CN106522368A - Annular stretch-draw integrated structure - Google Patents
Annular stretch-draw integrated structure Download PDFInfo
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- CN106522368A CN106522368A CN201610889135.7A CN201610889135A CN106522368A CN 106522368 A CN106522368 A CN 106522368A CN 201610889135 A CN201610889135 A CN 201610889135A CN 106522368 A CN106522368 A CN 106522368A
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
- E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
- E04B1/32—Arched structures; Vaulted structures; Folded structures
- E04B1/3205—Structures with a longitudinal horizontal axis, e.g. cylindrical or prismatic structures
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Abstract
The invention discloses an annular stretch-draw integrated structure. At present, no annular stretch-draw integrated structure with the overlapping rate among single bodies exists. The annular stretch-draw integrated structure is formed by combining m (m is a multiple of two) single bodies along the circumference with the radius being Rt in the mode that the ends are overlapped at the radius angle gamma. Each single body is composed of 2n joints, n pressing rods and 5n pulling ropes, wherein the 5n pulling ropes can be further divided into three groups including n vertical ropes, 2n saddle ropes and 2n diagonal ropes. All the joints are hinge points, and each joint is connected with five pulling ropes and one pressing rod. All the pulling ropes have pre-pulling force, all the pressing rods have pre-pressure, and the pre-pulling force of the pulling ropes and the pre-pressure of the pressing rods are mutually balanced. The annular stretch-draw integrated structure in the invention has rotation symmetry, every two continuous stretch-draw integrated single bodies form a basic repeatable unit, and the whole structure is provided with m/2 basic repeatable units.
Description
Technical field
A kind of a kind of the present invention relates to tension integral structure, more particularly to annulus with mn roots depression bar and 5mn root drag-lines
Shape tension integral structure.
Background technology
Tension integral structure is a kind of prestressing force self equilibrium systemses being made up of discrete depression bar and continuous drag-line, such
The rigidity of structure is provided by prestressing force, and component internal force is mutually balanced self, once losing prestressing force, structure no longer will be set up.
Tension integral structure has the advantages that light weight, span be big, beautiful design, receives the extensive concern of science and engineering circles.
In in the past few decades, the rule geometrical body such as plate shaped, prismatic, polyhedron shape, spherical is successively have developed
Tension integral structure.However, as a kind of common regular geometric shapes annular, being but seldom used as tensioning entirety
The basic configuration of structure, the annular tension integral structure for only having non-overlapping rate between monomer at present there is no
The annular tension integral structure of rate.
The content of the invention
The purpose of the present invention is to make up the pro forma deficiency of annular tension integral structure, there is provided there is weight between a kind of monomer
The annular tension integral structure of folded rate.
The purpose of the present invention is achieved through the following technical solutions：A kind of annular tension integral structure, it is single by m
The body ring that joins end to end is combined, and m is even number, with ring symmetry.Each monomer is numbered counterclockwise, is remembered successively
For monomer 1～monomer m；The torsional direction of the depression bar of adjacent two monomer is conversely, therefore the continuous monomer composition of each two one is minimum
Repeatable unit, referred to as elementary cell, are designated as first elementary cell～the m/2 substantially successively according to the number order of monomer
Unit.
Each monomer is respectively provided with former and later two positive n sides shape bottom surfaces and n root depression bars, and the node on each positive n sides shape bottom surface is by n
The homonymy end points of root depression bar is constituted, and the annulus axis of annular tension integral structure passes through the center of each bottom surface, each bottom
Face is each perpendicular to annulus axis.Each monomer to central angle beγ is Duplication when monomer head and the tail connect.
