CN107220396A - Solve the electric power pylon rod member calculation method for stress of singularity Singular Value sex chromosome mosaicism - Google Patents

Solve the electric power pylon rod member calculation method for stress of singularity Singular Value sex chromosome mosaicism Download PDF

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CN107220396A
CN107220396A CN201710092257.8A CN201710092257A CN107220396A CN 107220396 A CN107220396 A CN 107220396A CN 201710092257 A CN201710092257 A CN 201710092257A CN 107220396 A CN107220396 A CN 107220396A
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mtd
mrow
mtr
msub
node
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朱焱
徐剑峰
郭成功
葛乐
朱张蓓
朱富云
龚灯才
朱卫
吴晓楠
蒋徐勇
尹海海
林泳
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Nantong Power Supply Co of Jiangsu Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Jiangsu Electric Power Co Ltd
Nantong Power Supply Co of Jiangsu Electric Power Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

Abstract

The invention discloses a kind of electric power pylon rod member calculation method for stress for solving singularity Singular Value sex chromosome mosaicism, the finite element mechanical model of iron tower structure is set up first with Finite Element, and integrally-built discretization is carried out according to iron tower structure composition；Again to each unit generation unit stiffness matrix, with reference to the space angle relation and annexation between each rod member in iron tower structure, superposition generation Bulk stiffness matrix；Then, according to steel tower institute generation load array loaded, and using modal displacement array as unknown quantity, with Bulk stiffness matrix, load array composition matrix equation；Finally, by solution matrix equation, node strain is obtained, the stress of every rod member in iron tower structure is finally given.The present invention is directly accurately solved by mathematical method to electric power pylon rod member stress, can provide scientific basis for iron tower structure safety evaluation.

Description

Solve the electric power pylon rod member calculation method for stress of singularity Singular Value sex chromosome mosaicism
The application is application number：201410423136.3, the applying date：2014.8.26, title " one kind be based on finite element fraction The divisional application of the electric power pylon rod member calculation method for stress of analysis ".
Technical field
The present invention relates to a kind of method for carrying out structure mechanics analysis to electric power pylon and accurately calculating every rod member stress, Belong to transmission line of electricity running status safety evaluation field.
Background technology
Electrical energy production and the lifeblood that transmission is national economy social development, transmission line of electricity is even more the " life involved the interests of the state and the people Order line ".Transmission line of electricity is as important lifeline engineering, and efficient supply and reasonable distribution for electric power energy, which have been provided, tries hard to keep Card.The sustainable and healthy development of economic society, requirements at the higher level are proposed to the security and reliability that transmission line of electricity is run.However, by Vast in territory in China, transmission line of electricity path length, pylon are high, largely pass through remote mountains great river, even depopulated zone, naturally qi-regulating As complicated condition is changeable, transmission line of electricity is as the trunk of bulk power grid, and its own is a huge environmental hazard supporting body.For a long time Operational data shows that line security accident is caused by Mechanics of Machinery reason mostly.Although in layout of roads design, based on iron Tower tower material theoretical intensity calculation value, calculates allowable stress by specific operation condition and sets safety coefficient, ensureing to a certain degree The safe operation of circuit.But actual operating mode complexity and time-varying, and can not be completely by design specification institute, it is expected that the actual fortune of part Row stress may exceed secure threshold；Therefore though actual transmission line of electricity breaks, fallen strictly by Specification Design, construction, operation The security incidents such as tower still happen occasionally.
For 08 year especially big ice disaster, industry and educational circles expert generally believed that power network lacks scientific and effective prevent and reduce natural disasters Accident early warning combined system etc. is one of major reason that power outage occurs.The key for setting up this system is to transmission line of electricity Safe condition give scientific evaluation.Currently associated research is main by applying pulling force sensor, online design stress monitoring dress Put.Because hardware cost, device body easily the influence factor such as are destroyed by external force, its further genralrlization application receives restriction.Open Send out zero hardware cost a kind of, become without environmental constraints, reusable in the safety appraisement of structure systems of all operation transmission lines of electricity The task of top priority of electric power netting safe running, wherein it is key therein to carry out accurate stress distribution to calculate to steel tower rod member.
