CN105095576A - Stress calculation method for rod members of power transmission iron tower - Google Patents

Abstract

The invention discloses a stress calculation method for rod members of a power transmission iron tower. The stress calculation method comprises following steps: firstly, utilizing a finite element method to set up a finite element mechanical model of an iron tower structure and carrying out discretization on an overall structure based on the iron tower structure; secondly, generating an element stiffness matrix for each unit and generating a global stiffness matrix in an overlapped mode by combining space angle relations and connection relations of all the rod members of the structure of the iron tower; thirdly, generating load arrays based on loads applied on the iron tower, using joint displacement arrays as unknown quantities and forming a matrix equation by unknown quantities, the global stiffness matrix and the load arrays; and finally, acquiring joint strain by solving the matrix equation in order to obtain stress of all the rod members in the structure of the iron tower. The stress calculation method for rod members of the power transmission iron tower can provide a scientific basis for safety evaluation of the structure of the iron tower by directly and precisely solving stress of the rod members of the power transmission iron tower via a mathematical method.

Description

A kind of electric power pylon rod member calculation method for stress

The application is the divisional application of application number 201410423136.3, applying date 2014.8.26, title " a kind of electric power pylon rod member calculation method for stress based on finite element analysis ".

Technical field

The present invention relates to and a kind ofly structure mechanics analysis is carried out to electric power pylon and the method for accurate Calculation every root rod member stress, belong to transmission line of electricity running status safety evaluation field.

Background technology

Electrical energy production and transmission are the lifeblood of national economy social development, " lifeline " that transmission line of electricity involves the interests of the state and the people especially.Transmission line of electricity as important lifeline engineering, for the efficient supply of electric power energy and reasonable distribution provide strong guarantee.The sustainable and healthy development of economic society, the safety run transmission line of electricity and reliability propose requirements at the higher level.But because China is vast in territory, transmission line of electricity path length, pylon be high, pass through great river, remote mountains in a large number, or even depopulated zone, physical geography meteorological condition is complicated and changeable, and transmission line of electricity, as the trunk of bulk power grid, himself is a huge environmental hazard supporting body.Long-time running MSDS open-wire line road security incident is caused by Mechanics of Machinery reason mostly.Although in layout of roads design, based on tower material of iron tower theoretical intensity calculation value, calculated allowable stress by specific operation condition and arranged safety coefficient, to a certain degree having ensured the safe operation of circuit.But actual operating mode complicated and time become, and cannot be estimated by design specifications completely, parts actual motion stress may exceed secure threshold; Though therefore actual transmission line of electricity strictly presses Specification Design, construction, operation, broken string, the security incidents such as tower of falling still happen occasionally.

For 08 year especially big ice disaster, it was one of major reason of power outage generation that industry and educational circles expert generally believe that electrical network lacks scientific and effective accident early warning combined system etc. of preventing and reducing natural disasters.The key setting up this system gives scientific evaluation to the safe condition of transmission line of electricity.Current correlative study is mainly through applying pulling force sensor, online design monitor for stress.Because hardware cost, device body are subject to the influence factors such as outside destroy, the application of its further genralrlization receives restriction.Develop a kind of zero hardware cost, become the task of top priority of electric power netting safe running without environmental constraints, reusable in the safety appraisement of structure system of all operation transmission lines of electricity, wherein carrying out that accurate stress distribution calculates to steel tower rod member is key wherein.

For the stress distribution analytical calculation of electric power pylon, the technology path being seen in open report is all repeatedly simplify equivalence to iron tower structure, load suffered by steel tower is simply decomposed or is superposed, and ignores the elastic deformation of iron tower structure.The result that this kind of analytical approach provides, cannot provide stress data exactly for safety evaluation.Consider from the angle of mechanical analysis, out of true.Therefore the present invention proposes, finite element modeling is carried out to iron tower structure, consider the elastic deformation of iron tower structure, mechanical analysis is carried out to each root rod member, and rationally superpose according to the mechanical property of iron tower structure to single rod member, provide the accurate mechanical property of overall iron tower structure, to obtain the accurate stress distribution of iron tower structure under complex load.

