CN108090283B - Finite element analysis method for tunnel-vehicle coupled vibration under dynamic load of train - Google Patents
Finite element analysis method for tunnel-vehicle coupled vibration under dynamic load of train Download PDFInfo
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Abstract
The invention provides a finite element analysis method for tunnel-vehicle coupled vibration under dynamic load of a train, and relates to the field of automatic auxiliary design. The method comprises the following steps: (1) performing static analysis on the full bedrock three-dimensional finite element model before tunnel excavation; (2) establishing a three-dimensional finite element model of a bedrock-lining-bedrock coupling system based on the vehicle speed and the coupling theory; (3) eliminating the initial displacement of the coupling system by using an initial stress method; (4) automatically simulating the load of the train running time; (5) and automatically applying train running time load to the coupling system and calculating. The method uses a programmer in software and is based on the principle of coupling of vehicle speed and finite elements, the dynamic load of the train along with the time-space change is automatically applied, the modeling program is simplified, the calculation workload is reduced, and the method is suitable for the safety performance identification problem of the shield tunnel under the action of the dynamic load of the train.
Description
Technical Field
The invention relates to the field of automatic auxiliary design, in particular to a finite element analysis method for tunnel-vehicle coupling vibration under dynamic load of a train.
Background
With the continuous and rapid development of national economy, the contradiction between the continuously expanding population number and the increasingly worsened traffic conditions is increasingly prominent. Under huge traffic pressure, rail traffic lines such as subways and inter-city trains are sharply increased. The train can produce the dynamic load along with time and space change in the tunnel process of passing through to the tunnel lining through the basement bed. The influence of the dynamic load of the train on a bedrock-lining-bedbed coupling system is an important index for evaluating the safety performance of the tunnel.
The common characteristics of the tunnel engineering are that the length of a line is large, the uncertainty factor is large, the period for obtaining structural response through a field test is long, and the data discreteness is large. Finite element time-course analysis is the most convenient method for analyzing such time-course response problems. The main operation method is that based on a bedrock-lining-bedrock coupling model, a train dynamic load function is introduced to accurately simulate the vibration effect of a train, power time-course analysis is carried out, and the stress and deformation effect of a coupling system are extracted.
Because the tunnel structure has long line and large model, the size of the model grid needs to be determined by combining the running speed of the train, and the scale of the model is reduced by a coupling technology; and the train load has long time and fast space change, and the change of the load along with time and space cannot be simulated by depending on the manual loading of a user interface. At present, although documents are introduced for a train load exciting force function determined by referring to a rail irregularity model of the british railway technical center, a specific method for establishing a coupling system model based on the function and a system description of an automatic train time-course load application technology are not provided in a finite element analysis environment.
Disclosure of Invention
The technical problem solved by the invention is as follows: the invention provides a finite element analysis method for tunnel-vehicle coupled vibration under a dynamic load of a train, which solves the problems of model establishment and automatic train time load application under the coupling technology by relying on the programming function of an ANSYS software APDL language.
The technical scheme of the invention is as follows:
a finite element analysis method for tunnel-vehicle coupled vibration under dynamic load of a train comprises the following steps:
step 1: determining the type, shape, material attribute and the like of a model unit by bed rock layering and material, establishing a full-bed rock three-dimensional finite element model 1 before tunnel excavation, carrying out static analysis under the action of gravity, and storing the node stress and deformation results of the full model into a file 1 by an iswrite command;
the purpose of this analysis is to extract the initial stress and initial displacement under the action of gravity of the lining peripheral rock stratum, eliminate the initial displacement of gravity of the bedrock-lining-bedrock coupled system in the subsequent step 3 by the initial stress balance method, and retain the initial stress of the lining peripheral rock stratum. During modeling, original rock stratums are filled in the annular lining and the excavation part corresponding to the hollow tunnel in the lining, and solid and grid segmentation is performed.
