CN106934155A - A kind of cable-truss structure looks for shape method - Google Patents
A kind of cable-truss structure looks for shape method Download PDFInfo
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Abstract
Shape method is looked for this application discloses a kind of cable-truss structure, compared with prior art, the invention has the characteristics that and beneficial effect：Can given roofing or curtain wall geometry, keep being carried out on the premise of strut or hoist cable are vertical cable-truss structure look for shape, make to look for shape result to comply fully with expected architectural image；It is applied widely, can be used for various cable truss arrangements such as the roofing of multi-form or curtain wall curved surface, boundary shape and rung formula, run-in index, staggered form；The concept and one direction force density method of force density mode are proposed, the only z coordinate of more new node is looked for during shape, node x, y-coordinate meet equilibrium equation automatically, without being updated, so that strut or hoist cable keep vertical automatically；Control parameter is few, can be directed to given roofing or curtain wall geometry be quickly given it is a series of it is various sizes of look for shape result and corresponding internal force to be distributed, be easy to building scheme than choosing and structure optimization etc..
Description
Technical field
The invention belongs to the architectural design in architectural engineering and field of structural design, and in particular to a kind of cable-truss structure is looked for
Shape method.
Background technology
Cable-truss structure is arranged in a combination according to certain rules by a series of cable trusses, and common cable truss arrangement has car
Spoke, run-in index, staggered form etc..This structure type has from heavy and light, is applicable the features such as big span, easy construction, thus extensively
It is general to be applied in the construction styles such as all kinds of longspan structures, curtain wall construction.
The strut that the basic component units of cable-truss structure can be summarized as winding up between rope, last quarter rope and two-layer drag-line (or hangs
Rope), it is a kind of typical cable-strut tensile structure system.This class formation needs to form rigidity by introducing prestressing force, and then has
Standby bearing capacity.Introduce the configuration state before and after prestressing force and be referred to as nought state and initial state.For cable-truss structure, structure
Bearing capacity can be formed directly related with structural configuration, thus look for shape (form finding) be always cable-truss structure research and
One of key problem in design.The shape method of looking for for being applied to cable-truss structure at present mainly has finite element method, power pine
Relaxation method, force density method etc..After cable-truss structure configuration determines, the prestressing force point of structure can be obtained using balancing matrix theory etc.
Cloth, and determine stress distribution according to the rigidity of structure and requirement for bearing capacity, that is, obtain the initial state of cable-truss structure.
In engineering practice, building roof or curtain wall typically directly or are indirectly laid on cable-truss structure and wind up rope or last quarter rope
In residing face.To realize architectural effect, roofing or curtain wall geometry are generally determined by architect, i.e. cable truss winds up
(or lower edge) geometry gives, while strut (or hoist cable) typically keeps vertical.Therefore, need one kind can be in part in engineering
Component geometry looks for shape method to the cable-truss structure of timing, so as to find cable-truss structure on the premise of architectural effect is ensured
Initial state.
The content of the invention
For problems of the prior art, shape method is looked for it is an object of the invention to provide a kind of cable-truss structure,
It efficiently solves problems of the prior art.
