CN107292021A - A kind of icing transmission line of electricity based on limited particle method is uneven to deice analog analysing method - Google Patents
A kind of icing transmission line of electricity based on limited particle method is uneven to deice analog analysing method Download PDFInfo
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Abstract
Analog analysing method is deiced the invention discloses a kind of transmission line of electricity based on limited particle method is uneven, is comprised the following steps：First carry out particle attribute initialization, path unit is configured afterwards and powerline ice-covering is carried out and looks for shape, then set it is uneven deice scene, finally carry out deice dynamic analysis.The present invention completes that transmission line of electricity is uneven to deice sunykatuib analysis by the renewal iteration of the solution of the equation of motion and correlative.This method can solve the problem that existing finite element software carries out the problem of modeling is complicated, cumbersome before transmission pressure is dynamically analyzed, and can emulate a large amount of different complex scenes.The present invention be applied to have the discrepancy in elevation, without the discrepancy in elevation, uniform icing and uneven icing, it is uneven a variety of situations such as deice, it is applied widely, and calculating speed is very fast.
Description
Technical field
Analog analysing method is deiced the invention belongs to a kind of transmission line of electricity is uneven, it is particularly a kind of to be based on limited particle method
Icing transmission line of electricity uneven deice analog analysing method.
Background technology
With China's rapid development of economy, the requirement more and more higher to power system.Transmission line of electricity is used as network system
Important component, it is to ensure electric network security and the base of stability that various Mechanics Calculations and static and dynamic analysis are carried out to it
Plinth.Transmission pressure is not pressurized as flexible cable structure tension, and rigidity is low easily by ectocine, and ice load is used as transmission pressure
One of common loads, influence larger to transmission line safety.When transmission pressure deices vibration, shaft tower, insulator chain and gold utensil etc.
Withstand shocks load, and shaft tower bears unbalanced tensile force, may trigger broken string or even the mechanical accident such as tower；Alternate electric clearance subtracts
It is small, the electrical hazards such as flashover, short circuit may be triggered, the safe operation of serious threat power network.Therefore it is uneven to transmission pressure de-
It is particularly important that ice dynamically carries out analysis.
It is that Transmission Tower-line design, icing deice the important foundation of disaster prevention that transmission line of electricity is uneven, which to deice sunykatuib analysis,.
With the development of finite element software, analog analysing method is deiced existing transmission line of electricity is uneven, based on finite element software
It is one of most widely used method to carry out transmission line of electricity modeling and analysis.And step is more during finite element software modeling, shape is looked for answer
It is miscellaneous, cumbersome error-prone, analysis is deiced since shape is looked in modeling under different scenes, is difficult to emulate substantial amounts of scene；And
The nonlinear stiffness matrix of complexity is formed during solution, iterative calculation is comparatively laborious, and solution efficiency is low, calculates the time long.
The content of the invention
It is an object of the invention to provide a kind of simple to operate, applied widely, accuracy is high, efficiency high and calculating speed
The fast icing transmission line of electricity based on limited particle method is uneven to deice analog analysing method.
The technical solution for realizing the object of the invention is：A kind of transmission line of electricity based on limited particle method is uneven to be deiced
Analog analysing method, comprises the following steps：
Step 1：Overhead transmission line information and ice covering thickness information are read in, including：Span, the discrepancy in elevation, electric wire model, ice covering thickness
Etc. information；
Step 2：Grid locational and shape under being conducted oneself with dignity according to catenary equations；
Step 3：Division unit, initialization particle attribute, include quality, position and the speed of particle；
Step 4：The internal force and external force of particle are initialized, path unit is set, step-length and step number in path unit is determined；
Step 5：Automatic virtual blocks are set, powerline ice-covering is carried out and looks for shape；
Step 6：Set transmission pressure is uneven deice scene, update particle attribute；
Step 7：The equation of motion of particle is solved, particle displacement is calculated；
Step 8：Update displacement, internal force and the external force of particle；
Step 9：Judge whether to reach stopping criterion for iteration, if reached, icing transmission line of electricity is uneven to deice simulation
Analysis terminates, and otherwise goes to step 7.