Summary of the invention

In order to solve the problem, the present invention proposes a kind of electric power pylon rod member calculation method for stress based on finite element analysis, for the stress of the every root rod member of analytical calculation steel tower, comprises the steps:

Step 1: the finite element mechanical model setting up iron tower structure according to Finite Element, obtains steel tower node according to the mechanical model obtained; And by iron tower structure discretize, obtain and the same number of unit of rod member between steel tower two node, unit is only connected by node (in steel tower, main material is considered as node with oblique material, tiltedly material with the joint of oblique material with main material, main material) each other;

Step 2: for each unit and nodal displacement, respectively generation unit stiffness matrix [k] ^(e)with nodal displacement array and according to the annexation between the space angle relation between rod member, rod member, conversion superposes out steel tower Bulk stiffness matrix

Step 3: be displaced on node by uniformly distributed load suffered by steel tower and not a node load-transfer mechanism, forms panel load array (wherein ), and consider matrix equation singularity, introduce the displacement constraint of steel tower tower leg four node, solution matrix equation, obtains nodal displacement array

Step 4: calculate the strain of steel tower node, stress, obtains rod member weak in iron tower structure.

Wherein, the iron tower structure discretization method in step 1 is that material main in steel tower and main material, main material and oblique material, the tiltedly joint of material and oblique material are summed up as node, and the rod member between every two nodes is considered as a bar unit.

Nodal displacement array in step 2 with element stiffness matrix [k] ^(e)be respectively:

1) displacement array is put expression formula be:

$\begin{array}{cc}{\[\stackrel{\‾}{\mathrm{\δ}}\]}^{\left(e\right)}=\left[\begin{array}{c}{\[\stackrel{\‾}{\mathrm{\δ}}\]}_1\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_2\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_3\\ .\\ .\\ .\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_n\end{array}\right]& {\[\stackrel{\‾}{\mathrm{\δ}}\]}_i\left[\begin{array}{c}{u}_i\\ v_i\\ w_i\\ {\mathrm{\θ}}_{xi}\\ {\mathrm{\θ}}_{yi}\\ {\mathrm{\θ}}_{zi}\end{array}\right],i=1,2,\mathrm{...},n\end{array}$

Wherein, for the nodal displacement array in global coordinate system; it is the displacement array of the 1st node; it is the displacement array of the 2nd node; By that analogy it is the displacement array of the n-th node; u _i, v _i, w _iit is the displacement of the lines in the i-th node three directions in local coordinate system; θ _xi, θ _yi, θ _zibe the rotation of the i-th Nodes cross section around three coordinate axis, θ _xirepresent the torsion in cross section, θ _yi, θ _zirepresent the rotation of cross section in xz and xy coordinate surface respectively.

2) element stiffness matrix [k] ^(e)expression formula be:

Wherein, [k] ^(e)for the stiffness matrix of bar unit in unit local coordinate system; A is bar unit cross-sectional area; I _yfor cross sectional moment of inertia in xz face; I _zfor the cross sectional moment of inertia in xy face; I _pfor the torsional moment of inertia of unit; L is length; E and G is respectively elastic modulus and the modulus of shearing of material.

According to obtained element stiffness matrix [k] ^(e)and according to the annexation between the space angle relation between rod member, rod member, steel tower Bulk stiffness matrix can be obtained

Panel load matrix in step 3 for:

${\[\stackrel{\‾}{R}\]}^{\left(e\right)}=\left[\begin{array}{c}{\[\stackrel{\‾}{R}\]}_1\\ {\[\stackrel{\‾}{R}\]}_2\\ {\[\stackrel{\‾}{R}\]}_3\\ .\\ .\\ .\\ {\[\stackrel{\‾}{R}\]}_n\end{array}\right],{\[\stackrel{\‾}{R}\]}_i=\left[\begin{array}{c}{N}_{xi}\\ N_{yi}\\ N_{zi}\\ M_{xi}\\ M_{yi}\\ M_{zi}\end{array}\right],i=1,2,\mathrm{...}n$

Wherein, for panel load arrays all in overall coordinate; for the load column of i-th node in overall coordinate; N _xibe the axial force of i-th node, N _yi, N _zibe respectively the shearing of i-th node in xy and xz face; M _xibe the moment of torsion of i-th node, M _yi, M _zibe the moment of flexure of i-th node in xz and xy face.

Consider matrix equation in for singular matrix, for making system of equations have solution, introduce steel tower 4 column foots in the present invention and foundation connection is fixed, this constraint condition of rigid displacement of restriction iron tower structure, thus ensure that integral rigidity equation has unique solution.