Step 2: additionally storing the full bedrock three-dimensional model 1 established in the step 1 to generate a new model, sequentially excavating a soil body, establishing a lining and a bedbed, establishing a viscoelastic artificial boundary to form a bedrock-lining-bedbed coupling system three-dimensional finite element model 2, loading an APDL language self-programming program, and realizing the connection of the tunnel lining and the bedbed based on a node coupling theory;
and step 3: aiming at a three-dimensional finite element model 2 of the bedrock-lining-bedbed coupled system, an initial stress balancing method is used, the stress and deformation results of the bedrock nodes at the periphery of the lining layer in a file 1 are called by using an isfile command, the accumulated deformation of the bedrock-lining-bedbed coupled system under the action of gravity is eliminated, and the initial stress on the contact surface of a rock layer and a lining is introduced;
and 4, step 4: loading an APDL language self-programming program, and simulating the train running time load based on the rail irregularity exciting force function;
and 5: and loading an APDL language self-programming program, applying train running time load to the coupling system and calculating.
Further, in the step 2, the train load acting point is on the foundation bed node. In order to ensure that the moving load of the train is accurately applied along the longitudinal axis of the tunnel, the grid size of the foundation bed is controlled along the longitudinal direction of the tunnel to be not more than upsilon.DELTA.t, wherein upsilon is the running speed of the train, and DELTA t is the loading time step length. However, the coupling system has rich covering structure and long line, and if the lining and the foundation bed are subjected to common node processing, the modeling and calculation cost is increased greatly, so that the lining grid can be relatively extensive. Loading APDL language self-programming program, realizing the connection of coarse and fine grids between the tunnel lining and the foundation bed based on the node coupling theory, and the specific method comprises the following steps:
(1) selecting all nodes of the lining as an array cq, obtaining the total number of the nodes cqnum by a get command, and defining the array cqcount by a dim command;
(2) searching the node with the minimum number in the cq array, embedding a ndnext command in the do loop, searching nodes with adjacent numbers one by one, and sequentially storing the nodes into the array cqcount;
(3) selecting all nodes in a contact surface between a base bed and a lining as an array jc, obtaining the total number jcnum of the nodes by a get command, and defining the array jccount by a dim command;
(4) searching the node with the minimum number in the jc array, embedding a ndnext command in the do loop, searching the nodes adjacent to the number one by one, and sequentially storing the nodes in the jccount array;
(5) selecting all nodes of the cqcount array, embedding a nnear command in the do loop, searching nodes close to all nodes of the jccount array from 1 to jcnum, and excluding one cqcount node correspondingly;
(6) and coupling the base bed nodes and the lining nodes one by one from 1 to jcnum by embedding cq coupling commands in the do loop.
Further, in the step 4, the function of the excitation force of the track irregularity is considered as:
P(t)＝P0+P1sinω1t+P2sinω2t+P3sinω3t (1)
P1、P2、P3according to the driving stability, the line additional load and the vibration load under the waveform abrasion control condition, the calculation formula is as follows:
ωifor the vehicle round frequency, the calculation formula is:
ωi＝2πυ/li(i＝1,2,3) (3)
in the formula (1), P0The vehicle static load is obtained; in the formula (2), M0Is the unsprung mass of the train, aiIs a typical rise; in the formula (3), upsilon is the train running speed liTypical wavelength of geometric irregularity curve; according to the stability of the vehicle, wheni＝50m,ai16mm, wheni＝20m,ai9mm, wheni＝10m,ai5mm, according to the line additional load condition, when li＝5m,ai2.5mm, wheni＝2m,ai0.6mm, wheni＝1m,ai1.3mm, wear according to wave form, wheni＝0.5m,ai0.1mm, wheni＝0.02m,ai＝0.005mm；
Loading an APDL language self-programming program, and simulating the train running time load based on the rail irregularity exciting force function, wherein the specific method comprises the following steps:
(1) defining dynamic load parameters of the train, including the total length s of the tunnel, the distance d between the front axle and the rear axle of the train, the running speed upsilon of the train, the total running time ttime of the train in the tunnel, the loading time step length time, the total loading step number ti and the loading step i, wherein the dynamic load parameters of the train comprise the total running time ttime of the train in the tunnel, the loading time step length time
(2) Defining an array force1, implementing do cycle from loading steps 1 to ti, and defining the exciting force of any front wheel of the train along with time according to formulas (1) to (3) as follows:
force1(i)＝P0+P1sinω1(i·time)+P2sinω2(i·time)+P3sinω3(i.time) and when (i.time-s/ν) > 0, force1(i) ═ 0;
(3) defining an array force2, implementing do cycle from loading step 1 to ti, and defining the exciting force of any rear wheel of the train along with time according to formulas (1) to (3) as follows:
force2(i)＝P0+P1sinω1(i·time-d/υ)+P2sinω2(i·time-d/υ)+P3sinω3(i·time-d/υ)，
and if (i.time-d/upsilon) < 0, force2(i) ═ 0.
