CN113821865B - Finite element generation method, equipment and medium for three-dimensional stress of pull rod and dowel bar - Google Patents
Finite element generation method, equipment and medium for three-dimensional stress of pull rod and dowel bar Download PDFInfo
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Abstract
The invention relates to the technical field of stress simulation of road engineering, and discloses a finite element generation method, equipment and a medium for three-dimensional stress of a pull rod and a dowel bar, wherein the method comprises the following steps: constructing a three-dimensional finite element model of the pavement structure according to preset reference parameters; calculating the joint rigidity of the three-dimensional finite element model; calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness; according to the spring stiffness, constructing spring connection between plate side nodes in a three-dimensional finite element model so as to preliminarily simulate the connection form of a pull rod and a transmission rod; the spring connections between the board side nodes are converted to connector connections to further simulate tie rods and dowel bars and generate three-way stresses for tie rods and dowel bars. By adopting the method, the three-dimensional stress of the longitudinal dowel bar at the transverse seam of the carriageway, the longitudinal dowel bar at the transverse seam of the road shoulder and the transverse pull bar at the longitudinal seam of the carriageway-road shoulder cement slab can be analyzed, so that the deep analysis of the stress of the cement pavement structure is facilitated, and the design of the pull bar and the dowel bar is optimized.
Description
Technical Field
The invention relates to the technical field of stress simulation of road engineering, in particular to a finite element generation method of three-dimensional stress of a pull rod and a dowel bar, computer equipment and a computer readable storage medium.
Background
When the structural mechanics of the cement pavement is calculated, in order to obtain a more accurate finite element numerical calculation result, the simulation of a dowel bar between a cement plate and a cement plate transverse joint and a pull bar between longitudinal joints is particularly important.
At present, the methods for simulating the pull rod and the dowel bar of the cement board mainly comprise the following three methods:
firstly, a spring unit is adopted for simulation. The method needs to calculate the spring stiffness of each node position through a formula, the simulation is accurate, the manual adding workload is large, the spring in a finite element program can only output stress along the spring direction, and if the stress condition of the cement plate pull rod and the dowel bar in three directions (the driving direction, the depth direction and the cross section direction) under different working conditions is to be analyzed, the force cannot be used.
Secondly, arranging a virtual joint filling material. The method can avoid the problem that the units on the two sides are pierced in the stress process, but various simulation parameters of the virtual joint filling material are difficult to determine, the finite element setting is very complicated, and the involved nonlinear contact problem can not obtain a calculation result due to convergence.
And thirdly, defining the contact surface relation of the two cement boards as a bonding slippage state. However, the method is difficult to determine accurate stiffness parameters through an indoor test method, meanwhile, the interlayer problem also belongs to the contact problem, and the nonlinear contact problem also often cannot obtain a calculation result due to convergence.
Therefore, the existing methods cannot accurately simulate the pull rod and the dowel bar of the cement slab, and are not beneficial to deep analysis of the stress of the cement pavement structure and optimal design of the pull rod and the dowel bar.
Disclosure of Invention
The invention aims to solve the technical problem of providing a finite element generation method, computer equipment and a computer readable storage medium for the three-way stress of a pull rod and a dowel bar, which can analyze the three-way stress of a longitudinal dowel bar at a transverse seam of a roadway, a longitudinal dowel bar at a transverse seam of a road shoulder and a transverse pull rod at a longitudinal seam of a roadway-road shoulder cement slab.
In order to solve the technical problem, the invention provides a finite element generation method of three-dimensional stress of a pull rod and a dowel bar, which comprises the following steps: constructing a three-dimensional finite element model of the pavement structure according to preset reference parameters; calculating the joint stiffness of the three-dimensional finite element model; calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness; constructing spring connection between plate side nodes in the three-dimensional finite element model according to the spring stiffness so as to preliminarily simulate the connection form of a pull rod and a transmission rod, wherein the spring between the plate side nodes adopts the spring stiffness; and converting the spring connection between the side nodes of the plates into connector connection so as to further simulate a pull rod and a dowel bar and generate three-way stress of the pull rod and the dowel bar, wherein the three-way stress refers to traffic direction stress, depth direction stress and cross section direction stress.
As an improvement of the above, the step of calculating the joint stiffness of the three-dimensional finite element model includes: calculating the shear stiffness of the concrete to the support of the force transmission rod; calculating the self shearing spring stiffness of the dowel bar; calculating the combined shear stiffness of the dowel bars according to the shear stiffness and the shear spring stiffness; and calculating the rigidity of the joint per unit length according to the combined shear rigidity.
