CN104765925A - Cable-strut pretension structure stretch forming optimal selection method based on error sensitivity analysis - Google Patents

Abstract

The invention discloses a cable-strut pretension structure stretch forming optimal selection method based on error sensitivity analysis. The method includes the steps of firstly, establishing the basic relation, namely, the strut piece length error sensitivity analysis theory, of pretension deviation and strut piece length deviation based on three equations of a space hinge structure; secondly, deriving other basic relations of driven cable strut inner force deviation and strut piece length deviation under the condition of accurate control over driving stretch cable inner force and under the condition that the driving cable inner force deviation is zero to obtain inner force deviation formed by selecting different driving stretch cables and driven cable struts under various stretch forming schemes; thirdly, calculating the evaluation parameters of driven cable strut inner force deviation under various stretch forming schemes through the combination of a probability theory method and a mathematical statistics theory, and then evaluating error effects of the different stretch schemes. By analyzing and evaluating the error effects of the various construction schemes, the construction scheme which is low in error effect, convenient to construct and low in construction cost is selected as the stretch forming scheme of the structure, and theoretical guidance is provided for selecting the construction scheme of the project.

Description

Based on the rope bar pretension structure stretch-draw forming method for optimizing that error sensitivity is analyzed

Technical field

The present invention relates to pretension structure stressed-to form technology field, in particular based on the rope bar pretension structure stretch-draw forming method for optimizing that error sensitivity is analyzed.

Background technology

Cable-strut tensile structure to be a kind ofly made up of drag-line and depression bar, by the flexible tension structure of stretch-draw forming, because this system makes full use of the high epistasis of drag-line and the control advantage of pretension, thus make structure have the features such as span ability is strong, economic performance good, moulding is light and handy, be study hotspot and the developing direction from now on of Current Domestic external space large-span structure.Now there are some researches show, appropriate design and accurate applying of pretension are the key factors realizing the superior load-carrying properties of tension structure, there is no the reasonable Arrangement of pretension, just there is no good mechanical property and Stiffness Distribution, and accurately effective construction stretching is the prerequisite and the basis that realize pretension reasonable layout, pretension progressively generates along with the progressively stretch-draw of system, and finally completes along with work progress the final generation realizing pretension.Therefore, the rationality of tension structure construction stretching forming technique and validity are directly connected to the accurate validity that final pretension generates.