Further, the step 5 of loading the APDL language self-programming program and applying a train operation time-course load changing with time and space to the coupling system includes the following specific steps:
(1) selecting two rows of longitudinal nodes rolled by double rows of wheels on the upper edge of the foundation bed, and defining the running position of a front wheel as an array dist1 and the running position of a rear wheel as an array dist 2;
(2) implementing do loop from loading steps 1 to ti, corresponding to the ith loading step, respectively searching node numbers closest to the front wheel position and the rear wheel position by a node command, returning to arrays n1(i) and n2(i), selecting nodes n1(i) and n2(i), and respectively loading force1(i) and force2(i) by an F command, wherein the front wheel running position is dist1(i) ═ upsilon · i, the rear wheel running position is dist2(i) ═ d;
(3) and sequentially completing the loading of the train time-course load in all time steps, and carrying out time-course analysis on the coupled vibration system.
Compared with the prior art, the invention has the beneficial effects that: the invention realizes the technology of establishing a finite element model of a tunnel system by using a coupling theory and automatically simulating the influence of train exciting force. Based on a finite element coupling technology, a nesting program for coupling the foundation bed and the lining nodes is created, and the model calculation scale is greatly reduced; based on a time-course analysis principle, a nested program for automatically applying the train exciting force along with the time-space change is created, and the quick addition of the dynamic load of the train can be realized. The method is characterized in that ANSYS software is developed for the second time aiming at the problem of the dynamic performance analysis of the tunnel structure, the scale of the model is controlled by an automatic input means, and the calculation cost is reduced. The technology can be used for directly analyzing the power of various train transportation lines by engineering technicians.
Drawings
FIG. 1 is a flow chart of finite element analysis of tunnel-vehicle coupled vibration under dynamic load of a train.
FIG. 2 is a schematic diagram of a finite element model of a bedrock-lining-bedrock coupled system.
FIG. 3 is a schematic diagram of a lining-bed coupled finite element model.
Fig. 4 is a schematic diagram of the time course of the exciting force of the front wheel of the train.
Fig. 5 is a vertical displacement cloud chart of the bedrock-lining-bedrock coupled system with the distance t being 10 s.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the flow of implementing the present invention using ANSYS software is as follows:
step 1: establishing a three-dimensional finite element model of the whole bedrock before tunnel excavation, and carrying out static analysis: determining the type, shape, material attribute and the like of a model unit by bed rock layering and material, establishing a bed rock three-dimensional finite element model 1, performing static analysis under the action of gravity, and storing the node stress and deformation result of the full model into a file 1 by an iswrite command.
Step 2: establishing a three-dimensional finite element model of a bedrock-lining-bedbed coupling system, and realizing the connection of the tunnel lining and the bedbed based on a node coupling rationality: another new model is generated by the bedrock three-dimensional model 1, the soil body is excavated in sequence, the lining and the bedbed are established, the viscoelastic artificial boundary is established, and a bedrock-lining-bedbed coupling system three-dimensional finite element model 2 is formed, as shown in figure 2; controlling the size of a grid of a base bed along the longitudinal direction of the tunnel to be not more than upsilon.DELTA t, wherein upsilon is the running speed of the train, and DELTA t is the loading time step; loading an APDL language self-programming program, respectively defining node sets in contact surfaces of a base bed and a lining, embedding a cq coupling command in do circulation, and realizing coupling processing of base bed nodes with fine grids and lining nodes with coarse grids, as shown in FIG. 3.