As an improvement of the above, the step of calculating the joint stiffness of the three-dimensional finite element model includes: according to the formula DCI = [4 beta ]3/(2+βω)]EdIdCalculating the shear stiffness DCI of the concrete for the force transmission rod support, wherein beta is the relative stiffness of the force transmission rod and the concrete, omega is the width of a seam gap, and EdIs the elastic modulus, I, of dowel bars between cement concrete slabsdThe moment of inertia of the cross section of the dowel bar between the cement concrete slabs; according to the formula C = EdId/[ω3(1+φ)]Calculating the shearing spring stiffness C of the dowel bar, wherein phi is an intermediate parameter; calculating the combined shear stiffness D of the dowel according to the formula D =1/(1/DCI + 1/12C); and calculating the joint rigidity q of the joint unit length according to the formula q = D/s, wherein s is the distance between dowel bars between the cement concrete slabs.
As an improvement to the above, according to formula Id=πd4/64, calculating the section inertia moment I of the dowel bar between the cement concrete slabsdWherein d is the diameter of a dowel bar between cement concrete slabs; according to the formula β = [ Kd/(4E)dId)]1/4Calculating the relative rigidity beta of the dowel bar and the concrete, wherein K is the supporting modulus of the concrete to the dowel bar; according to the formula phi = 12EdId/(GdAdω2) Calculating an intermediate parameter phi, where Gd=Ed/[2(1+μd)] , Ad=0.225πd2,GdIs shear modulus, mu, of dowel bars between cement concrete slabsdIs the Poisson's ratio of the dowel bar between cement concrete slabs AdIs the effective cross-sectional area of the dowel bar between the cement concrete slabs.
As an improvement of the above solution, the step of calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness comprises: respectively calculating the plate angle spring stiffness of a target rod body, wherein the target rod body comprises a longitudinal dowel bar at a transverse seam of a roadway, a longitudinal dowel bar at a transverse seam of a road shoulder and a transverse pull rod at a longitudinal seam of the roadway-road shoulder cement plate; respectively calculating the plate edge spring stiffness of the target rod body; the in-plate spring rates of the target rods are calculated separately.
As an improvement of the above solution, the step of calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness comprises: according to formula k’ 1 =q×L/[4×(nr-1)(nc-1)]Calculating the plate-angle spring stiffness k of the target rod body’ 1Wherein q is the joint stiffness, L is the crack length, nrNumber of row of board side nodes corresponding to target rod body, ncThe number of the row of the board side nodes corresponding to the target rod body; according to formula k’ 2 =2×k’ 1Calculating the plate edge spring stiffness k of the target rod body’ 2(ii) a According to formula k’ 3 =4×k’ 1Calculating the spring rate k in the plate of the target rod body’ 3。
As an improvement of the above solution, the step of constructing the spring connection between the board side nodes in the three-dimensional finite element model according to the spring stiffness to preliminarily simulate the connection form of the pull rod and the transmission rod comprises: meshing the three-dimensional finite element model; generating a first modeling file after grid division; renumbering the board side nodes according to a preset sequencing rule, a Python programming mode and the first modeling file to generate a second modeling file; according to the second modeling file, writing a spring batch generation program in a Python programming mode to generate a third modeling file; copying the content of the third modeling file to the corresponding spring connection position in the second modeling file to generate a fourth modeling file; according to the fourth modeling file, all board side nodes which are renumbered are connected through springs, wherein the springs between the board side nodes adopt the spring stiffness.
As an improvement of the above solution, the step of converting the spring connection between the board side nodes into a connector connection to further simulate the tie rod and the dowel bar, and generating the three-way stress of the tie rod and the dowel bar comprises: according to the fourth modeling file, writing a conversion program in a Python programming mode to convert the spring connection between the board side nodes into a connector; and extracting corresponding connectors for analysis to generate three-way stress of the longitudinal dowel bars at the transverse seams of the carriageway, the longitudinal dowel bars at the transverse seams of the road shoulder and the transverse tie bars at the longitudinal seams of the carriageway-road shoulder cement boards under different working conditions.
Correspondingly, the invention further provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to realize the steps of the finite element generation method of the three-way stress of the pull rod and the dowel bar.
Accordingly, the present invention further provides a computer readable storage medium, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the above method for generating finite elements of tie rod and dowel pin three-way stress.