For first elementary cell, the front bottom surface of monomer 1, the rear bottom surface of monomer 1, the front bottom surface of monomer 2 and monomer 2
N node of bottom surface is designated as node 1～node n, node n+1～node 2n, node 2n+1～node 3n and node 3n+ successively afterwards
1～node 4n.Note node 1～node n, node n+1～node 2n, node 2n+1～node 3n and node 3n+1～node 4n institutes
The circumscribed circle center of circle of the positive n sides shape for constituting is followed successively by O11, O12, O21And O22.From the forward observation of 1 front bottom surface of monomer, node 1～
Node n is equidistantly arranged counterclockwise, node 1 and O11The angle of axis plane of line and annulus be designated as β0.Note
The relative rotation of two bottom surface of monomer is β, and node n+1～node 2n is relative to O12Position equivalent to by 1～node of node n around
O11β posterior nodal point 1～node n are turned over into annulus relative to O11Position, node 2n+1～node 3n is relative to O21Position phase
When in by node n+1～node 2n around O12π/n posterior nodal points n+1～node 2n is turned over into annulus relative to O12Position, node
3n+1～node 4n is relative to O22Position equivalent to by node 2n+1～node 3n around O21β posterior nodal point 2n+ are turned over to outside annulus
1～node 3n is relative to O21Position.The angle of the front bottom surface of the rear bottom surface of monomer 1 and monomer 2 is Duplication γ.Other are basic
The node location of unit and node serial number mode are identical with first elementary cell.
Each monomer also has 5n root drag-lines, and 5n root drag-lines are divided into three groups：The vertical rope of n roots, 2n root saddle ropes and 2n roots are diagonal
Rope.All of node is pin joint, and each node connects 5 drag-lines and 1 depression bar, and all drag-lines have pretension, all pressures
There is precompression in bar, the precompression of the pretension and depression bar of drag-line is mutually balanced.Vertical rope is same two end node of monomer of connection
Drag-line, saddle rope is the drag-line for connecting latter monomer front end node and current monolithic backend nodes, and diagonal rope is latter for connection
The drag-line or the previous monomer backend nodes of connection and current monolithic rear end of individual monomer front end node and current monolithic front end node
The drag-line of node.
The 2n roots depression bar of first elementary cell of annular tension integral structure is designated as into depression bar 1～depression bar 2n successively,
The vertical Suo Yici of 2n roots is designated as vertical rope 2n+1～vertical rope 4n, and 4n root saddle ropes are designated as saddle rope 4n+1～vertical rope 8n, 4n successively
The diagonal Suo Yici of root is designated as diagonal rope 8n+1～diagonal rope 12n.The Topology connection form of first elementary cell is：
1) depression bar：
Connect depression bar i between node i and node i+(n+1), wherein i=1,2 ..., n-1；
Connect depression bar n between node n and node n+1；
Node i+connect between (n+1) and node i+2n depression bar i, wherein i=n+1, n+2 ..., 2n-1；
Connect depression bar 2n between node 2n+1 and node 4n；
2) vertical rope：
Connect vertical rope i between node i-(2n-1) and node i-(n-1), wherein i=2n+1,2n+2 ..., 3n-1；
Connect vertical rope 3n between node 1 and node n+1；
Node i-(n-1) connects vertical rope i and node i+1 between, wherein i=3n+1,3n+2 ..., 4n-1；
Connect vertical rope 4n between node 2n+1 and node 3n+1；
3) saddle rope：
Connect saddle rope i between node i -4n and node i-(5-2m) n, wherein i=4n+1,4n+2 ..., 5n-1,5n；
Connect saddle rope i between node i -3n and node i-(4n-1), wherein i=5n+1,5n+2 ..., 6n-1；
Connect saddle rope 6n between node 3n and node n+1；
Connect saddle rope i between node i-(5n-1) and node i-(4n-1), wherein i=6n+1,6n+2 ..., 7n-1；
Connect saddle rope 7n between node n+1 and node 2n+1；
Connect saddle rope i between node i -4n and node i-(3n-1), wherein i=7n+1,7n+2 ..., 8n-1；
Connect saddle rope 8n between node 4n and node 4n+1.
4) diagonal rope：
Connect diagonal rope i between node i -8n and node i -6n, wherein i=8n+1,8n+2 ..., 9n-1,9n；
Connect diagonal rope i between node i-(10-2m) n and node i-(8n-1), wherein i=9n+1,9n+2 ..., 10n-1；
Connect diagonal rope 10n between node 2mn and node n+1；
Connect diagonal rope i between node i-(8n-1) and node i-(6n-1), wherein i=10n+1,10n+2 ..., 11n-1；
Connect diagonal rope 11n between node 2n+1 and node 4n+1；
The diagonal rope i of node i-connect between (10n-1) and node i -8n, wherein i=11n+1,11n+2 ..., 12n-1；
Connect diagonal rope 12n between node n+1 and node 4n.
