CN112800520A - Shape finding method of cable net structure - Google Patents
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Abstract
The invention discloses a shape finding method of a cable net structure, which comprises the following steps: the coordinates and the internal force of a group of cable nets are obtained by a classical force density method under a no-load state, the configuration is used as an initial configuration, under the action of a load, the node coordinates and the internal force of the structure under the load can be solved by continuously correcting the internal force of the structure, the configuration can be carried out, and the shape finding and force finding work is completed. According to the method, the coordinates and the internal force of the initial state are determined through a classical force density method, and the force density method is good in convergence and high in efficiency; the initial form is similar to the feasible form, and the partial inverse iteration method only corrects the internal force of the cable net structure, so that the possibility of algorithm divergence is reduced; can be combined with the existing large finite element analysis software (such as ANSYS, SAP2000 and the like), and has better universality.
Description
Technical Field
The invention relates to the technical field of architectural design and structural design, in particular to a shape finding method of a cable net structure.
Background
The cable net structure is a net-shaped flexible structure (the structure is shown in figure 1) composed of steel cables (the steel cable 01 and the steel cable 02) with opposite bidirectional curvatures. The cable net structure has the advantages of light dead weight, good spanning capability, rapid construction and the like, so the cable net structure is widely applied to building forms such as stadium roof, curtain wall structures and the like.
The geometric topology of the cable net structure belongs to a mechanism, and the cable net structure can be kept stable only by means of prestress, so that the cable net structure has certain bearing capacity. Defining the morphology of the structure and the corresponding pre-stress (form-finding) becomes one of the key tasks in the design and research of the cable-net structure. The shape-finding method applied to the cable net structure at present mainly comprises a nonlinear finite element method, a force density method, a dynamic relaxation method and the like, and the prestress of the structure is usually determined by a singular value decomposition method. The reverse iteration method can be combined with existing large-scale analysis software (such as ANSYS, SAP2000 and the like), so that the method is widely applied. The classical inverse iteration method randomly assigns a group of prestress for the cable net, and the cable net is close to feasible prestress and form by continuously correcting the coordinates of free nodes and the internal force of the member. However, when the boundary of the cable net is complex or the load distribution is uneven, the classical inverse iteration method is very inefficient and not easy to converge.
The applicant of the patent proposes a modified inverse iteration method, which is characterized in that a feasible configuration of a structure under the action of no external load is searched by a classical force density method, the configuration is used as an initial form, the internal force of a cable net under the load is modified by a partial inverse iteration method, and finally the internal force and coordinates (called feasible form) of the cable net under the load are obtained. The difference between the initial form and the prestress of the method and the feasible form is small, and the partial inverse iteration method can always maintain high calculation efficiency, so that the effective propulsion of the design work is ensured.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention aims to provide a shape finding method of a cable net structure, which aims to solve the technical problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a shape finding method of a cable net structure, which comprises the following steps: the coordinates and the internal force of a group of cable nets are obtained by a classical force density method under a no-load state, the configuration is used as an initial configuration, under the action of a load, the node coordinates and the internal force of the structure under the load can be solved by continuously correcting the internal force of the structure, the configuration can be carried out, and the shape finding and force finding work is completed.
As a further technical scheme, the method comprises the following steps:
s1: inputting a model A, and acquiring a geometric topological relation and constraint information of the model A;
s2: the designer specifies the force density of each cable net component according to experience;
s3: the number of components of the cable net is b, the number of nodes is n, and the integral degree of freedom is 3 n; forming a 3b multiplied by 3n dimensional branch point matrix C according to the topological relation of the rod pieces, wherein the rows of the matrix correspond to the rod piece information, and the columns correspond to the degree of freedom information;
for the ith member, if the node numbers at the two ends are j and k, the corresponding branch point matrix element is shown as formula (1):
according to whether the degree of freedom receives the constraint, the branch point matrix C can be divided into a free branch point matrix Cf and a constraint branch point matrix Cs according to columns, as shown in formula (2):
C＝[Cf，Cs] (2)
according to the balance relation, and the formulas (1) and (2) are carried, the following can be obtained finally:
CfTQCfNf+CfTQCsNs＝p (3)
in the formula: nf is a node coordinate corresponding to the unconstrained degree of freedom, and D is a coefficient matrix of CfTQCf; ns is a node coordinate corresponding to the constraint degree of freedom, and Df is a coefficient matrix of CfTQCs; q is a 3b x 3b dimensional force density matrix with force density qi for the ith member;
qi is Fi/Li, Fi is the internal force of the component, and Li is the length of the component;
then Q is formed as shown in equation (4):
Q(3i-2:3i)×(3i-2:3i)＝qiI3×3 (4)
s4: the classical force density method assumes that the external load p is 0, and then the node coordinate corresponding to the unconstrained degree of freedom can be directly obtained by solving the formula (5) after the force density matrix Q is determined;
Nf＝-D-1DfNs (5)
nf, determining the lengths of all the members, and further obtaining the prestress of the structure according to the force density specified in advance, wherein the cable net form is a model B; if the appearance of the cable net structure cannot meet the requirement of the building appearance, the appearance of the cable net can be changed by modifying the force density, and finally the appearance of the cable net structure and corresponding prestress which meet the requirement are obtained;
in order to ensure that the structure does not deviate from the form of the model B too much, the structure appearance is corrected by using a partial iteration method;
the specific implementation steps for correcting the structure appearance by using a partial iteration method are as follows: for the ith iteration step, solving the displacement di, the internal force Fi and the deformed coordinate Ni of the model B under the external load by using a nonlinear finite element method; calculating the length of the displacement di and judging whether the length is small enough; if the internal force is small enough, the iteration is considered to be completed, and the internal force Fi in the middle form and the deformed shape Ni are feasible forms of the cable net under the load action; otherwise, applying the internal force Fi as a prestress to the corresponding unit of the model B and repeating the contents of the iteration step until the length of the displacement di is small enough.