The invention combines a three-dimensional finite element model, theoretical joint stiffness, equivalent spring stiffness, spring simulation and connection simulation to form a method capable of analyzing the three-way stress of a longitudinal dowel bar at a transverse seam of a carriageway, a longitudinal dowel bar at a transverse seam of a road shoulder and a transverse pull bar at a longitudinal seam of a carriageway-road shoulder cement board, and specifically comprises the following steps:
according to the method, the joint stiffness and the spring stiffness of the three-dimensional finite element model are accurately calculated by adopting a theoretical method, so that a good theoretical basis is provided for the simulation of the pull rod and the dowel bar;
the invention is based on the principle of section rigidity equivalence, and the total rigidity of the spring unit is equivalent to the total rigidity of the joint section area, so that rigidity calculation algorithms of three different positions of a plate corner, a plate edge and a plate are established, and the accuracy is high;
the method adopts Python to compile a spring batch generation program, has high efficiency, can realize the setting of a plurality of layers of seam sections and any number of spring units, and has high simulation precision;
the invention also adopts Python to compile the program of converting springs into connectors in batches, can form the three-dimensional stress of the dowel bars between the cement boards and the transverse joints of the cement boards and the tie bars between the longitudinal joints, is convenient for deeply analyzing the stress of the cement pavement structure and optimally designing the tie bars and the dowel bars.
Drawings
FIG. 1 is a flow chart of an embodiment of a method for generating finite elements of three-dimensional stress of a tie rod and a dowel bar according to the present invention;
FIG. 2 is a schematic diagram of a board side node of the present invention;
FIG. 3 is a schematic diagram of the nomenclature of a single cement panel of the present invention;
FIG. 4 is a schematic diagram of the spring connection of the present invention after the board side nodes have been renumbered;
FIG. 5 is a schematic view of the spring connection of the cement board to the cement board according to the present invention;
FIG. 6 is a schematic diagram of a three-dimensional finite element model according to the present invention;
FIG. 7 is a schematic view of a pavement structure according to the present invention;
FIG. 8 is a schematic view of force analysis of three-layer springs in the traveling direction of the present invention;
FIG. 9 is a schematic diagram of the force analysis of the spring with three layers in the cross section direction in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 is a flow chart illustrating an embodiment of a finite element generation method for three-way stress of a tie rod and a dowel according to the present invention, which includes:
s101, constructing a three-dimensional finite element model of the pavement structure according to preset reference parameters.
It should be noted that the reference parameters include structural layer parameters and material parameters, and the specific reference parameters are shown in table 1:
accordingly, the reference parameters can be preset according to actual conditions, so that a three-dimensional finite element model aiming at the reference parameters is constructed.
And S102, calculating the joint rigidity of the three-dimensional finite element model.
The invention adopts a theoretical method to calculate the joint rigidity, and the specific calculation steps are as follows:
(1) the shear stiffness of the concrete to the strut support is calculated.
Specifically, the shear stiffness DCI of the concrete to the strut support is calculated according to the following formula:
DCI=[4β3/(2+βω)]EdId
β=[Kd/(4EdId)]1/4
Id=πd4/64
wherein:
beta is the relative stiffness of dowel bar-concrete in m-1；
Omega is the width of the seam gap, and the unit is m;
Edthe modulus of elasticity of a dowel bar between cement concrete slabs is MPa;
Idis the section inertia moment of a dowel bar between cement concrete slabs and has the unit of m4；
K is the supporting modulus of concrete to the force-transmitting rod and has the unit of MN/m3；
d is the diameter of the dowel bar between the cement concrete slabs and the unit is m.
(2) The shear spring rate of the dowel bar itself is calculated.
Specifically, the shear spring rate C of the dowel itself is calculated according to the following formula:
C=EdId/[ω3(1+φ)]
φ=12EdId/(GdAdω2)
Gd=Ed/[2(1+μd)]
Ad=0.225πd2
wherein:
phi is an intermediate parameter.
GdThe shear modulus of a dowel bar between cement concrete slabs is expressed in MPa;
Adis the effective cross-sectional area of the dowel bar between the cement concrete slabs and has the unit of m2；
μdIs the Poisson ratio of the dowel bars between the cement concrete slabs.
(3) And calculating the combined shear stiffness of the dowel bars according to the shear stiffness and the shear spring stiffness.
Specifically, the combined shear stiffness D of the dowel bars is calculated according to the following formula:
D=1/(1/DCI+1/12C)
(4) and calculating the rigidity of the joint per unit length according to the combined shear rigidity.