Compared with prior art, its remarkable advantage is the present invention：1) present invention is applied to have the discrepancy in elevation, without the discrepancy in elevation, uniformly cover
Ice, uneven icing, uniformly deice, it is uneven deice, the same period deices, not the same period the various scenes such as deice, the scope of application is wider；
2) present invention carries out that icing transmission pressure is uneven deices sunykatuib analysis using self-compiling program, can carry out the imitative of large amount of complex scene
Very；3) present invention, avoiding the complicated cumbersome modeling process of finite element software, nonlinear stiffness matrix is not necessarily formed；4) effect is calculated
Rate is high；5) solving speed is fast.
The present invention is described in further detail below in conjunction with the accompanying drawings.
Brief description of the drawings
Fig. 1, which is that the transmission pressure based on limited particle method is uneven, deices sunykatuib analysis flow chart.
Fig. 2 is the fantasy sport figure of unit, wherein scheme a) be unit virtual reverse movement figure, figure b) is the virtual of unit
Positive movement figure.
Fig. 3 is transmission pressure intermediate point displacement time-histories result schematic diagram.
Embodiment
With reference to accompanying drawing, a kind of icing transmission line of electricity based on limited particle method of the invention is uneven to deice sunykatuib analysis side
Method, comprises the following steps：
Step 1, acquisition overhead transmission line information and ice covering thickness information, including：Span, the discrepancy in elevation, electric wire model, ice covering thickness
Information；
Step 2, according to catenary equations conduct oneself with dignity under transmission line of electricity shape；The catenary formula is：
The formula is using left side hitch point as the origin of coordinates, in formula：
Y, x --- transmission pressure ordinate, abscissa everywhere；
σo--- horizontal stress under stringing temperature；
H --- along the discrepancy in elevation in load direction between adjacent two hitch point；
γ --- than carrying before wire icing；
LH=0--- catenary line length in the shelves of relative superiority or inferiority such as side-by-side mounting point；
L --- perpendicular to the projector distance in load direction, referred to as span between adjacent two hitch point.
Step 3, to transmission pressure carry out dividing elements, particle attribute is initialized afterwards, the particle attribute bag
Include quality, position and the speed of particle；
When being initialized to particle attribute, particle position catenary formula in step 2 is tried to achieve, and particle initial velocity is 0,
The all-mass of circuit is undertaken by particle, and the quality of unit is averagely allocated to both sides particle, point mass MiCalculation formula be：
M in formulai--- the quality of i-th of particle；
qi、qi+1--- the quality of i-th, i+1 unit.
Step 4, internal force and external force to particle are initialized, and path unit is set afterwards, are specifically to determine that path is single
Step-length and step number in first；
The base unit for setting path unit to be particle movement, makes hypothesis below in path unit：
(1) base frame for calculating displacement, deformation and internal force change is used as using the initial configuration of circuit；
(2) rotation, can be considered as the big rotation of moderate by the deformation very little of circuit；
(3) influence that Geometrical change is calculated the deformation of member and internal force is ignored；
(4) combination of component, property and constraint are constant；
(5) property of particle is constant in path unit, particle change of properties between path unit, the property bag of the particle
Include quality, quantity, internal force.
Step 5, damping is set to automatic virtual blocks, carrying out icing to transmission line of electricity looks for shape；It is specific to be entered using equation below
Line position, which is moved, to be solved and updates, and is completed icing and is looked for shape：
D in formulan+1、dn、dn-1--- displacement of the particle in the (n+1)th step, the n-th, (n-1)th step；
△ t --- time step；
The quality of M --- particle；
Fext、Fint--- equivalent particle internal force, external force；
μ --- damped coefficient.
Step 6, set that transmission pressure is uneven deices scene, particle attribute is updated afterwards；Set transmission pressure uneven
Scene is deiced, is specifically to determine and deices position, ratio and direction；
Update particle attribute and be specifically to determine particle external force, component calculation formula of the particle external force in y directions is：
In formula,--- component of the external force in y directions；
FIcing--- the equivalent power to particle of icing gravity；
G --- acceleration of gravity.