The main research structure of pretension structure construction forming technique obtains the method for tension force, implementation process and correlation technique, the solid enabling tension structure realize relaxing from one group to the process obtaining desirable design shape and prestress distribution, thus becomes reasonable, an efficient structure.Because system before flexible pretension structure formation is unstable, and along with rigid motion in forming process, stiffness matrix is unusual, therefore usually adopts " looking for shape " analytical approach in morphological analysis.Current construction forming technical research is many to be launched based on construction forming Scheme Choice and construction forming process simulation two aspect.Geiger proposes oblique cord forming arrangements under by outer and inner from coil to coil stretch-draw in 1988 Seoul Olympic Games gymnasium and fencing hall Cable dome roof design.The annular tension force cable truss canopy structure of Jeon Bongsoo to integrated symmetric proposes the construction forming scheme of radial cable in from coil to coil stretch-draw.Shen Zuyan etc. propose the former long control methods of rope, after determining the former length of Cable dome every root component, according to order assembling rod member, then successively by oblique cord stretch-draw to design length, need not stretch-draw repeatedly.Dong Shilin etc. propose seven kinds of construction forming schemes such as from coil to coil oblique cord stretching method, only outer ring oblique cord stretching method, from coil to coil montant top platen press, only outer ring montant top platen press, from coil to coil strop stretching method, only outer ring strop stretching method, the former long Method for Installation of from coil to coil oblique cord to Levy type cable dome structure, and simulate construction overall process based on the former length of control member and Dynamic Relaxation.Tang Jianmin etc., based on rigid body displacement supposition, adopt the work progress of finite element method to axisymmetric Geiger type cable dome structure to carry out sunykatuib analysis and experimental study.Luo Yaozhi adopts straight line pole unit, has followed the tracks of stretch-draw forming overall process, and analyze prestress Conduce Disciplinarian based on singular value decomposition method and geometrical non-linearity force method.Yuan Hangfei etc. based on the supposition of rigid body displacement and para-curve unit, by tearing bar method open to follow the tracks of be shaped the rod member motion in each stage and rope bar internal force rule.Huang Chengwei etc. adopt the mode alternately regulating strop, have carried out sunykatuib analysis and experimental study to the work progress of axisymmetric Geiger type cable dome structure.Deng Hua etc. propose based on para-curve unit, the former length of control cord, utilize thinking research rope bar tension force system stretch-draw forming each phase balancing state analytical approach of force density method.Zheng Jun China is fixed for Component-Based Development former long holidays, adopts finite element method and stretch-draw outer ring oblique cord forming process, stretch-draw outer ring notochord forming process and the stretch-draw outer ring strop forming process application at sunflower-shaped cable dome structure of combination model analysis of experiments.Guo Yanlin etc. utilize finite element method and Component-Based Development setting analysis former long holidays stadium, Bao'an, Shenzhen stretch-draw radial cable intending adopting is shaping, jacking flies the multiple stretch-draw forming schemes such as the shaping and stretch-draw strop of post is shaping.Yu Bin etc. analyze the integral tension lift technique that radial cable on pretensioning that to intend adopting in the constructing stadium of Bao'an, Shenzhen puts in place, radial cable puts in place under stretch-draw again, and propose a kind of scale fixed length design and construction control method.Jiang Leixin etc. analyze common upright method of hull section construction in existing cable-strut system stretch-draw forming and tear Computing Principle and the relative merits of method two kinds of construction methods open, and propose in stretch-draw forming process and improve constringent applying initial strain and assist convergence method and attachment beam element to assist convergence method.Ge Jiaqi etc. propose stretch-draw and respectively enclose radial oblique cord, stretch-draw each ring rope and multiple stretch-draw forming methods such as each ring rope of stretch-draw and interior oblique cord, and adopt finite element method and component surely to follow the tracks of stretch-draw forming overall process former long holidays.Wang Ze is strong etc. describes the application of Integral synchronous Lifting Technology in China's First cable dome structure-gouy flag nationwide fitness programs sports center, Inner Mongol Cable dome construction forming in detail, and the gordian technique such as the prestressed stretch-draw order described in construction forming and method, Construction Simulation and monitoring control.Leaf dogfaces etc. adopt mechanical dynamics analysis of multi rigid body system method, achieve the dynamic similation to the whole work progress of cable dome structure and control.Applicant once Kiewitt type cable dome structure be have employed that progressively stretch-draw outer ring oblique cord is shaped, disposable stretch-draw outer ring oblique cord is shaped and by outer and in progressively regulate depression bar to grow up to the multiple forming arrangements such as shape to former, and propose based on para-curve unit, control cord Duan Yuanchang, utilize Dynamic Relaxation to simulate the construction forming process of cable dome structure, but research method is confined to the error effects that component former long holidays are fixed, do not have the various forming arrangements of assay simultaneously equally.

Generally speaking, the stretch-draw forming theoretical research of pretension structure and test simulation technology have obtained certain achievement in research all, and correlation theory is necessarily applied in Practical Project.But existing stretch-draw forming theoretical research is many to be launched based on perfect condition condition, do not take into full account that in actual pretension structure construction procedure, the ubiquitous all kinds of construction errors such as component length error, block error that comprise are on construction stage and the impact becoming form and load state, simultaneously also the error effects of each stretch-draw forming scheme of assay not yet in effect and construction precision.

Therefore, prior art has yet to be improved and developed.