Specifically, the seam stiffness q per unit length of the seam is calculated according to the following formula:
q=D/s
wherein s is the distance between dowel bars between cement concrete slabs and the unit is m;
in general, the width omega =10mm =0.01m of the seam gap and the elastic modulus E of the dowel bar between the cement concrete slabs can be taken by referring to relevant specifications and datad=200GPa=2×105MPa =2E5MPa, the diameter d =32mm =0.032m of the dowel between the cement concrete slabs and the Poisson ratio mu of the dowel between the cement concrete slabsdAnd =0.3, and the space s of dowel bars between cement concrete slabs is =0.3 m. According to the calculation formulas of the above steps (1) to (4), the corresponding calculation results can be obtained as shown in table 2:
and S103, calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness.
Based on the principle of section rigidity equivalence, the invention equates the total rigidity of the spring unit to the total rigidity of the joint section area, thereby establishing rigidity calculation algorithms of three different positions in the plate corner, the plate edge and the plate.
As shown in fig. 2, the board side nodes may be divided into board corner nodes, board edge nodes and board middle nodes, where the board corner nodes are located at four corners of the board side, the board edge nodes are located on four edges of the board side, and the board edge nodes are located in the middle of the board side.
Specifically, the step of calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness comprises the following steps:
(1) and respectively calculating the plate angle spring stiffness of the target rod body.
The target rod body comprises a longitudinal dowel bar at a transverse joint of a roadway, a longitudinal dowel bar at a transverse joint of a road shoulder and a transverse pull rod at a longitudinal joint of the roadway-the road shoulder cement slab;
specifically, the plate angle spring rate of the target rod body is calculated according to the following formula:
k’ 1 =q×L/[4×(nr-1)(nc-1)]
wherein:
k’ 1 plate angle spring rate of target rod body in Nxm-1；
q is the seam stiffness;
l is the crack length in m;
nrthe number of row of the plate side nodes corresponding to the target rod body;
ncthe number of the corresponding board side node rows of the target rod body.
(2) And respectively calculating the plate edge spring stiffness of the target rod body.
Specifically, the plate edge spring rate of the target stick body is calculated according to the following formula:
k’ 2 =2×k’ 1
wherein k is’ 2Spring rate of plate edge with Nxm unit as target rod body-1。
(3) The in-plate spring rates of the target rods are calculated separately.
Specifically, the spring rate in the plate of the target rod body is calculated according to the following formula:
k’ 3 =4×k’ 1
wherein k is’ 3Spring rate in the plate of the target rod body in Nxm-1。
As shown in FIG. 2, in the present embodiment, the springs are designed to be three layers (i.e. n) of upper, middle and lower in the depth direction of the cement board jointr= 3); wherein the length of the traffic lane is 5m, and the width of the traffic lane is 4 m; the length of the road shoulder is 5m, and the width of the road shoulder is 2.5 m; when calculating the spring rate of the roadway, the roadway is divided into 14 equal parts (n) in the direction of travelc= 14), divided into 22 equal parts (n) in the transverse directionc= 22); when calculating the road shoulder spring stiffness, the road shoulder spring stiffness is divided into 10 equal parts (n) along the driving directionc= 10), divided into 22 equal parts (n) in the transverse directionc= 22); meanwhile, the joint stiffness q per unit length of the joint at the lane transverse seam is 782.1, the joint stiffness q per unit length of the joint at the shoulder transverse seam is 782.1, and the joint stiffness q per unit length of the joint at the lane-shoulder longitudinal seam is 80.4. So that it can be calculated:
the plate angle spring stiffness of the longitudinal dowel bar at the transverse seam of the traffic lane is as follows:
k’ 1 =q×L/[4×(nr-1)(nc-1)]=782.1×4/[4×(3-1)(14-1)]=3.0×107
the plate angle spring stiffness of the longitudinal dowel bar at the cross seam of the road shoulder is as follows:
k’ 1 =q×L/[4×(nr-1)(nc-1)]=782.1×2.5/[4×(3-1)(10-1)]=2.7×107
the plate angle spring stiffness of the pull rod at the longitudinal seam of the roadway-road shoulder is as follows:
k’ 1 =q×L/[4×(nr-1)(nc-1)]=80.4×2.5/[4×(3-1)(22-1)]=2.4×106
in conclusion, the spring stiffnesses of the plate center, the plate corner and the plate edge of the longitudinal dowel bar at the transverse joint of the traffic lane, the longitudinal dowel bar at the transverse joint of the road shoulder and the transverse pull bar at the longitudinal joint of the traffic lane-road shoulder cement plate are respectively shown in table 3.
And S104, constructing spring connection between the plate side nodes in the three-dimensional finite element model according to the spring stiffness so as to preliminarily simulate the connection form of the pull rod and the transmission rod.
