CN102841968A - Design method for shape control structure of cable network with positive Gaussian curvature based on initial reference state - Google Patents

Abstract

The invention discloses an active shape control structure for a cable network with a positive Gaussian curvature. During the active replacement work, a total strain epsilon a of a surface cable is equal to the sum of an initial strain epsilon 0 in an initial reference state and an active replacement strain epsilon d during the work, namely, epsilon a=epsilon 0+epsilon d. Because the active replacement work can be normally carried out in the shape control structure of the cable network within a certain allowable temperature difference range, the active replacement strain epsilon d comprises a stress-strain increment delta epsilon e and a temperature strain epsilon T, namely, epsilon d=delta epsilon e+epsilon T. As a result, during the active replacement work, a total stress-strain of the surface cable epsilon e=epsilon 0+delta epsilon e=epsilon 0+epsilon d-epsilon T. During the replacement between the reference condition and some operating condition, the active replacement strain of the surface cable epsilon d is a fixed value unrelated to the load, the specification and the elasticity modulus of the surface cable and the like. According to the invention, an optimization design method based on the initial reference condition is provided, and can rapidly optimize the initial pretension of an inhaul cable in the initial reference state, determine the specification of the inhaul cable and meet the performance requirement in the operating condition of the active replacement.

Description

Positive gauss curvature rope net form control structure method for designing based on the initial baseline attitude

Technical field

The invention belongs to the design and the analysis field of Cable Structure in the engineerings such as building, instrument and machinery, relate to a kind of active shape control structure, be optimized the method for design based on the initial baseline attitude to employing positive gauss curvature rope net.

Background technology

Drag-line generally only has extensional rigidity; Do not possess resistance to compression and bendind rigidity; Therefore the rope web frame that is made up of drag-line need be introduced initial pretension through modes such as stretch-draw, lays in enough pre-tensile stress in advance, thereby drag-line is in tension state all the time in the assurance work use.Therefore, the initial pretension of confirming drag-line is one of important content of rope web frame design.

Face rope net with positive gauss curvature can't form the structure of pretension self-equilibrating.And in the arranged outside of face rope net radially behind the rope, face rope net and radially rope can constitute the positive gauss curvature rope web frame of pretension self-equilibrating.In addition, in work is used, can regulate and control the radially length of rope, impel face rope net to form different curved surfaces, thereby realize positive gauss curvature rope net form control structure through equipment such as actuator or lifting jack.

In work is used, carry a control structure and be load (as deadweight, temperature become, wind carries and snow load etc.) the down passive generation deformationization of effect and reach new equilibrium state; And the shape control structure is the certain bits shape when satisfying work, not only stands load action, also under the effect of regulating and controlling mechanism, initiatively is indexed to preset target bit shape and causes that internal force changes.Therefore, the variation of the internal force of shape control structure comes from two aspects: loads change and initiatively displacement.

The benchmark attitude of shape control structure is the initial configuration before the preparation work, and operating conditions is for the initiatively duty of displacement takes place.Therefore initiatively both position shapes all are the conditions of work of being scheduled to, and the material strain that causes of displacement also is scheduled to, and then also the cross section property with the elastic modulus of material and member is relevant in the variation of stress and internal force.

Use for reference the conventional control structure that carries, the basic ideas of carrying out the design of positive gauss curvature rope net active shape control structure are:

1) sets known conditions, comprising: the permissible load of the structure position shape condition of how much topological relations, drag-line material behavior, loading condition, edge-restraint condition, benchmark attitude and operating conditions of rope net, the strain tolerant of drag-line and regulating and controlling mechanism, the alternative specification of drag-line etc.

2) first specification and initial pretension of establishing drag-line.

3) performance analysis comprises initial baseline attitude and a plurality of operating conditions.

4) checking of bearing capacity of drag-line and regulating and controlling mechanism.

5), then adjust the cross section specification and initial pretension of drag-line if bearing capacity does not meet the demands.

6) repeat 3) to 5), satisfy convergence until iteration.

Adopt conventional mentality of designing of carrying control structure to carry out the design of rope net form control structure, focus on performance analysis,,, cause design efficiency low, fail to demonstrate fully the work characteristics of shape control structure because the operating conditions operating mode of shape control structure is too much although thinking is simple.