Stress distribution for electric power pylon analyzes calculating, and the technology path for being seen in open report is that iron tower structure is entered Row repeatedly simplifies equivalent, and the progress loaded of steel tower institute is simply decomposed or is superimposed, and ignores the elastic deformation of iron tower structure.This Plant the result that analysis method is provided, it is impossible to provide stress data exactly for safety evaluation.From the point of view of mechanical analysis, no Accurately.Therefore the present invention is proposed, finite element modeling is carried out to iron tower structure, it is contemplated that the elastic deformation of iron tower structure, to each Rod member carries out mechanical analysis, and the mechanical property of single rod member is rationally superimposed according to iron tower structure, provides overall steel tower The accurate mechanical property of structure, to obtain accurate stress distribution of the iron tower structure under complex load.
The content of the invention
In order to solve the above problems, the present invention proposes a kind of electric power pylon rod member Stress calculation side based on finite element analysis Method, the stress of every rod member of steel tower is calculated for analyzing, is comprised the following steps：
Step 1：The finite element mechanical model of iron tower structure is set up according to Finite Element, is obtained according to obtained mechanical model Take steel tower node；And by iron tower structure discretization, obtain the same number of unit of rod member between the node of steel tower two, unit each other it Between be only connected by node (main material is considered as node with oblique material, oblique material with main material, main material with the joint of oblique material in steel tower)；
Step 2：For each unit and modal displacement, difference generation unit stiffness matrix [k](e)With modal displacement arrayAnd according to the annexation between the space angle relation between rod member, rod member, conversion is superimposed out steel tower integral rigidity Matrix
Step 3：Uniform load suffered by steel tower and not a node load-transfer mechanism are displaced on node, panel load array is formed(wherein), and in view of matrix equationInIt is unusual Property, the displacement constraint of the node of steel tower tower leg four is introduced, solution matrix equation obtains modal displacement array
Step 4：Strain, the stress of steel tower node are calculated, rod member weak in iron tower structure is obtained.
Wherein, the iron tower structure discretization method in step 1 is by main material in steel tower and main material, main material and oblique material, oblique material The rod member being attributed to the joint of oblique material between node, each two node is considered as a bar unit.
Modal displacement array in step 2With element stiffness matrix [k](e)Respectively：
1) displacement array is putExpression formula be：
Wherein,For the modal displacement array in global coordinate system；For the displacement array of the 1st node；For The displacement array of 2nd node；By that analogyFor the displacement array of n-th of node；ui, vi, wiSat for the i-th node local The displacement of the lines in three directions in mark system；θxi, θyi, θziIt is section at the i-th node around the rotation of three reference axis, θxiRepresent section Torsion, θyi, θziRotation of the section in xz and xy coordinate surfaces is represented respectively.
2) element stiffness matrix [k](e)Expression formula be：
Wherein, [k](e)For stiffness matrix of the bar unit in unit local coordinate system；A is bar unit cross-sectional area；Iy For in xz faces inner section the moment of inertia；IzFor the cross sectional moment of inertia in xy faces；IpFor the torsional moment of inertia of unit；L is length；E and G is respectively the modulus of elasticity and modulus of shearing of material.
According to the element stiffness matrix [k] obtained(e)And according between the space angle relation between rod member, rod member Annexation, you can obtain steel tower Bulk stiffness matrix
Panel load matrix in step 3For：
Wherein,For all panel load arrays in overall coordinate；For the load row of i-th of node in overall coordinate Battle array；NxiFor the axial force of i-th of node, Nyi、NziShearing of respectively i-th node in xy and xz faces；MxiFor i-th of section The moment of torsion of point, Myi、MziFor moment of flexure of i-th of node in xz and xy faces.
In view of matrix equationInFor singular matrix, to cause equation group to have solution, the present invention Middle introducing 4 column foots of steel tower are fixed with foundation connection, this constraints of the rigid displacement of limitation iron tower structure, so as to protect Card integral rigidity equation has unique solution.
The strain and stress formula of calculating steel tower node is in step 4：
Wherein, σx, σy, σzFor reference axis x, y, 3 direct stress components on z directions；τxy, τyz, τzxFor in x/y plane, yz 3 shearing stress components in plane, zx planes；Respectively steel tower space structure is occurring During deformation, node is in the line strain component of the generation on tri- directions of reference axis x, y, z； It is steel tower space structure in deformation, node is in x/y plane, yz planes, zx planes 3 shearing strain components of interior generation.；U=u (x, y, z), v=v (x, y, z), w=w (x, y, z) is respectively steel tower space structure In deformation, node is in reference axis x, y, the displacement in z directions；E is the modulus of elasticity of rod member；μ is Poisson's ratio.
The technique effect of the present invention：
1) elastic deformation of iron tower structure is taken into full account, mechanical analysis is carried out to each rod member, according to iron tower structure pair The mechanical property of single rod member is overlapped so that analysis result is more accurate.