Further, the invention can adopt Python programming mode to write the spring batch generation program, and the concrete steps include:
(1) carrying out mesh division on the three-dimensional finite element model;
as shown in fig. 2, the established three-dimensional finite element model is divided into meshes, the number of the equal divisions is consistent with that of the nodes, and the traffic lane is divided into 14 equal divisions (n) along the traffic directionc= 14), divided into 22 equal parts (n) in the transverse directionc= 22); dividing the road shoulder into 10 equal parts (n) along the driving directionc= 10), divided into 22 equal parts (n) in the transverse directionc= 22). Meanwhile, it is divided into two equal parts in the thickness direction.
(2) And generating a first modeling file after the meshing is performed.
Finite element software (such as ABAQUS software) is adopted for modeling, and a first modeling file (named as inp-1) after the grid is divided is derived.
(3) And renumbering the board side nodes according to a preset sequencing rule, a Python programming mode and the first modeling file to generate a second modeling file.
And newly building a file, importing the first modeling file again, selecting mesh- > edge mesh- > number in ABAQUS software, and numbering the nodes on the side face of the board again in a mode suitable for Python programming according to a preset sequencing rule.
As shown in FIG. 3, the slab is a schematic representation of a roadway cement slab, with the X direction being the cross-sectional direction and the Y direction being the longitudinal direction; the length of the plate is 5m, the width of the plate is 4m, the cross section direction is divided into 14 equal parts, and the longitudinal section direction is divided into 22 equal parts; therefore, the board side nodes are numbered in sequence according to a preset ordering principle (such as increasing sequence) to facilitate programming. After the renumbering of the involved board side nodes is completed, the second modeling file (named as inp-2) is exported again.
(4) And writing a spring batch generation program by adopting a Python programming mode according to the second modeling file to generate a third modeling file.
And writing a spring batch generation program by using Python according to a writing rule of spring connection between the plate side nodes in the second modeling file, and generating and outputting a third modeling file (named as inp-3). When writing the batch spring generation program using Python, the spring rate calculated in step S103 needs to be set as the spring rate between the board-side nodes.
(5) And copying the content of the third modeling file to the corresponding spring joint in the second modeling file to generate a fourth modeling file.
And copying and pasting the content of the third modeling file to the corresponding spring joint in the second modeling file, and saving the content as a fourth modeling file (named as inp-4).
(6) According to the fourth modeling document, all board side nodes which are renumbered are connected through springs.
After the ABAQUS software is closed, the ABAQUS software is restarted, a fourth modeling file is imported into the ABAQUS software, at which time the transverse seams 2 between the slab-side nodes of all the renumbered concrete slabs 3 are connected by the springs 1 (see fig. 4 and 5), and the springs 2 between the slab-side nodes adopt the spring stiffness calculated in step S103.
Therefore, the nodes are renumbered in a mode suitable for Python programming according to a certain rule, and programming is convenient. Meanwhile, a spring batch generation program is compiled by adopting Python, spring connection between nodes is generated in batches for the nodes after heavy numbering, the efficiency is high, the arrangement of multiple layers of seam sections and any number of spring units can be realized, and the simulation precision is high.
And S105, converting the spring connection between the board side nodes into connector connection so as to further simulate the pull rod and the dowel bar and generate three-way stress of the pull rod and the dowel bar.
In the invention, the three-dimensional stress refers to the traffic direction stress, the depth direction stress and the cross section direction stress.
It should be noted that, in step S104, the spring is used to simulate the dowel bar between the cement board and the cement board transverse seam and the tie bar between the longitudinal seams, and the spring can only output the stress along the spring direction, but cannot output the three-way stress condition of the cement board tie bar and the dowel bar under different working conditions (e.g., working conditions such as half-clearance at the board corner, full-clearance at the board corner, etc.), so that the spring unit needs to be converted into a connector unit, and the three-way stress data can be output through the connector unit.
Specifically, the step of converting the spring connection between the board side nodes to a connector connection to further simulate tie rods and dowel bars and generate three-way stresses for the tie rods and dowel bars includes:
(1) according to the fourth modeling file, a conversion program is written in a Python programming manner to convert the spring connection between the board side nodes into a connector.
And operating the ABAQUS- > file- > import in the ABAQUS software, and then operating the file- > run script to execute the script spring to connector.
It should be noted that, a Python writing conversion program spring to connector is adopted, and the main content is to convert the corresponding renumbered spring connection in the original inp file into connector connection according to the connector writing rule in the inp file. Specifically, in the conversion process, the connection element attribute is checked from the interaction module (namely, whether the connection element is a spring is judged), so that whether the connection element is changed into a connector is judged, and meanwhile, the connection spring between the sides of the originally defined renumbered back plate is deleted, so that the situation that the rigidity is doubled is avoided.
