CN113378265B - Bridge dynamic performance evaluation method based on multi-body dynamics - Google Patents
Bridge dynamic performance evaluation method based on multi-body dynamics Download PDFInfo
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Abstract
The method for evaluating the dynamic performance of the bridge based on the multi-body dynamics reflects the bridge information by the structural rigidity and the mode matrix, adopts the mode superposition method, greatly improves the calculation efficiency, by introducing the virtual body and marking points, the position of the point to be loaded can be quickly established, and by endowing the virtual body with moving speed, the method can realize quick establishment of the moving load, is convenient for quickly evaluating the vertical dynamic response, can well evaluate the transverse dynamic response, can conveniently realize the combined action of the moving load and the non-moving load, realizes the superposition calculation of various loads, has high calculation efficiency, simplifies the calculation model, meets the actual application requirement of bridge dynamic analysis under the action of a vehicle in the novel bridge engineering, and is particularly suitable for the condition of quickly comparing the dynamic behavior of the bridge during the selection scheme of the bridge.
Description
Technical Field
The invention belongs to the technical field of bridge dynamics, and relates to a bridge dynamic performance evaluation method based on multi-body dynamics.
Background
The bridge is used as a supporting structure for driving and pedestrians, a certain rigidity requirement is required to be met during design, and dynamic response calculation of the bridge is required when whether the rigidity meets the requirement is judged. The dynamic response calculation of the bridge is always a major key problem concerned in the bridge design and operation stage, and more factors need to be considered: for example, the power problem of a bridge caused by vehicle (pedestrian) load is prominent, and the road bridge can generate excessive dynamic displacement due to the automobile overload problem, so that great discomfort is caused to people on a sidewalk; the railway bridge has high train speed, if the power problem is not considered in design, the possibility of resonance can occur under the operation speed, the linear change of the bridge can be caused by the action of an automobile along with the increasing span of a highway-railway co-constructed bridge, the overlarge power response can further be caused when a train passes through, and the modeling of the coupling influence relationship between the train and the bridge is a complicated process; although the load of a pedestrian bridge is generally gentle, regular pedestrian loads can also cause the bridge to resonate.
With the vigorous development of novel rail transit, such as air rails, magnetic levitation and the like, the design of novel rail transit bridges is more and more, but the power problems of the bridges have no mature experience. In addition to the dynamic bridge deck loads described above, there are a range of other loads such as wind loads, seismic loads, rockfall impact loads, ship crash loads, sea wave loads, and the like. The current analysis method mainly comprises the following steps of (1) solving the dynamic response problem of a bridge under the action of vehicles (pedestrians) according to different loads and different action mechanisms of the loads: firstly, building vehicle models such as automobiles/trains and bridge models, building an interactive dynamic equation through the interaction relationship, and obtaining the dynamic response of the bridge through theoretical solution; secondly, directly establishing a bridge finite element model, and solving by adopting a transient analysis method through force loading in general finite element software.
However, different equation relationships need to be established according to different vehicle topological structures in the mode of establishing the vehicle and bridge models, and the connection structures are different, so that one excitation load carries one analysis model, the universality is poor, and the calculation efficiency is low.
Disclosure of Invention
The invention aims to overcome the defects that external excitation factors faced by the dynamic response calculation of a bridge are increasingly complex as more and more novel rail transit bridges are provided in the prior art, and the existing evaluation method is poor in universality and causes the efficiency of bridge dynamic performance analysis to be low, and provides a bridge dynamic performance evaluation method based on multi-body dynamics.
In order to achieve the above purpose, the invention provides the following technical scheme:
a bridge dynamic performance evaluation method based on multi-body dynamics comprises the following steps:
a. establishing a bridge finite element model to obtain the structural rigidity and the modal matrix of the bridge, and introducing the structural rigidity and the modal matrix of the bridge into a multi-body dynamics analysis platform in a flexible body form to establish a multi-body dynamics model of the bridge;
b. dynamic analysis of bridge deck live load: establishing a plurality of virtual bodies, endowing a corresponding hinge of each virtual body with a moving speed, correspondingly setting a movable first mark point on a bridge floor, keeping the first mark point consistent with the moving track of the corresponding virtual body, applying a corresponding vertical load or load time course to the corresponding first mark point through a first force element, setting simulation time to carry out power analysis, and obtaining a first displacement and a first acceleration of a bridge, wherein the first force element comprises the wheel pressure of an automobile, the wheel pair vertical force of a train or the load of a pedestrian;
c. if the first displacement is smaller than or equal to the first preset displacement and the first acceleration meets the requirement that is smaller than or equal to the first preset acceleration, the vertical dynamic response of the bridge meets the design requirement, and if the horizontal dynamic response of the bridge meets the design requirement, the dynamic performance of the bridge meets the design requirement.
