CN111797459B - Construction method of ballasted track-bridge dynamic coupling model - Google Patents
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Abstract
The invention discloses a construction method of a dynamic coupling model of a ballasted track and a bridge. The method comprises the following steps: establishing a ballast bed discrete element model reflecting the complex appearance and contact relation of the ballast by using a discrete unit method, wherein the model is used for representing a particle unit stacking structure, the contact force of particles and a coupling surface and an equivalent node transplanting load; establishing a continuous medium sleeper finite element model and a bridge finite element model by utilizing a multi-body finite element method, wherein the continuous medium sleeper finite element model and the bridge finite element model are used for representing a continuous body grid structure, node displacement deformation, surface node position coordinates and unit connection relations; and constructing a ballasted track-bridge dynamic coupling model based on a discrete element and multi-body finite element coupling method. The invention fully considers the irregular shape of the railway ballast at the microscopic level and the mutual occlusion stacking relation, and simultaneously can reflect the interaction between the macroscopic railway ballast bed and the upper and lower structures, thereby realizing the fine simulation of the complex mechanical behavior of the ballast track on the bridge under the action of train load.
Description
Technical Field
The invention relates to the technical field of track construction, in particular to a construction method of a dynamic coupling model of a ballasted track-bridge.
Background
In the construction process of the high-speed railway, in order to avoid the fertile farmland and save the land, the construction policy of replacing the road with a bridge is advocated, so that the mass of the high-speed railway on the bridge is huge. For example, the bridge foundation of the jinghu high-speed rail accounts for more than 80% of the whole line. The ballasted track and the ballastless track are main track structures of the high-speed railway, and compared with the ballasted track, the ballasted track has the advantages of low manufacturing cost, small vibration noise, strong adaptability, convenient maintenance and repair and the like, so that the high-speed railway on the bridge in China mainly uses the ballasted track, and the ballasted track is more necessarily selected especially in long and large bridge sections. However, the ballast bed is used as a discrete structure, the contact relation among particles and the mechanical behavior of the ballast bed are extremely complex, and the track panel-ballast bed-bridge is used as a multilayer heterostructure, so that the interlayer mechanical mechanism is difficult to ascertain. How to realize the fine simulation of the multilayer structure of the ballast track and the bridge, and the definition of the mechanical characteristics of the train under the action of the load is the key for ensuring the safe operation of the train.
Along with the development of computer technology, numerical simulation has become the mainstream method of theoretical research of ballasted tracks on bridges, and has the advantages of low cost, easy variable regulation and control, visual mechanism, and the like. Currently, common numerical simulation methods include a finite element method and a discrete element method.
The finite element method is mainly studied for continuous media, and the basic idea is to divide a continuous body into units with different shapes such as triangles, quadrilaterals and the like, and adjacent units are connected in a node mode. In the calculation process, firstly, constructing a unit function to calculate and analyze the displacement and mechanical characteristics of the unit; then, constructing equivalent node load to realize the transmission of forces between units; and finally, forming the whole load vector of the structure by all node loads according to a certain coding sequence, and calculating the structural displacement by combining boundary conditions. The finite element method has been widely used in a variety of engineering fields since its proposal. In consideration of the unique advantages of the finite element method in the continuous body simulation, a large number of students build a ballasted track-bridge model by using the method. For example, melaku establishes a ballasted track-bridge finite element model to analyze the effect of interactions between multiple layers on bridge dynamic response. Li Shaozheng (railway standard design, 2019,63 (5): 11-16) and the like establish a turnout-bridge-pier integrated finite element model for researching nonlinear resistance and related influence factors of a ballasted track seamless turnout on a bridge. Chen Haorui ("longitudinal force research of seamless lines on bridge under different load patterns", railway construction, 2020 (2): 3) and the like establish a ballasted track-bridge model based on the method, and research on the influence rule of train load on the longitudinal force of the seamless lines on bridge. However, the existing ballasted track-bridge model established based on the finite element method can reflect the continuous medium characteristics of sleepers and bridges, but cannot accurately represent the characteristic of the shot body of the ballasted track bed.