The strain and stress formula calculating steel tower node in step 4 is:

$\left[\begin{array}{c}{\mathrm{\σ}}_x\\ {\mathrm{\σ}}_y\\ {\mathrm{\σ}}_z\\ {\mathrm{\τ}}_{xy}\\ {\mathrm{\τ}}_{yz}\\ {\mathrm{\τ}}_{zx}\end{array}\right]=\frac{E(1-\mathrm{\μ})}{(1+\mathrm{\μ})(1-2\mathrm{\μ})}\left[\begin{array}{cccccc}1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& 0& 0& 0\\ 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}& 0& 0\\ 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}& 0\\ 0& 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\mathrm{\γ}}_{xy}\\ {\mathrm{\γ}}_{yz}\\ {\mathrm{\γ}}_{zx}\end{array}\right]$

Wherein, σ _x, σ _y, σ _zfor the normal stress component of 3 on coordinate axis x, y, z direction; τ _xy, τ _yz, τ _zxfor in xy plane, yz plane, 3 shearing stress components in zx plane; be respectively steel tower space structure when there is deformation, the line strain component of the generation of Nodes on coordinate axis x, y, z tri-directions; for steel tower space structure is when deformation, Nodes in xy plane, yz plane, 3 the shearing strain components produced in zx plane.; U=u (x, y, z), v=v (x, y, z), w=w (x, y, z) is respectively steel tower space structure when deformation, and node is in the displacement in coordinate axis x, y, z direction; E is the elastic modulus of rod member; μ is Poisson ratio.

Technique effect of the present invention:

1) take into full account the elastic deformation of iron tower structure, mechanical analysis is carried out to each root rod member, superpose according to the mechanical property of iron tower structure to single rod member, make analysis result more accurate.

2) under not only can analyzing single operating mode, iron tower structure is stressed, also has superior performance to the iron tower structure force analysis under Analysis of Complex operating mode.

3) introduce steel tower 4 column foots and foundation connection is fixed in calculating, this constraint condition of rigid displacement of restriction iron tower structure, thus guarantee integral rigidity equation has unique solution, solves matrix equation dexterously in the singularity problem of singularity matrix.

Accompanying drawing explanation

Fig. 1 is that 220kV does font steel tower schematic diagram.

Fig. 2 is that in iron tower model, column foot imposes restriction condition schematic diagram.

Embodiment

Based on an electric power pylon rod member calculation method for stress for finite element analysis, can be summarized as four-stage: process in early stage, FEM mechanics analysis, operating mode load treatment and post-processed.In earlier stage process the finite element mechanical model comprising and set up iron tower structure and sliding-model control is carried out to one-piece construction; Namely FEM mechanics analysis is analyzed the finite element mechanical model of iron tower structure, and in conjunction with the space angle relation between rod member each in iron tower structure and annexation, superposition generates Bulk stiffness matrix; Operating mode load treatment is displaced on node by uniformly distributed load, not a node load-transfer mechanism suffered by steel tower, forms panel load array; Post-processed is namely using nodal displacement array as unknown quantity, and with Bulk stiffness matrix, load array composition matrix equation, and solution matrix equation, to egress strain, finally find out rod member weak in iron tower structure.The method mainly comprises the steps:

Step 1: the finite element mechanical model setting up iron tower structure according to Finite Element, obtains steel tower node according to the mechanical model obtained; And by iron tower structure discretize, obtain and the same number of unit of rod member between steel tower two node, unit is only connected by node (in steel tower, main material is considered as node with oblique material, tiltedly material with the joint of oblique material with main material, main material) each other;

Step 2: for each unit and nodal displacement, respectively generation unit stiffness matrix [k] ^(e)with nodal displacement array and according to the annexation between the space angle relation between rod member, rod member, conversion superposes out steel tower Bulk stiffness matrix

Step 3: be displaced on node by uniformly distributed load suffered by steel tower and not a node load-transfer mechanism, forms panel load array (wherein ), and consider matrix equation in singularity, introduce the displacement constraint of steel tower tower leg four node, solution matrix equation, obtains nodal displacement array

Step 4: calculate the strain of steel tower node, stress, obtains rod member weak in iron tower structure.

