A method for determining the cable-bar configuration of cable structures based on the initial configuration equilibrium of the upper grid

Abstract

The present invention relates to the technical field of prestressed cable structures in civil engineering, and in particular to a method for determining the morphology of a lower cable-bar system based on the initial configuration equilibrium of an upper grid. Generally, the cable structure design first determines the configuration of the lower cable-bar system according to the functional requirements of the internal space of the building and similar engineering experience, and then determines its prestress through force analysis. For more complex projects, it is difficult to achieve the target requirements only through force analysis. The present invention proposes a method for optimizing the morphology of a cable-bar system. Under the premise that the local control cable force is known, an iterative method is used to simultaneously update the coordinates of the configuration nodes and the pretension of the force-finding unit, and the configuration and prestress of the global cable-bar system are optimized, thereby greatly improving the efficiency of structural design and realizing a constant load equilibrium state based on the initial configuration of the upper grid, that is, under the joint action of the constant load and the prestress, the vertical displacement of the upper grid is close to 0, and the deformation and force of the upper grid are minimized.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering prestressed cable structures, in particular to a method for determining the shape of a lower cable rod system based on an upper grid initial configuration balance. Background Art

[0002] With the development of the times and social progress, some large public buildings have become cultural symbols and symbols of strength of a country or region. Large-span cable structures have become one of the most popular structural types for building large public buildings in modern society due to their strong plasticity of appearance and full utilization of structural materials. Modern cable structures often use high-strength cable materials and prestressed technology to optimize structural performance, reduce structural deadweight, and achieve light spans across large spaces, such as cable-stayed truss structures, cable-supported dome structures, cable-supported grid structures, cable-stayed grid structures, cable dome structures, cable truss structures, cable net structures, cable suspension structures, etc., which have been widely used in large stadiums, exhibition centers, transportation hubs, etc. Among them, the cable-stayed truss structure, suspend-dome structure, cable-supported grid structure, cable dome structure, cable truss structure, etc. all belong to the double-layer structural system. For example, the suspend-dome structure and the cable-supported grid structure are both composed of an upper grid shell and a lower cable rod system. Through the application of prestress, the lower cable rod system supports the upper grid shell and provides elastic support points for the upper grid shell; the cable dome structure and the cable truss structure are both composed of an upper cable net and a lower cable rod system. The support rods are supported between the upper and lower cables. Through the application of prestress, the prestress of the upper and lower cables is balanced with each other.

[0003] Large-span spatial cable structures exhibit geometric nonlinear characteristics under load, and reach equilibrium after undergoing large deformation from the initial geometry. In general cable structure design, the shape of the upper grid is determined by the architectural design, while the shape of the lower cable-bar system (including position and prestress) needs to be determined in the structural design. Usually, one of the goals of the cable-bar system shape design is that in the structural constant load state (equilibrium state under the combined action of constant load and prestress), the vertical displacement of the upper grid is close to 0, that is, the upper grid is maintained in the initial position, achieving the minimum deformation and force of the upper grid.

[0004] To achieve the above goals, it is necessary not only to adjust the prestress of the cable-bar system, but also to adjust the configuration of the cable-bar system. The former belongs to the category of force-finding analysis, and the latter belongs to the category of form-finding analysis. Generally, the configuration of the lower cable-bar system is first determined according to the functional requirements of the internal space of the building and the experience of similar projects, and then its prestress is determined through force-finding analysis. For more complex projects, it is difficult to achieve the target requirements only through force-finding analysis. Therefore, it is necessary to repeatedly adjust the configuration of the cable-bar system, which has a great impact on the efficiency of structural design. Summary of the invention

[0005] In view of the above problems, the present invention provides a method for determining the shape of a cable-bar system of a cable structure based on the initial configuration equilibrium of an upper grid. The basic principle is as follows: based on the configuration and internal force of the structural equilibrium state under the joint action of load and prestress, the node coordinates and prestress of the cable-bar system are simultaneously updated, so that the new prestress of the cable-bar system balances the load in the new configuration and reduces the structural displacement. The method is iterated cyclically until the structural displacement is close to 0. In order to control the overall prestress level and obtain a unique solution, it is necessary to reasonably select force control units in the cable-bar system to apply known prestress.