The discrete unit method is provided based on the principle of molecular dynamics at the earliest, and is mainly researched aiming at the bulk medium. The basic idea is that the bulk material is discretized into a plurality of rigid body units with certain mass, each unit is mutually independent, the stress and the motion condition among each unit at each moment of the microcosmic layer are obtained by a time-step iteration mode on the premise of meeting Newton's second law and contact relation, and then the integral mechanical and kinematic relation of the microcosmic layer material is obtained. The discrete element method does not need to meet the deformation coordination condition among the units in the finite element method, and the particle units move mutually independently, so that the intrinsic properties of the bulk aggregate can be accurately simulated. Discrete unit processes have played an irreplaceable key role in the field of discrete body particles since their proposal. Considering the dispersion medium characteristics of the ballast track bed, a large number of students establish a ballast track-bridge model by adopting a discrete unit method. Through analysis, the ballasted track model on the bridge established based on the discrete unit method can effectively reflect the dispersion medium characteristics of the ballasted track bed, but simplifies the sleeper and the bridge into a fixed wall body, so that the interaction among the multilayer structures is difficult to truly simulate.
The existing numerical simulation method for the ballasted track on the bridge mainly has the following defects: 1) The finite element method regards the ballast bed as a homogeneous whole, performs unitization processing by considering the geometric outline of the ballast bed, and satisfies displacement continuous relation among units, and although a complete track-bridge system model can be established, the instantaneous mechanical state of the ballast bed under the action of load can only be studied from a macroscopic level, and the occlusion relation of ballast particles of the ballast bed of a dispersion ballast bed and the plastic deformation caused by the long-term action of load can not be simulated. 2) The discrete element method only focuses on the local ballast bed structure, considers the complex appearance of the ballast, and researches the accumulated influence of long-term load on the change of the ballast bed state, but has a certain deviation with the mechanical state of the ballast bed on a real bridge due to the difficulty in considering the interaction of the ballast bed and the upper and lower structures.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a construction method of a dynamic coupling model of a ballasted track-bridge, which is established based on a discrete element and multi-body finite element coupling method, so that the irregular shape of railway ballasts at a microscopic level and the mutual occlusion stacking relationship are fully considered, and the interaction between a macroscopic railway bed and an upper and lower structure can be reflected, thereby realizing the fine simulation of the complex mechanical behavior of the ballasted track on the bridge under the action of train load.
The invention provides a construction method of a dynamic coupling model of a ballasted track and a bridge. The method comprises the following steps:
establishing a ballast track bed discrete element model reflecting the complex appearance and contact relation of the ballast by using a discrete element method, wherein the model is used for representing a particle unit stacking structure, the contact force of particles and a coupling surface and an equivalent node transplanting load;
establishing a continuous medium sleeper finite element model and a bridge finite element model by utilizing a multi-body finite element method, wherein the continuous medium sleeper finite element model and the bridge finite element model are used for representing a continuous body grid structure, node displacement deformation, surface node position coordinates and unit connection relations;
and constructing a ballasted track-bridge dynamic coupling model based on a discrete element and multi-body finite element coupling method.
In one embodiment, constructing the ballasted track-bridge dynamic coupling model based on the discrete element and multi-body finite element coupling method comprises the following steps:
based on the coupling of the discrete element and the multi-body finite element, adopting bidirectional coupling solution, and in the first direction, the discrete element transmits the contact force and the contact position between the ballast bed and the bridge to the multi-body finite element, and the contact force and the contact position are equivalently transplanted to the corresponding bridge deck grid node as the mechanical boundary condition analyzed by the multi-body finite element method; in the second direction, the multi-body finite element transmits bridge deformation information to the discrete element discrete ballast bed.
In one embodiment, in the two-way coupling solution, the contact force of particles acting on the coupling surface is converted into equivalent node force, meanwhile, the multi-body finite element bridge is meshed, and bridge outer surface wall units with the same node positions are generated in discrete elements based on the bridge outer surface node coordinate information after the meshing, so that the same meshing mode of the coupling bridge deck part in the multi-body finite element and the discrete elements is realized.
In one embodiment, a tetrahedral entity division mode is adopted for the multi-body finite element bridge division grid, and the wall body grids in the corresponding discrete elements are all triangular grids.