And step 3: and (3) calling a static calculation result of a bedrock model by using an initial stress balance method, and eliminating initial displacement under the action of the gravity of the bedrock-lining-bedbed coupling system: aiming at a three-dimensional finite element model 2 of a bedrock-lining-bedrock coupled system, the stress and deformation results of bedrock nodes at the periphery of a lining layer in a file 1 are called by using an isfile command, the accumulated deformation under the action of the gravity of a rock stratum is eliminated, and the initial stress on the contact surface of the rock stratum and the lining is introduced.
And 4, step 4: based on the track irregularity excitation force function, the train operation time-course load is simulated: according to the formulas (1) - (3), constructing a train exciting force function by using the static load of a vehicle, the unsprung mass of the train, the running speed of the train, the typical rise and the typical wavelength of a geometric irregularity curve; loading APDL language self-programming program, inputting tunnel total length, distance between front axle and rear axle of the train, train running speed, total running time of the train in the tunnel, loading time step length and total loading step number in a parameterization mode, implementing do cycle program aiming at all time steps, and defining exciting force of front wheels and rear wheels of each time step, as shown in figure 4.
And 5: applying train running time load to the coupling system and calculating: loading an APDL language self-programming sequence, implementing a do cycle program aiming at all time steps, determining the positions of front and rear wheel loading points at each time step, and applying front and rear wheel exciting forces at the nearest nodes of wheel loading; loading of train travel loads in all time steps is completed in sequence, time course analysis is carried out on the coupled vibration system, and a time course analysis result is obtained, as shown in fig. 5.
Example (c): automatic modeling and calculation of tunnel-vehicle coupled vibration system
Step 1: and establishing a three-dimensional finite element model of the whole bedrock before tunnel excavation, and carrying out static analysis. The 550m long underground tunnel is used as an analysis object, the buried depth of the tunnel is 23m, the diameter of the tunnel is 6.1m, bedrocks are respectively a clay layer and a medium sand layer from top to bottom, the model unit type is determined to be solid45, and the tunnel material is concrete C50. Giving material attributes, establishing a three-dimensional finite element model 1 of the bedrock, carrying out static analysis under the action of gravity, and storing the node stress and deformation results of the full model into a file 1 by using an iswrite command.
Step 2: and establishing a three-dimensional finite element model of a bedrock-lining-bedbed coupling system, and realizing the connection of the tunnel lining and the bedbed based on a node coupling rationality. A new model is additionally stored and generated by the bedrock three-dimensional model 1, soil bodies are excavated in sequence, lining and a bedbed are established, a combination 14 unit simulated viscoelastic artificial boundary is established, and a bedrock-lining-bedbed coupling system three-dimensional finite element model 2 is formed; controlling the grid size of a base bed along the longitudinal direction of the tunnel to be not more than upsilon.DELTA.t as 0.56m by the train running speed upsilon as 200km/h and the loading time step length delta t as 0.01 s; and loading an APDL language self-programming program, respectively defining node sets jc and cq in contact surfaces of the base bed and the lining, and embedding a cq coupling command in do circulation to realize coupling processing of the base bed nodes with fine grids and the lining nodes with coarse grids.
And step 3: and (3) using an initial stress balance method, calling a static calculation result of a bedrock model, and eliminating initial displacement under the action of the gravity of the bedrock-lining-bedbed coupling system. Aiming at a three-dimensional finite element model 2 of a bedrock-lining-bedbed coupled system, the stress and deformation results of the residual bedrock after excavation at the periphery of a lining layer in a file 1 are called by using an isfile command, the accumulated deformation under the action of the gravity of a rock stratum is eliminated, and the initial stress on the contact surface of the rock stratum and the lining is introduced.
And 4, step 4: train operation time-course load simulation based on rail irregularity exciting force function. According to the formulas (1) to (3), the vehicle static load P080kN, unsprung mass M of train0750kg, 200km/h as train running speed upsilon, and typical wavelength and typical rise of geometric irregularity curve l1＝10m,a1＝5mm，l2＝2m,a2＝0.6mm，l3＝0.5m,a3Constructing a train excitation force function as 0.1 mm; loading an APDL language self-programming program, inputting 550m of the total length of a tunnel, 17.5m of the distance between the front axle and the rear axle of a train, 200km/h of the running speed of the train, about 10s of the total running time of the vehicle in the tunnel, 10s of the loading time step length and 1000 of the loading total step number in a parameterization manner, implementing a do cycle program aiming at all time steps, and defining front and rear wheel excitation force arrays for 1(i) and for 2(i) before each time step.