Positive gauss curvature rope net form control structure comprises face rope net and rope radially, through initiatively regulating and control the radially length of rope, realizes that face rope net curved surface initiatively is indexed to different working attitude position shape.According to functional requirement; The position shape of the benchmark attitude of rope net form control structure and operating conditions is confirmed; Therefore initiatively being indexed to the deformation that operating conditions produces from the benchmark attitude also confirms; Promptly initiatively the strain of displacement generation is a definite value, has nothing to do with the mechanical characteristic of material, the cross section property and the external applied load of member.In active displacement work, the rope net can run into also that temperature becomes, wind carries and loads change such as snow load.When running into abominable loading condition such as strong wind or heavy snow; Rope net form control structure should stop initiatively displacement work; But normally initiatively displacement work in certain permission temperature range, the strain that therefore produces in the active displacement work has comprised ess-strain increment and temperature strain.When warm variable load and one timing of line of material expansion coefficient, the temperature strain in the drag-line also is definite value.

Therefore; Through analyzing the difference of benchmark attitude and operating conditions shape on the throne and temperature aspect in advance; The strain that displacement and the temperature variation of having the initiative in hands causes then can be carried out the design of rope net form control structure based on initial baseline attitude (single operating mode), and need not to carry out the analysis repeatedly of operating conditions (a plurality of operating mode); This has obviously improved the design efficiency of rope net form control structure, but has increased the analysis difficulty of initial baseline attitude.

Positive gauss curvature rope net is the initial baseline attitude optimal design of shape control structure initiatively, and technical difficult points is: 1. how reasonably to limit face rope initial strain scope and set radially rope initial tension; 2. how based on the position shape of initial baseline attitude, seek and rope initial tension radially and the face rope initial tension that balances each other from heavy load; 3. face rope net generally is formed by connecting through bearing pin drag-line and web member; And drag-line is made up of cable body and rope head two parts; Therefore the elastic modulus of drag-line receives length and the rigidity of length and elastic modulus, the rope head of cable body, the influence of web member size in the practical structures, and how this pay attention in online element analysis model; 4. how according to the initial tension and the initial strain limited range of face rope, preferred drag-line cross section specification.

Summary of the invention

Technical matters: the objective of the invention is to the active displacement shape control structure that adopts positive gauss curvature rope net, provide a kind of and improve design efficiency, improve face rope strain energy deposit and rope net displacement recovery capability, improve radially cable force and the initial strain of face rope homogeneity, alleviate the positive gauss curvature rope net form control structure method for designing based on the initial baseline attitude of drag-line weight.

Technical scheme: face rope overall strain ε when initiatively displacement is worked _aEqual the initial strain ε of initial baseline attitude ₀Active displacement strain stress during with work _d, that is: ε _a=ε ₀+ ε _dBecause the normally initiatively displacement work of rope net form control structure, therefore active displacement strain stress in certain permission temperature range _dComprised ess-strain increment Delta ε _eWith temperature strain ε _T, that is: ε _d=Δ ε _e+ ε _TFace rope total stress strain stress when therefore, initiatively displacement is worked _e=ε ₀+ Δ ε _e=ε ₀+ ε _d-ε _TBetween benchmark attitude and certain operating conditions during displacement, the active displacement strain stress of face rope _dBe definite value, the specification of this and load, face rope and elastic modulus etc. are irrelevant.At temperature expansion coefficient one timing of drag-line material, temperature strain ε _TAlso only relevant with the line of material expansion coefficient with temperature variation.Positive gauss curvature rope net active shape control structure mentality of designing based on the initial baseline attitude is: according to active displacement strain and the temperature strain and the strain tolerant of face rope, confirm the face rope initial strain allowed band of initial baseline attitude; According to the regulation and control of rope radially allowable load scope, confirm the radially rope initial tension of initial baseline attitude; Based on the position shape of initial baseline attitude, that carries out face rope initial tension looks for the power analysis, seeks to satisfy with rope initial tension radially with from heavy load the face rope initial tension of static balance condition; According to initial strain allowed band, initial tension and the elastic modulus of face rope, be that principle is optimized face rope cross section specification to alleviate drag-line weight.

The positive gauss curvature rope net form control structure method for designing that the present invention is based on the initial baseline attitude comprises following steps:

1) finite element analysis model is prepared and is set up in analysis:

At first confirm how much topological relations of rope net, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shape, operating conditions structure position shape, the strain tolerant [ε] of drag-line, the permissible load upper limit [F of regulating and controlling mechanism _JU] and lower limit [F _JL], the alternative specification of drag-line and work allows temperature to become Δ T;

In finite element analysis software, set up finite element analysis model according to said rope net how much topological relations, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shapes then;

2) confirm the face rope temperature strain ε that warm variable load Δ T causes _T: ε _T=Δ T * α, wherein α is a drag-line line temperature expansion coefficient;

Simultaneously, in finite element analysis software, initial baseline attitude structure position shape and operating conditions structure position shape are compared, thereby confirm the face rope strain stress that initiatively displacement causes _dHigher limit ε _DUWith lower limit ε _DL