Below each step is described in further detail:

In step 1: the finite element mechanical model setting up iron tower structure according to Finite Element, obtain steel tower node according to the mechanical model obtained; And by iron tower structure discretize, obtain and the same number of unit of rod member between steel tower two node, unit is only connected by node (in steel tower, main material is considered as node with oblique material, tiltedly material with the joint of oblique material with main material, main material) each other, and its implementation process is:

First set up the finite element mechanical model of iron tower structure, with the x-axis of the cross-arm direction of steel tower coordinate system as a whole, line direction is as y-axis, and vertical direction as z-axis, and meets the right-hand rule; Using bar unit place straight line as the x-axis of unit local coordinate system, rod member overlaps with the x-axis direction under local coordinate system, and its positive dirction is consistent with global coordinate system x-axis positive dirction.

Electric power pylon is as space bar member system, carry out discrete with bar-beam element (being called for short bar unit) later, in the present invention, material main in steel tower and main material, main material and oblique material, the tiltedly joint of material and oblique material are turned to node, the rod member between every two nodes is considered as a bar unit.Due to the complicated structure of steel tower, rod member number is many, if structural separationization namely division unit time, it is less that unit divides, number of unit is more, and computing time is longer, therefore considers to divide according to the natural structure of steel tower itself, both improve computational accuracy, additionally reduce amount of calculation.

In step 2: for each unit and nodal displacement, generation unit stiffness matrix [k] respectively ^(e)with nodal displacement array and according to the annexation between the space angle relation between rod member, rod member, conversion superposes out steel tower Bulk stiffness matrix

After iron tower structure discretize, mechanical characteristic analysis to be carried out to unit, the relation namely between determining unit nodal force and nodal displacement.In order to analyze and determine this relation, need to select displacement model, displacement function is displacement that unit the is put function to the coordinate of point, this method polynomial expression of the coordinate of unit internal point represents, rod member in space, each node has 6 degree of freedom, and namely rod member is except bearing the effect of one dimension axle power, bidimensional shearing and bidimensional moment of flexure, also may bear the effect of one dimension moment of torsion.And, space framed rods bears one dimension axle power, bidimensional shearing, bidimensional moment of flexure, one dimension moment of torsion, namely correspond to 6 degree of freedom of node, be respectively the displacement of the lines on 3 directions and the rotation in Nodes cross section around 3 coordinate axis, because the polynomial expression of the coordinate of this element internal point can be expressed as δ=k ₁u+k ₂v+k ₃w+k ₄θ _x+ k ₅θ _y+ k ₆θ _z, accordingly, the displacement array of all nodes can be formed

$\begin{array}{cc}{\[\stackrel{\‾}{\mathrm{\δ}}\]}^{\left(e\right)}=\left[\begin{array}{c}{\[\stackrel{\‾}{\mathrm{\δ}}\]}_1\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_2\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_3\\ .\\ .\\ .\\ {\[\stackrel{\‾}{\mathrm{\δ}}\]}_n\end{array}\right]& {\[\stackrel{\‾}{\mathrm{\δ}}\]}_i\left[\begin{array}{c}{u}_i\\ v_i\\ w_i\\ {\mathrm{\θ}}_{xi}\\ {\mathrm{\θ}}_{yi}\\ {\mathrm{\θ}}_{zi}\end{array}\right],i=1,2,\mathrm{...},n\end{array}$

Wherein, for the nodal displacement array in global coordinate system; it is the displacement array of the 1st node; it is the displacement array of the 2nd node; By that analogy it is the displacement array of the n-th node; u _i, v _i, w _iit is the displacement of the lines in the i-th node three directions in local coordinate system; θ _xi, θ _yi, θ _zibe the rotation of the i-th Nodes cross section around three coordinate axis, θ _xirepresent the torsion in cross section, θ _yi, θ _zirepresent the rotation of cross section in xz and xy coordinate surface respectively.

The basic step setting up stiffness equation is: on the basis of assuming unit displacement function, according to theory of elastic mechanics, sets up strain, relational expression between stress and nodal displacement.Then according to the principle of virtual displacement, try to achieve the relation between cell node power and nodal displacement, thus draw following element stiffness matrix [k] ^(e):

Wherein, [k] ^(e)for the stiffness matrix of bar unit in unit local coordinate system; A is bar unit cross-sectional area; I _yfor cross sectional moment of inertia in xz face; I _zfor the cross sectional moment of inertia in xy face; I _pfor the torsional moment of inertia of unit; L is length; E and G is respectively elastic modulus and the modulus of shearing of material.