In one embodiment, the ballasted track bed discrete meta-model is built according to the following steps:
three-dimensional laser scanning is adopted to reconstruct the appearance of the railway ballast, and sphere units with the number more than 8 are adopted to simulate railway ballast with complex appearance;
and building a ballast bed discrete element model by layering ballast particles with different shapes.
In one embodiment, after converting the contact force of the particles on the coupling face to an equivalent node force, further comprising: and updating the node coordinates after the nodes of the multi-body finite element are deformed under stress, and updating the node information on the outer surface of the multi-body finite element at a new moment to each node of the discrete element coupling shell wall unit so as to update the coordinate positions of the coupling wall unit in the discrete element and finish one-time bidirectional coupling data transmission.
In one embodiment, the sleeper finite element model adopts a rigid body to simulate sleeper structure, and the bridge finite element model adopts a railway single-line box girder.
Compared with the prior art, the invention has the advantages that the ballasted track-bridge coupling model provided by the invention can truly reflect the continuous medium characteristics of the sleeper and the bridge, so that the interaction between the ballasted track and the bridge multilayer heterostructure can be accurately calculated, and therefore, the model provided by the invention has higher calculation accuracy. Compared with the ballasted track-bridge finite element model, the ballasted track-bridge dynamic coupling model provided by the invention can effectively characterize the granule characteristics of a ballasted track bed, and truly simulate the complex appearance of the ballasts and the contact and engagement relationship among particles. Therefore, the coupling model provided by the invention has higher precision and more comprehensive functions.
Other features of the present invention and its advantages will become apparent from the following detailed description of exemplary embodiments of the invention, which proceeds with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a simulation model of the appearance and refinement of a ballast particle according to one embodiment of the present invention;
FIG. 2 is a finite element model of a tie according to one embodiment of the invention;
FIG. 3 is a finite element model of a bridge according to one embodiment of the invention;
FIG. 4 is a flow chart of a discrete element and finite element flexible body coupling calculation according to one embodiment of the present invention;
FIG. 5 is a triangle cell diagram according to one embodiment of the invention;
FIG. 6 is a ballasted track-bridge dynamic coupling model according to one embodiment of the invention;
FIG. 7 is a graphical illustration of a comparison of model simulation and measured sleeper acceleration in accordance with an embodiment of the present invention.
Detailed Description
Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that: the relative arrangement of the components and steps, numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise.
The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses.
Techniques, methods, and apparatus known to one of ordinary skill in the relevant art may not be discussed in detail, but are intended to be part of the specification where appropriate.
In all examples shown and discussed herein, any specific values should be construed as merely illustrative, and not a limitation. Thus, other examples of exemplary embodiments may have different values.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further discussion thereof is necessary in subsequent figures.
Briefly, the construction method of the dynamic coupling model of the ballasted track and the bridge provided by the invention comprises the following steps: firstly, establishing a ballasted ballast bed model reflecting complex appearance and contact relation of a ballast by using a discrete unit method; establishing a continuous medium sleeper and a bridge model by utilizing a multi-body finite element method; and establishing a ballasted track-bridge dynamic coupling model based on a discrete element and multi-body finite element coupling method. Hereinafter, a ballast track bed discrete element model, a sleeper and bridge finite element model and a ballast track-bridge dynamics coupling model will be respectively described.
1. Discrete element model for ballast bed
In one embodiment, a three-dimensional laser scanning method is used for reconstructing the appearance of the railway ballast in three dimensions. The three-dimensional coordinates, the reflectivity, the texture and other information of a large number of dense points on the outer surface of the measured object can be rapidly obtained by scanning the two placing positions of the railway ballast by 360 degrees except the bottom surface. The scanner automatically synthesizes the two scanning results by adopting a spatial profile overlapping method, thereby realizing three-dimensional reconstruction of the real appearance of the railway ballast in a computer. Preferably, the calculation accuracy and efficiency of the discrete element model of the ballast bed are comprehensively considered, and the ballasts with complex shapes are simulated by adopting spherical units with the number more than 8, as shown in fig. 1. Further, a ballast bed discrete element model is built through layered accumulation of ballast particles with different shapes. For example, the width of the bottom surface of the model is 4.5m, the thickness of the ballast bed is 0.35m, and the slope of the ballast bed is 1:1.75, the pile height of the ballast shoulder is 0.15m, and the material parameters are shown in table 1.