2) iron tower structure stress under single operating mode can be not only analyzed, to the iron tower structure force analysis under analysis complex working condition Also there is superior performance.
3) calculate in introduce 4 column foots of steel tower fixed with foundation connection, limitation iron tower structure rigid displacement this Constraints, so as to ensure that integral rigidity equation has unique solution, dexterously solves matrix equation InSingularity matrix singularity problem.
Brief description of the drawings
Fig. 1 is that 220kV does font steel tower schematic diagram.
Fig. 2 is column foot application constraints schematic diagram in iron tower model.
Embodiment
A kind of electric power pylon rod member calculation method for stress based on finite element analysis, can be summarized as four-stage：At early stage Reason, FEM mechanics analysis, operating mode load treatment and post-processing.Early stage processing includes setting up the finite element dynamics of iron tower structure Model and to overall structure carry out sliding-model control；FEM mechanics analysis is that the finite element mechanical model of iron tower structure is carried out Analysis, with reference to the space angle relation and annexation between each rod member in iron tower structure, superposition generation Bulk stiffness matrix；Work Uniform load, not a node load-transfer mechanism suffered by steel tower are displaced on node by condition load treatment, form panel load array；Afterwards Phase processing is i.e. using modal displacement array as unknown quantity, and with Bulk stiffness matrix, load array constitutes matrix equation, and solves square Battle array equation, gives egress strain, finally finds out rod member weak in iron tower structure.This method mainly comprises the following steps：
Step 1：The finite element mechanical model of iron tower structure is set up according to Finite Element, is obtained according to obtained mechanical model Take steel tower node；And by iron tower structure discretization, obtain the same number of unit of rod member between the node of steel tower two, unit each other it Between be only connected by node (main material is considered as node with oblique material, oblique material with main material, main material with the joint of oblique material in steel tower)；
Step 2：For each unit and modal displacement, difference generation unit stiffness matrix [k](e)With modal displacement arrayAnd according to the annexation between the space angle relation between rod member, rod member, conversion is superimposed out steel tower integral rigidity Matrix
Step 3：Uniform load suffered by steel tower and not a node load-transfer mechanism are displaced on node, panel load array is formed(wherein), and in view of matrix equationInIt is unusual Property, the displacement constraint of the node of steel tower tower leg four is introduced, solution matrix equation obtains modal displacement array
Step 4：Strain, the stress of steel tower node are calculated, rod member weak in iron tower structure is obtained.
Each step is described in further detail below：
In step 1：The finite element mechanical model of iron tower structure is set up according to Finite Element, according to obtained mechanical model Obtain steel tower node；And by iron tower structure discretization, the same number of unit of rod member between the node of steel tower two is obtained, unit is each other Between be only connected by node (main material is considered as node with oblique material, oblique material with main material, main material with the joint of oblique material in steel tower), in fact The process of applying is：
The finite element mechanical model of iron tower structure is initially set up, using the cross-arm direction of steel tower as the x-axis of global coordinate system, Line direction is as y-axis, and vertical direction meets the right-hand rule as z-axis；Straight line where using bar unit is locally sat as unit The x-axis of system is marked, rod member is overlapped with the x-axis direction under local coordinate system, and its positive direction is consistent with global coordinate system x-axis positive direction.
Electric power pylon as space bar member system, carried out with bar-beam element (later abbreviation bar unit) it is discrete, the present invention in The joint of main material in steel tower and main material, main material and oblique material, oblique material and oblique material is turned to the rod member between node, each two node It is considered as a bar unit.Because the structure of steel tower is more complicated, rod member number is relatively more, if being division unit in structural separation When, it is smaller that unit divides, and number of unit is more, and the calculating time is longer, therefore considers the natural structure according to steel tower in itself Divide, both improve computational accuracy, amount of calculation is reduced again.