And 5: and applying train running time load to the coupling system and calculating. Loading an APDL language self-programming sequence, implementing a do loop program for all time steps, determining positions dist1(i) and dist2(i) of loading points of a front wheel and a rear wheel at each time step, searching the most adjacent nodes by a node command, and respectively applying exciting forces of the front wheel and the rear wheel by an F command; and sequentially completing the loading of the train time-course load in all time steps, and carrying out time-course analysis on the coupled vibration system.
The method can realize the numerical analysis of the tunnel safety performance under the influence of the dynamic load of the train, and the method for considering the coupling modeling and automatically applying the dynamic load of the train along with the time-space change based on the speed is not available in other analysis methods. The above examples are merely examples for clarity of illustration and are not intended to limit the scope of the embodiments. Modifications may be made without departing from the principles of the invention and these modifications are to be considered within the scope of the invention and all such implementations are not necessarily or exclusively exhaustive.
Claims (5)
1. A finite element analysis method for tunnel-vehicle coupled vibration under dynamic load of a train is characterized by comprising the following steps: the method comprises the following steps:
step 1: determining the type, shape and material attribute of a model unit by bed rock layering and material, establishing a full-bed rock three-dimensional finite element model 1 before tunnel excavation, carrying out static analysis under the action of gravity, and storing the node stress and deformation results of the full model into a file 1 by an iswrite command;
step 2: additionally storing the full bedrock three-dimensional model 1 established in the step 1 to generate a new model, sequentially excavating a soil body, establishing a lining and a bedbed, establishing a viscoelastic artificial boundary to form a bedrock-lining-bedbed coupling system three-dimensional finite element model 2, loading an APDL language self-programming program, and realizing the connection of the tunnel lining and the bedbed based on a node coupling theory;
and step 3: using an initial stress balancing method, using an isfile command to call in the stress and deformation results of the bedrock nodes at the periphery of the lining layer in the file 1, eliminating the accumulated deformation under the action of the gravity of a bedrock-lining-bedrock coupling system, and introducing the initial stress on the contact surface of the rock layer and the lining;
and 4, step 4: loading an APDL language self-programming program, and simulating the train running time load based on the rail irregularity exciting force function;
and 5: and loading an APDL language self-programming program, applying train running time load to the coupling system and calculating.
2. The finite element analysis method of tunnel-vehicle coupled vibration under dynamic load of train as claimed in claim 1, wherein: in the step 2, in order to ensure that the moving load of the train is accurately applied along the longitudinal axis of the tunnel, the grid size of the foundation bed is controlled along the longitudinal direction of the tunnel to be not more than upsilon.DELTA t, wherein upsilon is the running speed of the train, DELTA t is the loading time step length, APDL language self-programming programs are loaded, and the connection of coarse and fine grids between the tunnel lining and the foundation bed is realized based on the node coupling theory, and the specific method comprises the following steps:
(1) selecting all nodes of the lining as an array cq, obtaining the total number of the nodes cqnum by a get command, and defining the array cqcount by a dim command;
(2) searching the node with the minimum number in the cq array, embedding a ndnext command in the do loop, searching nodes adjacent to the node with the minimum number one by one, and sequentially storing the nodes in the array cqcount;
(3) selecting all nodes in a contact surface between a base bed and a lining as an array jc, obtaining the total number jcnum of the nodes by a get command, and defining the array jccount by a dim command;
(4) searching the node with the minimum number in the jc array, embedding a ndnext command in the do loop, searching the nodes adjacent to the number one by one, and sequentially storing the nodes in the jccount array;
(5) selecting all nodes of the cqcount array, embedding a nnear command in the do loop, searching nodes close to all nodes of the jccount array from 1 to jcnum, and excluding one cqcount node correspondingly;
(6) and coupling the base bed nodes and the lining nodes one by one from 1 to jcnum by embedding cq coupling commands in the do loop.