By adopting the technical scheme, the invention has the following beneficial effects:
1. the coordinate and the internal force of the initial state are determined by a classical force density method, and the force density method is good in convergence and high in efficiency.
2. The initial form is similar to the feasible form, and the partial inverse iteration method only corrects the internal force of the cable net structure, thereby reducing the possibility of algorithm divergence.
3. Can be combined with the existing large finite element analysis software (such as ANSYS, SAP2000 and the like), and has better universality.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic diagram of a prior art structure;
FIG. 2 is a model (i.e., model A) for determining geometric topological relationships;
FIG. 3 is a cable net structure (initial form, namely model B) under the no-load effect, which is obtained by solving through a classical force density method;
FIG. 4 is a schematic diagram of the reverse iteration method employed in the present invention;
FIG. 5 is a schematic diagram of the final cable net structure obtained by the inverse iteration method (feasible form, i.e., model C);
FIG. 6 is a general flow chart of the algorithm of the present invention.
Wherein: the model B is characterized in that 1 is a first inhaul cable, 2 is a second inhaul cable, 3 is a cable net boundary, 4 is an external load, 5 is a form corresponding to the model B, 6 is an intermediate form in the reverse iteration process, and 7 is a final cable net form (namely the model C) after the reverse iteration is finished.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
As shown in fig. 2-6, the cable net structure is formed by connecting two groups of cables (cable one 1 and cable two 2) with different curvatures in different directions, and the boundary (cable net boundary 3) is three-way constraint. Model a may not have a reasonable coordinate because it only provides topology and boundary information, with an outer load of 0.
The number of components of the cable net is b, the number of nodes is n, and the total degree of freedom is 3 n. A3 b multiplied by 3n dimensional branch point matrix C can be formed according to the topological relation of the rod pieces, the rows of the matrix correspond to the rod piece information, and the columns correspond to the degree of freedom information. For the ith root member, if the node numbers at the two ends are j and k, the corresponding branch point matrix element is as shown in (1):
according to whether the degree of freedom receives the constraint, the branch point matrix C can be divided into a free branch point matrix Cf and a constraint branch point matrix Cs according to columns, as shown in formula (2):
C＝[Cf，Cs] (2)
according to the balance relation, and the formulas (1) and (2) are carried, the following can be obtained finally:
CfTQCfNf+CfTQCsNs＝p (3)
in the formula: nf is a node coordinate corresponding to the unconstrained degree of freedom, and D is a coefficient matrix of CfTQCf; ns is a node coordinate corresponding to the constraint degree of freedom, and Df is a coefficient matrix of CfTQCs; q is a 3b × 3b dimensional force density matrix, and for the ith member, the force density is qi (qi is Fi/Li, Fi is the member internal force, and Li is the member length), and Q is configured as shown in formula (4):
Q(3i-2:3i)×(3i-2:3i)＝qiI3×3 (4)
the classical force density method assumes that the external load p is 0, and then the node coordinates corresponding to the unconstrained degree of freedom can be directly obtained by solving equation (5) after the force density matrix Q is determined.
Nf＝-D-1DfNs (5)
Nf is determined, the lengths of all the members are determined, and the prestress of the structure can be further determined according to the predetermined force density, and the cable net form is the model B according to the above description, as shown in fig. 2. If the appearance of the cable net structure can not meet the requirement of building appearance, the appearance of the cable net can be changed by modifying the force density, and finally, the appearance of the cable net structure and corresponding prestress can be obtained. For a structure in actual engineering, the state after construction is finished is not only influenced by prestress, but also influenced by an external load 4 as shown in 4 in fig. 3. The forces in the cable net are redistributed under the action of load, and the shape is also changed.