In step 2：For each unit and modal displacement, difference generation unit stiffness matrix [k](e)With modal displacement battle array RowAnd according to the annexation between the space angle relation between rod member, rod member, it is integrally firm that conversion is superimposed out steel tower Spend matrix
After iron tower structure discretization, mechanical characteristic analysis, i.e. determining unit nodal force and node position are carried out to unit Relation between shifting.In order to analyze and determine this relation, it is necessary to select displacement model, displacement function is the displacement put on unit To the function of the coordinate of point, this method is represented with the multinomial of the coordinate of unit internal point, the rod member in space, each node With 6 frees degree, i.e. rod member in addition to bearing the effect of one-dimensional axle power, bidimensional shearing and bidimensional moment of flexure, it is also possible to bear one Tie up the effect of moment of torsion.Also, space framed rods bear one-dimensional axle power, bidimensional shearing, bidimensional moment of flexure, one-dimensional moment of torsion, that is, correspond to Displacement of the lines on 6 frees degree of node, respectively 3 directions and at node section around 3 reference axis rotation, it is therefore single The multinomial of the coordinate of first internal point is represented by δ=k1u+k2v+k3w+k4θx+k5θy+k6θz, accordingly, all nodes can be formed Displacement array
Wherein,For the modal displacement array in global coordinate system；For the displacement array of the 1st node；For The displacement array of 2nd node；By that analogyFor the displacement array of n-th of node；ui, vi, wiSat for the i-th node local The displacement of the lines in three directions in mark system；θxi, θyi, θziIt is section at the i-th node around the rotation of three reference axis, θxiRepresent section Torsion, θyi, θziRotation of the section in xz and xy coordinate surfaces is represented respectively.
The basic step for setting up stiffness equation is：It is assumed that on the basis of element displacement function, according to Elasticity Theory, to set up the relational expression between strain, stress and modal displacement.Then according to the principle of virtual displacement, cell node power is tried to achieve Relation between modal displacement, so as to draw following element stiffness matrix [k](e)：
Wherein, [k](e)For stiffness matrix of the bar unit in unit local coordinate system；A is bar unit cross-sectional area；Iy For in xz faces inner section the moment of inertia；IzFor the cross sectional moment of inertia in xy faces；IpFor the torsional moment of inertia of unit；L is length；E and G is respectively the modulus of elasticity and modulus of shearing of material.
Unit element stiffness matrix [k](e)After obtaining, according to the connection between the space angle relation between rod member, rod member Relation, conversion is superimposed out steel tower Bulk stiffness matrixIts specific implementation process is as follows：
First, it is assumed that local coordinate is x, y, z；Overall coordinate isWith from the x-axis positive direction of local coordinate system Move clockwise to global coordinate systemAxle positive direction is just, then the direction cosines of x-axis is：
The direction cosines of y-axis are
The direction cosines of z-axis are
Order
The then element stiffness matrix in global coordinate systemIt is expressed as：
Wherein,[λ0] it is node Transition matrix, [λ] is coordinate conversion matrix, [k](e)For stiffness matrix of the bar unit in unit local coordinate system.
The integrated rule of Bulk stiffness matrix is as follows：
1) stiffness matrix [k] of each unit is first obtained(e)；
2) willEach sub-blockThe progress number of changing, changes corresponding overall numbering into；
3) later block will be changed into be sent on the correspondence position in Bulk stiffness matrix；
If 4) corresponding sub block for having several units on same position is sent to, it should be overlapped.
After above-mentioned steps, it is possible to each sub-block in Bulk stiffness matrix is obtained, so as to form integral rigidity Matrix
Wherein,When producing unit displacement for j-th of node, nodal force caused by i-th of node, referred to as rigidity Submatrix.It is worth noting that：In each sub-block be 6 × 6 rank matrixes, if overall structure has n node, then Exponent number 6n × 6n of Bulk stiffness matrix.
Uniform load suffered by steel tower and not a node load-transfer mechanism are displaced on node by step 3, form panel load array(wherein), and in view of matrix equationInIt is unusual Property, the displacement constraint of the node of steel tower tower leg four is introduced, solution matrix equation obtains modal displacement arrayIts is specific Implementation process is：
Uniform load, not a node load-transfer mechanism suffered by steel tower are displaced on node first, panel load array is formedRod member in space, each node has 6 frees degree, i.e., rod member is except bearing axle power, shearing and the effect of moment of flexure Outside, it is also possible to bear the effect of moment of torsion.Also, space framed rods bear one-dimensional axle power, bidimensional shearing, bidimensional moment of flexure, one-dimensional torsion Square, that is, correspond to 6 frees degree of node.The bar unit of electric power pylon exactly space framed rods.
Wherein,For all panel load arrays in overall coordinate；For the load row of i-th of node in overall coordinate Battle array；NxiFor the axial force of i-th of node, Nyi、NziShearing of respectively i-th node in xy and xz faces；MxiFor i-th of section The moment of torsion of point, Myi、MziFor moment of flexure of i-th of node in xz and xy faces.
