A method for analyzing the dynamics of flexible central buckle

Abstract

The present invention discloses a method for dynamic analysis of a flexible central buckle, and relates to the technical field of bridge dynamic analysis. The method comprises: equating the cable structure of the flexible central buckle to a group of parallel truss units and hook units; obtaining the mechanical parameters of the truss unit and the hook unit according to the constitutive relationship of the truss unit and the constitutive relationship of the hook unit; establishing a finite element model of the flexible central buckle according to the mechanical parameters of the truss unit and the hook unit; and performing dynamic simulation calculations based on the finite element model of the flexible central buckle by using time history analysis to obtain the stress time history curve of the flexible central buckle. The method solves the problem that in the prior art, when performing dynamic analysis on the flexible central buckle, the flexible central buckle is generally analyzed as an equivalent truss unit, so that the equivalent truss unit exhibits the characteristics of a truss that can be subjected to both tension and compression, which is inconsistent with the actual property of the flexible central buckle that can only be subjected to tension but not compression during analysis, and the dynamic analysis result is inaccurate.

Description

Technical Field

[0001] The invention relates to the technical field of bridge dynamic analysis, and in particular to a flexible central buckle dynamic analysis method. Background Art

[0002] One of the effective measures to improve the rigidity of a suspension bridge is to connect the main cable and the stiffening beam in the middle of the main span with a central buckle. There are two ways to set the central buckle: use a rigid triangular truss to connect the main cable and the stiffening beam so that the cable and beam are relatively fixed in the middle of the span, which is a rigid central buckle; add one or more pairs of oblique slings in the middle of the span to establish the longitudinal constraint of the cable beam, which is a flexible central buckle.

[0003] For vehicle loads, under the action of vehicles, the stiffening beams and main cables of suspension bridges will produce longitudinal and lateral displacements, and the displacements of the main cables and main beams are not synchronized, causing the cables to bend. The addition of flexible central buckles can effectively improve the stress performance and bending resistance of short cables near the mid-span. For wind loads, the biggest role of the flexible central buckle is to significantly increase the antisymmetric torsion frequency of the structure, so that the torsion-bending frequency ratio under the antisymmetric modal combination increases, which is beneficial to improving the wind resistance of the bridge. However, for seismic loads with significant energy, the installed flexible central buckle of the suspension bridge is less favorable under such loads and is prone to damage. Therefore, energy-absorbing devices such as buckling shock absorbers are generally used in combination with flexible central buckles to improve the comprehensive stress performance of the structure under multiple loads such as earthquakes, vehicles and wind. Compared with traditional supports, the stiffness and strength of buckling shock absorbers in compression and tension are basically the same. When conducting structural vibration response analysis, the load-deformation relationship of the buckling shock absorber can be processed in the same way as the bilinear hysteresis model of traditional steel structures. The flexible central buckle is a super-flexible structure with large geometric deformation. The static geometric nonlinear effect is very significant, and the force under dynamic action is more complicated.

[0004] In the prior art, when performing dynamic analysis on the flexible central buckle, the flexible central buckle is generally analyzed as equivalent to a truss unit, so that the equivalent truss unit exhibits truss characteristics that can withstand both tension and compression. This is inconsistent with the actual property of the flexible central buckle that can only withstand tension but not compression during analysis, resulting in inaccurate dynamic analysis results. Summary of the invention

[0005] In view of the defects existing in the prior art, the purpose of the present invention is to provide a flexible central buckle dynamic analysis method, which can solve the problem that in the prior art, when performing dynamic analysis on the flexible central buckle, the flexible central buckle is generally analyzed as equivalent to a truss unit, so that the equivalent truss unit exhibits truss characteristics that can withstand both tension and compression, which is inconsistent with the actual property of the flexible central buckle that can only withstand tension but not compression during analysis, resulting in inaccurate dynamic analysis results.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] This scheme provides a flexible central buckle force analysis method, including:

[0008] The cable structure of the flexible central buckle is equivalent to a set of parallel truss units and hook units;

[0009] According to the constitutive relation of the truss unit and the constitutive relation of the hook unit, the mechanical parameters of the truss unit and the mechanical parameters of the hook unit are obtained;

[0010] According to the mechanical parameters of the truss unit and the hook unit, a finite element model of the flexible central buckle is established;

[0011] Based on the finite element model of the flexible central buckle, time history analysis is used to perform dynamic simulation calculations to obtain the force time history curve of the flexible central buckle.