TABLE 1 ballast parameters
2. Finite element model for sleeper and bridge
In one embodiment, a continuous medium model of ties, bridges, etc. is built using a multi-body finite element method.
For the sleeper model, under the action of train load, the deformation of the sleeper is negligible relative to the settlement of the whole ballasted track. Thus, preferably, the sleeper structure is simulated using a rigid body, as shown in FIG. 2, with the main parameters shown in Table 2.
Table 2 sleeper model parameters
For the bridge model, in one embodiment, the bridge uses railway single line box girders, as shown in fig. 3. The bridge material was C55 concrete and the material parameters are shown in table 3.
TABLE 3 bridge model parameters
3. Dynamic coupling model for ballasted track and bridge
1) Principle of coupling discrete elements and multi-body finite elements
The invention adopts a bidirectional coupling method based on the coupling of discrete elements and multi-body finite elements, and the key of coupling solution is that the contact force and the contact position between a track bed and a bridge are accurately and equivalently transplanted to the corresponding bridge deck grid nodes as the mechanical boundary conditions analyzed by the multi-body finite element method, and the bridge deformation is transferred to the discrete track bed of the discrete element part. The coupling transition boundary is expressed as a wall unit in discrete elements and is a shell grid unit formed by triangular one-sided surfaces. In finite element analysis, load is typically applied to the nodes, but in coupling solutions the contact forces on the grid face of the discrete element shell wall element cells tend not to be on the grid nodes. Because the particle sizes of the particles contacting the coupling surface are different, a very small grid is required if the grid cell nodes are selected as the contact points, and a plurality of contact points may exist on each triangular piece grid, which makes the analysis process very complex and inaccurate. It is necessary to convert the contact force of the particles acting on the coupling surface into an equivalent node force and acquire the equivalent node force by adopting a shape function interpolation method and the like. Meanwhile, the multi-body finite element bridge is firstly meshed, a tetrahedron entity meshing mode (the wall body meshes in the corresponding discrete elements are triangular meshes) is adopted, and bridge outer surface wall units with the same node positions are generated in the discrete elements based on bridge outer surface node coordinate information after meshing, so that the mesh meshing mode of the coupling bridge deck part in the multi-body finite element and the discrete elements is realized, and the complexity of transmitting contact force to the finite element nodes by the coupling transition boundary is greatly simplified. The calculation flow of the coupling of the two is shown in fig. 4, wherein the finite element method is shown as a finite element flexible body method, and the calculation process comprises the steps of establishing a continuous body grid structure, acquiring node displacement deformation, acquiring surface node position coordinates and unit connection relation. The discrete element method comprises the steps of establishing a particle unit stacking structure, acquiring contact force between particles and a coupling surface, and acquiring an equivalent node transplanting load. The bi-directional coupling between the finite element method and the discrete element method is embodied in: the discrete element method transmits the particle acting force information to the finite element method and is used as a mechanical boundary condition for finite element method analysis; the finite element method transmits wall displacement speed information to the discrete element method so that the discrete element method can consider interaction between the ballast bed and the upper and lower structures.
The following derives the equivalent migration of contact forces acting on the faces of the triangular mesh to the cell nodes.
In fig. 5, a triangular unit of surface acted on by a particle M is shown, the x-y-z coordinate system is centered on the triangular unit, and the x-y plane coincides with the plane of the triangular unit, which is the local coordinate system of the unit plane.
The relationship of the local coordinate system X-Y-Z to the global coordinate system X-Y-Z is expressed as:
{x,y,z} T ＝[T trans,1 ]{X,Y,Z} T (1)
in the formula (1) [ T ] trans,1 ]Is a 3 x 3 conversion matrix.
For the bending response of the shell and the panel, each node has six degrees of freedom, including three displacements and three angles. Displacement matrix { U } 6×1 Can be expressed as:
{U} 6×1 ＝[N] 6×18 {A} 18×1 (2)
in the formula (2) [ N ]] 6×18 Is a triangle unit node shape function matrix, { A } 18×1 Is the node displacement.