Due to matrix equationInFor singular matrix, equation group is without solution, to solve the equation, Constraints is must be introduced into, the rigid displacement of iron tower structure is limited, it is ensured that integral rigidity equation has unique solution.Displacement constraint Effect be make the node in structure displacement component be constant value, i.e. δi=δ0.Displacement constraint is introduced, is sought to δi =δ0It is incorporated into structure global stiffness equation.
In the present invention, 1 method is put using diagonal element, by δi=δ0Introduce Bulk stiffness matrix
For in 4 tower legs of electric power pylon, the part being connected with basis is that fixing end is constrained, therefore δ0=0；By K's The elements in a main diagonal K of i-th rowii1 is put, remaining element is reset, and by the load R of the i-th rowiUse δ0Instead of above formula is changed into
By putting 1 method by displacement constraint δi=δ0It is incorporated into integral rigidity equation, does not change in matrix K and R Each element storage sequence, and matrix K remains as symmetrical matrix.
In computational methods of the present invention, the submatrix of pair 4 leg nodes being connected with basis, which is used, puts 1 method, you can substitute into 24 displacement boundary conditions, eliminate the singularity of Bulk stiffness matrix, so as to carry out matrix equation solution using Gaussian elimination method.
Step 4：Calculate node strain, stress etc., find out rod member most weak in iron tower structure, and its implementation process is as follows：
Gone out by the Bulk stiffness matrix equation solution of iron tower structure after the displacement δ of each node, it is possible to obtain each unit Modal displacement δe.After iron tower structure stress, its interior point will be subjected to displacement along x, y, tri- change in coordinate axis direction of z.If each point Along x, y, the displacement of tri- change in coordinate axis direction of z is represented with u, v, w, and they are the coordinate function of point, i.e. u=u (x, y, z), v=v (x, y, z), w=w (x, y, z).
Iron tower structure has 3 line strain component ε in deformation at internal any pointx, εy, εzAnd 3 pairs of shearing strains point Measure γxy=γyx, γyz=γzy, γzx=γxz.Relation between Elasticity, strain and displacement is geometric equation For：
ε in formulax, εy, εzFor be respectively steel tower space structure when deforming upon, node is in tri- sides of reference axis x, y, z The components of strain of upward generation；γxy, γyz, γzxIt is steel tower space structure in deformation, node is in x/y plane, yz is put down 3 components of strain produced in face, zx planes.
When iron tower structure is acted on, the stress state at internal any point is also three-dimensional, there is 3 direct stress components σx, σy, σzAnd three couples of shearing stress component τxy=τyx, τyz=τzy, τzx=τxz。
In linear-elastic range, stress and strain is represented with equation below：
Wherein, σx, σy, σzFor reference axis x, y, 3 direct stress components on z directions；τxy, τyz, τzxFor in x/y plane, yz 3 shearing stress components in plane, zx planes；Respectively steel tower space structure is occurring During deformation, node is in the line strain component of the generation on tri- directions of reference axis x, y, z； It is steel tower space structure in deformation, node is in x/y plane, yz planes, zx planes 3 The shearing strain component produced in individual plane；E is the modulus of elasticity of rod member；μ is Poisson's ratio.
The content not being described in detail in this manual belongs to the known technology of those skilled in the art.

Claims (6)

1. a kind of electric power pylon rod member calculation method for stress for solving singularity Singular Value sex chromosome mosaicism, it is characterised in that：Including Following steps：
Step 1：The finite element mechanical model of iron tower structure is set up according to Finite Element, iron is obtained according to obtained mechanical model Tap node；And by iron tower structure discretization, obtain between the node of steel tower two between the same number of unit of rod member, unit only It is connected by node；Main material is considered as node with main material, main material and the joint of oblique material, oblique material and oblique material in steel tower；
Step 2：For each unit and modal displacement, difference generation unit stiffness matrix [k](e)With modal displacement array And according to the annexation between the space angle relation between rod member, rod member, conversion is superimposed out steel tower Bulk stiffness matrix
Step 3：Uniform load suffered by steel tower and not a node load-transfer mechanism are displaced on node, panel load array is formedWhereinAnd in view of matrix equationInSingularity, The displacement constraint of the node of steel tower tower leg four is introduced, solution matrix equation obtains modal displacement array
Step 4：Strain, the stress of steel tower node are calculated, every rod member stress of iron tower structure is obtained；
Modal displacement array in the step 2With element stiffness matrix [k](e)Respectively：
1) modal displacement arrayExpression formula be：
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Wherein,For the modal displacement array in global coordinate system；For the displacement array of the 1st node；For the 2nd The displacement array of node；By that analogyFor the displacement array of n-th of node；ui, vi, wiIt is the i-th node in local coordinate system In three directions displacement of the lines；θxi, θyi, θziIt is section at the i-th node around the rotation of 3 reference axis, θxiRepresent the rotation in section Angle, θyi, θziRotational angle of the section in xz and xy coordinate surfaces is represented respectively；