The Topology connection form of other elementary cells is corresponding identical with the Topology connection form of first elementary cell.
Further, the concrete composition of whole annular tension integral structure is uniquely determined by following parameter：Ring monomer
Number m, the depression bar number n of each monomer, the radius Rt of annulus axis, circumradius r of the positive n sides shape bottom surface of monomer, monomer
Positive n sides shape bottom surface relative to axis plane initial corner β0, two bottom surface of monomer relative rotation β and monomer head and the tail connect
When Duplication γ.
Further, the feasible pre-stressed mode of the annular tension integral structure has ring symmetry, therefore is asking
During the feasible pre-stressed mode of solution total, the feasible pre-stressed mode of first elementary cell of analysis and solution is only needed,
The pre-stressed mode of other elementary cells is identical with first elementary cell.
Further, for the solution of the pre-stressed mode of first elementary cell is specially：According to the geometric form of structure
State and topological relation are balanced matrix, then carry out the basic course laboratory that singular value decomposition tries to achieve its kernel to balancing matrix, if
The linear combination of each column vector (i.e. independent self-stress modes) of existence foundation solution system can meet annular tension integral structure
The tension and compression condition of all units, then the annular tension integral structure under parameter current value there is feasible pre-stressed mode.
The invention has the beneficial effects as follows：This annular tension integral structure of the present invention compensate for existing annular
The pro forma deficiency of tension integral structure, there is provided there is the annular tension integral structure of Duplication between a kind of monomer, it is this kind of
There is potential use in fields such as building roof structure, apparatus for building, arch porch, sculpture, light fixtures in structure.
Description of the drawings
Fig. 1 is the parameter schematic diagram of the annular tension integral structure in the present invention, and wherein (a) figure is top view, in figure
Give r, Rt, γ and α definition, 1. represent monomer 1,2. represent monomer 2,3. represent 3～monomer of monomer m according to monomer 1,
2 identical modes are arranged, and 4. represent the inner ring circle of annulus, 5. represent the outer ring circle of annulus, 6. represent axis, as shown in 7.
Radial direction thick segment represents the positive n sides shape bottom surface of each monomer, the section on n summit of the positive n sides shape bottom surface of the digitized representation by line segment
Point numbering, centers of the origin O for annulus in figure, z-axis is perpendicular to annulus axis place plane and points to outside paper, and x-axis is by original
Point points to the center of the positive n sides shape bottom surface that 1～n of node is located, and y-axis is determined by right-hand rule；B () figure is that 1～n of node places are cut
The schematic diagram in face, gives β in figure0Definition (shown in figure, direction is β0Positive direction) and 1～n of node numbering,
8. represent 4～node of node n-1 equally withSpacing arrangement；C () figure is the schematic diagram in node n+1～2n places section, figure
In give the definition positive direction of β (direction shown in figure be) of β, point 1 ' be node 1 along axis project to node n+1～
The center of the positive n sides shape bottom surface that node n+1～2n is located is pointed in corresponding position during the bottom surface of 2n places, x ' axles by origin, 9.
Represent node n+4～node 2n-1 equally withSpacing arrangement.
Fig. 2 is the topology connections maps of the annular tension integral structure in the present invention, and is observed from the medial surface of annulus
Obtain, wherein (a) figure is node serial number schematic diagram, (b) figure is element number schematic diagram, and in figure, thick line represents depression bar, fine rule
Drag-line is represented, positive direction of the arrow direction for each unit, wherein unit 2n+1～4n represent vertical rope, unit 4n+1～8n
Saddle rope is represented, unit 8n+1～12n represents diagonal rope.
Fig. 3 is annular tension integral structure in the present invention in m=6, n=3, Rt=5m, r=0.75m, β0=60 °, β
=10 °, schematic diagram during γ=15 °, corresponding to example 1, wherein (a) figure is plan, and (b) figure is stereogram, thick line in figure
Depression bar is represented, fine rule represents drag-line.