To achieve the above object, the present invention uses following technical scheme：
Look for the shape method, methods described of a kind of cable-truss structure comprise the following steps：
1) foundation meets given roofing or the cable-truss structure of curtain wall geometry winds up or lower-chord panel point, according to topological relation
Each node is connected, the geometrical model of obtain winding up rope or last quarter rope；
2) will respectively wind up or lower-chord panel point vertically downwards or offsets up any distance, obtain each lower edge or wind up
The initial position of node, the corresponding upper and lower chord node of connection obtains the initial geometric model of strut or hoist cable；
3) the lower or upper extreme point of constraint outer shroud support node and strut or hoist cable, obtains looking for power model, is named as model A；
4) another building looks for shape Model B：According to step 2) in the initial position of lower edge or upper chord node set up last quarter rope or wind up
The initial geometric model of rope, and constrain outer shroud support node；
5) group collects the balancing matrix of model A and carries out singular value decomposition, obtains its self-stress modes；
6) self-stress modes of model A are carried out into linear combination, extract the corresponding numerical value of strut or hoist cable in combined result,
When self-stress modes are unique, the corresponding numerical value of strut or hoist cable in mode is directly extracted, acquired results are used as outer when looking for shape
Load；
7) x of Model B is set up to, to equilibrium equation group, the coefficient matrix of group collection equation group claims with y by variable of force density
Be force density balancing matrix, singular value decomposition carried out to matrix, obtain Model B meet x to force density mould from y to equilibrium condition
State；
8) the force density mode of Model B is carried out into linear combination, when force density mode is unique, can be directly multiplied by adjustment system
Number, acquired results are used as the force density for looking for shape to use；
9) using step 8) force density that obtains, and by step 6) external load that obtains is applied to the respective nodes of Model B,
Force density method with load is carried out to Model B and looks for shape, be met lower edge that equilibrium condition and strut or hoist cable require vertically or
Wind up node coordinate, because x, the y-coordinate of looking for each node during shape meet balance automatically, can only update z coordinate, therefore be referred to as
One direction force density method；
10) using winding up in model A or lower-chord panel point coordinate and lower edge or upper chord node after shape in Model B is looked for sit
Mark, sets up the whole geometry model of cable-truss structure, is named as MODEL C；
11) whether the physical dimension of inspection model C meets the requirement related to building function, and follow-up step is entered if meeting
Suddenly, the return to step 8 if being unsatisfactory for), force density modality combinations coefficient or regulation coefficient are updated, and re-start and look for shape, until
Obtain physical dimension and meet desired cable-truss structure；
12) group collects the balancing matrix of MODEL C and carries out singular value decomposition, obtains the cable-truss structure seif-citing rate mould for looking for shape to complete
State；Consider deadweight or other loads to looking for shape result to be modified afterwards.
Further, step 7) described in force density balancing matrix and force density mode concrete meaning and computational methods be：
For i-th node of Model B set up x to y to equilibrium equation：
Wherein (xi,yi) it is i-th x of node, y-coordinate, n is to be connected to i-th element number of node, Lk、fkWith
(xk,yk) (k=1,2 ..., n) it is respectively x, the y for being connected to i-th length, internal force and another end points of k-th unit of node
Coordinate；Introduce force density qk=fk/Lk, formula (1) can be transformed to：
In formula (2), (xi,yi)、(xk,yk) horizontal level according to each node gives, and qkIt is unknown, therefore can be with
Formula (2) is considered as on qkEquation group；For all nodes of Model B set up same equilibrium equation, write as rectangular after group collection
Formula：
[Aq] { q }={ 0 } (3)
Matrix [A in formula (3)q] it is referred to as the force density balancing matrix of Model B, { q } puts down to meet each knee level of Model B
The force density of weighing apparatus condition；
By [Aq] singular value decomposition is carried out, one group of vector { s can be obtainedj(j=1,2 ...), meet：
[Aq]{sj}={ 0 } (4)
Then { sjIt is the general solution of system of homogeneous linear equations formula (3), referred to as force density mode.
Further, step 9) described in one direction force density method principle and implementation process be：
Each node of Model B is applied along z to external load pi, then the equilibrium equation of i-th node of Model B be：
Wherein (xi,yi,zi) it is i-th x, y, z coordinate of node, n is to be connected to i-th element number of node, Lk、fk
(xk,yk,zk) (k=1,2 ..., n) it is respectively length, internal force and another end points for being connected to i-th k-th unit of node
X, y, z coordinate；Introduce force density qk=fk/Lk, formula (5) can be written as：
From formula (1)-formula (4), when using step 8) force density that obtains when, the first two equation of formula (6) it is automatic into
It is vertical, the 3rd equation need to only be solved；
If Model B has b unit, m node, wherein the quantity point of the node of shape to be looked for and fixed outer shroud support node
Wei not mfAnd mc, introduce the topological matrix of b × m：
Before the node of shape to be looked for is arranged in into outer shroud support node in [C], [C] can be split as free node topology
Matrix [Cf] and constraint node topology matrix [Cc], i.e. C=[[Cf][Cc]]；All nodes to Model B list z to balance side
Journey simultaneously organizes collection, can be write as：
[Cf]T[Q][Cf]{zf}+[Cf]T[Q][Cc]{zc}={ p } (8)
Wherein { zfIt is node z coordinate vector to be solved, { zcIt is the z coordinate vector of outer shroud support node, { p } is section
Point external load vector, [Q] is force density diagonal matrix；Solution formula (8), obtains final product the z coordinate of free node：
{zf}=([Cf]T[Q][Cf])-1({p}-[Cf]T[Q][Cc]{zc}) (9)
More than solve mean Model B look for shape during only need the z coordinate of more new node, and x, y-coordinate will not be sent out
Changing, thus strut or hoist cable can automatically keep vertical；Due to the method achieve only in z to look for shape, therefore it is referred to as
One direction force density method.