{U} 6×1 and {A}18×1 Can be expressed as:
{U} T ＝{u x ,u y ,u z ,θ x ,θ y ,θ z } (3)
{A} T ＝{u xi ,u yi ,u zi ,θ xi ,θ yi ,θ zi ............,u xk ,u yk ,u zk ,θ xk ,θ yk ,θ zk } (4)
in the formula ,ux ,u y ,u z ,θ x ,θ y ,θ z The displacements of the triangular units in six different degrees of freedom, including linear displacement and angular displacement, respectively. u (u) xi ,u yi ,u zi ,θ xi ,θ yi ,θ zi ............,u xk ,u yk ,u zk ,θ xk ,θ yk ,θ zk The displacements of the three nodes (i, j, k) constituting the triangle unit in six degrees of freedom, respectively.
The external virtual work generated by the contact force is:
in the formula (3), the amino acid sequence of the compound,for the contact force vector acting at the contact point M, M is the number of particle contact points acting on the triangular unit. Substitution can be obtained:
in the formula (6) [ N ] m ]Is a matrix of functions shaped in relation to the point of contact m of the particles with the surface element. Then the equivalent node forces of the local coordinate system are according to the above equationCan be expressed as:
thus, the contact forces in the local and global coordinate systems can be related by coordinate transformation, i.e.:
in the formula (8) [ T ] trans,2 ]Is a 6 x 6 conversion matrix.
Also, the equivalent node forces in the local coordinate system and the global coordinate system can be related by the following equation (10):
in the formula (11) [ T ] trans,3 ] 18×18 Is an 18 x 18 conversion matrix.
Substituting equation (7) and equation (8) into equation (10) yields a node force for calculating the global coordinate system, which is equivalent to the contact force in the global coordinate system.
Through the process, the conversion from the contact force of the particles and the triangular surface units to the equivalent node force of each node is completed. And updating the node coordinates after the nodes of the multi-body finite element are deformed under stress, and updating the node information on the outer surface of the multi-body finite element at a new moment to each node of the discrete element coupling shell wall unit so as to update the coordinate positions of the coupling wall unit in the discrete element and finish one-time bidirectional coupling data transmission. It should be noted that, in the coupling calculation, the time-step division of the discrete element and the multi-volume finite element model is a multiple relationship, and since the discrete element needs a smaller time step to ensure the convergence of the calculation, the discrete element model usually calculates several time steps to perform data exchange with the multi-volume finite element once.
2) Establishing a dynamic coupling model of the ballasted track and the bridge
According to the above establishment of each substructure model, in one embodiment, the ballasted track-bridge dynamics model established based on the discrete element and multi-body finite element coupling method is shown in fig. 6. The model established in the mode can effectively reflect the dispersion medium characteristics of the ballast bed and simulate the interaction among the multilayer structures.
In order to further verify the effect of the invention, external force load is applied to the ballasted track-bridge coupling model, and the dynamic characteristics of the train running through the ballasted track and bridge multilayer structure are calculated and analyzed. The accuracy and reliability of the model are verified by comparing with the vibration acceleration of the sleeper actually measured on site.
1) Train load
The invention realizes fitting of on-site actually measured dynamic pressure on the pillow through self-programming external force function. The expression of the train load applied to the rail bearing groove at one end of the sleeper is as follows:
wherein n is the number of carriages, F z Is the axle weight, v is the train running speed, t is the train running time, y jk The relative position of the wheel relative to the sampling point is χ, which is a load factor, expressed as follows.
2) Contrast verification
When the train runs on the bridge with the span of 32m at the speed of 30km/h, the vibration acceleration of the ballasted track sleeper on the bridge is actually measured on site, as shown in fig. 7 (a), and the amplitude is 2.49g. Parameters of the ballasted track-bridge coupling model are adjusted to enable the calculation working conditions to be the same as the actual working conditions on site, and the obtained sleeper vibration acceleration is shown in fig. 7 (b) and has the amplitude of 2.23g. The comparison analysis shows that the two are only different by 0.26g, and the accuracy of the coupling model of the invention is verified.