Fig. 4 is annular tension integral structure in the present invention in m=8, n=4, Rt=5m, r=0.75m, β0=0 °, β
=10 °, schematic diagram during γ=15 °, corresponding to example 2, wherein (a) figure is plan, and (b) figure is stereogram, thick line in figure
Depression bar is represented, fine rule represents drag-line.
Specific embodiment
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings, the purpose of the present invention and effect will
Become apparent from.
First, the description of annular tension integral structure of the present invention
Annular tension integral structure of the present invention is combined by the m monomer ring that joins end to end, and wherein m is necessary for
Even number.Each monomer is made up of 2n node, n roots depression bar and 5n root drag-lines, is located on same bottom surface and is constituted per n node
One positive n sides shape, the axis of annulus pass through the center of each bottom surface, and each plane perpendicular is in the axis of annulus.Whole circle
The concrete composition of Tensegrity torus is uniquely determined by following parameter：Ring number of monomers m, the depression bar number n of each monomer, circle
The radius R of ring axist, monomer positive n in circumradius r, the positive n of monomer of shape bottom surface shape bottom surface relative to axis
The initial corner β of plane0, two bottom surface of monomer relative rotation β and monomer head and the tail connect when Duplication γ.
The annular tension integral structure has 2mn node, 5mn roots drag-line and mn root depression bars, and all drag-lines bear
Pretension, all depression bars bear precompression.5mn roots drag-line can be further subdivided into 3 groups of vertical ropes, saddle rope and diagonal
Rope, respectively has mn roots, 2mn roots and 2mn roots.Wherein, vertical rope is the drag-line of connection same tensioning entirety two end node of monomer, saddle rope
For latter tensioning entirety monomer front end node of connection and the drag-line of current tensioning entirety monomer backend nodes, diagonal rope is connection
The drag-line or the previous tensioning of connection of latter tensioning entirety monomer front end node and current tensioning entirety monomer front end node is whole
The drag-line of body monomer backend nodes and current tensioning entirety monomer backend nodes.
The annular tension integral structure has a ring symmetry, the continuous tensioning entirety monomer of each two be one most
I repetitive, referred to as elementary cell.Each elementary cell has 4n node, 10n roots drag-line and 2n root depression bars, wherein
10n roots drag-line includes vertical rope 2n roots, saddle rope 4n roots and diagonal rope 4n roots.2mn section of the annular tension integral structure
Point is designated as node 1～node 2mn successively.4n node of first elementary cell is designated as node 1～node 4n, 2n root pressures successively
Bar is designated as depression bar 1～depression bar 2n successively, and the vertical Suo Yici of 2n roots is designated as vertical rope 2n+1～vertical rope 4n, and 4n root saddle ropes are remembered successively
For saddle rope 4n+1～vertical rope 8n, the diagonal Suo Yici of 4n roots is designated as diagonal rope 8n+1～diagonal rope 12n.First elementary cell
Topology connection form is：
1) depression bar：
Connect depression bar i between node i and node i+(n+1), wherein i=1,2 ..., n-1；
Connect depression bar n between node n and node n+1；
Node i+connect between (n+1) and node i+2n depression bar i, wherein i=n+1, n+2 ..., 2n-1；
Connect depression bar 2n between node 2n+1 and node 4n；
2) vertical rope：
Connect vertical rope i between node i-(2n-1) and node i-(n-1), wherein i=2n+1,2n+2 ..., 3n-1；
Connect vertical rope 3n between node 1 and node n+1；
Node i-(n-1) connects vertical rope i and node i+1 between, wherein i=3n+1,3n+2 ..., 4n-1；
Connect vertical rope 4n between node 2n+1 and node 3n+1；
3) saddle rope：
Connect saddle rope i between node i -4n and node i-(5-2m) n, wherein i=4n+1,4n+2 ..., 5n-1,5n；
Connect saddle rope i between node i -3n and node i-(4n-1), wherein i=5n+1,5n+2 ..., 6n-1；
Connect saddle rope 6n between node 3n and node n+1；
Connect saddle rope i between node i-(5n-1) and node i-(4n-1), wherein i=6n+1,6n+2 ..., 7n-1；
Connect saddle rope 7n between node n+1 and node 2n+1；
Connect saddle rope i between node i -4n and node i-(3n-1), wherein i=7n+1,7n+2 ..., 8n-1；
Connect saddle rope 8n between node 4n and node 4n+1.