Simultaneously; According to the alternative specification of drag-line, select the cable body sectional area initial value

of the cable body sectional area of smallest cross-sectional specification as the face rope

3) confirm the face rope initial strain ε of initial baseline attitude ₀The upper limit [ε _0U] and lower limit [ε _0L]: the face rope initial strain ε that at first calculates the initial baseline attitude ₀The permitted maximum range be :-ε _DL+ ε _T<ε ₀<[ε]-ε _DU-ε _T, in this scope, choose [ε then _OU] and [ε _0L], that is :-ε _DL+ ε _T<[ε _0L]≤ε ₀≤[ε _0U]<[ε]-ε _DU-ε _T

Simultaneously, confirm the radially rope initial tension P of initial baseline attitude _J: the permissible load upper limit [F that gets regulating and controlling mechanism _JU] and lower limit [F _JL] mean value;

4) confirm that face rope net synthetical elastic modulus

is then in finite element analysis model; Apply from heavy load according to loading condition; Saidly comprise cable body, rope head, web member and appendicular weight from heavy load; Wherein, J is an iterations, and its initial value is 0: the method for said definite face rope net synthetical elastic modulus

is:

At first, according to the conversion elastic modulus of each face rope of computes;

$E_m^{\left(j\right)}=\frac{L_s^{\&prime;}}{(\frac{L_{\mathrm{sb}}^{\left(j\right)}}{E_b{A}_b^{\left(j\right)}}+\frac{{\left(L_{\mathrm{sh}}^{\left(j\right)}\right)}^2\&times;{\mathrm{\&rho;}}_h\&times;g}{E_h{G}_h})A_b^{\left(j\right)}}$

Wherein, G _h, ρ _hWeight, density for the rope head; G is an acceleration of gravity;

The cable body section of steel wire that is the j time iteration is long-pending; E _bBe the cable body elastic modulus; E _hBe rope head elastic modulus;

For with Actual rope head length, the actual cable body length of the j time corresponding iteration; L ' _sLength for cable elements in the analytical model;

Convert the weighted mean value of elastic modulus then according to each face rope of computes, as face rope net synthetical elastic modulus

$E_{m0}^{\left(j\right)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_m^{(j,i)}\&times;L_s^{(j,i)}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{L}_s^{(j,i)}}$

Wherein, i is the i root drag-line of veil rope; N is the total radical of the drag-line of veil rope;

That 5) adopts that submissile mould alternative manner carries out face rope initial tension looks for the power analysis, promptly based on the position shape of initial baseline attitude, seeks the radially rope initial tension P with the initial baseline attitude _JWith the face rope initial tension that satisfies static balance condition from heavy load

Concrete steps are:

51) in finite element analysis model, set and initiatively to regulate and control radially that the elastic modulus of rope is virtual little value E' _JGiving radially, rope applies fixed radially rope initial tension P _JWith from heavy load; The iterative initial value of confirming face rope initial tension does

Face rope initial tension iteration convergence error [ζ _Pm];

52) finite element analysis model being carried out static(al) finds the solution; Suo Li

k that obtains face rope net is an iterations, and its initial value is 0;

53) if

then stops iteration; With

as face rope initial tension otherwise; Make

and upgrade face rope initial tension, promptly use

replacement

get back to 52);

6) confirm the initial strain of face rope ${\mathrm{\&epsiv;}}_0^{\left(j\right)}:{\mathrm{\&epsiv;}}_0^{\left(j\right)}=P_M^{\left(j\right)}/(A_b^{\left(j\right)}\&times;E_{m0}^{\left(j\right)});$

7) judging whether to satisfy

is then to stop iteration; And long-pending

face rope initial tension

the face rope net synthetical elastic modulus

of the cable body section of steel wire of finally confirming the face rope otherwise; Choose the smallest cross-sectional specification of satisfied and upgrade face rope cross section specification, get back to step 4).