In summary, the ballasted track-bridge model based on the coupling of the discrete elements and the multi-body finite elements can simultaneously consider complex shapes and contact relations of the ballast particles and interaction among the multi-layer heterostructures, and improves the calculation accuracy and the function of the model. According to the invention, the ballast bed model is built by adopting a discrete unit method, the complex appearance of ballast particles can be accurately simulated, sleeper and bridge models are built by adopting multi-body finite elements, and further interlayer displacement and stress information are transmitted based on coupling of the sleeper and the bridge models, so that the fine simulation of interaction among multi-layer structures is realized. The invention can provide scientific theoretical guidance for construction, operation and maintenance of the ballasted track on the high-speed railway bridge.
The present invention may be a system, method, and/or computer program product. The computer program product may include a computer readable storage medium having computer readable program instructions embodied thereon for causing a processor to implement aspects of the present invention.
The computer readable storage medium may be a tangible device that can hold and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include the following: portable computer disks, hard disks, random Access Memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static Random Access Memory (SRAM), portable compact disk read-only memory (CD-ROM), digital Versatile Disks (DVD), memory sticks, floppy disks, mechanical coding devices, punch cards or in-groove structures such as punch cards or grooves having instructions stored thereon, and any suitable combination of the foregoing. Computer-readable storage media, as used herein, are not to be construed as transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., optical pulses through fiber optic cables), or electrical signals transmitted through wires.
The computer readable program instructions described herein may be downloaded from a computer readable storage medium to a respective computing/processing device or to an external computer or external storage device over a network, such as the internet, a local area network, a wide area network, and/or a wireless network. The network may include copper transmission cables, fiber optic transmissions, wireless transmissions, routers, firewalls, switches, gateway computers and/or edge servers. The network interface card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium in the respective computing/processing device.
Computer program instructions for carrying out operations of the present invention may be assembly instructions, instruction Set Architecture (ISA) instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, c++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions may be executed entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (for example, through the Internet using an Internet service provider). In some embodiments, aspects of the present invention are implemented by personalizing electronic circuitry, such as programmable logic circuitry, field Programmable Gate Arrays (FPGAs), or Programmable Logic Arrays (PLAs), with state information for computer readable program instructions, which can execute the computer readable program instructions.
Various aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer-readable program instructions.
These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable medium having the instructions stored therein includes an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.
The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer, other programmable apparatus or other devices implement the functions/acts specified in the flowchart and/or block diagram block or blocks.
The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. It is well known to those skilled in the art that implementation by hardware, implementation by software, and implementation by a combination of software and hardware are all equivalent.
The foregoing description of embodiments of the invention has been presented for purposes of illustration and description, and is not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the various embodiments described. The terminology used herein was chosen in order to best explain the principles of the embodiments, the practical application, or the technical improvements in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.
Claims (7)
1. A construction method of a dynamic coupling model of a ballasted track and a bridge comprises the following steps:
establishing a ballast track bed discrete element model reflecting the complex appearance and contact relation of the ballast by using a discrete element method, wherein the model is used for representing a particle unit stacking structure, the contact force of particles and a coupling surface and an equivalent node transplanting load;
establishing a continuous medium sleeper finite element model and a bridge finite element model by utilizing a multi-body finite element method, wherein the continuous medium sleeper finite element model and the bridge finite element model are used for representing a continuous body grid structure, node displacement deformation, surface node position coordinates and unit connection relations;
constructing a ballasted track-bridge dynamic coupling model based on a discrete element and multi-body finite element coupling method;
the construction of the ballast track-bridge dynamic coupling model based on the coupling method of the discrete element and the multi-body finite element comprises the following steps:
based on the coupling of the discrete element and the multi-body finite element, adopting bidirectional coupling solution, and in the first direction, the discrete element transmits the contact force and the contact position between the ballast bed and the bridge to the multi-body finite element, and the contact force and the contact position are equivalently transplanted to the corresponding bridge deck grid node as the mechanical boundary condition analyzed by the multi-body finite element method; in the second direction, the multi-body finite element transmits bridge deformation information to a discrete-element discrete ballast bed;
in the two-way coupling solution, the contact force of particles acting on a coupling surface is converted into equivalent node force, meanwhile, a multi-body finite element bridge is meshed, and bridge outer surface wall units with the same node positions are generated in discrete elements based on the bridge outer surface node coordinate information after the meshing, so that the same meshing mode of a coupling bridge deck part in the multi-body finite element and the discrete elements is realized;
wherein, in the coupling solving process, the converting the contact force of the particles acting on the coupling surface into the equivalent node force includes:
step S51, establishing a corresponding relation between a local coordinate system and a global coordinate system of the triangle unit, wherein the relation is expressed as follows:
{x,y,z} T ＝[T trans,1 ]{X,Y,Z} T ，[T trans,1 ]is a 3 x 3 conversion matrix;
step S52, for the bending response of the shell and the panel, each node has six degrees of freedom including three displacements and three angles, displacement matrix { U } 6×1 Expressed as:
{U} 6×1 ＝[N] 6×18 {A} 18×1
wherein ,[N]6×18 Is a triangle unit node shape function matrix, { A } 18×1 The displacement is the node displacement;
step S53, the external virtual work generated by the contact force is expressed as:
wherein ,for the contact force vector acting at contact point M, M is the number of particle contact points acting on the triangular unit, substituted to:
wherein ,[Nm ]A matrix of functions in the form of a shape, associated with the particles and with the contact points m;
step S54, equivalent node forces of the local coordinate systemExpressed as:
step S55, linking the contact force under the local coordinate system and the global coordinate system through coordinate transformation, which is expressed as:
wherein ,[Ttrans,2 ]Conversion matrix of 6×6:
step S56, the equivalent node forces in the local coordinate system and the global coordinate system are related according to the following formula:
step S57, obtaining an equivalent node force in the global coordinate system, expressed as:
2. the method of claim 1, wherein the multi-body finite element bridge division grid adopts a tetrahedral entity division mode, and the wall grids in the corresponding discrete elements are all triangular grids.
3. The method of claim 1, wherein the ballasted track bed discrete meta-model is built according to the steps of:
three-dimensional laser scanning is adopted to reconstruct the appearance of the railway ballast, and sphere units with the number more than 8 are adopted to simulate railway ballast with complex appearance;
and building a ballast bed discrete element model by layering ballast particles with different shapes.
4. The method of claim 1, wherein after converting the contact force of the particle on the coupling face to an equivalent node force, further comprising: and updating the node coordinates after the nodes of the multi-body finite element are deformed under stress, and updating the node information on the outer surface of the multi-body finite element at a new moment to each node of the discrete element coupling shell wall unit so as to update the coordinate positions of the coupling wall unit in the discrete element and finish one-time bidirectional coupling data transmission.
5. The method of claim 1, wherein the sleeper finite element model employs a rigid body to simulate sleeper structure and the bridge finite element model employs a railway single line box girder.
6. A computer readable storage medium having stored thereon a computer program, wherein the program when executed by a processor realizes the steps of the method according to any of claims 1 to 5.
7. A computer device comprising a memory and a processor, on which memory a computer program is stored which can be run on the processor, characterized in that the processor implements the steps of the method according to any one of claims 1 to 5 when the program is executed.
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| CN112668087B (en) * | 2021-01-11 | 2022-06-14 | 武汉理工大学 | Ballasted track modeling analysis method and system based on finite element and discrete element coupling |
| CN112364553B (en) * | 2021-01-13 | 2021-06-25 | 西南交通大学 | Method for evaluating coupling of finite element-discrete element of surface layer seepage corrosion of ballastless track foundation bed of high-speed rail |
| CN113128102B (en) * | 2021-03-25 | 2023-10-03 | 北京交通大学 | Method for quickly constructing multi-scale analysis model of ballast invaded matters of railway ballast bed |
| CN113392531B (en) * | 2021-06-23 | 2024-03-08 | 北京交通大学 | Numerical simulation method for humidifying ballasted ballast bed |
| CN113642075B (en) * | 2021-08-12 | 2023-12-22 | 北京交通大学 | Optimization method for ballasted ballast bed-large machine tamping depth |
| CN116427221B (en) * | 2023-05-11 | 2024-05-10 | 武汉大学 | Rapid nondestructive testing method for degradation state of ballast bed |
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