4) diagonal rope：
Connect diagonal rope i between node i -8n and node i -6n, wherein i=8n+1,8n+2 ..., 9n-1,9n；
Connect diagonal rope i between node i-(10-2m) n and node i-(8n-1), wherein i=9n+1,9n+2 ..., 10n-1；
Connect diagonal rope 10n between node 2mn and node n+1；
Connect diagonal rope i between node i-(8n-1) and node i-(6n-1), wherein i=10n+1,10n+2 ..., 11n-1；
Connect diagonal rope 11n between node 2n+1 and node 4n+1；
The diagonal rope i of node i-connect between (10n-1) and node i -8n, wherein i=11n+1,11n+2 ..., 12n-1；
Connect diagonal rope 12n between node n+1 and node 4n.
The Topology connection form of other elementary cells is corresponding identical with the Topology connection form of first elementary cell.2nd,
The present invention relates to primary variables, node coordinate, balancing matrix etc.
ri=Rmri-4n, i=4n+1,4n+2 ..., 2mn.
Ai=ri+(n+1)-ri, wherein i=1,2 ..., n-1；
An=rn+1-rn；
Ai=ri+2n-ri+(n+1), wherein i=n+1, n+2 ..., 2n-1；
A2n=r4n-r2n+1；
Ai=ri-(n-1)-ri-(2n-1), wherein i=2n+1,2n+2 ..., 3n-1；
A3n=rn+1-r1；
Ai=ri+1-ri-(n-1), wherein i=3n+1,3n+2 ..., 4n-1；
A4n=r3n+1-r2n+1；
Ai=ri-(5-2m)n-ri-4n, wherein i=4n+1,4n+2 ..., 5n-1,5n；
Ai=ri-(4n-1)-ri-3n, wherein i=5n+1,5n+2 ..., 6n-1；
A6n=rn+1-r3n；
Ai=ri-(4n-1)-ri-(5n-1), wherein i=6n+1,6n+2 ..., 7n-1；
A7n=r2n+1-rn+1；
Ai=ri-(3n-1)-ri-4n, wherein i=7n+1,7n+2 ..., 8n-1；
A8n=r4n+1-r4n；
Ai=ri-6n-ri-8n, wherein i=8n+1,8n+2 ..., 9n-1,9n；
Ai=ri-(8n-1)-ri-(10-2m)n, wherein i=9n+1,9n+2 ..., 10n-1；
A10n=rn+1-r2mn；
Ai=ri-(6n-1)-ri-(8n-1), wherein i=10n+1,10n+2 ..., 11n-1；
A11n=r4n+1-r2n+1；
Ai=ri-8n-ri-(10n-1), wherein i=11n+1,11n+2 ..., 12n-1；
A12n=r4n-rn+1。
Note：MatrixIn Ai、BiOr CiIn matrix i-th arranges, and remaining each row is null vector O, wherein O=[0 0
0]T.MatrixThe i-th row be with regard to node i.
Ai(i.e. direction cosines × unit is long for the molecular moiety of the direction cosines of the unit i in first elementary cell
Degree)；
BiThe list of the unit i of first elementary cell is corresponded in the previous elementary cell of first elementary cell
The molecular moiety of the direction cosines of unit,
CiThe list of the unit i of first elementary cell is corresponded in latter elementary cell of first elementary cell
The molecular moiety of the direction cosines of unit, Ci=RmAi；
Relative rotation angle of the adjacent tensioning entirety monomers of α around the center of annular tension integral structure,
RmSpin matrix,
Matrix is obtained after the length factor of balancing matrix A each element is proposed；
3rd, the determination of pre-stressed mode of the invention
Because the annular tension integral structure has ring symmetry, the continuous tensioning entirety monomer of each two is one
Individual elementary cell (minimum repeatable unit).Therefore when the feasible pre-stressed mode of total is solved, first need to be analyzed only
Elementary cell, tries to achieve the feasible pre-stressed mode of first elementary cell, the pre-stressed mode of other elementary cells and
One elementary cell is identical.