[0006] The present invention adopts the following technical solution:

[0007] The method for determining the cable-bar system morphology of a cable structure based on the initial configuration balance of the upper grid of the present invention comprises the following steps:

[0008] 1) Establish the initial model of the double-layer cable structure and apply loads and boundary conditions;

[0009] 2) Select the shape control node in the lower cable-bar system of the model Determine shape control nodes Shape control direction, set shape control node The iterative convergence value u cvg ;

[0010] 3) Select the form-finding node in the lower cable-bar system of the model Determine the form nodes The form-finding direction;

[0011] 4) Select the force control unit in the lower cable-bar system of the model The small elastic modulus method is used to apply a known prestress is the applied load in step 1);

[0012] 5) Select the force-finding unit in the lower cable-bar system of the model exist The initial value of the prestress iteration p is applied i(0) ;

[0013] 6) For the model, load, boundary conditions and initial value of prestress iterative applied in the force-finding unit in step 1), step 4) and step 5), perform the first geometric nonlinear static solution to obtain the equilibrium state after structural deformation;

[0014] 7) Update the shape node for the kth iteration The coordinate value c i(k) and force-finding unit The prestress p i(k) , the specific iteration strategy is:

[0015] For form nodes: c i(k) =ci(k-1) +β×u i(k-1) , where c i(k-1) and u i(k-1) are the coordinates and displacement of the i-th form-finding node in the form-finding direction in the k-1-th iteration respectively; β is the iteration acceleration coefficient, and β≥1.0;

[0016] For the force-seeking unit: p i(k) =σ i(k-1) , where σ i(k-1) is the axial stress of the i-th force-finding unit in the equilibrium state at the k-1-th iteration;

[0017] 8) According to the kth iteration updated form node coordinates and force unit prestress, perform the k+1th geometric nonlinear static solution to obtain the equilibrium state after structural deformation

[0018] 9) According to the iterative convergence value u in step 2) cvg , to determine whether the convergence criteria are met: If satisfied, the iteration ends; if not satisfied, return to step 7) and iterate again.

[0019] The cable structure cable-bar system shape determination method based on the upper grid initial configuration equilibrium of the present invention, the iterative convergence criterion is the shape control node in the equilibrium state Maximum displacement in the shape control direction

[0020] The method for determining the shape of a cable-strut system of a cable structure based on the initial shape balance of an upper grid described in this invention, wherein the shape control node is a node connecting the strut in the lower cable-strut system with the upper grid.

[0021] In the method for determining the shape of a cable-bar system of a cable structure based on the initial configuration balance of an upper grid described in the present invention, the shape-finding node is a node where a brace and a cable are connected in the lower cable-bar system.

[0022] In the method for determining the shape of a cable-bar system of a cable structure based on the initial configuration balance of an upper grid described in the present invention, the shape-finding direction can be a single direction or multiple directions.

[0023] In the cable structure cable-bar system morphology determination method based on the upper grid initial configuration equilibrium described in the present invention, the force control unit is a cable unit or a bar unit with a known axial force in the lower cable-bar system in a structural equilibrium state.

[0024] In the cable structure cable rod system morphology determination method based on the upper grid initial configuration balance described in the present invention, the force-seeking units are the struts and cables in the lower cable rod system except the force control units.

[0025] The cable structure cable rod system morphology determination method based on the upper grid initial configuration equilibrium of the present invention, the small elastic modulus method is to adjust the material elastic modulus of the corresponding unit to a small value, so that after the double-layer cable structure model is deformed, the elastic stress generated by the relative displacement of the two end nodes of the unit is small, and the axial stress of the corresponding unit is consistent with the applied prestress; the force control unit e i ctrl The axial stress σ in the equilibrium state i ctrl Equal to the known p i ctrl , the corresponding unit is not affected by the prestress update of the force-finding unit and the coordinate update of the form-finding node.