Summary of the invention

The technical problem to be solved in the present invention is, for the above-mentioned defect of prior art, provides the rope bar pretension structure stretch-draw forming method for optimizing analyzed based on error sensitivity.Be intended to the error effects by the various arrangement and method for construction of assay thus the arrangement and method for construction that Select Error effect is low, easy construction, construction cost are low as the stretch-draw forming scheme of structure, for the scheme choice of such engineering provides theoretical direction.

The technical scheme that technical solution problem of the present invention adopts is as follows:

Based on the rope bar pretension structure stretch-draw forming method for optimizing that error sensitivity is analyzed, wherein, comprise step:

A, to build the fundamental relation of pretension deviations and rod member length variation based on three large equations of space articulated structure, i.e. rod member error in length sensitivity analysis theory;

B, accurately can to control initiatively i.e. rustling sound internal force deviation based on active stretch-draw rustling sound internal force be under zero condition, derive all the other by the fundamental relation of dynamic search bar internal force deviation and rod member length variation, under trying to achieve various stretch-draw forming scheme, (selects different initiatively stretching rope) by dynamic search bar internal force deviation;

C, join probability opinion method and mathematical statistics calculate various stretch-draw forming scheme by the evaluating of dynamic search bar internal force deviation, and then evaluate the error effects of different stretching plan.

The rope bar pretension structure stretch-draw forming method for optimizing analyzed based on error sensitivity provided by the present invention, by the error effects of the various arrangement and method for construction of assay thus the arrangement and method for construction that Select Error effect is low, easy construction, construction cost are low as the Tension Forming scheme of structure, for the scheme choice of such engineering provides theoretical direction.

Accompanying drawing explanation

Fig. 1 is the embodiment process flow diagram of the rope bar pretension structure stretch-draw forming method for optimizing based on error sensitivity analysis of the present invention.

Fig. 2 is the preferred application embodiment annular cable-strut tensile structure three-dimensional plot of the rope bar pretension structure stretch-draw forming method for optimizing based on error sensitivity analysis of the present invention

Fig. 3 is the preferred application embodiment annular cable-strut tensile structure sectional view of the rope bar pretension structure stretch-draw forming method for optimizing based on error sensitivity analysis of the present invention and corresponding physical dimension.

Embodiment

For making object of the present invention, technical scheme and advantage clearly, clearly, developing simultaneously referring to accompanying drawing, the present invention is described in more detail for embodiment.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

As shown in Figure 1 be the embodiment process flow diagram of rope bar pretension structure stretch-draw forming method for optimizing analyzed based on error sensitivity of the present invention, said method comprising the steps of:

S100, to build the fundamental relation of pretension deviations and rod member length variation based on three large equations of space articulated structure, i.e. rod member error in length sensitivity analysis theory; Can the stretch-draw forming scheme of effective departure effect for exploring, first the error sensitivity analysis theories that to build with rod member error in length be variable, namely rod member length changes and structural internal force variation relation, carrys out the error effects (comprising pretension deviation and form variations) that analytical structure rod member error in length is brought thus.The rod member number making a spatial cable-strut structure (using drag-line as bar unit process) is b, and nodes is n, and support restraint number is c.As rod member existing defects length e ₀time (b × 1), set up following three fundamental equations:

Balance equation At=P (1)

Physical equation t=M (e-e ₀) (2)

Geometric equation Bd=e (3)

In formula, t is force vector (b × 1) in rod member, and P is joint load vector ((3n-c) × 1), and d is nodal displacement vector ((3n-c) × 1), and e is rod member stroke (b × 1), e ₀for the initial stroke of rod member (b × 1), M is element stiffness diagonal matrix (b × b), M _ii=E _ia _i/ l _i, E _i, A _i, l _ibe respectively the elastic modulus of i-th rod member, sectional area and length, A is that balancing matrix ((3n-c) × b), B are for coordinating matrix (b × (3n-c)), B=A ^t.