The flat of first elementary cell (node 1～node 4n) is obtained by the Topology connection of analytical structure and geometrical relationship
Weighing apparatus equation, obtains matrix after the length factor of balancing matrix A each element is proposedIn given ring unit number m, each tensioning
The mean value R of the depression bar number n and annulus outer ring radius of circle and inner ring radius of circle of overall monomertThe feelings of the value of these three parameters
Under condition, by arranging with regard to r, β0, 4 layers of β and γ values circulation carry out tentative calculation (spacing of the scope and value of tentative calculation are according to setting
Meter it needs to be determined that)：Every kind of parameter value situation is substituted intoExpression formula be obtained specificallyMatrix, it is rightCarry out unusual
Value decomposition is obtainedKernel basic course laboratory, if each column vector (i.e. independent self-stress modes) of existence foundation solution system
Linear combination can meet the tension and compression condition of all units of annular tension integral structure, then the annular under parameter current value
Overall structure is drawn to there is feasible pre-stressed mode.Parameter needed for finally selecting in the case of it there is feasible pre-stressed mode takes
Value situation, drawsKernel basic course laboratory, with each column vector of suitable constant coefficient combination foundation solution systemIt is (i.e. independent
Self-stress modes) the feasible pre-stressed mode of force density form is obtainedWillItems be multiplied by its corresponding list respectively
First length is required feasible pre-stressed mode s.
Example 1：Work as m=6, annular tension integral structure T (6-3) during n=3, Rt=5m.
Analysis process is as follows：
Arrange with regard to r, β0, 4 layers of β and γ values circulation carry out tentative calculation (spacing of the scope and value of tentative calculation are according to setting
Meter it needs to be determined that)：Every kind of parameter value situation is substituted intoExpression formula be obtained specificallyIt is rightCarry out singular value point
Solution is obtainedKernel basic course laboratory, if each column vector (i.e. independent self-stress modes) of existence foundation solution system is linear
Combination can meet the tension and compression condition of all units of annular tension integral structure, then the annular tensioning under parameter current value is whole
There is feasible pre-stressed mode in body structure.
Then, the parameter value situation needed for selecting in the case of it there is feasible pre-stressed mode.R=is selected in this example
0.75m, β0=60 °, β=10 °, this group of γ=15 ° value is used as required parameter value.Each parameter is substituted intoExpression formula
It is obtained specificIt is rightCarry out singular value decomposition to obtainKernel basic course laboratoryWith
With constant coefficient C1And C2CombinationWithSo thatMeet annular tension integral structure to own
The tension and compression condition of unit, makes C here1=-1, C2=0.25, then now have：
Again because the geometrical length of each unit is：
WillItems be multiplied by its corresponding unit length respectively, then acquired results are standardized, can obtain standardized feasible pre-
Stress mode is as follows：
Example 2：Work as m=8, annular tension integral structure T (8-4) during n=4, Rt=5m.
Analysis process is as follows：
Arrange with regard to r, β0, 4 layers of β and γ values circulation carry out tentative calculation (spacing of the scope and value of tentative calculation are according to setting
Meter it needs to be determined that)：Every kind of parameter value situation is substituted intoExpression formula be obtained specificallyIt is rightCarry out singular value point
Solution is obtainedKernel basic course laboratory, if each column vector (i.e. independent self-stress modes) of existence foundation solution system is linear
Combination can meet the tension and compression condition of all units of annular tension integral structure, then the annular tensioning under parameter current value is whole
There is feasible pre-stressed mode in body structure.