Beneficial effect: according to the work characteristics of positive gauss curvature rope net form control structure; Through analyzing the difference of benchmark attitude and operating conditions shape on the throne and temperature aspect between the operating period in advance; The strain that displacement and the temperature variation of having the initiative in hands causes; Limit the face rope initial strain allowed band in high level, narrow interval and set radially rope initial tension; Through looking for the power analysis to seek to satisfy the face rope initial tension of static balance condition with rope initial tension radially with from heavy load, thereby allow initial strain to limit down to alleviate the cross section specification that deadweight is a principle optimization drag-line at the face rope based on initial baseline attitude position shape.Adopt conventional mentality of designing of carrying control structure relatively, carry out rope net form control structure optimal design, need not to carry out the analysis repeatedly of operating conditions (a plurality of operating mode), obviously improved design efficiency based on initial baseline attitude (single operating mode).In the design, the face rope initial strain that limits the initial baseline attitude helps the even of face rope initial stress in higher level and narrower interval, improves face rope strain energy deposit and rope net displacement recovery capability, increases the radially minimum value of Suo Li, alleviates drag-line weight; The unified mean value of setting the radially rope initial tension of initial baseline attitude for the upper and lower limit of regulation and control permissible load, help rope initial tension radially evenly, and adjusting device is in running status preferably; That adopts that submissile mould alternative manner carries out face rope initial tension looks for the power analysis; The iteration fast and stable; Face rope initial tension after the convergence is balance with rope initial tension radially and from heavy load on the shape of the position of initial baseline attitude, therefore need not to carry out the conformal analysis of looking for of initial baseline attitude; Adopt the synthetical elastic modulus of the weighted mean value of each face rope conversion elastic modulus as face rope net; Both considered the influence of length and rigidity, the web member size of length and elastic modulus, the rope head of cable body in the practical structures, and also avoided large-scale rope web frame to set the loaded down with trivial details of different elastic modulus for every face rope the drag-line elastic modulus.

Description of drawings

Fig. 1 is based on the positive gauss curvature rope net form control structure method for designing process flow diagram of initial baseline attitude.

Fig. 2 is 500m bore radio telescope (Five-hundred-meter-Aperture Spherical Telescope is called for short FAST) reflecting surface rope web frame block mold figure.

Fig. 3 is a FAST reflecting surface rope web frame partial view.

Fig. 4 is an initiatively displacement work synoptic diagram of FAST reflecting surface rope web frame.

Have among the figure: face rope 1, radially rope 2, periphery supporting structure 3, actuator 4, benchmark sphere 5, work parabola 6, feed 7, feed track 8, sphere centre 9, celestial body 10.

Embodiment

Positive gauss curvature rope net form control structure method for designing based on the initial baseline attitude of the present invention may further comprise the steps:

1) finite element analysis model is prepared and is set up in analysis:

At first confirm how much topological relations of rope net, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shape, operating conditions structure position shape, the strain tolerant [ε] of drag-line, the permissible load upper limit [F of regulating and controlling mechanism _JU] and lower limit [F _JL], the alternative specification of drag-line and work allows temperature to become Δ T;

In finite element analysis software, set up finite element analysis model according to said rope net how much topological relations, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shapes then;

2) confirm the face rope temperature strain ε that warm variable load Δ T causes _T: ε _T=Δ T * α, wherein α is a drag-line line temperature expansion coefficient;

Simultaneously, in finite element analysis software, initial baseline attitude structure position shape and operating conditions structure position shape are compared, thereby confirm the face rope strain stress that initiatively displacement causes _dHigher limit ε _DUWith lower limit ε _DL, ε _DL≤ε _d≤ε _DU

Simultaneously; According to the alternative specification of drag-line, select the cable body sectional area initial value

of the cable body sectional area of smallest cross-sectional specification as the face rope

3) confirm the face rope initial strain ε of initial baseline attitude ₀The upper limit [ε _OU] and lower limit [ε _0L]: for guaranteeing face rope elastic working under design conditions, the ess-strain of face rope should satisfy: O<ε _e<[ε], then the maximum magnitude of face rope initial strain is :-ε _DL+ ε _T<ε ₀<[ε]-ε _DU-ε _TIn this overall range, leaving under the prerequisite of certain safety margin, choose the upper limit [ε of face rope initial strain _OU] and lower limit [ε _OL], that is :-ε _DL+ ε _T<[ε _OL]≤ε ₀≤[ε _0U]<[ε]-ε _DU-ε _T, the permission initial strain of face rope net is limited in higher level and the narrower interval; To allow initial strain to be limited to higher level, help improving face rope strain energy deposit and rope net displacement recovery capability, increase the radially minimum value of Suo Li, alleviate drag-line weight; To allow initial strain to be limited to narrower interval, help the even of face rope initial stress;

Simultaneously, confirm the radially rope initial tension P of initial baseline attitude _J: the permissible load upper limit [F that gets regulating and controlling mechanism _JU] and lower limit [F _JL] mean value, i.e. P _J=([F _JU]+[F _JL])/2;

4) confirm that face rope net synthetical elastic modulus

is then in finite element analysis model; Apply from heavy load according to loading condition; Saidly comprise cable body, rope head, web member and appendicular weight from heavy load; Wherein, j is an iterations, and its initial value is 0.