(2) And extracting corresponding connectors for analysis to generate three-way stress of the longitudinal dowel bars at the transverse seams of the carriageway, the longitudinal dowel bars at the transverse seams of the road shoulder and the transverse tie bars at the longitudinal seams of the carriageway-road shoulder cement boards under different working conditions.
The different working conditions can be working conditions such as plate corner half-void and plate corner full-void, wherein the plate corner half-void means that only voids exist under a loaded plate of a cement concrete slab, and the plate corner full-void means that voids exist under the loaded plate and a non-loaded plate, and the voids are in the same shape.
Returning to the step module, and checking CTF1, CTF2 and CTF3 aiming at the connector force output; submitting analysis, and obtaining the three-dimensional stress conditions of the cement plate pull rod and the dowel bar under different working conditions by checking the CTF after the calculation is completed.
Therefore, the Python is adopted to write the springs and convert the springs into a connector program in batches, the three-way stress of the dowel bars between the cement boards and the transverse joints of the cement boards and the three-way stress of the pull bars between the longitudinal joints of the cement boards can be output, the deep analysis of the stress of the cement pavement structure is facilitated, and the optimized design of the pull bars and the dowel bars is facilitated.
In conclusion, the joint stiffness and the spring stiffness of the three-dimensional finite element model are accurately calculated by adopting a theoretical method, so that a good theoretical basis is provided for the simulation of the pull rod and the dowel bar; meanwhile, the invention is based on the principle of section rigidity equivalence, and the total rigidity of the spring unit is equivalent to the total rigidity of the joint section area, so that rigidity calculation algorithms of three different positions of a plate corner, a plate edge and a plate are established, and the accuracy is high; in addition, the method adopts Python to compile a spring batch generation program, has high efficiency, can realize the setting of a plurality of layers of seam sections and any number of spring units, and has high simulation precision; and the invention also adopts Python to compile the procedure of converting springs into connectors in batches, can form the three-dimensional stress of the dowel bar between the cement board and the cement board transverse joint and the tie bar between the longitudinal joints, is convenient for deep analysis of the stress of the cement pavement structure, and the optimized design of the tie bar and the dowel bar.
The invention is further described below with reference to specific examples:
establishing a three-dimensional finite element model by using ABAQUS finite element analysis software, and assuming that the pavement structure layer material is completely uniform and isotropic by using a C3D8R unit; convention X, Y, Z is the direction of traffic, the direction of depth, and the direction of cross section, respectively. X, Y, Z the dimensions are 10.02m, 3m and 5m respectively. When the void simulation is not carried out, the soil foundation adopts a winkler foundation model; when the void simulation is performed (see fig. 6), the soil foundation is an enlarged foundation, the bottom surface of the enlarged soil foundation is an ENCASTRE (all degrees of freedom are constrained, i.e., U1= U2= U3= UR1= UR2= UR3= 0) constraint condition, and the two side surfaces are XSYMM (a symmetric boundary condition in which a symmetric surface is a plane perpendicular to the coordinate axis X, i.e., U1-UR 2-UR 3= 0) and ZSYMM (a symmetric boundary condition in which a symmetric surface is a plane perpendicular to the coordinate axis Z, i.e., U3-UR 1-UR 2= 0) constraint conditions, respectively. The other layers constrain U1 and U3 in the X direction; one side of the Z direction adopts a spring simulation pull rod, and the other side adopts a free boundary. And a dowel bar between the two cement concrete plates is simulated by a spring, and the model is solved by using Dynamic Explicit. Specifically, the pavement structure is shown in fig. 7, the asphalt concrete layer thickness D1=6cm, the cement concrete layer thickness D2=28cm, the cement stabilized macadam layer thickness D3=18cm, and the soil layer thickness D4 are not limited at the moment, and the reference parameters are shown in table 4.
In the embodiment, the void shape is simulated by adopting a prism with an isosceles right triangle section, the height of the prism is the same as that of the base layer, and the side length (referred to as void size for short) of the isosceles right triangle is 0.4 m; the method is characterized by adopting a modulus reduction mode to represent the void degree, taking 0MPa to represent the void degree as 1 (complete void), and selecting two void forms of plate corner semi-void and plate corner full void, wherein the plate corner semi-void means that only the cement concrete plate has void under a loaded plate, and the plate corner full void means that the loaded plate and the unloaded plate have voids, and the void forms are the same.