Then, the parameter value situation needed for selecting in the case of it there is feasible pre-stressed mode.R=is selected in this example
0.75m, β0=0 °, β=10 °, this group of γ=15 ° value is used as required parameter value.Each parameter is substituted intoExpression formula can
Obtain specificIt is rightCarry out singular value decomposition to obtainKernel basic course laboratoryWith
With constant coefficient C1And C2CombinationWithSo thatMeet annular tension integral structure to own
The tension and compression condition of unit, makes C here1=1, C2=0.515, then now have：
Again because the geometrical length of each unit is：
WillItems be multiplied by its corresponding unit length respectively, then acquired results are standardized, can obtain standardized feasible pre-
Stress mode is as follows：
Claims (4)
1. a kind of annular tension integral structure, it is characterised in that the annular tension integral structure is by m monomer head and the tail phase
To combining, m is even number to the chain of rings, with ring symmetry.Each monomer is numbered counterclockwise, monomer 1 is designated as successively
～monomer m；The torsional direction of the depression bar of adjacent two monomer is conversely, therefore continuous one minimum of monomer composition of each two is repeatable single
Unit, referred to as elementary cell, are designated as m/2 elementary cell of first elementary cell～the successively according to the number order of monomer.
Each monomer is respectively provided with former and later two positive n sides shape bottom surfaces and n root depression bars, and the node on each positive n sides shape bottom surface is by n root pressures
The homonymy end points of bar is constituted, and the annulus axis of annular tension integral structure passes through the center of each bottom surface, and each bottom surface is equal
Perpendicular to annulus axis.Each monomer to central angle beγ is Duplication when monomer head and the tail connect.
For first elementary cell, the rear bottom of the front bottom surface of monomer 1, the rear bottom surface of monomer 1, the front bottom surface of monomer 2 and monomer 2
The n node in face is designated as node 1～node n successively, and node n+1～node 2n, node 2n+1～node 3n and node 3n+1～
Node 4n.Note node 1～node n, node n+1～node 2n, node 2n+1～node 3n and node 3n+1～node 4n institutes structure
Into the circumscribed circle center of circle of positive n sides shape be followed successively by O11, O12, O21And O22.From the forward observation of 1 front bottom surface of monomer, 1～section of node
Point n is equidistantly arranged counterclockwise, node 1 and O11The angle of axis plane of line and annulus be designated as β0.Note is single
The relative rotation of two bottom surface of body is β, and node n+1～node 2n is relative to O12Position equivalent to by node 1～node n around O11
β posterior nodal point 1～node n are turned over into annulus relative to O11Position, node 2n+1～node 3n is relative to O21Position it is suitable
In by node n+1～node 2n around O12π/n posterior nodal points n+1～node 2n is turned over into annulus relative to O12Position, node 3n
+ 1～node 4n is relative to O22Position equivalent to by node 2n+1～node 3n around O21β posterior nodal point 2n+1 are turned over to outside annulus
～node 3n is relative to O21Position.The angle of the front bottom surface of the rear bottom surface of monomer 1 and monomer 2 is Duplication γ.Other are basic
The node location of unit and node serial number mode are identical with first elementary cell.
Each monomer also has 5n root drag-lines, and 5n root drag-lines are divided into three groups：The vertical rope of n roots, 2n root saddle ropes and the diagonal rope of 2n roots.Institute
Some nodes are pin joint, and each node connects 5 drag-lines and 1 depression bar, and all drag-lines have pretension, and all depression bars are present
Precompression, the precompression of the pretension and depression bar of drag-line are mutually balanced.Vertical rope is the drag-line for connecting same two end node of monomer,
Saddle rope is the drag-line for connecting latter monomer front end node and current monolithic backend nodes, before diagonal rope is for latter monomer of connection
The drawing of the drag-line or the previous monomer backend nodes of connection and current monolithic backend nodes of end node and current monolithic front end node
Rope.