The virtual bodies are small enough to be ignored for the established bridge system, the number of the virtual bodies is determined according to the number of systems applying acting force and the number of contact points between a single system and the bridge, the moving speed is determined according to the design speed of the bridge, and various speeds in the design speed range need to be included during analysis so as to discuss dynamic response of the bridge at different speeds.
The transverse dynamic response of the bridge is mainly other loads due to the non-live load effect, and can be obtained by adopting a mode in the prior art, such as directly establishing a bridge finite element model and carrying out corresponding point loading on non-moving loads.
In the method, the vehicles and other systems are established in a virtual body mode, the vehicles are acted on the bridge in a load mode, the problem of axle coupling does not exist, coupling iteration is not needed between the vehicles and the bridge, and therefore solution is easier; meanwhile, the bridge in the multi-body dynamics analysis platform is a flexible body and contains modal information, the deformation solution of the bridge flexible body is solved by a vibration mode superposition method and is not a rigidity matrix, a damping matrix and a quality matrix in a motion equation any more, and the equation solution efficiency is greatly improved. Meanwhile, compared with the prior art, different complex vehicle models need to be established according to different vehicle topological structures, one train vehicle needs to be simplified into 7 rigid system systems, and then a multi-rigid system is formed to carry out dynamic response.
Preferably, step b further comprises performing kinetic analysis of other loads: establishing a plurality of second mark points in a geodetic coordinate system, wherein the position of each second mark point is overlapped with the position of a third mark point, the third mark points are positioned on the bridge, the second mark points apply corresponding loads or load time courses to the corresponding third mark points through second force elements, simulation time is set for dynamic analysis, and second displacement and second acceleration of the bridge are obtained, wherein other loads comprise wind loads and seismic loads;
in step c, if the second displacement is less than or equal to the second preset displacement and the second acceleration is less than or equal to the second preset acceleration, the lateral dynamic response of the bridge meets the design requirement.
The third mark point is the position of the load acting on the bridge and is selected according to the acting characteristic of the load.
Different from a highway bridge, a railway bridge is designed based on rigidity as a key point, in live load, the maximum vertical deflection of a train is solved in an influence line loading mode by static live load, live load and pedestrian load of the live load, the real load of the train is not considered, and the dynamic impact effect cannot be considered, and when the span of the bridge is large or the structural style is complex, axle coupling dynamic analysis is generally required to evaluate the dynamic response of the bridge. At the moment, the problem of coupling of moving load and non-moving load is encountered, so that the model is established more complexly and has large limitation, because when a motion equation is adopted for solving, the deformation of the bridge is further increased due to the loading of the non-moving load on the bridge, and when the coupling analysis between the vehicle and the bridge is caused, the equation can meet the convergence condition after the equation is iterated for more times under each sub-step, and the calculation of the next step is carried out. The method adopts a multi-body dynamics analysis platform to carry out dynamic analysis under the superposition of moving load and non-moving load, the deformation solution of the bridge with the flexible body is solved by a vibration mode superposition method, and a rigidity matrix, a damping matrix and a mass matrix in a motion equation are not needed, so that the equation solution efficiency is greatly improved, the superposition calculation of various loads is favorably realized, the calculation efficiency is high, and the calculation difficulty is low.
Preferably, in step a, the structural rigidity and the modal matrix of the bridge are obtained by a substructure analysis method. The information of a single unit can be obtained to represent the whole bridge structure, and a multi-body dynamics analysis platform is convenient to introduce.
Preferably, the platform for the multi-body kinetic analysis is SIMPACK or UM.