Further, step 12) middle consideration is conducted oneself with dignity or other loads are to the detailed process for looking for shape result to be modified：Look for shape
After the completion of, the specification and prestressing force of each component of cable-truss structure are determined by Preliminary design, obtain structure design model, referred to as model
D；The prestressing force of each struts of extraction model D or hoist cable；The all z by the node of looking for shape to obtain of restricted model D to the free degree,
Static Calculation is carried out under dead load or other load actions, each constraint reaction value is superimposed into corresponding strut or hoist cable in advance should
Power, as the external load that amendment is used；Apply the respective nodes of external load to Model B；The force density mode of Model B is entered into line
Property combination, when force density mode is unique, can directly be multiplied by regulation coefficient, the force density that acquired results are used as amendment；It is right
Model B carries out the one direction force density method with load and looks for shape；According to looking for shape modified result model D's to look for shape node coordinate, if repairing
Model D physical dimensions after just are unsatisfactory for requiring that then renewal force density modality combinations coefficient or regulation coefficient, re-starts and repair
Just, until the physical dimension of model D meets requirement；Said process is repeated, until single amendment amplitude is less than pre-set limit；Finally
Look for the rope of shape part long and corresponding force density value according to model D, calculate amendment looks for shape partial prestressing.
The present invention has following Advantageous Effects：
1. can in given roofing or curtain wall geometry, keep carrying out looking for for cable-truss structure on the premise of strut or hoist cable are vertical
Shape, makes to look for shape result to comply fully with expected architectural image；
2. applied widely, can be used for the roofing of multi-form or curtain wall curved surface, boundary shape and rung formula, parallel
Various cable truss arrangements such as formula, staggered form；
3. the concept and one direction force density method of force density mode are proposed, the only z coordinate of more new node, section is looked for during shape
Point x, y-coordinate meet equilibrium equation automatically, without being updated, so that strut or hoist cable keep vertical automatically；
4. control parameter is few, can quickly provide a series of various sizes of for given roofing or curtain wall geometry
Look for shape result and corresponding internal force to be distributed, be easy to building scheme than choosing and structure optimization；
5. look for shape process relatively independent with makeover process, looking for during shape need not carry out Static Calculation, therefore cut with component
Face size and load are unrelated, can make to look for shape quicker, convenient；
6. look for after the completion of shape and consider that deadweight or other loads are modified, cable-truss structure initial state can be made several with nought state
What configuration is basically identical.
Brief description of the drawings
Fig. 1 looks for shape method flow diagram for of the invention；
Fig. 2 is modification method flow chart of the invention；
Fig. 3 be the cable-truss structure that geometry gives wind up rope geometrical model and strut initial geometric model composition look for power mould
Type, i.e. model A；
Fig. 4 is to look for shape model, i.e. Model B based on what cable-truss structure last quarter rope initial geometric model was formed；
Fig. 5 is the Model B for looking for shape to complete；
Fig. 6 is the cable-truss structure for looking for shape to complete, i.e. MODEL C；
Fig. 7 is model A partial structural diagrams；
Fig. 8 is Model B partial structural diagram；
Fig. 9 is the Model B partial structural diagram for looking for shape to complete；
Figure 10 is MODEL C partial structural diagram；
Figure 11 is inner ring floor projection and cable truss floor projection geometrical relationship schematic diagram；
Wherein：1 is upper chord node, and 2 is the rope that winds up, and 3 is lower-chord panel point, i.e. strut lower extreme point, and 4 is strut, and 5 is outer shroud branch
Block node, 6 is last quarter rope, and 7 look for the external load of shape use for Model B；8 is inner ring floor projection；9 is cable truss floor projection.