Step 7, the equation of motion to particle are solved, and obtain particle displacement；Specifically include following steps：
Step 7-1, the equation of motion for building particle, its formula is：
Ma=Fext+Fint+Fdmp
Fdmp=-μM v
In formula, a --- particle acceleration vector；
Fext、Fint、Fdmp--- equivalent particle internal force, external force and damping force；
V --- particle velocity vector；
Step 7-2, using central difference method particle velocity, accelerometer are shown as：
In formula, vn、an--- the speed of the step of particle n-th, vector acceleration；
Step 7-3, judge calculate the moment whether be to deice initial time, if it is perform step 7-4, otherwise perform step
Rapid 7-5；
Step 7-4, structure deice the displacement calculation formula of initial time：
The formula of central difference method is substituted into the equation of motion, then the displacement for obtaining the (n+1)th step is：
D in formula1、d0--- particle is in the 1st step, the displacement of initial time；
v0--- the velocity vector of particle initial time；
Step 7-5, the formula of central difference method substituted into the equation of motion, then the displacement for obtaining the (n+1)th step is：
Step 8, the displacement confrontation point obtained using step 7 are updated, and the content of renewal includes the displacement of particle and interior
Power；The particle internal force updates formula used：
Fext=f1-f2
F in formula1, f2--- the internal force of particle two ends connection unit；
From taMoment is to tbFormula used in moment element force is：
F in formulaB'--- unit AB is in tbThe internal force at moment；
σ --- unit AB is in taThe stress at moment；
S --- unit sectional area；
E --- modulus of elasticity；
lA'B'、lAB--- unit is in tb、taThe length at moment；
eA'B'--- unit AB is in tbThe direction vector at moment；
Particle external force updates according to the component calculation formula in particle external force y directions.
Step 9, judge whether reach stopping criterion for iteration, if reach, icing transmission line of electricity is uneven to deice simulation
Analysis terminates, and otherwise goes to step 7.
The present invention be applied to have the discrepancy in elevation, without the discrepancy in elevation, uniform icing, uneven icing, uniformly deice, uneven deice, together
Phase deices, not the same period the various scenes such as deice, the scope of application is wider.
It is described in more detail below.
Referring to Fig. 1, Fig. 1, which is that the transmission pressure based on limited particle method is uneven, deices analog analysing method, specific as follows：
The first step, reads in overhead transmission line information and ice covering thickness information, including span, the discrepancy in elevation, wire type, ice covering thickness
Deng.
Second step, grid locational and shape under being conducted oneself with dignity according to catenary equations, using left side hitch point as seat
Origin is marked, calculation formula is as follows：
Y, x in formula --- transmission pressure ordinate, abscissa everywhere；
σo--- horizontal stress under stringing temperature, it can be checked in by stringing design drawing or formula is calculated and obtained；
H --- along the discrepancy in elevation in load direction between adjacent two hitch point；
γ --- than carrying before wire icing, γ is q*g/A；
LH=0--- catenary line length in the shelves of relative superiority or inferiority such as side-by-side mounting point；
L --- perpendicular to the projector distance in load direction, referred to as span between adjacent two hitch point；
3rd step, initializes particle attribute, with particle come discrete and analyze transmission pressure, particle attribute after division unit
Quality, position and speed including particle.Particle position catenary formula in second step is tried to achieve, and particle initial velocity is 0, structure
All-mass undertaken by particle, the quality of unit is averagely allocated to both sides particle, and the calculation formula of point mass is：
M in formulai--- the quality of i-th of particle；
qi、qi+1--- the quality of i-th, i+1 unit；
4th step, sets path unit to determine the base unit of particle movement, with limited particle in tiny time section
Motion be that path unit approaches the continuous motion of structure over time and space, hypothesis below is made in path unit：
(1) base frame for calculating displacement, deformation and internal force change is used as using the initial configuration of component；
(2) rotation, can be considered as the big rotation of moderate by the deformation very little of component；
(3) influence that Geometrical change is calculated the deformation of member and internal force can be ignored；
(4) combination of component, property and constraint are constant.
When component geometry deformation or larger rotation, it can use component in one group of approach element analysis, each approach unit
Deformation be considered as small deformation and moderate and rotate to handle.Property (quality, quantity, internal force) constant, road of particle in path unit
Particle change of properties between the unit of footpath.
5th step, sets virtual damper force to increase the dynamic response that damping energy dissipation cuts down structure, so as to carry out transmission line of electricity
Icing looks for shape, therefore it is static after transmission pressure icing when powerline ice-covering looks for shape to set larger virtual damper force to try to achieve
State.