Compared with the prior art, the invention has the beneficial effects that: the method disclosed by the invention embodies bridge information by a structural rigidity and modal matrix, adopts a modal superposition method, greatly improves the calculation efficiency, can quickly establish the position of a point to be loaded by introducing a virtual body and a mark point, can realize quick establishment of a moving load by endowing the virtual body with a moving speed, is convenient for quickly evaluating vertical dynamic response, can be better suitable for evaluating transverse dynamic response, can be convenient for the combined action of the moving load and a non-moving load, realizes superposition calculation of various loads, has high calculation efficiency and simplified calculation model, is suitable for the actual application requirement of bridge dynamic analysis under the action of a vehicle in novel bridge engineering, and is particularly suitable for the condition of quickly comparing bridge dynamic behaviors in a bridge selection scheme.
Drawings
FIG. 1 is a flow chart of a method for evaluating dynamic performance of a bridge based on multi-body dynamics according to the present invention;
FIG. 2 is a schematic view of the vehicle load of a single automobile in embodiment 1;
FIG. 3 is a vertical displacement time course diagram of each span of the bridge in the embodiment 1 at the vehicle speed of 100 km/h;
FIG. 4 is a vertical acceleration time course diagram of each span of the bridge in the embodiment 1 at the vehicle speed of 100 km/h;
FIG. 5 is a vehicle speed-maximum vertical displacement relationship diagram in a main span of an axle in embodiment 1;
FIG. 6 is a vehicle speed-maximum vertical acceleration map in the main span of the bridge in embodiment 1;
fig. 7 is a schematic view of the bridge seismic load in example 1.
Detailed Description
The present invention will be described in further detail with reference to examples and embodiments. It should be understood that the scope of the above-described subject matter is not limited to the following examples, and any techniques implemented based on the disclosure of the present invention are within the scope of the present invention.
Example 1
A bridge dynamic performance evaluation method based on multi-body dynamics is shown in figure 1 and comprises the following steps:
a. establishing a bridge finite element model to obtain the structural rigidity and the modal matrix of the bridge, and introducing the structural rigidity and the modal matrix of the bridge into a multi-body dynamics analysis platform in a flexible body form to establish a multi-body dynamics model of the bridge;
b. dynamic analysis of bridge deck live load: establishing a plurality of virtual bodies, endowing a corresponding hinge of each virtual body with a moving speed, correspondingly setting a movable first mark point on a bridge floor, keeping the first mark point consistent with the moving track of the corresponding virtual body, applying a corresponding vertical load or load time course to the corresponding first mark point through a first force element, setting simulation time to carry out power analysis, and obtaining a first displacement and a first acceleration of a bridge, wherein the first force element comprises the wheel pressure of an automobile, the wheel pair vertical force of a train or the load of a pedestrian;
c. if the first displacement is smaller than or equal to the first preset displacement and the first acceleration meets the requirement that is smaller than or equal to the first preset acceleration, the vertical dynamic response of the bridge meets the design requirement, and if the horizontal dynamic response of the bridge meets the design requirement, the dynamic performance of the bridge meets the design requirement.
Specifically, taking a 3-span highway-railway dual-purpose continuous steel truss bridge as an example, the dynamic performance evaluation of the bridge under highway automobile load is carried out, a bridge finite element model is established according to a designed bridge scheme, and the structural rigidity and the modal matrix of the bridge are obtained, for example, through a substructure analysis method, the structural rigidity comprises vertical dynamic response and transverse dynamic response. And then, introducing the structural rigidity and the modal matrix of the bridge into a multi-body dynamics analysis platform in a flexible body form to establish a bridge multi-body dynamics model, wherein the multi-body dynamics analysis platform is multi-body dynamics software such as SIMPACK or UM. In the form of a flexible body, namely a body of the bridge system which can deform under the action of external force.