Specific embodiment
Below, refer to the attached drawing, is more fully illustrated to the present invention, shown in the drawings of exemplary implementation of the invention
Example.However, the present invention can be presented as various multi-forms, the exemplary implementation for being confined to describe here is not construed as
Example.And these embodiments are to provide, so that the present invention is fully and completely, and will fully convey the scope of the invention to this
The those of ordinary skill in field.
As shown in figure 1, looking for shape method invention provides a kind of cable-truss structure, comprise the following steps：
Step 1：Foundation meets chord node 1 on the cable-truss structure of given roofing geometry, each according to topological relation connection
Node, the geometrical model of the rope 2 that obtains winding up；
Step 2：Each upper chord node 1 is offset into any distance vertically downwards, the initial bit of each lower-chord panel point 3 is obtained
Put, the corresponding upper and lower chord node of connection obtains the initial geometric model of strut 4；
Step 3：The lower extreme point 3 of constraint outer shroud support node 5 and strut 4, obtains looking for power model, life shown in Fig. 3 and Fig. 7
Entitled model A；
Step 4：Another building look for shape Model B shown in Fig. 4 and Fig. 8, and the initial position according to lower-chord panel point in step 23 is set up
The initial geometric model of last quarter rope 6, and constrain outer shroud support node 5；
Step 5：The balancing matrix of group collection model A simultaneously carries out singular value decomposition, obtains its unique self-stress modes；
Step 6：The corresponding numerical value of strut in extraction model A self-stress modes, acquired results are used as external load when looking for shape
7；
Step 7：The x of Model B is set up to, to equilibrium equation group, group collects the coefficient square of equation group with y by variable of force density
Battle array, referred to as force density balancing matrix carries out singular value decomposition to matrix, obtain Model B meet x to y to equilibrium condition only
One force density mode；
Step 8：The force density mode of Model B is multiplied by regulation coefficient, acquired results are used as the force density for looking for shape to use；
Step 9：The force density obtained using step 8, and the external load 7 that step 6 is obtained is applied to the corresponding section of Model B
Point 3, the force density method with load is carried out to Model B and looks for shape, obtain shown in Fig. 5 and Fig. 9 meet equilibrium condition and strut 4 is vertical
It is required that the coordinate of lower-chord panel point 3, because x, the y-coordinate of looking for each node 3 during shape meet balance automatically, can only update z coordinate,
Therefore referred to as one direction force density method；
Step 10：Using the coordinate of upper chord node 1 in model A and the coordinate of lower-chord panel point 3 after shape in Model B is looked for, set up
Cable-truss structure whole geometry model shown in Fig. 6 and Figure 10, is named as MODEL C；
Step 11：Whether the physical dimension of inspection model C meets the requirement related to building function, after entering if meeting
Continuous step, return to step 8 if being unsatisfactory for update force density mode regulation coefficient, and re-start and look for shape, until obtaining geometry
Size meets desired cable-truss structure；
Step 12：The balancing matrix of group collection MODEL C simultaneously carries out singular value decomposition, and the cable-truss structure for obtaining looking for shape to complete certainly should
Power mode.
Above-mentioned steps do not consider dead load or the influence of other loads.Look for after the completion of shape, rope is determined by Preliminary design
The specification and prestressing force of each component of purlin structure, obtain structure design model, referred to as model D.Afterwards as shown in Figure 2 step to looking for shape
Result is modified, and makeover process is：The prestressing force of each struts 4 of extraction model D；The z of all lower-chord panel points 3 of restricted model D to
The free degree, Static Calculation is carried out under dead load or other load actions, and each constraint reaction value is superimposed into corresponding strut 4
Prestressing force, as the external load that amendment is used；Apply the respective nodes 3 of external load to Model B；By the force density mode of Model B
It is multiplied by regulation coefficient, the force density that acquired results are used as amendment；The one direction force density method with load is carried out to Model B to look for
Shape；According to the coordinate of lower-chord panel point 3 for looking for shape modified result model D, if revised model D physical dimensions are unsatisfactory for requiring,
Force density mode regulation coefficient is updated, amendment is re-started, until the physical dimension of model D meets requiring；Repeat said process,
Until single amendment amplitude is less than pre-set limit；Finally according to each length of last quarter rope 6 of model D and corresponding force density value, calculating is repaiied
The positive prestressing force of last quarter rope 6.The makeover process is only finely adjusted to the shape and prestressing force of cable-truss structure last quarter rope 6, Bu Huigai
Become the geometry of the rope 2 that winds up, and strut 4 is remained on vertically.After amendment, the geometry structure of cable-truss structure initial state and nought state
Shape is basically identical.