2) element stiffness matrix [k](e)Expression formula be：
Wherein, [k](e)For stiffness matrix of the bar unit in unit local coordinate system；A is bar unit cross-sectional area；IyFor Xz faces inner section the moment of inertia；IzFor the cross sectional moment of inertia in xy faces；；IpFor the torsional moment of inertia of unit；L is length；E and G points Not Wei material modulus of elasticity and modulus of shearing；
So, according to the element stiffness matrix [k] obtained(e)And according between the space angle relation between rod member, rod member Annexation, you can obtain steel tower Bulk stiffness matrix
The integrated rule of Bulk stiffness matrix is as follows：
1) stiffness matrix [k] of each unit is first obtained(e)；
2) willEach sub-blockThe progress number of changing, changes corresponding overall numbering into；
3) later block will be changed into be sent on the correspondence position in Bulk stiffness matrix；
If 4) corresponding sub block for having several units on same position is sent to, it should be overlapped；
After above-mentioned steps, it is possible to each sub-block in Bulk stiffness matrix is obtained, so as to form Bulk stiffness matrix
Wherein,When producing unit displacement for j-th of node, nodal force caused by i-th of node, the referred to as sub- square of rigidity Battle array；；
The strain and stress formula of calculating steel tower node is in step 4：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;sigma;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;sigma;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;sigma;</mi> <mi>z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;tau;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;tau;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;tau;</mi> <mrow> <mi>z</mi> <mi>x</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;mu;</mi> <mo>)</mo> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mfrac> <mi>&amp;mu;</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> </mrow> </mfrac> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>&amp;mu;</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>&amp;mu;</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>&amp;mu;</mi> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;epsiv;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;epsiv;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;epsiv;</mi> <mi>z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>z</mi> <mi>x</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein, σx, σy, σzFor reference axis x, y, 3 direct stress components on z directions；τxy, τyz, τzxFor in x/y plane, yz is put down 3 shearing stress components in face, zx planes；；Respectively shape is occurring for steel tower space structure During change, node is in the line strain component of the generation on tri- directions of reference axis x, y, z； It is steel tower space structure in deformation, node is in x/y plane, yz planes, zx planes The 3 shearing strain components produced；；U=u (x, y, z), v=v (x, y, z), w=w (x, y, z) are respectively that steel tower space structure exists During deformation, node is in reference axis x, y, the displacement in z directions；E is the modulus of elasticity of rod member；μ is Poisson's ratio.
2. the electric power pylon rod member calculation method for stress according to claim 1 for solving singularity Singular Value sex chromosome mosaicism, It is characterized in that：Step 1：The finite element mechanical model of iron tower structure is set up according to Finite Element, according to obtained mechanics mould Type obtains steel tower node；And by iron tower structure discretization, obtain the same number of unit of rod member between the node of steel tower two, unit that Only it is connected between this by node.
3. the electric power pylon rod member calculation method for stress according to claim 1 for solving singularity Singular Value sex chromosome mosaicism, It is characterized in that：Main material is considered as node with main material, main material and the joint of oblique material, oblique material and oblique material in steel tower.
4. the electric power pylon rod member calculation method for stress according to claim 1 for solving singularity Singular Value sex chromosome mosaicism, It is characterized in that：Step 2：For each unit and modal displacement, difference generation unit stiffness matrix [k](e)With modal displacement battle array RowAnd according to the annexation between the space angle relation between rod member, rod member, it is integrally firm that conversion is superimposed out steel tower Spend matrix
5. the electric power pylon rod member calculation method for stress according to claim 1 for solving singularity Singular Value sex chromosome mosaicism, It is characterized in that：Step 3：Uniform load suffered by steel tower and not a node load-transfer mechanism are displaced on node, panel load is formed ArrayWhereinAnd in view of matrix equationInIt is strange The opposite sex, introduces the displacement constraint of the node of steel tower tower leg four, and solution matrix equation obtains modal displacement array
6. the electric power pylon rod member calculation method for stress according to claim 1 for solving singularity Singular Value sex chromosome mosaicism, It is characterized in that：Step 4：Strain, the stress of steel tower node are calculated, every rod member stress of iron tower structure is obtained.
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