Then, dynamic analysis of bridge deck live load is carried out, a virtual body is established first, and the virtual body is establishedI.e. a volume of sufficiently small mass, e.g. setting the virtual volume to a mass of less than 10-5kg, so that the influence of the virtual bodies on a general bridge system can be ignored, the number of the virtual bodies is determined according to the number of systems applying acting force and the number of contact points between a single system and a bridge, if 15 cars are considered, one virtual body is correspondingly arranged for each pair of wheel pairs and used for simulating car load, 75 virtual bodies are arranged in total by taking a truck comprising 5 wheel pairs as an example, the single truck is represented by 5 virtual bodies, and the distance between the virtual bodies is determined according to the wheel pair distance in the specification, as shown in fig. 2 (the virtual bodies are not shown). Because each body in the multi-body dynamics analysis platform is provided with the corresponding hinge, the moving speed is given to the corresponding hinge according to the design speed per hour of the bridge and the analysis requirement. The method includes the steps of correspondingly setting movable first mark points on a bridge deck, enabling the first mark points to be consistent with motion tracks of corresponding virtual bodies, and enabling the virtual bodies to apply corresponding vertical loads or load time courses to the corresponding first mark points through first force elements, wherein the first mark points are in 5 circles in fig. 2, the vertical forces of fixed values are taken as examples, and the fixed values of different wheel pairs take values according to specifications, such as numerical values shown in fig. 2. According to the embodiment, the first force element is road automobile load, and the first force element is automobile wheel pressure. If the virtual bodies are train loads or pedestrian loads, the number of the virtual bodies is correspondingly set according to the number of wheel pairs of a carriage of the train and the number of the carriages, the first force element corresponds to the wheel pair vertical force of the train, different complex vehicle models do not need to be established according to topological structures of different vehicle types, if the virtual bodies are maglev trains, the uniform force can be replaced by a mode of concentrating the vertical force, the number of the virtual bodies is automatically selected, and then the vertical force is uniformly distributed on all the virtual bodies; and for the pedestrian load, establishing the number of virtual bodies according to the pedestrian number distribution characteristics of the bridge, wherein the first force element corresponds to the pedestrian load. The setting method of the virtual body aims at the highway and railway dual-purpose bridge and the novel track bridge, is convenient and quick to model, and is convenient for analyzing the automobile load, the train load and the like independently or in combination. And then, setting simulation time to carry out dynamic analysis, and obtaining a first displacement and a first acceleration of the bridge. In the embodiment, the hinges of the virtual body are respectively endowed with the vehicle speeds of 20, 40, 60, 80 and 100km/h,for example, when the automobile speed is 100km/h, the displacement time interval and the acceleration time interval (0-6 s) of each span of the bridge are respectively shown in fig. 3 and 4, and the maximum displacement and the maximum acceleration of each span of the bridge under different automobile speeds are respectively shown in fig. 5 and 6.
If the first displacement is less than or equal to the first predetermined displacement and the first acceleration is less than or equal to the first predetermined acceleration, i.e. when the corresponding maximum vertical displacement of 23.45mm at 40km/h meets the specification requirement and the corresponding maximum vertical acceleration of 0.034m/s at 60km/h2And if the standard requirement is met, the vertical dynamic response of the bridge meets the design requirement.
Meanwhile, if the transverse dynamic response of the bridge meets the design requirement, the dynamic performance of the bridge meets the design requirement. The transverse dynamic response of the bridge is mainly other loads such as wind load and earthquake load due to the non-live load effect, and can be obtained by adopting a mode in the prior art, such as directly establishing a bridge finite element model and carrying out corresponding point loading on the non-moving load.
And if the vertical dynamic response or the transverse dynamic response of the bridge is not satisfied, readjusting the structural parameters of the bridge, repeating the steps a-c, and analyzing the vertical dynamic response or the transverse dynamic response again.
Of course, dynamic analysis may also be performed in a multi-body dynamic platform to determine the lateral dynamic response of the bridge. Establishing a plurality of second mark points in the geodetic coordinate system, wherein the position of each second mark point is overlapped with the position of a third mark point, the third mark points are positioned on the bridge, and the second mark points apply corresponding loads or load time courses to the corresponding third mark points through second force elements. If the earthquake load is the earthquake load, the position of the third mark point is arranged at the bottom of a pier or at a support, the number of the third mark points is determined according to the number of the piers, the second mark point which is overlapped with the position of the third mark point is arranged on the geodetic coordinate system, and then the horizontal force is applied by the second force element instead of the load time course. As shown in fig. 7, wherein the second and third marker points, the second force element is shown with arrows representing Fy and Fz. And also can be wind load, the position of the third mark point is arranged at the beam, the pier or the tower, and the number is determined according to the specific arrangement mode. And then setting simulation time to carry out dynamic analysis to obtain a second displacement and a second acceleration of the bridge, wherein if the second displacement is less than or equal to a second preset displacement and the second acceleration meets the requirement of the second preset acceleration, the transverse dynamic response of the bridge meets the design requirement.