Force density balancing matrix described in step 7 and force density mode concrete meaning and computational methods are：
For i-th lower-chord panel point of Model B set up x to y to equilibrium equation：
Wherein (xi,yi) it is i-th x of node 3, y-coordinate, n is to be connected to i-th quantity of the last quarter rope of node 36,
Lk、fk(xk,yk) (k=1,2 ..., n) it is respectively and is connected to the length of i-th kth root last quarter rope 6 of node 3, internal force and another
The x of end point, y-coordinate.Introduce force density qk=fk/Lk, formula (1) can be transformed to：
In formula (2), (xi,yi)、(xk,yk) horizontal level according to each node 3 gives, and qkIt is unknown, therefore can
It is considered as on q with by formula (2)kEquation group.For all nodes 3 of Model B set up same equilibrium equation, write as matrix after group collection
Form：
[Aq] { q }={ 0 } (3)
Matrix [A in formula (3)q] it is referred to as the force density balancing matrix of Model B, { q } is to meet each level of node 3 of Model B
The force density of equilibrium condition；
By [Aq] singular value decomposition is carried out, one group of vector { s can be obtainedj(j=1,2 ...), meet：
[Aq]{sj}={ 0 } (4)
Then { sjIt is the general solution of system of homogeneous linear equations formula (3), referred to as force density mode.By system of homogeneous linear equations general solution
Property understand, vector { sjLinear combination be still the solution of formula (3), therefore force density mode can be carried out linear combination,
Be met x to force density from y to equilibrium condition.Arranged by rational structure, Model B can be made to possess unique force density
Mode, is now multiplied by force density mode regulation coefficient and can obtain force density.
For the rung formula cable-truss structure of the present embodiment, structure is projected to horizontal plane, then the lower chord joint of each in inner ring
The projection of point 3 is respectively connected with the inner ring projection 8 and Pin cable trusses projection 9 of both sides, as shown in figure 11.When the projection of every Pin cable trusses
When the 9 angular bisector directions for projecting angle along corresponding inner ring 8 are arranged, the force density mode of Model B existence anduniquess, while this
It is the adequate condition of model A existence anduniquess self-stress modes in step 5.
The principle and implementation process of one direction force density method described in step 9 be：
Each lower-chord panel point 3 to Model B applies (to use p to the external load 7 in (i.e. strut direction) along ziRepresent), then model
The equilibrium equation of i-th node of B 3 is：
Wherein (xi,yi,zi) it is i-th x, y, z coordinate of node 3, n is to be connected to i-th number of the last quarter rope of node 36
Amount, Lk、fk(xk,yk,zk) (k=1,2 ..., n) it is respectively length, the internal force for being connected to i-th kth root last quarter rope of node 3
With the x, y, z coordinate of another end points.Introduce force density qk=fk/Lk, formula (5) can be written as：
From formula (1)-formula (4), when the force density obtained using step 8, the first two equation of formula (6) it is automatic into
It is vertical, the 3rd equation (i.e. z is to equilibrium equation) need to only be solved.
If Model B has b roots last quarter rope 6, m node, wherein the lower-chord panel point 3 of shape to be looked for and fixed outer shroud support node
5 quantity is respectively mfAnd mc, introduce the topological matrix of b × m：
Before lower-chord panel point 3 is arranged in into outer shroud support node 5 in [C], [C] can be split as free node topology square
Battle array [Cf] and constraint node topology matrix [Cc], i.e. [C]=[[Cf][Cc]]；All nodes 3 to Model B list z to balance side
Journey simultaneously organizes collection, can be write as：
[Cf]T[Q][Cf]{zf}+[Cf]T[Q][Cc]{zc}={ p } (8)
Wherein { zfBe node 3 to be solved z coordinate vector, { zcIt is the z coordinate vector of outer shroud support node 5, { p }
It is the vector of node external load 7, [Q] is force density diagonal matrix；Solution formula (8), obtains final product the z coordinate of free node：
{zf}=([Cf]T[Q][Cf])-1({p}-[Cf]T[Q][Cc]{zc}) (9)
More than solve mean Model B look for shape during only need the z coordinate of more new node 3, and x, y-coordinate will not be sent out
Changing, thus strut can automatically keep vertical；Due to the method achieve only in z to look for shape, therefore referred to as one direction
Force density method.