Face rope net generally is formed by connecting through bearing pin drag-line and web member, and drag-line is made up of cable body and rope head two parts.In the analytical model, the rope web frame often is reduced to the line model of element, and the end points of cable elements is the web member center.And length and the rigidity and the web member size of the length of the drag-line elastic modulus considered cable body in the practical structures and elastic modulus, rope head.Therefore, need be the elastic modulus of the cable elements in the analytical model with the elastic modulus conversion of actual drag-line.If web member is firm territory, the computing formula of the conversion elastic modulus of single rope is:

$E_m^{\left(j\right)}=\frac{L_s^{\&prime;}}{(\frac{L_{\mathrm{sb}}^{\left(j\right)}}{E_b{A}_b^{\left(j\right)}}+\frac{L_{\mathrm{sh}}^{\left(j\right)}}{E_h{A}_h^{\left(j\right)}})A_b^{\left(j\right)}}=\frac{L_s^{\&prime;}}{(\frac{L_{\mathrm{sb}}^{\left(j\right)}}{E_b{A}_b^{\left(j\right)}}+\frac{{\left(L_{\mathrm{sh}}^{\left(j\right)}\right)}^2\&times;{\mathrm{\&rho;}}_h\&times;g}{E_h{G}_h})A_b^{\left(j\right)}}$

（1）

Wherein, G _h, ρ _hThe weight of-rope head, density; G-acceleration of gravity;

The cable body section of steel wire of-the j time iteration is long-pending; E _b-cable body elastic modulus; E _h-rope head elastic modulus;

-with

Actual drag-line length, actual rope head length, the actual cable body length of the j time corresponding iteration, $L_s^{\left(j\right)}=L_{\mathrm{Sh}}^{\left(j\right)}+L_{\mathrm{Sb}}^{\left(j\right)}=L_s^{\&prime;\left(j\right)}-(B_1^{\left(j\right)}+B_2^{\left(j\right)})/2;$ L ' _sThe length of cable elements in the-analytical model;

The pin-and-hole center overall diameter of drag-line two end connections of-the j time iteration.

The conversion elastic modulus of every face rope is all different in the face rope net.For large-scale rope web frame, setting different moduli of elasticity for every face rope can be very loaded down with trivial details.Therefore the elastic modulus of face rope can be simplified the unified synthetical elastic modulus that adopts in the analytical model.According to the weighted mean value of each face rope conversion elastic modulus of computes, as face rope net synthetical elastic modulus

$E_{m0}^{\left(j\right)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_m^{(j,i)}\&times;L_s^{(j,i)}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{L}_s^{(j,i)}}$

（2）

Wherein, the i root drag-line of i-veil rope; The total radical of drag-line of n-veil rope;

Comprise structure and appendicular weight from heavy load, wherein dead load comprises the weight of cable body, rope head and web member.Web member and adjunct all can concentrated force or the form of lumped mass be applied on the node.Because the web member size of the cable body density of every kind of specification drag-line, rope head weight and correspondence is all different, cable elements length is the length between the node in the analytical model in addition, and actual drag-line length is the distance between the pin-and-hole center on two end connections.For accurately applying drag-line weight, with the difference between the weight of the weight of actual drag-line and cable elements, to divide equally with the form of nodal force and to act on bitter end two nodes, computing formula is:

$\mathrm{\&Delta;}{F}_s^{\left(j\right)}=(G_s^{\left(j\right)}-G_s^{\&prime;\left(j\right)})/2=(G_{\mathrm{sh}}^{\left(j\right)}+L_{\mathrm{sb}}^{\left(j\right)}\&times;q_{\mathrm{sb}}^{\left(j\right)}-G_s^{\&prime;\left(j\right)})/2$

$=[G_{\mathrm{sh}}^{\left(j\right)}+(L_s^{\left(j\right)}-L_{\mathrm{sh}}^{\left(j\right)})\&times;q_{\mathrm{sb}}^{\left(j\right)}-G_s^{\&prime;\left(j\right)}]/2$

$=[G_{\mathrm{sh}}^{\left(j\right)}+(L_s^{\&prime;}-(B_1^{\left(j\right)}+B_2^{\left(j\right)})/2-L_{\mathrm{sh}}^{\left(j\right)})\&times;q_{\mathrm{sh}}^{\left(j\right)}-L_s^{\&prime;\left(j\right)}\&times;q_s^{\&prime;\left(j\right)}]/2$

（3）

Wherein,

Heavy and the gross weight of the line of the cable elements of the j time iteration in-the analytical model,

-actual cable body line is heavy;

-actual drag-line weight, rope head weight and cable body weight, $G_s^{\left(j\right)}=G_{\mathrm{Sh}}^{\left(j\right)}+G_{\mathrm{Sb}}^{\left(j\right)},$ $G_{\mathrm{Sb}}^{\left(j\right)}=L_{\mathrm{Sb}}^{\left(j\right)}\&times;q_{\mathrm{Sb}}^{\left(j\right)}.$