Unit element stiffness matrix [k] ^(e)after obtaining, according to the annexation between the space angle relation between rod member, rod member, conversion superposes out steel tower Bulk stiffness matrix its specific implementation process is as follows:

First, suppose that local coordinate is x, y, z; Overall coordinate is with the x-axis positive dirction forwarding global coordinate system from the x-axis positive dirction of local coordinate system clockwise to for just, then the direction cosine of x-axis are:

$l_{x\stackrel{\‾}{x}}=cos(x,\stackrel{\‾}{x}),l_{x\stackrel{\‾}{y}}=cos(x,\stackrel{\‾}{y}),l_{x\stackrel{\‾}{z}}=cos(x,\stackrel{\‾}{z})$

The direction cosine of y-axis are

$l_{y\stackrel{\‾}{x}}=cos(y,\stackrel{\‾}{x}),l_{y\stackrel{\‾}{y}}=cos(y,\stackrel{\‾}{y}),l_{y\stackrel{\‾}{z}}=cos(y,\stackrel{\‾}{z})$

The direction cosine of z-axis are

$l_{z\stackrel{\‾}{x}}=cos(z,\stackrel{\‾}{x}),l_{z\stackrel{\‾}{y}}=cos(z,\stackrel{\‾}{y}),l_{z\stackrel{\‾}{z}}=cos(z,\stackrel{\‾}{z})$

Order

${\[\mathrm{\λ}\]}_{01}=\left[\begin{array}{ccc}{l}_{x\stackrel{\‾}{x}}& l_{x\stackrel{\‾}{y}}& l_{x\stackrel{\‾}{z}}\\ l_{y\stackrel{\‾}{x}}& l_{y\stackrel{\‾}{y}}& l_{y\stackrel{\‾}{z}}\\ l_{z\stackrel{\‾}{x}}& l_{z\stackrel{\‾}{y}}& l_{z\stackrel{\‾}{z}}\end{array}\right]$

Element stiffness matrix then in global coordinate system be expressed as:

${\[\stackrel{\‾}{k}\]}^{\left(e\right)}={\[\mathrm{\λ}\]}^T{\[k\]}^{\left(e\right)}\[\mathrm{\λ}\]$

Wherein, [λ ₀] be node transition matrix, [λ] is coordinate conversion matrix, [k] ^(e)for the stiffness matrix of 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) will each sub-block carry out the number of changing, change corresponding entirety numbering into;

3) will change on correspondence position that later block delivers in Bulk stiffness matrix;

4) if when having the corresponding sub block of several unit to deliver on same position, then should superpose.

After above-mentioned steps, just can obtain each sub-block in Bulk stiffness matrix, thus define Bulk stiffness matrix

Wherein, for jth node produce unit displacement time, the nodal force that i-th node causes, is called rigidity submatrix.It should be noted that: in each sub-block be 6 × 6 rank matrixes, if one-piece construction has n node, so exponent number 6n × 6n of Bulk stiffness matrix.

Uniformly distributed 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 consider matrix equation in singularity, introduce the displacement constraint of steel tower tower leg four node, solution matrix equation, obtains nodal displacement array its specific implementation process is:

First uniformly distributed load, not a node load-transfer mechanism suffered by steel tower are displaced on node, form panel load array rod member in space, each node has 6 degree of freedom, and namely rod member is except bearing the effect of axle power, shearing and moment of flexure, also may bear the effect of moment of torsion.Further, space framed rods bears one dimension axle power, bidimensional shearing, bidimensional moment of flexure, one dimension moment of torsion, namely correspond to 6 degree of freedom of node.The bar unit space framed rods just of electric power pylon.

${\[\stackrel{\‾}{R}\]}^e=\left[\begin{array}{c}{\[\stackrel{\‾}{R}\]}_1\\ {\[\stackrel{\‾}{R}\]}_2\\ {\[\stackrel{\‾}{R}\]}_3\\ .\\ .\\ .\\ {\[\stackrel{\‾}{R}\]}_n\end{array}\right],{\[\stackrel{\‾}{R}\]}_i=\left[\begin{array}{c}{N}_{xi}\\ N_{yi}\\ N_{zi}\\ M_{xi}\\ M_{yi}\\ M_{zi}\end{array}\right],i=1,2,\mathrm{...},n$

Wherein, for panel load arrays all in overall coordinate; for the load column of i-th node in overall coordinate; N _xibe the axial force of i-th node, N _yi, N _zibe respectively the shearing of i-th node in xy and xz face; M _xibe the moment of torsion of i-th node, M _yi, M _zibe the moment of flexure of i-th node in xz and xy face.