[0026] Beneficial Effects

[0027] The present invention provides a method for determining the cable-bar morphology of a cable structure based on the initial configuration balance of an upper grid, and proposes a morphology optimization method. On the premise that the local control cable force is known, the global cable-bar morphology and prestress are optimized and determined simultaneously, thereby achieving a load equilibrium state based on the initial configuration of the upper grid and greatly improving the efficiency of structural design.

[0028] The cable structure cable-bar system morphology determination method based on the initial configuration balance of the upper grid provided by the present invention, under the premise that the local control cable force is known, the axial force of the force control unit at that location is maintained constant by the small elastic modulus method, and the coordinates of the form-finding node and the prestress of the force-finding unit are simultaneously updated by the iteration method, and the configuration and prestress of the global cable-bar system are optimized and determined, thereby greatly improving the efficiency of structural design, and realizing the load equilibrium state based on the initial configuration of the upper grid, that is, under the joint action of the load and the prestress, the vertical displacement of the upper grid is close to 0, and the deformation and stress of the upper grid are minimized. In addition, there is no need to construct a complex mathematical analytical formula according to specific engineering conditions, the iteration strategy is simple and clear, and has strong versatility in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 The flow chart for determining the shape of the lower cable rod system applicable to the present invention is as follows

[0030] Figure 2 It is an overall three-dimensional axonometric diagram of the cantilevered roof of a stadium to which the present invention is applicable;

[0031] Figure 3 The overall plan view of the cantilevered roof of a stadium to which the present invention is applicable;

[0032] Figure 4 It is a three-dimensional axonometric diagram of the lower cable rod system of the cantilevered roof of a stadium to which the present invention is applicable;

[0033] Figure 5 It is a plan view of the lower cable rod system of the cantilevered roof of the stadium to which the present invention is applicable;

[0034] Figure 6 The invention relates to a shape control node, a shape finding node, a force control unit and a force finding unit of a cantilevered roof of a stadium to which the invention is applicable.

[0035] Explanation of the reference numerals: upper grid 1, lower cable-rod system 2, oblique cable 3, ring cable 4, strut 5, shape control node 6, shape-finding node 7, force control unit 8, force-finding unit 9. DETAILED DESCRIPTION

[0036] In order to make the purpose and technical solution of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] The canopy roof of a certain stadium is a large-opening cable-supported grid structure, in which the upper grid 1 is a single-layer lattice shell with a large cantilever in the east-west direction and a small cantilever in the north-south direction; the lower cable-bar system 2 is composed of oblique cables 3, ring cables 4 and struts 5, which are double-ring rib ring type in the east-west direction and gradually transform into a single-ring rib ring type in the north-south direction, in which the upper node of the strut 5 is hinged to the upper grid 1. The overall roof has a unique shape and a large difference in vertical stiffness distribution. According to preliminary analysis, the roof exhibits significant vertical bending under the constant load prestressed state, and the bending stress of the upper grid 1 is relatively large. Therefore, it is necessary to optimize the position and prestress of the lower cable-bar system 2 to achieve a vertical displacement of the vertex of the strut 5 close to 0 under the constant load equilibrium state, thereby reducing the bending stress of the upper grid 1. The specific implementation steps are as follows:

[0038] 1) Establish the initial model of the cantilever roof structure, and apply the dead load including the structure, roof system, and horseway. The boundary condition of the roof support is radial sliding hinge.

[0039] 2) Determine the shape control nodes in the lower cable-bar system 2 is the upper node of all struts 5, the shape control direction is vertical, and the iterative convergence value u cvg is 1.0mm.

[0040] 3) Determine the form-finding nodes in the lower cable-bar system 2 It is the lower node of all struts 5, and the shape-finding direction is vertical.

[0041] 4) Determine the force control unit in the lower cable rod system 2 It is the 4-unit ring cable at the junction of the single ring and the double ring. The prestress is known.

[0042] 5) Determine the force-finding unit in the lower cable-bar system 2 In addition to the force control unit All the inclined cables 3, ring cables 4 and struts 5 except for 3 are installed, and the initial value of prestress iteration of 200 MPa is applied to the inclined cable 3.