That 5) adopts that submissile mould alternative manner carries out face rope initial tension looks for the power analysis, promptly based on the position shape of initial baseline attitude, seeks the radially rope initial tension P with the initial baseline attitude _JWith the face rope initial tension that satisfies static balance condition from heavy load

Concrete steps are:

51) in finite element analysis model, set and initiatively to regulate and control radially that the elastic modulus of rope is virtual little value E' _J(this little value and material behavior are irrelevant, but under convergence condition, should look for the power analysis efficiency with raising as far as possible for a short time); Giving radially, rope applies fixed radially rope initial tension P _JWith from heavy load; The iterative initial value of confirming face rope initial tension does

Face rope initial tension iteration convergence error [ζ _Pm];

52) finite element analysis model being carried out static(al) finds the solution; Suo Li

k that obtains face rope net is an iterations, and its initial value is 0;

53) if

then stops iteration; With

as face rope initial tension

otherwise; Make

and upgrade face rope initial tension, promptly use

replacement get back to 52);

6) confirm the initial strain of face rope ${\mathrm{\&epsiv;}}_0^{\left(j\right)}:{\mathrm{\&epsiv;}}_0^{\left(j\right)}=P_M^{\left(j\right)}/(A_b^{\left(j\right)}\&times;E_{m0}^{\left(j\right)});$

7) judging whether to satisfy is then to stop iteration; And long-pending

face rope initial tension

the face rope net synthetical elastic modulus

of the cable body section of steel wire of finally confirming the face rope otherwise; Choose the smallest cross-sectional specification of satisfied

and upgrade face rope cross section specification, get back to step 4).

Below in conjunction with FAST reflecting surface rope web frame to further explain of the present invention.

The FAST engineering is a 500m bore radio telescope, its reflecting surface rope web frame by positive gauss curvature surface rope net and radially rope constitute.Sphere rope net forms according to the braiding of short distance line style grid mode, and each main rope net node connects a radially control cord, and radially the rope lower end links to each other with the ground actuator, through controlling the actuator stretching or loosening radially Suo Shixian reflecting surface displacement.Initiatively displacement is the maximum characteristics of FAST reflecting surface, forms the instantaneous parabola of 300m bore to converge electromagnetic wave through ACTIVE CONTROL in observed ray, and parabola moves along with observation celestial body and on 500m bore spherical crown, moves during observation, thereby realizes tracking observation.

The initial baseline attitude optimal design step of FAST reflecting surface rope web frame is:

1) finite element analysis model is prepared and is set up in analysis.

Confirm known conditions and set up finite element analysis model.The drag-line material adopts finished product high strength steel strand bundle rope, and cable body tensile strength standard value is 1860MPa, the cable body elastic modulus E _b=190GPa, temperature line expansion coefficient α=1.2 * 10 ^-5, strain tolerant [ε]=3.54 * 10 ^-3The alternative specification of face rope from smallest cross-sectional specification OVM.ST15-2 to the maximum cross-section specification OVM.ST15-11J3, totally 20 kinds; Load mainly comprises: the deadweight of drag-line, web member and back of the body frame and 25 ℃ warm variable load; Between face rope net and the periphery supporting structure, and radially be hinged between rope and the lower end actuator; Face rope net is the sphere of bore 500m and radius 300m during the benchmark attitude, and the parabola of bore 300m is at the online mobile observation of face rope during operating conditions; Radially rope is regulated and control the permissible load upper limit [F _JU] be 50kN, lower limit [F _JL] be 10kN.

2) confirm the face rope temperature strain ε that warm variable load Δ T (=25 ℃) causes _T: ε _T=25 * 1.2 * 10 ^-5=0.0003;

Simultaneously, in finite element analysis software, initial baseline attitude structure position shape and operating conditions structure position shape are compared, thereby confirm the face rope strain stress that initiatively displacement causes _dHigher limit ε _DUFor+0.00047 with lower limit ε _DLBe-0.00165.

Simultaneously; According to the alternative specification of drag-line, select the cable body sectional area initial value

of the cable body sectional area of smallest cross-sectional specification OVM.ST15-2 as the face rope

3) confirm the face rope initial strain ε of initial baseline attitude ₀The upper limit [ε _OU] and lower limit [ε _0L]: for guaranteeing face rope elastic working under design conditions, the ess-strain of face rope should satisfy: O<ε _e=ε ₀+ ε _d-ε _T<[ε], then the maximum magnitude of face rope initial strain is: 0.00195<ε ₀<0.00277; In this overall range, leaving under the prerequisite of certain safety margin, choose the upper limit [ε of face rope initial strain _0U] be 0.0025, lower limit [ε _0L] be 0.00215.