Due to matrix equation in for singular matrix, system of equations, without solution, to solve this equation, must introduce constraint condition, the rigid displacement of restriction iron tower structure, ensures that integral rigidity equation has unique solution.The effect of displacement constraint makes the displacement component of structural node be constant value, i.e. δ _i=δ ₀.Introducing displacement constraint, is exactly will by δ _i=δ ₀be incorporated in structure collectivity stiffness equations.

In the present invention, diagonal element is adopted to put 1 method, by δ _i=δ ₀introduce Bulk stiffness matrix

$\left[\begin{array}{cccccc}{K}_{11}& K_{12}& \mathrm{...}& K_{1i}& \mathrm{...}& K_{1n}\\ K_{21}& K_{22}& \mathrm{...}& K_{2i}& \mathrm{...}& K_{2n}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ K_{i1}& K_{i2}& \mathrm{...}& K_{ii}& \mathrm{...}& K_{in}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ K_{n1}& K_{n2}& \mathrm{...}& K_{ni}& \mathrm{...}& K_{nn}\end{array}\right]\left[\begin{array}{c}{\mathrm{\δ}}_1\\ {\mathrm{\δ}}_2\\ .\\ .\\ .\\ {\mathrm{\δ}}_i\\ .\\ .\\ .\\ {\mathrm{\δ}}_n\end{array}\right]=\left[\begin{array}{c}{R}_1\\ R_2\\ .\\ .\\ .\\ R_i\\ .\\ .\\ .\\ R_n\end{array}\right]$

For in 4 tower legs of electric power pylon, the part be connected with basis is that stiff end retrains, therefore δ ₀=0; By the elements in a main diagonal K of i-th row of K _iiput 1, all the other elements reset, and by the load item R of the i-th row _iuse δ ₀replace, above formula becomes

$\left[\begin{array}{cccccc}{K}_{11}& K_{12}& \mathrm{...}& 0& \mathrm{...}& K_{1n}\\ K_{21}& K_{22}& \mathrm{...}& 0& \mathrm{...}& K_{2n}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ 0& 0& \mathrm{...}& 1& \mathrm{...}& 0\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ K_{n1}& K_{n2}& \mathrm{...}& 0& \mathrm{...}& K_{nn}\end{array}\right]\left[\begin{array}{c}{\mathrm{\δ}}_1\\ {\mathrm{\δ}}_2\\ .\\ .\\ .\\ {\mathrm{\δ}}_i\\ .\\ .\\ .\\ {\mathrm{\δ}}_n\end{array}\right]=\left[\begin{array}{c}{R}_1\\ R_2\\ .\\ .\\ .\\ 0\\ .\\ .\\ .\\ R_n\end{array}\right]$

By putting 1 method by displacement constraint δ _i=δ ₀be incorporated in integral rigidity equation, do not change each element storage sequence in matrix K and R, and matrix K be still symmetric matrix.

In computing method of the present invention, the submatrix of 4 leg nodes be connected with basis is adopted and puts 1 method, 24 displacement boundary conditions can be substituted into, eliminate the singularity of Bulk stiffness matrix, thus adopt Gaussian elimination method to carry out matrix equation to solve.

Step 4: computing node strain, stress etc., find out rod member the weakest in iron tower structure, its implementation process is as follows:

Solved the displacement δ of each node by the Bulk stiffness matrix Solving Equations of iron tower structure after, just can obtain the nodal displacement δ of each unit ^e.After iron tower structure is stressed, its interior point will be subjected to displacement along x, y, z tri-change in coordinate axis direction.If each point represents along the displacement of x, y, z tri-change in coordinate axis direction with u, v, w, they are coordinate functions of point, i.e. u=u (x, y, z), v=v (x, y, z), w=w (x, y, z).