In order to prevent the structure from deviating too much from the form 5 corresponding to the model B, the structure shape is modified by using a partial iteration method, and the specific implementation steps are as shown in fig. 4: for the ith iteration step, the displacement di, the internal force Fi and the deformed coordinate Ni of the model B under the external load are solved by using a nonlinear finite element method (namely the intermediate form 6 in the inverse iteration process shown as 6 in FIG. 4). The length of the displacement di is determined and it is determined whether the length is sufficiently small (less than 1 e-3). If the internal force Fi is small enough, the iteration is considered to be finished, and the internal force Fi in the middle form and the deformed shape Ni are the final cable net form 7 (namely the model C) after the reverse iteration of the cable net under the load action is finished. Otherwise, applying the internal force Fi as a prestress to the corresponding unit of the model B and repeating the contents of the iteration step until the length of the displacement di is small enough.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A shape finding method of a cable net structure is characterized by comprising the following steps: the coordinates and the internal force of a group of cable nets are obtained by a classical force density method under a no-load state, the configuration is used as an initial configuration, under the action of a load, the node coordinates and the internal force of the structure under the load can be solved by continuously correcting the internal force of the structure, the configuration can be carried out, and the shape finding and force finding work is completed.
2. A method of form-finding a cable net structure according to claim 1, comprising the steps of:
s1: inputting a model A, and acquiring a geometric topological relation and constraint information of the model A;
s2: the designer specifies the force density of each cable net component according to experience;
s3: the number of components of the cable net is b, the number of nodes is n, and the integral degree of freedom is 3 n; forming a 3b multiplied by 3n dimensional branch point matrix C according to the topological relation of the rod pieces, wherein the rows of the matrix correspond to the rod piece information, and the columns correspond to the degree of freedom information;
for the ith member, if the node numbers at the two ends are j and k, the corresponding branch point matrix element is shown as formula (1):
according to whether the degree of freedom receives the constraint, the branch point matrix C can be divided into a free branch point matrix Cf and a constraint branch point matrix Cs according to columns, as shown in formula (2):
C＝[Cf，Cs] (2)
according to the balance relation, and the formulas (1) and (2) are carried, the following can be obtained finally:
CfTQCfNf+CfTQCsNs＝p (3)
in the formula: nf is a node coordinate corresponding to the unconstrained degree of freedom, and D is a coefficient matrix of CfTQCf; ns is a node coordinate corresponding to the constraint degree of freedom, and Df is a coefficient matrix of CfTQCs; q is a 3b x 3b dimensional force density matrix with force density qi for the ith member;
qi is Fi/Li, Fi is the internal force of the component, and Li is the length of the component;
then Q is formed as shown in equation (4):
Q(3i-2:3i)×(3i-2:3i)＝qiI3×3 (4)
s4: the classical force density method assumes that the external load p is 0, and then the node coordinate corresponding to the unconstrained degree of freedom can be directly obtained by solving the formula (5) after the force density matrix Q is determined;
Nf＝-D-1DfNs (5)
nf, determining the lengths of all the members, and further obtaining the prestress of the structure according to the force density specified in advance, wherein the cable net form is a model B; if the appearance of the cable net structure cannot meet the requirement of the building appearance, the appearance of the cable net can be changed by modifying the force density, and finally the appearance of the cable net structure and corresponding prestress which meet the requirement are obtained;
in order to ensure that the structure does not deviate from the form of the model B too much, the structure appearance is corrected by using a partial iteration method;
the specific implementation steps for correcting the structure appearance by using a partial iteration method are as follows: for the ith iteration step, solving the displacement di, the internal force Fi and the deformed coordinate Ni of the model B under the external load by using a nonlinear finite element method; calculating the length of the displacement di and judging whether the length is small enough; if the internal force is small enough, the iteration is considered to be completed, and the internal force Fi in the middle form and the deformed shape Ni are feasible forms of the cable net under the load action; otherwise, applying the internal force Fi as a prestress to the corresponding unit of the model B and repeating the contents of the iteration step until the length of the displacement di is small enough.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080300831A1 (en) * | 2006-12-19 | 2008-12-04 | Board Of Governors For Higher Education, State Of Rhode Island And Providence | System and method for finite element based on topology optimization |
| CN106934147A (en) * | 2017-03-09 | 2017-07-07 | 北京理工大学 | A kind of geometry such as space truss rope net antenna look for shape method |
| CN106934155A (en) * | 2017-03-13 | 2017-07-07 | 北京市建筑设计研究院有限公司 | A kind of cable-truss structure looks for shape method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080300831A1 (en) * | 2006-12-19 | 2008-12-04 | Board Of Governors For Higher Education, State Of Rhode Island And Providence | System and method for finite element based on topology optimization |
| CN106934147A (en) * | 2017-03-09 | 2017-07-07 | 北京理工大学 | A kind of geometry such as space truss rope net antenna look for shape method |
| CN106934155A (en) * | 2017-03-13 | 2017-07-07 | 北京市建筑设计研究院有限公司 | A kind of cable-truss structure looks for shape method |
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