Simultaneously, confirm the radially rope initial tension P of initial baseline attitude _J: because the intensification of warm variable load and the extreme value of cooling are antisymmetric; The epirelief and the recessed displacement extreme value of relative datum sphere also are antisymmetric during parabola active displacement; So relative sphere benchmark attitude, it also is antisymmetric that the radially Suo Li of the most unfavorable processing condition changes extreme value.Therefore, the radially rope initial tension of initial baseline attitude is got the mean value of its upper limit value and lower limit value, i.e. P _J=30kN;

4) confirm that face rope net synthetical elastic modulus then in finite element analysis model, applies from heavy load according to loading condition.

In the analytical model, the rope web frame is reduced to the line model of element.If web member is firm territory, the cable body elastic modulus E _b=190GPa, rope head elastic modulus E _h=206GPa, rope head density p _h=7850kg/m ³, gravity acceleration g=9.8m/s ², the concrete size and the weight of cable body, rope head and web member are not listed at this in detail.Calculate the conversion elastic modulus of each face rope according to formula (1), calculate the synthetical elastic modulus E of face rope net then according to formula (2) _M0

Comprise the weight of cable body, rope head, web member and back of the body frame from heavy load, wherein web member and back of the body frame all can concentrated force or the form of lumped mass be applied on the node.Because the web member size of the cable body line of every kind of specification drag-line weight, rope head weight and correspondence is all different, cable elements length is the length between the node in the analytical model in addition, and actual drag-line length is the distance between the pin-and-hole center on two end connections.For accurately applying drag-line weight, calculate the difference between the weight of weight and cable elements of actual drag-line according to formula (3), divide equally with the form of nodal force and act on bitter end two nodes.

That 5) adopts that submissile mould alternative manner carries out face rope initial tension looks for the power analysis, promptly based on the position shape of initial baseline attitude, seeks the radially rope initial tension P with the initial baseline attitude _JWith the face rope initial tension that satisfies static balance condition from heavy load

Concrete steps are:

51) in finite element analysis model, set and initiatively to regulate and control radially that the elastic modulus of rope is virtual little value E' _J=190MPa; Giving radially, rope applies fixed radially rope initial tension P _JWith from heavy load; The iterative initial value of confirming face rope initial tension does $P_M^{(j,0)}=\left[{\mathrm{\&epsiv;}}_{0U}\right]\&times;E_{m0}^{\left(j\right)}\&times;A_b^{\left(j\right)}=0.0025\&times;E_{m0}^{\left(0\right)}\&times;A_b^{\left(0\right)},$ Face rope initial tension iteration convergence error [ζ _Pm]=0.01;

52) finite element analysis model being carried out static(al) finds the solution; Suo Li

k that obtains face rope net is an iterations, and its initial value is 0;

53) if then stops iteration; With as face rope initial tension

otherwise; Make

and upgrade face rope initial tension, promptly use

replacement get back to 52);

After the power of looking for was analyzed, the radially cable force of initial sphere benchmark attitude was 29.955 ~ 30.032kN; The Suo Li of face rope is 82.358 ~ 1120kN; The maximum node displacement is 0.987mm.

6) confirm the initial strain of face rope ${\mathrm{\&epsiv;}}_0^{\left(j\right)}:{\mathrm{\&epsiv;}}_0^{\left(j\right)}=P_M^{\left(j\right)}/(A_b^{\left(j\right)}\&times;E_{m0}^{\left(j\right)});$

7) judging whether to satisfy

is then to stop iteration; And long-pending

face rope initial tension

the face rope net synthetical elastic modulus

of the cable body section of steel wire of finally confirming the face rope otherwise; Choose the smallest cross-sectional specification of satisfied

and upgrade face rope cross section specification, get back to step 4).

Initial baseline attitude rope net design result is: face Suo Chongliang is 1174T, and radially Suo Chongliang is 57T, and web member weight is 396T, and face rope net synthetical elastic modulus is 213.8GPa.