As shown in fig. 8, when the clearance degree is 1, the spring mainly simulates the mechanical behavior of the longitudinal seam pull rod under the conditions of half clearance of the plate angle and full clearance of the plate angle, and the main stress direction is the cross section direction; in FIG. 8, the abscissa is the displacement from the centerline of the transverse slot, and the displacement of the spring on the loaded plate from the centerline is given as negative, and the displacement of the spring on the unloaded plate from the centerline is given as positive.
As shown in fig. 9, when the degree of clearance is 1, the spring mainly simulates the mechanical behavior of the transverse joint dowel bar under the conditions of half clearance of the plate angle and full clearance of the plate angle, and the main stress direction is the driving direction; in FIG. 9, the abscissa is the displacement from the centerline of the longitudinal seam, and the displacement of the spring on the loaded plate from the centerline is given as negative and the displacement of the spring on the unloaded plate from the centerline is given as positive.
In summary, the following results can be obtained:
(1) along with the change of the position of the spring layer, the mechanical distribution rules of the springs at the longitudinal seam along the cross section are greatly different, the first layer of springs positioned on the top surface of the cement board are mainly stressed, the third layer of springs positioned on the bottom surface of the cement board are mainly stressed, and the middle second layer of springs are in a tension-compression alternating state; the mechanical distribution rules of the springs of the first layer and the third layer are approximately in parabolic distribution; along with the change of the position of the spring layer, the mechanical distribution rules of the springs at the transverse seam along the driving direction are greatly different, the springs at the first layer and the third layer of the cement board are in a double-curve distribution form, but the directions are opposite, and the springs at the second layer are in a tension-compression alternating state; the first layer of springs on the top surface of the loaded cement board are mainly under tension, and the third layer of springs are mainly under pressure; the first layer of springs of the non-loaded plate mainly bear pressure, and the third layer of springs mainly bear tension. It can be seen that the spring in the area of the void is in torsional shear when the void is present.
(2) The mechanical behavior in two different directions indicates that: the stress of the spring near the void area is large, and the stress of the spring far away from the void area is small and gradually approaches zero; it is shown that the springs do not work simultaneously when they resist deformation due to the emptying, but that the part of the springs close to the area of emptying is involved. The tension and the pressure of the second layer of spring are irregular and are in a tension and pressure transition state.
(3) When the spring stiffness is constant, the absolute values of the tension and the pressure near the void area slightly increase with the increase of the void area, but the tension and the pressure of the adjacent spring increase greatly, which indicates that the working state of the seam load transfer system is a change process: the springs in the vicinity of the void area participate in the work and then the larger range of springs begin to work in tandem as the void size or degree increases and as the restraining action can no longer increase as the springs "yield" in the vicinity of the void area.
Therefore, through the three-dimensional stress analysis of the dowel bars between the cement boards and the transverse seams of the cement boards and the pull rods between the longitudinal seams, the deep analysis of the stress of the cement pavement structure and the optimal design of the pull rods and the dowel bars can be facilitated.
Correspondingly, the invention further provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to realize the steps of the finite element generation method of the three-way stress of the pull rod and the dowel bar. Meanwhile, the invention also provides a computer readable storage medium, wherein a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the steps of the finite element generation method for the three-way stress of the pull rod and the dowel bar are realized.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (10)
1. A finite element generation method for three-dimensional stress of a pull rod and a dowel bar is characterized by comprising the following steps:
constructing a three-dimensional finite element model of the pavement structure according to preset reference parameters;
calculating the joint stiffness of the three-dimensional finite element model;
calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness, wherein the spring stiffness comprises the spring stiffness of a plate center, a plate corner and a plate edge of a longitudinal dowel bar at a lane transverse joint, a longitudinal dowel bar at a road shoulder transverse joint and a transverse pull bar at a lane-road shoulder cement plate longitudinal joint;
constructing spring connection between plate side nodes in the three-dimensional finite element model according to the spring stiffness so as to preliminarily simulate the connection form of a pull rod and a transmission rod, wherein the spring between the plate side nodes adopts the spring stiffness;
and converting the spring connection between the side nodes of the plates into connector connection so as to further simulate a pull rod and a dowel bar and generate three-way stress of the pull rod and the dowel bar, wherein the three-way stress refers to traffic direction stress, depth direction stress and cross section direction stress.
2. The method of claim 1, wherein the step of calculating the joint stiffness of the three-dimensional finite element model comprises:
calculating the shear stiffness of the concrete to the support of the force transmission rod;
calculating the self shearing spring stiffness of the dowel bar;
calculating the combined shear stiffness of the dowel bars according to the shear stiffness and the shear spring stiffness;
and calculating the rigidity of the joint per unit length according to the combined shear rigidity.