Iron tower structure is when deformation, and there are 3 line strain component ε at inner any point place _x, ε _y, ε _zand 3 couples of shearing strain component γ _xy=γ _yx, γ _yz=γ _zy, γ _zx=γ _xz.From Elasticity, the relation between strain and displacement and geometric equation are:

${\mathrm{\ϵ}}_x=\frac{\∂u}{\∂x},{\mathrm{\γ}}_{xy}=\frac{\∂u}{\∂y}+\frac{\∂v}{\∂x}$

${\mathrm{\ϵ}}_y=\frac{\∂v}{\∂y},{\mathrm{\γ}}_{yz}=\frac{\∂v}{\∂z}+\frac{\∂w}{\∂y}$

${\mathrm{\ϵ}}_z=\frac{\∂w}{\∂z},{\mathrm{\γ}}_{zx}=\frac{\∂w}{\∂x}+\frac{\∂u}{\∂z}$

${\mathrm{\δ}}^e=\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\mathrm{\γ}}_{\mathrm{xy}}\\ {\mathrm{\γ}}_{yz}\\ {\mathrm{\γ}}_{zx}\end{array}\right]$

ε in formula _x, ε _y, ε _zfor being respectively steel tower space structure when there is deformation, the components of strain of the generation of Nodes on coordinate axis x, y, z tri-directions; γ _xy, γ _yz, γ _zxfor steel tower space structure is when deformation, Nodes in xy plane, yz plane, produce in zx plane 3 components of strain.

When iron tower structure is subject to acting on, the stress state at inner any point place is also three-dimensional, has 3 normal stress component σ _x, σ _y, σ _zand three couples of shearing stress component τ _xy=τ _yx, τ _yz=τ _zy, τ _zx=τ _xz.

In linear-elastic range, the following the Representation Equation of stress and strain:

$\left[\begin{array}{c}{\mathrm{\σ}}_x\\ {\mathrm{\σ}}_y\\ {\mathrm{\σ}}_z\\ {\mathrm{\τ}}_{xy}\\ {\mathrm{\τ}}_{yz}\\ {\mathrm{\τ}}_{zx}\end{array}\right]=\frac{E(1-\mathrm{\μ})}{(1+\mathrm{\μ})(1-2\mathrm{\μ})}\left[\begin{array}{cccccc}1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& 0& 0& 0\\ 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}& 0& 0\\ 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}& 0\\ 0& 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2(1-\mathrm{\μ})}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\mathrm{\γ}}_{xy}\\ {\mathrm{\γ}}_{yz}\\ {\mathrm{\γ}}_{zx}\end{array}\right]$

Wherein, σ _x, σ _y, σ _zfor the normal stress component of 3 on coordinate axis x, y, z direction; τ _xy, τ _yz, τ _zxfor in xy plane, yz plane, 3 shearing stress components in zx plane; be respectively steel tower space structure when there is deformation, the line strain component of the generation of Nodes on coordinate axis x, y, z tri-directions; for steel tower space structure is when deformation, Nodes in xy plane, yz plane, the shearing strain component produced in zx plane 3 planes; E is the elastic modulus of rod member; μ is Poisson ratio.

The content be not described in detail in this manual belongs to the known technology of those skilled in the art.

Claims (1)

1. an electric power pylon rod member calculation method for stress, is characterized in that: comprise the steps:

Step 1: the finite element mechanical model setting up iron tower structure according to Finite Element, obtains steel tower node according to the mechanical model obtained; And by iron tower structure discretize, obtain and the same number of unit of rod member between steel tower two node, unit is only connected by node each other; In steel tower, main material and main material, main material and oblique material, the tiltedly joint of material and oblique material are considered as node;

Step 2: for each unit and nodal displacement, respectively generation unit stiffness matrix [k] ^(e)with nodal displacement array and according to the annexation between the space angle relation between rod member, rod member, conversion superposes out steel tower Bulk stiffness matrix

Step 3: be displaced on node by uniformly distributed load suffered by steel tower and not a node load-transfer mechanism, forms panel load array wherein ${\[\stackrel{\‾}{R}\]}^{\left(e\right)}={\[\stackrel{\‾}{K}\]}^{\left(e\right)}{\[\stackrel{\‾}{\mathrm{\δ}}\]}^{\left(e\right)},$ And consider matrix equation ${\[\stackrel{\‾}{K}\]}^{\left(e\right)}={\[\stackrel{\‾}{\mathrm{\δ}}\]}^{\left(e\right)}{\[\stackrel{\‾}{R}\]}^{\left(e\right)}$ In singularity, introduce the displacement constraint of steel tower tower leg four node, solution matrix equation, obtains nodal displacement array