It is described above simply to illustrate that of the invention, it is understood that the invention is not limited in above example, meet
The various variants of inventive concept are within protection scope of the present invention.
Claims (4)
1. a kind of cable-truss structure looks for shape method, it is characterised in that methods described comprises the following steps：
1) foundation meets given roofing or the cable-truss structure of curtain wall geometry winds up or lower-chord panel point, is connected according to topological relation
Each node, the geometrical model of obtain winding up rope or last quarter rope；
2) will respectively wind up or lower-chord panel point vertically downwards or offsets up any distance, obtain each lower edge or upper chord node
Initial position, the corresponding upper and lower chord node of connection obtains the initial geometric model of strut or hoist cable；
3) the lower or upper extreme point of constraint outer shroud support node and strut or hoist cable, obtains looking for power model, is named as model A；
4) another building looks for shape Model B：According to step 2) in the initial position of lower edge or upper chord node set up last quarter rope or the rope that winds up
Initial geometric model, and constrain outer shroud support node；
5) group collects the balancing matrix of model A and carries out singular value decomposition, obtains its self-stress modes；
6) self-stress modes of model A are carried out into linear combination, the corresponding numerical value of strut or hoist cable in combined result is extracted, when certainly
When stress mode is unique, the corresponding numerical value of strut or hoist cable in mode is directly extracted, acquired results are used as external load when looking for shape；
7) x of Model B is set up to, to equilibrium equation group, group collects the coefficient matrix of equation group, referred to as power with y by variable of force density
Density balance matrix, singular value decomposition is carried out to matrix, obtain Model B meet x to force density mode from y to equilibrium condition；
8) the force density mode of Model B is carried out into linear combination, when force density mode is unique, can be directly multiplied by regulation coefficient,
Acquired results are used as the force density for looking for shape to use；
9) using step 8) force density that obtains, and by step 6) external load that obtains is applied to the respective nodes of Model B, to mould
Type B carries out the force density method with load and looks for shape, is met equilibrium condition and strut or the vertical desired lower edge of hoist cable or winds up
Node coordinate, because x, the y-coordinate of looking for each node during shape meet balance automatically, can only update z coordinate, therefore referred to as folk prescription
To force density method；
10) using winding up in model A or lower-chord panel point coordinate and the lower edge or the node coordinate that winds up after shape in Model B are looked for, is built
The whole geometry model of vertical cable-truss structure, is named as MODEL C；
11) whether the physical dimension of inspection model C meets the requirement related to building function, and subsequent step is entered if meeting,
The return to step 8 if being unsatisfactory for), force density modality combinations coefficient or regulation coefficient are updated, and re-start and look for shape, until obtaining
Physical dimension meets desired cable-truss structure；
12) group collects the balancing matrix of MODEL C and carries out singular value decomposition, obtains the cable-truss structure self-stress modes for looking for shape to complete；
Consider deadweight or other loads to looking for shape result to be modified afterwards.
2. cable-truss structure according to claim 1 looks for shape method, it is characterised in that step 7) described in force density balance square
Battle array and force density mode concrete meaning and computational methods are：
For i-th node of Model B set up x to y to equilibrium equation：
Wherein (xi,yi) it is i-th x of node, y-coordinate, n is to be connected to i-th element number of node, Lk、fk(xk,yk)
(k=1,2 ..., n) it is respectively length, the x of internal force and another end points, the y-coordinate for being connected to i-th k-th unit of node；
Introduce force density qk=fk/Lk, formula (1) can be transformed to：
In formula (2), (xi,yi)、(xk,yk) horizontal level according to each node gives, and qkIt is unknown, therefore can be by formula
(2) it is considered as on qkEquation group；For all nodes of Model B set up same equilibrium equation, write as matrix form after group collection：
[Aq] { q }={ 0 } (3)
Matrix [A in formula (3)q] it is referred to as the force density balancing matrix of Model B, { q } is to meet each knee level balance strip of Model B
The force density of part；
By [Aq] singular value decomposition is carried out, one group of vector { s can be obtainedj(j=1,2 ...), meet：
[Aq]{sj}={ 0 } (4)
Then { sjIt is the general solution of system of homogeneous linear equations formula (3), referred to as force density mode.