3. The finite element analysis method of tunnel-vehicle coupled vibration under dynamic load of train as claimed in claim 1, wherein: in the step 4, the function of the exciting force considering the track irregularity is as follows:
P(t)＝P0+P1sinω1t+P2sinω2t+P3sinω3t (1)
P1、P2、P3according to the driving stability, the line additional load and the vibration load under the waveform abrasion control condition, the calculation formula is as follows:
ωifor the vehicle round frequency, the calculation formula is:
ωi＝2πυ/li(i＝1,2,3) (3)
in the formula (1), P0The vehicle static load is obtained; in the formula (2), M0Is the unsprung mass of the train, aiIs a typical rise; in the formula (3), upsilon is the train running speed liTypical wavelength of geometric irregularity curve; according to the stability of the vehicle, wheni＝50m,ai16mm, wheni＝20m,ai9mm, wheni＝10m,ai5mm, according to the line additional load condition, when li＝5m,ai2.5mm, wheni＝2m,ai＝0.6mmWhen l isi＝1m,ai1.3mm, wear according to wave form, wheni＝0.5m,ai0.1mm, wheni＝0.02m,ai＝0.005mm；
Loading an APDL language self-programming program, and simulating the train running time load based on the rail irregularity exciting force function, wherein the specific method comprises the following steps:
(1) defining train dynamic load parameters including the total length s of the tunnel, the distance d between the front axle and the rear axle of the train, the running speed upsilon of the train, the total running time ttime of the train in the tunnel, the loading time step length time, the total loading step number ti and the loading step i, wherein the parameters include the total length s of the tunnel, the distance d between the front axle and the rear axle of the train, the running speed ups
(2) Defining an array force1, implementing do cycle from loading step 1 to ti, and defining the exciting force of any front wheel of the train along with time according to formulas (1) to (3) as follows:
force1(i)＝P0+P1sinω1(i·time)+P2sinω2(i·time)+P3sinω3(i.time) and if (i.time-s/ν) > 0, force1(i) ═ 0;
(3) defining an array force2, implementing do cycle from loading step 1 to ti, and defining the exciting force of any rear wheel of the train along with time according to formulas (1) to (3) as follows:
force2(i)＝P0+P1sinω1(i·time-d/υ)+P2sinω2(i·time-d/υ)+P3sinω3(i · time-d/ν), and if (i · time-d/ν) < 0, force2(i) ═ 0.
4. The finite element analysis method of tunnel-vehicle coupled vibration under dynamic load of train as claimed in claim 1, wherein: step 5, loading an APDL language self-programming program, and applying train operation time-course load changing along with time and space to the coupling system, wherein the specific method comprises the following steps:
(1) selecting two rows of longitudinal nodes rolled by double rows of wheels on the upper edge of the foundation bed, and defining the running position of a front wheel as an array dist1 and the running position of a rear wheel as an array dist 2;
(2) implementing do loop from loading steps 1 to ti, corresponding to the ith loading step, respectively searching node numbers closest to the front wheel position and the rear wheel position by a node command, returning to arrays n1(i) and n2(i), selecting nodes n1(i) and n2(i), and respectively loading force1(i) and force2(i) by an F command, wherein the front wheel operating position is dist1(i) ═ upsilon · i, the rear wheel operating position is dist2(i) ═ upsilon · i-d;
(3) and sequentially completing the loading of the train time-course load in all time steps, and carrying out time-course analysis on the coupled vibration system.
5. The finite element analysis method of tunnel-vehicle coupled vibration under dynamic load of train as claimed in claim 1, wherein: and 3, aiming at the three-dimensional finite element model 2 of the bedrock-lining-bedrock coupled system, using an initial stress balance method, and using an isfile command to call in the stress and deformation results of the bedrock nodes at the periphery of the lining layer in the file 1, eliminating the accumulated deformation under the action of the gravity of the rock stratum, and introducing the initial stress on the contact surface between the rock stratum and the lining.
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