[0012] In some optional schemes, the mechanical parameters of the truss element are obtained according to the constitutive relationship of the truss element, including:

[0013] The stress, equivalent tangent modulus and axial stiffness of the cable are determined based on the chord length, cross-sectional area, elastic modulus, cable force and bulk density of the cable.

[0014] In some alternative schemes, according to the formula: , , , determine the stress, equivalent tangent modulus and axial stiffness of the cable;

[0015] in, is the axial stiffness, is the cross-sectional area of ​​the cable, is the length of the cable, is the equivalent tangent modulus of the cable, is the elastic modulus of the cable, is the bulk density of the rope, is the horizontal projection length of the cable, is the stress of the cable, For the force.

[0016] In some optional schemes, the mechanical parameters of the hook unit are obtained according to the constitutive relationship of the hook unit, including:

[0017] Based on the axial stiffness and the initial spacing of the hooks, the stiffness of the hooks and the cable force are determined.

[0018] In some alternative schemes, according to the formula: , , determine the stiffness of the hook and the cable force;

[0019] in, is the stiffness of the hook, is the displacement of the hook, is the initial clearance of the hook.

[0020] In some optional schemes, before establishing the finite element model of the flexible central buckle, the flexible central buckle is also connected in series with a buckling type shock absorber and a dynamic analysis is performed together.

[0021] In some optional solutions, the flexible central buckle is also connected in series with a buckling type shock absorber and the dynamic analysis is carried out together, including:

[0022] The buckling type shock absorber is equivalent to a hysteresis system and connected in series with the parallel truss unit and hook unit;

[0023] According to the constitutive relation of the hysteresis system, the parameters of the hysteresis system are obtained;

[0024] According to the hysteresis system parameters, the finite element model of the flexible central buckle and the buckling shock absorber is established. Based on the finite element model of the flexible central buckle and the buckling shock absorber, the time history analysis is used to perform dynamic simulation calculation to obtain the force time history curve of the flexible central buckle and the buckling shock absorber.

[0025] In some optional schemes, the hysteresis system parameters are obtained according to the constitutive relation of the hysteresis system, including:

[0026] According to the formula: , , , , , obtain the hysteresis system parameters;

[0027] in, is the preflexion stiffness, is the post-buckling stiffness, is the support yield force, is the yield displacement, is the ratio of stiffness before and after flexion, is the initial yield strength, is the equivalent stiffness, is the equivalent displacement, is the equivalent damping ratio.

[0028] In some optional schemes, the hook unit includes two rods that are arranged in parallel and spaced apart and partially staggered in the length direction. A stop block is provided at one end of the two rods that are staggered with each other. The two stop blocks overlap in the projection part of the length direction of the rods, and are used to hold the two rods together when they move away from each other. The other ends of the two rods are respectively connected to the two ends of the truss unit.

[0029] In some optional solutions, when the truss unit is connected in parallel with the hook unit, both ends are fully rigidly connected.

[0030] Compared with the prior art, the advantages of the present invention are as follows: the present invention equates the cable structure of the flexible central buckle to a group of parallel truss units and hook units; obtains the mechanical parameters of the truss unit and the hook unit according to the constitutive relationship of the truss unit and the constitutive relationship of the hook unit; establishes a finite element model of the flexible central buckle according to the mechanical parameters of the truss unit and the hook unit; and obtains the force time history curve of the flexible central buckle by using time history analysis based on the finite element model of the flexible central buckle. This solves the problem that in the prior art, when performing dynamic analysis on the flexible central buckle, the flexible central buckle is generally analyzed as equivalent to a truss unit, so that the equivalent truss unit exhibits the characteristics of a truss that can be subjected to both tension and compression, which is inconsistent with the actual property of the flexible central buckle that can only be subjected to tension but not compression during analysis, and the dynamic analysis result is inaccurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0032] Figure 1 It is a schematic diagram of the process of the flexible central buckle force analysis method in an embodiment of the present invention;

[0033] Figure 2 Schematic diagram of a dynamic analysis model of a flexible central buckle in an embodiment of the present invention;

[0034] Figure 3 is a schematic diagram of a model of a truss unit in an embodiment of the present invention;

[0035] Figure 4 Schematic diagram of the constitutive relationship of the hook unit in an embodiment of the present invention;

[0036] Figure 5 Schematic diagram of constitutive relationship of the buckling type shock absorber in the embodiment of the present invention;

[0037] In the figure: 1. Hook unit; 2. Truss unit; 3. Lag system. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0039] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0040] like Figure 1 As shown, the present invention provides a flexible central buckle force analysis method, comprising:

[0041] S1: The cable structure of the flexible central buckle is equivalent to a set of parallel truss elements and hook elements.

