mid-level net
The excessively small part of lattice gives transition with Kai Weite reticulated shell (3), forms single layer spiral reticulated shell.
2. a kind of constructive method of bionical spiral reticulated shell according to claim 1, it is characterised in that: triumphant in step (IV)
Six ring of Witter reticulated shell (3) broadwise, outermost totally 36 nodes.
3. a kind of constructive method of bionical spiral reticulated shell according to claim 1, it is characterised in that: step (VII), step
No. I spatially spiral line (4), No. II spatially spiral line (5) array are 36 times in (VIII).
4. a kind of constructive method of bionical spiral reticulated shell according to claim 1, it is characterised in that: the single layer spiral net
Rod piece in shell uses welding box-shaped rod piece (9), and the welding box-shaped rod piece (9) welds No. I gusset plate by cross partition
(7), No. II gusset plate (8) is connected.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101614045A (en) * | 2009-07-22 | 2009-12-30 | 薛晓光 | Double-tower vestibule spiral building |
| CN104060740A (en) * | 2014-06-11 | 2014-09-24 | 江苏科技大学 | Double-layer column surface net shell with lower chord being prestressed stay rope |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101614045A (en) * | 2009-07-22 | 2009-12-30 | 薛晓光 | Double-tower vestibule spiral building |
| CN104060740A (en) * | 2014-06-11 | 2014-09-24 | 江苏科技大学 | Double-layer column surface net shell with lower chord being prestressed stay rope |
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