In the method, the vehicles and other systems are established in a virtual body mode, the vehicles are acted on the bridge in a load mode, the problem of axle coupling does not exist, coupling iteration is not needed between the vehicles and the bridge, and therefore solution is easier; meanwhile, the bridge in the multi-body dynamics analysis platform is a flexible body and contains modal information, the deformation solution of the bridge flexible body is solved by a vibration mode superposition method and is not a rigidity matrix, a damping matrix and a quality matrix in a motion equation any more, and the equation solution efficiency is greatly improved. Meanwhile, compared with the prior art, different complex vehicle models need to be established according to different vehicle topological structures, one train vehicle is simplified into 7 rigid system systems, and then a multi-rigid system is formed to carry out dynamic response, the method has the advantages that the contact between the vehicle or the pedestrian and the bridge is represented by the virtual body, the real contact force between the vehicle or the pedestrian and the bridge is represented by the force element of the mark point on the virtual body and the bridge, the original multi-rigid system can be replaced by only one rigid body, the system freedom degree is greatly reduced, the calculation efficiency is obviously improved, the initial evaluation of the bridge dynamic response is facilitated, the method is particularly suitable for bridge dynamic analysis of railway bridges and highway bridges under the action of the vehicle, is particularly suitable for carrying out rapid comparison and selection during bridge selection schemes, and can facilitate the combined action of moving load and non-moving load, the superposition calculation of various loads is realized, and the calculation efficiency is high.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the present invention shall be covered thereby. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (4)
1. A bridge dynamic performance evaluation method based on multi-body dynamics is characterized by comprising the following steps:
a. establishing a bridge finite element model to obtain the structural rigidity and the modal matrix of the bridge, and introducing the structural rigidity and the modal matrix of the bridge into a multi-body dynamics analysis platform in a flexible body form to establish a multi-body dynamics model of the bridge;
b. dynamic analysis of bridge deck live load: establishing a plurality of virtual bodies, endowing a corresponding hinge of each virtual body with a moving speed, correspondingly setting a movable first mark point on a bridge floor, keeping the first mark point consistent with the moving track of the corresponding virtual body, applying a corresponding vertical load or load time course to the corresponding first mark point by a first force element, setting simulation time to carry out power analysis by the first force element, and obtaining a first displacement and a first acceleration of the bridge, wherein the virtual body is a body with a small mass which can be ignored for an established bridge system;
c. if the first displacement is smaller than or equal to the first preset displacement and the first acceleration meets the requirement that is smaller than or equal to the first preset acceleration, the vertical dynamic response of the bridge meets the design requirement, and if the horizontal dynamic response of the bridge meets the design requirement, the dynamic performance of the bridge meets the design requirement.
2. The method of claim 1, wherein in step b, further comprising performing a kinetic analysis of the other loads: establishing a plurality of second mark points in a geodetic coordinate system, wherein the position of each second mark point is respectively superposed with the position of one third mark point, the third mark points are positioned on the bridge, the second mark points apply corresponding horizontal loads or load time courses to the corresponding third mark points through second force elements, simulation time is set for dynamic analysis, and second displacement and second acceleration of the bridge are obtained, wherein other loads comprise wind loads and earthquake loads;
in step c, if the second displacement is less than or equal to the second preset displacement and the second acceleration is less than or equal to the second preset acceleration, the lateral dynamic response of the bridge meets the design requirement.
3. The method of claim 1, wherein in step a, the structural stiffness and mode matrix of the bridge are obtained by a substructure analysis method.
4. A method according to any one of claims 1 to 3 wherein the platform for multi-body kinetic analysis is SIMPACK or UM.
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| CN111829738A (en) * | 2020-07-20 | 2020-10-27 | 唐堂 | Impact load-based bridge bearing capacity lightweight evaluation method |
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