Claims (1)

1. positive gauss curvature rope net form control structure method for designing based on the initial baseline attitude is characterized in that the method includes the steps of:

1) finite element analysis model is prepared and is set up in analysis:

At first confirm how much topological relations of rope net, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shape, operating conditions structure position shape, the strain tolerant [ε] of drag-line, the permissible load upper limit [F of regulating and controlling mechanism _JU] and lower limit [F _JL], the alternative specification of drag-line and work allows temperature to become Δ T;

In finite element analysis software, set up finite element analysis model according to said rope net how much topological relations, drag-line material behavior, loading condition, edge-restraint condition, initial baseline attitude structure position shapes then;

2) confirm the face rope temperature strain ε that warm variable load Δ T causes _T: ε _T=Δ T * α, wherein α is a drag-line line temperature expansion coefficient;

Simultaneously, in finite element analysis software, initial baseline attitude structure position shape and operating conditions structure position shape are compared, thereby confirm the face rope strain stress that initiatively displacement causes _dHigher limit ε _DUWith lower limit ε _DL

Simultaneously; According to the alternative specification of drag-line, select the cable body sectional area initial value

of the cable body sectional area of smallest cross-sectional specification as the face rope

3) confirm the face rope initial strain ε of initial baseline attitude ₀The upper limit [ε _0U] and lower limit [ε _0L]: the face rope initial strain ε that at first calculates the initial baseline attitude ₀The permitted maximum range be :-ε _DL+ ε _T<ε ₀<[ε]-ε _DU-ε _T, in this scope, choose [ε then _0U] and [ε _0L], that is :-ε _DL+ ε _T<[ε _0L]≤ε ₀≤[ε _0U]<[ε]-ε _DU-ε _T

Simultaneously, confirm the radially rope initial tension P of initial baseline attitude _J: the permissible load upper limit [F that gets regulating and controlling mechanism _JU] and lower limit [F _JL] mean value;

4) confirm that face rope net synthetical elastic modulus

is then in finite element analysis model; Apply from heavy load according to loading condition; Saidly comprise cable body, rope head, web member and appendicular weight from heavy load; Wherein, J is an iterations, and its initial value is 0: the method for said definite face rope net synthetical elastic modulus

is:

At first, according to the conversion elastic modulus of each face rope of computes;

$E_m^{\left(j\right)}=\frac{{L^{\&prime;}}_s}{(\frac{L_{\mathrm{sb}}^{\left(j\right)}}{E_b{A}_b^{\left(j\right)}}+\frac{{\left(L_{\mathrm{sh}}^{\left(j\right)}\right)}^2\&times;{\mathrm{\&rho;}}_h\&times;g}{E_h{G}_h})A_b^{\left(j\right)}}$

Wherein, G _h, ρ _hWeight, density for the rope head; G is an acceleration of gravity;

The cable body section of steel wire that is the j time iteration is long-pending; E _bBe the cable body elastic modulus; E _hBe rope head elastic modulus;

For with

Actual rope head length, the actual cable body length of the j time corresponding iteration; L ' _sLength for cable elements in the analytical model;

Convert the weighted mean value of elastic modulus then according to each face rope of computes, as face rope net synthetical elastic modulus

$E_{m0}^{\left(j\right)}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{E}_m^{(j,i)}\&times;L_s^{(j,i)}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{L}_s^{(j,i)}}$

Wherein, i is the i root drag-line of veil rope; N is the total radical of the drag-line of veil rope;

That 5) adopts that submissile mould alternative manner carries out face rope initial tension looks for the power analysis, promptly based on the position shape of initial baseline attitude, seeks the radially rope initial tension P with the initial baseline attitude _JWith the face rope initial tension that satisfies static balance condition from heavy load

Concrete steps are:

51) in finite element analysis model, set and initiatively to regulate and control radially that the elastic modulus of rope is virtual little value E ' _JGiving radially, rope applies fixed radially rope initial tension P _JWith from heavy load; The iterative initial value of confirming face rope initial tension does

Face rope initial tension iteration convergence error [ξ _Pm];

52) finite element analysis model being carried out static(al) finds the solution; Suo Li

k that obtains face rope net is an iterations, and its initial value is 0;

53) if $\left|\frac{F_M^{(j,k)}-P_M^{(j,k)}}{P_M^{(j,k)}}\right|\&le;\left[{\mathrm{\&xi;}}_{\mathrm{Pm}}\right],$ Then stop iteration, will

As face rope initial tension Otherwise, order

And the face of renewal rope initial tension, promptly use

Replacement

Get back to 52);

6) confirm the initial strain of face rope

${\mathrm{\&epsiv;}}_0^{\left(j\right)}=P_M^{\left(j\right)}/(A_b^{\left(j\right)}\&times;E_{m0}^{\left(j\right)});$

7) judge whether to satisfy

Be then to stop iteration, and confirm that finally the cable body section of steel wire of face rope is long-pending

Face rope initial tension

Face rope net synthetical elastic modulus

Otherwise, choose satisfied $A_b^{(j+1)}\&GreaterEqual;P_M^{\left(j\right)}/\left(\right[{\mathrm{\&epsiv;}}_{0U}]\&times;E_{m0}^{\left(j\right)})$ The smallest cross-sectional specification upgrade face rope cross section specification, get back to step 4).

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