[0043] 6) Perform geometric nonlinear static solutions to obtain the equilibrium state of the structure after deformation.

[0044] 7) Update the shape-finding node for the kth iteration The coordinate value c i(k) and force-finding unit The prestress p i(k) , the specific iteration strategy is:

[0045] (1) For shape-finding node 7: c i(k) =c i(k-1) +β×u i(k-1) , where c i(k-1) and u i(k-1) are the coordinates and displacement of the i-th form-finding node 7 in the form-finding direction in the k-1-th iteration respectively; β is the iteration acceleration coefficient, which is 5.0;

[0046] (2) For force-finding unit 9: p i(k) =σ i(k-1) , where σ i(k-1) is the axial stress of the i-th force-finding unit (9) in the equilibrium state at the k-1-th iteration.

[0047] 8) After the 15th iteration, the maximum vertical displacement of the node on the strut 5 is Satisfy the convergence criteria: End the iteration.

[0048] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for determining the cable-bar shape of a cable structure based on the initial configuration equilibrium of the upper grid. Features: Here are the steps: 1) Establish the initial model of the double-layer cable structure and apply loads and boundary conditions; 2) Select the shape control node in the lower cable-bar system of the model Determine shape control nodes Shape control direction, set shape control node The iterative convergence value u cvg ; 3) Select the form-finding node in the lower cable-bar system of the model Determine the form nodes The form-finding direction; 4) Select the force control unit in the lower cable-bar system of the model The small elastic modulus method is used to apply a known prestress is the applied load in step 1); 5) Select the force-finding unit in the lower cable-bar system of the model exist The initial value of the prestress iteration p is applied i(0) ; 6) For the model, load, boundary conditions and initial value of prestress iterative applied in the force-finding unit in step 1), step 4) and step 5), perform the first geometric nonlinear static solution to obtain the equilibrium state after structural deformation; 7) Update the shape node for the kth iteration The coordinate value c i(k) and force-finding unit The prestress p i(k) , the specific iteration strategy is: For form nodes: c i(k) =c i(k-1) +β×u i(k-1) , where c i(k-1) and u i(k-1) are the coordinates and displacement of the i-th form-finding node in the form-finding direction in the k-1-th iteration respectively; β is the iteration acceleration coefficient, and β≥1.0; For the force-seeking unit: p i(k) =σ i(k-1) , where σ i(k-1) is the axial stress of the i-th force-finding unit in the equilibrium state at the k-1-th iteration; 8) According to the k-th iteration updated form-finding node coordinates and force-finding unit prestress, perform the k+1th geometric nonlinear static solution to obtain the equilibrium state after structural deformation; 9) According to the iterative convergence value u in step 2) cvg , to determine whether the convergence criteria are met: If satisfied, the iteration ends; if not satisfied, return to step 7) and iterate again.

2. According to the method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid according to claim 1, Features: The iterative convergence criterion is the shape control node in the equilibrium state Maximum displacement in the shape control direction 3. According to the method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid according to claim 1, Features: The shape control node is a node where the support rod in the lower cable-rod system is connected to the upper grid.

4. According to claim 1, the method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid, Features: The form-finding node is a node where the brace and the cable are connected in the lower cable-rod system.

5. According to claim 1, the method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid, Features: The shape-finding direction may be a single direction or multiple directions.

6. The method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid according to claim 1, Features: The force control unit is a cable unit or a rod unit with a known axial force in the lower cable-rod system in a structural equilibrium state.

7. The method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid according to claim 1, Features: The force-seeking unit is the support rod and the cable in the lower cable rod system except the force control unit.

8. The method for determining the cable-bar system morphology of a cable structure based on the initial configuration equilibrium of the upper grid according to claim 1, Features: The small elastic modulus method is to adjust the material elastic modulus of the corresponding unit to a small value, so that after the double-layer cable structure model is deformed, the elastic stress generated by the relative displacement of the nodes at both ends of the unit is small, and the axial stress of the corresponding unit is consistent with the applied prestress; the force control unit Axial stress in equilibrium Equal to the known The corresponding elements are not affected by the prestress update of the force-finding element and the coordinate update of the form-finding node.

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