6th step, sets that transmission pressure is uneven deices scene, it is determined that deicing position, ratio and direction, is deicing scene
On the basis of update particle attribute, such as point mass, external force.
7th step, equation of particle motion follows Newton's second law, and the solution of the equation of motion is carried out using central difference method,
Equation of motion formula is：
The quality of M, a in formula --- particle, vector acceleration；
Fext、Fint、Fdmp--- equivalent particle internal force, external force and damping force；
μ, v --- damped coefficient, particle velocity vector.
Particle velocity, acceleration can be expressed as in central difference method：
D in formulan+1、dn、dn-1--- displacement of the particle in the (n+1)th step, the n-th, (n-1)th step；
△ t --- time step；
vn、an--- the speed of the step of particle n-th, vector acceleration.
The formula of central difference method is substituted into the equation of motion, then the displacement for obtaining the (n+1)th step is：
The solution that can carry out displacement by formula 4 updates, and during initial time n=0, d1Solve as follows：
The displacement of known initial time and speed, eliminate d-1Obtain：
8th step, particle displacement is updated after equation of motion solution, and the internal force of particle passes through fantasy sport and unit
Pure deformation is derived, and particle external force is changed according to the situation that deices.
In this paper transmission pressure deices analysis, particle external force changes when deicing the not same period, and external force is before deicing
Deadweight and icing gravity, it is deadweight plus the icing weight after initially deicing to deice initial time, according to covering in dynamic analysis process
The situation that deices in the scape of ice stadium sets the modification of progress external force, updated.And particle internal force derives from the unit being connected with particle, transmission of electricity
Lead unit uses bar unit, and bar unit occurs that axial deformation produces axle power and acting in opposition is on particle.
Fantasy sport includes reverse movement and positive movement, as shown in figures 2 a and 2b.Such as particle A and the list of particle B connections
First AB is in taMoment element length is lAB, arrive separately at A ' and B by two particles of △ t ' position, unit A ' B ' length is
lA'B'.It is required that unit A ' B ' are in tb=taThe internal force of+△ ts, the virtual reverse movement for first passing through Fig. 2 a tries to achieve axial deformation position
Move, unit A ' B ' reach A " B " by virtual reverse translation and virtual backwards rotation, and bar unit keeps linear state before and after deformation,
The incremental deformation of bar unit is only related to element length, so the axial deformation displacement of unit is in △ t
△ u=(lA'B'-lAB)eAB(formula 8)
L in formulaA'B'、lAB--- unit is in tb、taThe length at moment；
eAB--- the now direction vector of unit.
Time step is smaller in path unit, unit experience small deformation, and the unit axle power after deformation is
F in formulaα, σ --- unit AB is in taThe unit axle power and stress at moment；
△fα--- unit AB is by taTo tbInternal force increment；
E --- modulus of elasticity；
S --- unit sectional area.
According to the static balance condition of bar unit, unit two ends internal force is equal in magnitude, in the opposite direction.Try to achieve the list of virtual location
After first internal force, the element force of actual position is tried to achieve by Fig. 2 b virtual positive movement.During positive movement, rigid motion
When internal force size it is constant, direction change, so unit is in tbThe internal force at moment is
E in formulaA'B'--- unit is in tbThe direction vector at moment.
Element force is reversely added on the particle of two ends, you can try to achieve the internal force at each particle each moment, particle external force, internal force
It is expressed as：
In formula--- component of the external force in v directions；
FIcing--- the equivalent power to particle of icing gravity；
f1, f2--- the internal force of particle two ends connection unit.
9th step, is terminated when arrival time finally walks, and intermediate point time-histories displacement result is as shown in Figure 3.