Step 4: calculate the strain of steel tower node, stress, obtains iron tower structure every root rod member stress;

Computing node strain, stress etc. in step 4, find out rod member the weakest in iron tower structure, its implementation process is as follows:

Solved the displacement δ of each node by the Bulk stiffness matrix Solving Equations of iron tower structure after, just can obtain the nodal displacement δ of each unit ^e; After iron tower structure is stressed, its interior point will be subjected to displacement along x, y, z tri-change in coordinate axis direction; If each point represents along the displacement of x, y, z tri-change in coordinate axis direction with u, v, w, they are coordinate functions of point, i.e. u=u (x, y, z), v=v (x, y, z), w=w (x, y, z);

Iron tower structure is when deformation, and there are 3 line strain component ε at inner any point place _x, ε _y, ε _zand 3 couples of shearing strain component γ _xy=γ _yx, γ _yz=γ _zy, γ _zx=γ _xz; From Elasticity, the relation between strain and displacement and geometric equation are:

${\mathrm{\ϵ}}_x=\frac{\∂u}{\∂x},{\mathrm{\γ}}_{xy}=\frac{\∂u}{\∂y}+\frac{\∂v}{\∂x}$

${\mathrm{\ϵ}}_y=\frac{\∂v}{\∂y},{\mathrm{\γ}}_{yz}=\frac{\∂v}{\∂z}+\frac{\∂w}{\∂y}$

${\mathrm{\ϵ}}_z=\frac{\∂w}{\∂z},{\mathrm{\γ}}_{zx}=\frac{\∂w}{\∂x}+\frac{\∂u}{\∂z}$

${\mathrm{\δ}}^e=\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\mathrm{\γ}}_{xy}\\ {\mathrm{\γ}}_{yz}\\ {\mathrm{\γ}}_{zx}\end{array}\right]$

ε in formula _x, ε _y, ε _zfor being respectively steel tower space structure when there is deformation, the components of strain of the generation of Nodes on coordinate axis x, y, z tri-directions; γ _xy, γ _yz, γ _zxfor steel tower space structure is when deformation, Nodes in xy plane, yz plane, produce in zx plane 3 components of strain;

When iron tower structure is subject to acting on, the stress state at inner any point place is also three-dimensional, has 3 normal stress component σ _x, σ _y, σ _zand three couples of shearing stress component τ _xy=τ _yx, τ _yz=τ _zy, τ _zx=τ _xz;

In linear-elastic range, the following the Representation Equation of stress and strain:

$\left[\begin{array}{c}{\mathrm{\σ}}_x\\ {\mathrm{\σ}}_y\\ {\mathrm{\σ}}_z\\ {\mathrm{\τ}}_{xy}\\ {\mathrm{\τ}}_{yz}\\ {\mathrm{\τ}}_{zx}\end{array}\right]=\frac{E\left(1-\mathrm{\μ}\right)}{\left(1+\mathrm{\μ}\right)\left(1-2\mathrm{\μ}\right)}\left[\begin{array}{cccccc}1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 0& 0& 0\\ \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& \frac{\mathrm{\μ}}{1-\mathrm{\μ}}& 1& 0& 0& 0\\ 0& 0& 0& \frac{1-2\mathrm{\μ}}{2\left(1-\mathrm{\μ}\right)}& 0& 0\\ 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2\left(1-\mathrm{\μ}\right)}& 0\\ 0& 0& 0& 0& 0& \frac{1-2\mathrm{\μ}}{2\left(1-\mathrm{\μ}\right)}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x\\ {\mathrm{\ϵ}}_y\\ {\mathrm{\ϵ}}_z\\ {\mathrm{\γ}}_{xy}\\ {\mathrm{\γ}}_{yz}\\ {\mathrm{\γ}}_{zx}\end{array}\right]$

Wherein, σ _x, σ _y, σ _zfor the normal stress component of 3 on coordinate axis x, y, z direction; τ _xy, τ _yz, τ _zxfor in xy plane, yz plane, 3 shearing stress components in zx plane; be respectively steel tower space structure when there is deformation, the line strain component of the generation of Nodes on coordinate axis x, y, z tri-directions; for steel tower space structure is when deformation, Nodes in xy plane, yz plane, the shearing strain component produced in zx plane 3 planes; E is the elastic modulus of rod member; μ is Poisson ratio.