3. cable-truss structure according to claim 1 looks for shape method, it is characterised in that step 9) described in one direction force density
The principle and implementation process of method be：
Each node of Model B is applied along z to external load pi, then the equilibrium equation of i-th node of Model B be：
Wherein (xi,yi,zi) it is i-th x, y, z coordinate of node, n is to be connected to i-th element number of node, Lk、fkWith
(xk,yk,zk) (k=1,2 ..., n) it is respectively the length, internal force and another end points that are connected to i-th k-th unit of node
X, y, z coordinate；Introduce force density qk=fk/Lk, formula (5) can be written as：
From formula (1)-formula (4), when using step 8) force density that obtains when, the first two equation of formula (6) is set up automatically, only
3rd equation need to be solved；
If Model B has b unit, m node, wherein the quantity of the node of shape to be looked for and fixed outer shroud support node is respectively
mfAnd mc, introduce the topological matrix of b × m：
Before the node of shape to be looked for is arranged in into outer shroud support node in [C], [C] can be split as free node topological matrix
[Cf] and constraint node topology matrix [Cc], i.e. C=[[Cf][Cc]]；Z is listed to all nodes of Model B to equilibrium equation simultaneously
Group collection, can be write as：
[Cf]T[Q][Cf]{zf}+[Cf]T[Q][Cc]{zc}={ p } (8)
Wherein { zfIt is node z coordinate vector to be solved, { zcIt is the z coordinate vector of outer shroud support node, { p } is outside node
Load vector, [Q] is force density diagonal matrix；Solution formula (8), obtains final product the z coordinate of free node：
{zf}=([Cf]T[Q][Cf])-1({p}-[Cf]T[Q][Cc]{zc}) (9)
More than solve mean Model B look for shape during only need the z coordinate of more new node, and x, y-coordinate will not become
Change, thus strut or hoist cable can automatically keep vertical；Due to the method achieve only in z to look for shape, therefore referred to as folk prescription
To force density method.
4. cable-truss structure according to claim 1 looks for shape method, it is characterised in that step 12) in consider deadweight or other
Load is to the detailed process for looking for shape result to be modified：Look for after the completion of shape, each component of cable-truss structure is determined by Preliminary design
Specification and prestressing force, obtain structure design model, referred to as model D；The prestressing force of each struts of extraction model D or hoist cable；Constraint
Model D it is all by look for shape obtain node z to the free degree, carry out static(al) meter under dead load or other load actions
Calculate, each constraint reaction value is superimposed to corresponding strut or hoist cable prestressing force, as the external load that amendment is used；Apply external load
To the respective nodes of Model B；The force density mode of Model B is carried out into linear combination, when force density mode is unique, can directly be multiplied
With the force density that regulation coefficient, acquired results are used as amendment；The one direction force density method with load is carried out to Model B to look for
Shape；According to looking for shape modified result model D's to look for shape node coordinate, if revised model D physical dimensions are unsatisfactory for requiring, more
New force density modality combinations coefficient or regulation coefficient, re-start amendment, until the physical dimension of model D meets requiring；Repeat
Said process, until single amendment amplitude is less than pre-set limit；The rope of shape part force density long and corresponding is looked for finally according to model D
Value, calculate amendment looks for shape partial prestressing.
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| CN108256251A (en) * | 2018-01-26 | 2018-07-06 | 东南大学 | A kind of symmetrical cable-rod structure of height for considering datum mark mechanical balance looks for shape method |
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| CN114996793A (en) * | 2022-04-11 | 2022-09-02 | 北京市建筑设计研究院有限公司 | Suspension cable morphology analysis method |
| CN114996793B (en) * | 2022-04-11 | 2022-11-18 | 北京市建筑设计研究院有限公司 | Suspension cable morphology analysis method |
| CN114781142B (en) * | 2022-04-11 | 2023-03-10 | 北京市建筑设计研究院有限公司 | Morphological analysis method for single-ring cable wheel spoke type cable truss structure |
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