[0042] S2: According to the constitutive relation of the truss unit and the constitutive relation of the hook unit, the mechanical parameters of the truss unit and the mechanical parameters of the hook unit are obtained.

[0043] S3: According to the mechanical parameters of the truss unit and the hook unit, a finite element model of the flexible central buckle is established.

[0044] S4: Based on the finite element model of the flexible central buckle, time history analysis is used to perform dynamic simulation calculations to obtain the force time history curve of the flexible central buckle.

[0045] In some optional embodiments, obtaining the mechanical parameters of the truss unit according to the constitutive relationship of the truss unit includes:

[0046] The stress, equivalent tangent modulus and axial stiffness of the cable are determined based on the chord length, cross-sectional area, elastic modulus, cable force and bulk density of the cable.

[0047] like Figure 3 The model schematic diagram of the truss unit is shown. In some optional embodiments, according to the formula: , , , determine the stress, equivalent tangent modulus and axial stiffness of the cable;

[0048] in, is the axial stiffness, is the cross-sectional area of ​​the cable, is the length of the cable, is the equivalent tangent modulus of the cable, is the elastic modulus of the cable, is the bulk density of the rope, is the horizontal projection length of the cable, is the stress of the cable, For the force.

[0049] In this embodiment, the geometric nonlinearity of the cable structure is mainly caused by its sag effect, and the equivalent tangent modulus is used to consider the sag effect.

[0050] like Figure 4The figure shows a schematic diagram of the constitutive relationship of the hook unit. In some optional embodiments, according to the constitutive relationship of the hook unit, the mechanical parameters of the hook unit are obtained, including:

[0051] Based on the axial stiffness and the initial spacing of the hooks, the stiffness of the hooks and the cable force are determined.

[0052] In some optional embodiments, according to the formula: , , determine the stiffness of the hook and the cable force;

[0053] in, is the stiffness of the hook, is the displacement of the hook, is the initial clearance of the hook.

[0054] In this embodiment, the initial gap of the hook is 0.

[0055] In some optional embodiments, before establishing the finite element model of the flexible central buckle, the flexible central buckle is also connected in series with a buckling shock absorber and a dynamic analysis is performed together.

[0056] In some optional embodiments, the flexible central buckle is also connected in series with a buckling type shock absorber and dynamic analysis is performed together, including:

[0057] The buckling type shock absorber is equivalent to a hysteresis system and connected in series with the parallel truss unit and hook unit;

[0058] According to the constitutive relation of the hysteresis system, the parameters of the hysteresis system are obtained;

[0059] According to the hysteresis system parameters, the finite element model of the flexible central buckle and the buckling shock absorber is established. Based on the finite element model of the flexible central buckle and the buckling shock absorber, the time history analysis is used to perform dynamic simulation calculation to obtain the force time history curve of the flexible central buckle and the buckling shock absorber.

[0060] like Figure 5 The figure shows a schematic diagram of the constitutive relationship of the buckling type shock absorber. In some optional embodiments, according to the constitutive relationship of the hysteresis system, the hysteresis system parameters are obtained, including:

[0061] According to the formula: , , , , , obtain the hysteresis system parameters;

[0062] in, is the preflexion stiffness, is the post-buckling stiffness, is the support yield force, is the yield displacement, is the ratio of stiffness before and after flexion, is the initial yield strength, is the equivalent stiffness, is the equivalent displacement, is the equivalent damping ratio.

[0063] In this embodiment, the stiffness ratio before and after flexion is 3% to 5%.

[0064] like Figure 2 Shown is the dynamic analysis model of the flexible central buckle, including hook element 1, truss element 2 and hysteresis system 3.

[0065] In some optional embodiments, the hook unit includes two rods that are arranged in parallel and spaced apart and partially staggered in the length direction. A stop block is provided at one end of the two rods that are staggered with each other. The projections of the two blocks in the length direction of the rods overlap, and are used to hold the two rods together when they move away from each other. The other ends of the two rods are respectively connected to the two ends of the truss unit.

[0066] In some optional embodiments, when the truss unit and the hook unit are connected in parallel, both ends are completely rigidly connected.