The 2n roots depression bar of first elementary cell of annular tension integral structure is designated as into depression bar 1～depression bar 2n, 2n roots successively
Vertical Suo Yici is designated as vertical rope 2n+1～vertical rope 4n, and 4n root saddle ropes are designated as saddle rope 4n+1～vertical rope 8n, 4n roots pair successively
Angle rope is designated as diagonal rope 8n+1～diagonal rope 12n successively.The Topology connection form of first elementary cell is：
1) depression bar：
Connect depression bar i between node i and node i+(n+1), wherein i=1,2 ..., n-1；
Connect depression bar n between node n and node n+1；
Node i+connect between (n+1) and node i+2n depression bar i, wherein i=n+1, n+2 ..., 2n-1；
Connect depression bar 2n between node 2n+1 and node 4n；
2) vertical rope：
Connect vertical rope i between node i-(2n-1) and node i-(n-1), wherein i=2n+1,2n+2 ..., 3n-1；
Connect vertical rope 3n between node 1 and node n+1；
Node i-(n-1) connects vertical rope i and node i+1 between, wherein i=3n+1,3n+2 ..., 4n-1；
Connect vertical rope 4n between node 2n+1 and node 3n+1；
3) saddle rope：
Connect saddle rope i between node i -4n and node i-(5-2m) n, wherein i=4n+1,4n+2 ..., 5n-1,5n；
Connect saddle rope i between node i -3n and node i-(4n-1), wherein i=5n+1,5n+2 ..., 6n-1；
Connect saddle rope 6n between node 3n and node n+1；
Connect saddle rope i between node i-(5n-1) and node i-(4n-1), wherein i=6n+1,6n+2 ..., 7n-1；
Connect saddle rope 7n between node n+1 and node 2n+1；
Connect saddle rope i between node i -4n and node i-(3n-1), wherein i=7n+1,7n+2 ..., 8n-1；
Connect saddle rope 8n between node 4n and node 4n+1.
4) diagonal rope：
Connect diagonal rope i between node i -8n and node i -6n, wherein i=8n+1,8n+2 ..., 9n-1,9n；
Connect diagonal rope i between node i-(10-2m) n and node i-(8n-1), wherein i=9n+1,9n+2 ..., 10n-1；
Connect diagonal rope 10n between node 2mn and node n+1；
Connect diagonal rope i between node i-(8n-1) and node i-(6n-1), wherein i=10n+1,10n+2 ..., 11n-1；
Connect diagonal rope 11n between node 2n+1 and node 4n+1；
The diagonal rope i of node i-connect between (10n-1) and node i -8n, wherein i=11n+1,11n+2 ..., 12n-1；
Connect diagonal rope 12n between node n+1 and node 4n.
The Topology connection form of other elementary cells is corresponding identical with the Topology connection form of first elementary cell.
2. annular tension integral structure according to claim 1, it is characterised in that whole annular tension integral structure
Concrete composition is uniquely determined by following parameter：Ring number of monomers m, the depression bar number n of each monomer, the radius Rt of annulus axis,
The positive n of the monomer initial corner β of shape bottom surface relative to axis plane in circumradius r, the positive n of monomer of shape bottom surface0、
Duplication γ when the relative rotation β of two bottom surface of monomer and monomer head and the tail connect.
3. annular tension integral structure according to claim 1, it is characterised in that the annular tension integral structure
Feasible pre-stressed mode has ring symmetry, therefore when the feasible pre-stressed mode of total is solved, only needs analysis and solution
The feasible pre-stressed mode of first elementary cell, the pre-stressed mode of other elementary cells and first elementary cell phase
Together.
4. annular tension integral structure according to claim 3, it is characterised in that pre- for first elementary cell should
The solution of power mode is specially：Matrix is balanced according to the geometric shape of structure and topological relation, then balancing matrix is carried out
Singular value decomposition tries to achieve the basic course laboratory of its kernel, if each column vector (i.e. independent self-stress modes) of existence foundation solution system
Linear combination can meet the tension and compression condition of all units of annular tension integral structure, then the annular under parameter current value
There is feasible pre-stressed mode in tension integral structure.
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| CN106930404A (en) * | 2017-03-28 | 2017-07-07 | 浙江大学 | A kind of tensioning Integral rectangular truss structural |
| CN109853726A (en) * | 2019-01-10 | 2019-06-07 | 浙江大学 | A kind of New Ring-like Type tension integral structure |
| CN110847369A (en) * | 2019-10-28 | 2020-02-28 | 东南大学 | Method for constructing irregular grid structure determined by longitudinal symmetric plane of rod piece |
| CN113463762A (en) * | 2021-07-08 | 2021-10-01 | 浙江大学 | Thirty-rod spherical tension integral structure |
| CN114575461A (en) * | 2022-03-16 | 2022-06-03 | 中山大学 | Nested annular tensioning integral structure spliced in modularization mode |
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