3. A finite element generation method of three-way stress of a tie rod and a dowel according to claim 1 or 2, wherein the step of calculating the joint stiffness of the three-dimensional finite element model comprises:
according to the formula DCI = [4 beta ]3/(2+βω)]EdIdCalculating the shear stiffness DCI of the concrete for the force transmission rod support, wherein beta is the relative stiffness of the force transmission rod and the concrete, omega is the width of a seam gap, and EdIs the elastic modulus, I, of dowel bars between cement concrete slabsdThe moment of inertia of the cross section of the dowel bar between the cement concrete slabs;
according to the formula C = EdId/[ω3(1+φ)]Calculating the shearing spring stiffness C of the dowel bar, wherein phi is an intermediate parameter;
calculating the combined shear stiffness D of the dowel according to the formula D =1/(1/DCI + 1/12C);
and calculating the joint rigidity q of the joint unit length according to the formula q = D/s, wherein s is the distance between dowel bars between the cement concrete slabs.
4. A method for generating finite element of three-dimensional stress of tie rod and dowel as claimed in claim 3, wherein the method is based on formula Id=πd4/64, calculating the section inertia moment I of the dowel bar between the cement concrete slabsdWherein d is the diameter of a dowel bar between cement concrete slabs;
according to the formula β = [ Kd/(4E)dId)]1/4Calculating the relative rigidity beta of the dowel bar and the concrete, wherein K is the supporting modulus of the concrete to the dowel bar;
according to the formula phi = 12EdId/(GdAdω2) Calculating an intermediate parameter phi, where Gd=Ed/[2(1+μd)] , Ad=0.225πd2,GdIs shear modulus, mu, of dowel bars between cement concrete slabsdIs the Poisson's ratio of the dowel bar between cement concrete slabs AdIs the effective cross-sectional area of the dowel bar between the cement concrete slabs.
5. The method of claim 1, wherein the step of calculating the spring rate of the three-dimensional finite element model based on the joint stiffness comprises:
respectively calculating the plate angle spring stiffness of a target rod body, wherein the target rod body comprises a longitudinal dowel bar at a transverse seam of a roadway, a longitudinal dowel bar at a transverse seam of a road shoulder and a transverse pull rod at a longitudinal seam of the roadway-road shoulder cement plate;
respectively calculating the plate edge spring stiffness of the target rod body;
the in-plate spring rates of the target rods are calculated separately.
6. A finite element generation method of three-way stress of a pull rod and a dowel according to claim 1 or 5, wherein the step of calculating the spring stiffness of the three-dimensional finite element model according to the joint stiffness comprises the following steps:
according to formula k’ 1 =q×L/[4×(nr-1)(nc-1)]Calculating the plate-angle spring stiffness k of the target rod body’ 1Wherein q is the joint stiffness, L is the crack length, nrNumber of row of board side nodes corresponding to target rod body, ncThe number of the row of the board side nodes corresponding to the target rod body;
according to formula k’ 2 =2×k’ 1Calculating the target barEdge spring rate k of body’ 2；
According to formula k’ 3 =4×k’ 1Calculating the spring rate k in the plate of the target rod body’ 3。
7. The method of claim 1, wherein the step of constructing a spring connection between plate side nodes in a three-dimensional finite element model based on spring rate to initially simulate the connection of tie rods and dowel rods comprises:
meshing the three-dimensional finite element model;
generating a first modeling file after grid division;
renumbering the board side nodes according to a preset sequencing rule, a Python programming mode and the first modeling file to generate a second modeling file;
according to the second modeling file, writing a spring batch generation program in a Python programming mode to generate a third modeling file;
copying the content of the third modeling file to the corresponding spring connection position in the second modeling file to generate a fourth modeling file;
according to the fourth modeling file, all board side nodes which are renumbered are connected through springs, wherein the springs between the board side nodes adopt the spring stiffness.
8. A method for finite element generation of three-way stresses in tie rods and transfer rods as set forth in claim 7, wherein said step of converting the spring connection between the plate side nodes to a connector connection to further simulate tie rods and transfer rods and generating three-way stresses in tie rods and transfer rods comprises:
according to the fourth modeling file, writing a conversion program in a Python programming mode to convert the spring connection between the board side nodes into a connector;
and extracting corresponding connectors for analysis to generate three-way stress of the longitudinal dowel bars at the transverse seams of the carriageway, the longitudinal dowel bars at the transverse seams of the road shoulder and the transverse tie bars at the longitudinal seams of the carriageway-road shoulder cement boards under different working conditions.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of any of claims 1 to 8.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 8.
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