[0067] In summary, the present invention equates the cable structure of the flexible central buckle to a group of parallel truss units and hook units; obtains the mechanical parameters of the truss unit and the hook unit according to the constitutive relationship of the truss unit and the constitutive relationship of the hook unit; establishes a finite element model of the flexible central buckle according to the mechanical parameters of the truss unit and the hook unit; and based on the finite element model of the flexible central buckle, uses time-history analysis to perform dynamic simulation calculations to obtain the force time-history curve of the flexible central buckle. This solves the problem that in the prior art, when performing dynamic analysis on the flexible central buckle, the flexible central buckle is generally analyzed as equivalent to a truss unit, so that the equivalent truss unit exhibits truss characteristics that can withstand both tension and compression, which is inconsistent with the actual property of the flexible central buckle that can only withstand tension but not compression during analysis, and the dynamic analysis result is inaccurate.

[0068] In the description of the present application, it should be noted that the terms "upper", "lower", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0069] It should be noted that, in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0070] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A flexible central buckle force analysis method, characterized in that: include: The cable structure of the flexible central buckle is equivalent to a set of parallel truss units and hook units; According to the constitutive relation of the truss unit and the constitutive relation of the hook unit, the mechanical parameters of the truss unit and the mechanical parameters of the hook unit are obtained; According to the mechanical parameters of the truss unit and the hook unit, a finite element model of the flexible central buckle is established; Based on the finite element model of the flexible central buckle, the dynamic simulation calculation is carried out by using time history analysis to obtain the force time history curve of the flexible central buckle; The hook unit includes two rods that are arranged in parallel and spaced apart and partially staggered in the length direction. A stopper is provided at one end of the two rods that are staggered with each other. The projections of the two blocks in the length direction of the rods overlap and are used to hold the two rods together when they move away from each other. The other ends of the two rods are respectively connected to the two ends of the truss unit.

2. The flexible central buckle force analysis method according to claim 1, characterized in that: According to the constitutive relationship of the truss element, the mechanical parameters of the truss element are obtained, including: The stress, equivalent tangent modulus and axial stiffness of the cable are determined based on the chord length, cross-sectional area, elastic modulus, cable force and bulk density of the cable.

3. The flexible central buckle force analysis method according to claim 2, characterized in that: According to the formula: , , , determine the stress, equivalent tangent modulus and axial stiffness of the cable; in, is the axial stiffness, is the cross-sectional area of ​​the cable, is the length of the cable, is the equivalent tangent modulus of the cable, is the elastic modulus of the cable, is the bulk density of the rope, is the horizontal projection length of the cable, is the stress of the cable, For the force.

4. The flexible central buckle force analysis method according to claim 3, characterized in that: According to the constitutive relationship of the hook element, the mechanical parameters of the hook element are obtained, including: Based on the axial stiffness and the initial spacing of the hooks, the stiffness of the hooks and the cable force are determined.

5. The flexible central buckle force analysis method according to claim 4, characterized in that: According to the formula: , , determine the stiffness of the hook and the cable force; in, is the stiffness of the hook, is the displacement of the hook, is the initial clearance of the hook.

6. The flexible central buckle force analysis method according to claim 1, characterized in that: Before establishing the finite element model of the flexible central buckle, a buckling type shock absorber was connected in series with the flexible central buckle and dynamic analysis was performed together.

7. The flexible central buckle force analysis method according to claim 6, characterized in that: The flexible central buckle is also connected in series with a buckling type shock absorber and the dynamic analysis is carried out together, including: The buckling type shock absorber is equivalent to a hysteresis system and connected in series with the parallel truss unit and hook unit; According to the constitutive relation of the hysteresis system, the parameters of the hysteresis system are obtained; According to the hysteresis system parameters, the finite element model of the flexible central buckle and the buckling shock absorber is established. Based on the finite element model of the flexible central buckle and the buckling shock absorber, the time history analysis is used to perform dynamic simulation calculation to obtain the force time history curve of the flexible central buckle and the buckling shock absorber.

8. The flexible central buckle force analysis method according to claim 7, characterized in that: According to the constitutive relation of the hysteresis system, the parameters of the hysteresis system are obtained, including: According to the formula: , , , , , obtain the hysteresis system parameters; in, is the preflexion stiffness, is the post-buckling stiffness, is the support yield force, is the yield displacement, is the ratio of stiffness before and after flexion, is the initial yield strength, is the equivalent stiffness, is the equivalent displacement, is the equivalent damping ratio.

9. The flexible central buckle force analysis method according to claim 1, characterized in that: When the truss unit is connected in parallel with the hook unit, both ends are fully rigidly connected.

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