Embodiment
Wire LGJ500/45 is chosen, wire parameter and operating mode set as shown in table 1：
The wire characteristic parameter of table 1 and operating mode
| Parameter | Unit | Numerical value |
| Sectional area | mm2 | 531.68 |
| Wire diameter | mm | 30 |
| Unit mass | kg/m | 1.688 |
| Modulus of elasticity | MPa | 65000 |
| Calculate pull-off force | N | 128100 |
| Initial tension | N | 23058 |
| Horizontal span | m | 300 |
| The discrepancy in elevation | m | 0 |
| Ice covering thickness | mm | 10 |
Full shelves carry out 100% and deiced, and emulate 20s, damped coefficient takes 0.2, and the centre position of distinct methods deices jump
The height results that jump are as shown in table 2：
The each method jump height of table 2
| Method | Result of jumping (m) | The calculating time (s) |
| ANSYS | 1.5878 | / |
| Finite Element | 1.5904 | 602.6 |
| Limited particle method | 1.5926 | 135.4 |
The ANSYS calculating times can not accurately count as can be seen from Table 2, but early stage models complex, limited particle method
The calculating time it is smaller, calculating speed is very fast.
A kind of uneven analog analysing method that deices of transmission line of electricity based on limited particle method of the present invention can solve the problem that now
Some finite element softwares carry out transmission pressure look for the modeling of shape process it is complicated, it is cumbersome the problem of, a large amount of different answer can be emulated
Miscellaneous scene, it is adaptable to have the discrepancy in elevation, without the discrepancy in elevation, uniform icing, uneven icing and uneven a variety of situations, the scope of application such as deice
Extensively, computational efficiency is high, and solving speed is fast.
Claims (8)
1. a kind of icing transmission line of electricity based on limited particle method is uneven to deice analog analysing method, it is characterised in that including
Following steps：
Step 1, acquisition overhead transmission line information and ice covering thickness information, including：Span, the discrepancy in elevation, electric wire model, ice covering thickness letter
Breath；
Step 2, according to catenary equations conduct oneself with dignity under transmission line of electricity shape；
Step 3, to transmission pressure carry out dividing elements, particle attribute is initialized afterwards, the particle attribute include matter
Quality, position and the speed of point；
Step 4, internal force and external force to particle are initialized, and path unit is set afterwards, is specifically to determine in path unit
Step-length and step number；
Step 5, damping is set to automatic virtual blocks, carrying out icing to transmission line of electricity looks for shape；
Step 6, set that transmission pressure is uneven deices scene, particle attribute is updated afterwards；
Step 7, the equation of motion to particle are solved, and obtain particle displacement；
Step 8, the displacement confrontation point obtained using step 7 are updated, and the content of renewal includes displacement and the internal force of particle；
Step 9, judge whether reach stopping criterion for iteration, if reach, icing transmission line of electricity is uneven to deice sunykatuib analysis
Terminate, otherwise go to step 7.
2. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that catenary formula is in step 2：
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The formula is using left side hitch point as the origin of coordinates, in formula：
Y, x --- transmission pressure ordinate, abscissa everywhere；
σo--- horizontal stress under stringing temperature；
H --- along the discrepancy in elevation in load direction between adjacent two hitch point；
γ --- than carrying before wire icing；
LH=0--- catenary line length in the shelves of relative superiority or inferiority such as side-by-side mounting point；
L --- perpendicular to the projector distance in load direction, referred to as span between adjacent two hitch point.
3. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that when step 3 is initialized to particle attribute, particle position catenary formula in step 2 is tried to achieve, matter
Point initial velocity is 0, and the all-mass of circuit is undertaken by particle, and the quality of unit is averagely allocated to both sides particle, point mass Mi
Calculation formula be：
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M in formulai--- the quality of i-th of particle；
qi、qi+1--- the quality of i-th, i+1 unit.
4. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that step 4 sets the base unit that path unit is particle movement, and hypothesis below is made in path unit：
(1) base frame for calculating displacement, deformation and internal force change is used as using the initial configuration of circuit；
(2) rotation, can be considered as the big rotation of moderate by the deformation very little of circuit；
(3) influence that Geometrical change is calculated the deformation of member and internal force is ignored；
(4) combination of component, property and constraint are constant；
(5) property of particle is constant in path unit, particle change of properties between path unit, and the property of the particle includes matter
Amount, quantity, internal force.
5. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that displacement is carried out using equation below in step 5 and solved and renewal, icing is completed and looks for shape：
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</msub>
</mrow>
D in formulan+1、dn、dn-1--- displacement of the particle in the (n+1)th step, the n-th, (n-1)th step；
△ t --- time step；
The quality of M --- particle；
Fext、Fint--- equivalent particle internal force, external force；
μ --- damped coefficient.
6. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that set that transmission pressure is uneven deices scene in step 6, is specifically to determine and deices position, ratio and side
To；
Update particle attribute and be specifically to determine particle external force, component calculation formula of the particle external force in y directions is：
In formula,--- component of the external force in y directions；
FIcing--- the equivalent power to particle of icing gravity；
G --- acceleration of gravity.
7. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that step 7 is solved to the equation of motion of particle, is comprised the following steps：
Step 7-1, the equation of motion for building particle, its formula is：
Ma=Fext+Fint+Fdmp
Fdmp=-μM v
In formula, a --- particle acceleration vector；
Fext、Fint、Fdmp--- equivalent particle internal force, external force and damping force；
V --- particle velocity vector；
Step 7-2, using central difference method particle velocity, accelerometer are shown as：
<mrow>
<msub>
<mi>v</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mn>2</mn>
<msub>
<mi>d</mi>
<mi>n</mi>
</msub>
<mo>+</mo>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>&Delta;t</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
In formula, vn、an--- the speed of the step of particle n-th, vector acceleration；
Step 7-3, judge to calculate whether the moment is to deice initial time, if it is perform step 7-4, otherwise perform step 7-
5；
Step 7-4, structure deice the displacement calculation formula of initial time：
The formula of central difference method is substituted into the equation of motion, then the displacement for obtaining the (n+1)th step is：
<mrow>
<msub>
<mi>d</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>d</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;tv</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mi>&Delta;t</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msup>
<mi>F</mi>
<mrow>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>F</mi>
<mi>int</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>M</mi>
</mrow>
</mfrac>
</mrow>
D in formula1、d0--- particle is in the 1st step, the displacement of initial time；
v0--- the velocity vector of particle initial time；
Step 7-5, the formula of central difference method substituted into the equation of motion, then the displacement for obtaining the (n+1)th step is：
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>2</mn>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mi>&mu;</mi>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<msup>
<mi>&Delta;t</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msup>
<mi>F</mi>
<mrow>
<mi>e</mi>
<mi>x</mi>
<mi>t</mi>
</mrow>
</msup>
<mo>+</mo>
<msup>
<mi>F</mi>
<mi>int</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
<mi>M</mi>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mi>&mu;</mi>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>d</mi>
<mi>n</mi>
</msub>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>-</mo>
<mi>&mu;</mi>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mi>&mu;</mi>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>.</mo>
</mrow>
8. a kind of icing transmission line of electricity based on limited particle method according to claim 1 is uneven to deice sunykatuib analysis side
Method, it is characterised in that the particle internal force in step 8 updates formula used and is：
Fext=f1-f2
F in formula1, f2--- the internal force of particle two ends connection unit；
From taMoment is to tbFormula used in moment element force is：
<mrow>
<msub>
<mi>f</mi>
<msup>
<mi>B</mi>
<mo>&prime;</mo>
</msup>
</msub>
<mo>=</mo>
<mo>&lsqb;</mo>
<mi>&sigma;</mi>
<mi>S</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mi>E</mi>
<mi>S</mi>
</mrow>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>l</mi>
<mrow>
<msup>
<mi>A</mi>
<mo>&prime;</mo>
</msup>
<msup>
<mi>B</mi>
<mo>&prime;</mo>
</msup>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>l</mi>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<msub>
<mi>e</mi>
<mrow>
<msup>
<mi>A</mi>
<mo>&prime;</mo>
</msup>
<msup>
<mi>B</mi>
<mo>&prime;</mo>
</msup>
</mrow>
</msub>
</mrow>
F in formulaB′--- unit AB is in tbThe internal force at moment；
σ --- unit AB is in taThe stress at moment；
S --- unit sectional area；
E --- modulus of elasticity；
lA'B'、lAB--- unit is in tb、taThe length at moment；
eA'B'--- unit AB is in tbThe direction vector at moment；
Particle external force updates according to the component calculation formula in particle external force y directions.
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| CN112580243A (en) * | 2020-12-23 | 2021-03-30 | 广东电网有限责任公司佛山供电局 | Power transmission line deicing jump dynamic response simulation analysis method |
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