Be easy to get by formula (1), (2), (3):

t＝MA ^T(AMA ^T) ^-1P+M(A ^T(AMA ^T) ^-1AM-I)e ₀(4)

＝t _P+t _e

Above formula reflects defect length e ₀, external load P and rod member axle power t relation, wherein I is unit matrix, t _pfor the rod member internal force caused by load, t _efor the rod member internal force caused by the initial length defect of rod member.Therefore, when external load P is constant, the pretension deviation in rope bar pretension structure can be described as being caused by the former long change of rod member, when the former length of rod member is changed to δ e ₀time, then knots modification (hereinafter referred to as pretension deviation) the δ t trying to achieve structural member axle power by formula (4) is:

δt＝M(A ^T(AMA ^T) ^-1AM-I)δe ₀＝S _tδe ₀(5)

S in formula _t=M (A ^t(AMA ^t) ^-1aM-I) be internal force sensitivity matrix (b × b), its element (S _t) _ijreflect the enlargement factor of the former long change of rod member j to rod member i internal force deviation.Visible, formula (5) has set forth the fundamental relation of rod member length variation and pretension deviation, can be used to the error sensitivity evaluating each rod member.

S200, accurately can to control initiatively i.e. rustling sound internal force deviation based on active stretch-draw rustling sound internal force be under zero condition, derive all the other by the fundamental relation of dynamic search bar internal force deviation and rod member length variation, under trying to achieve various stretch-draw forming scheme, (selects different initiatively stretching rope) by dynamic search bar internal force deviation.Usually drag-line is divided into initiatively stretching rope and passive stretching rope in Practical Project, initiatively the length of drag-line can regulate in stretching process, and in it, force value can directly be obtained by lifting jack reading; Passive stretching rope is according to the rope that design former progress row setting-out is blocked before construction stretching, and in stretching process, its internal force is according to equilibrium condition and deformation compatibility condition is passive sets up.Component internal force deviation according to active drag-line internal force deviation δ t _cwith by dynamic search internal force deviation δ t _uclassification, long error of keeping vegetarian is also according to the long error delta e of active rustling sound _c0error delta e long with passive rustling sound _u0classify, sensitivity matrix S _twrite as the form of piecemeal, formula (5) can be written as following form:

$\left\{\begin{array}{c}{\mathrm{\δt}}_c\\ \mathrm{\δ}{t}_u\end{array}\right\}\left\{\begin{array}{cc}{S}_{\mathrm{cc}}& S_{\mathrm{cu}}\\ S_{\mathrm{uc}}& S_{\mathrm{uu}}\end{array}\right\}\left\{\begin{array}{c}{\mathrm{\δe}}_{c0}\\ {\mathrm{\δe}}_{u0}\end{array}\right\}---\left(6\right)$

Control initiatively rope, the internal force deviation finally making initiatively rope is zero.According to formula (6), the regulated value that initiatively rustling sound is long can be obtained:

$\begin{array}{c}{\mathrm{\δe}}_c=-S_{\mathrm{cc}}^{-1}{\mathrm{\δt}}_c\\ =-S_{\mathrm{cc}}^{-1}\left[\begin{array}{cc}{S}_{\mathrm{cc}}& S_{\mathrm{cu}}\end{array}\right]\left\{\begin{array}{c}{\mathrm{\δe}}_{c0}\\ {\mathrm{\δe}}_{u0}\end{array}\right\}=-\left[\begin{array}{cc}I& S_{\mathrm{cc}}^{-1}{S}_{\mathrm{cu}}\end{array}\right]\left\{\begin{array}{c}{\mathrm{\δe}}_{c0}\\ {\mathrm{\δe}}_{u0}\end{array}\right\}=-{\mathrm{\δe}}_{c0}+S_{\mathrm{cc}}^{-1}{S}_{\mathrm{cu}}{\mathrm{\δe}}_{u0}\end{array}---\left(7\right)$

Therefore the length adjustment value of each rope of construction stretching is: δ e={ δ e _c0} ^t, the internal force deviation obtained thus by dynamic search is last is:

${\mathrm{\δt}}_u=\left[\begin{array}{cc}{S}_{\mathrm{uc}}& S_{\mathrm{uu}}\end{array}\right]\left\{\begin{array}{c}{\mathrm{\δe}}_{c0}\\ {\mathrm{\δe}}_{u0}\end{array}\right\}{+S}_{\mathrm{uc}}{\mathrm{\δe}}_c=(S_{\mathrm{uu}}-S_{\mathrm{uc}}{S}_{\mathrm{cc}}^{-1}{S}_{\mathrm{cu}}){\mathrm{\δe}}_{u0}=R_t\mathrm{\δ}{e}_{u0}---\left(8\right)$

When there being s root active stretching rope, formula (8) R _t=S _uu-S _ucs _c ^- _c ¹s _cuunder active cable force deviation is zero prerequisite, by the sensitivity matrix of dynamic search pretension deviation ((b-s) × (b-s)).R _tijfor under active cable force controlled condition, the pretension deviate of i-th rope that the long error of jGen rope unit rope causes.Comparison expression (5) and formula (8) can find, control initiatively stretch-draw cable force and change the long error of rope to by the impact of dynamic search initial prestress deviation.

Formula (8) can be used to analyze Pretensioned structural element by (selecting certain active rope) during certain stretch-draw forming scheme respectively by dynamic search bar component pretension deviation, rope internal force deviation when adopting different stretch-draw forming scheme by com-parison and analysis same structure, can evaluate the construction precision of various stretch-draw forming scheme.

S300, join probability opinion method and mathematical statistics calculate various stretch-draw forming scheme by the evaluating of dynamic search bar internal force deviation, and then evaluate the error effects of different stretching plan.According to regulation in China " Cable Structure technical regulation " (JGJ257-2012), finished guy cable will meet table 1, the requirement of 2 with delivery length admissible deviation compared with design length of pull bar.Consider that component length deviation is the effect that a large amount of slight influence combined factors is got up, such as temperature, humidity change, the change of vibrations, cutting angle, tool wear, bearing wear, raw material change etc. simultaneously.If each little error is independent, and be just or for negative probability etc. possible, according to Edward Lindberg-Lai fibrillar center limit theorem, then total error Normal Distribution.Suppose every root rod member error in length Normal Distribution N ~ (μ _ei, σ _ei), μ _eibe the average of i-th rod member error in length, σ _eiit is the distribution variance of i-th rod member error in length.According to Probability Principles, the probability during error drops on [μ-3 σ, μ+3 σ] is 99.74%, therefore when rod member error in length range of control is between [a, b], then has:

$\begin{array}{cc}\mathrm{\μ}=\frac{a+b}{2}& \mathrm{\σ}=\frac{1}{6}(b-a)\end{array}---\left(9\right)$

In formula: a, b are the bound allowing the long error of rope, and its value can refer in China " Cable Structure technical regulation " (JGJ257-2012) table 1,2 and specifies.Mean value and the standard deviation of the drag-line of Normal Distribution and the distribution of pull bar length variation can be obtained, as shown in Table 3, 4 according to formula (9).

Table 1 rope length permissible variation table 2 pull bar length permissible variation

Table 3 guy cable length error distribution character table 4 pull bar error in length distribution character

According to formula (5) and probability statistics knowledge, when the long error independent distribution of every root rope, the initial prestress deviation also Normal Distribution N ~ (μ of every root rope can be obtained _ti, σ _ti), μ _tibe the average of i-th cable force deviation, σ _tiit is the distribution variance of i-th cable force deviation.Wherein:

$\begin{array}{cc}{\mathrm{\μ}}_{\mathrm{ti}}=\underset{j=1}{\overset{b}{\mathrm{\Σ}}}{S}_{\mathrm{tij}}{\mathrm{\μ}}_{\mathrm{ej}}& {\mathrm{\σ}}_{\mathrm{ti}}^2=\underset{j=1}{\overset{b}{\mathrm{\Σ}}}{S}_{\mathrm{tij}}^2{\mathrm{\σ}}_{\mathrm{ej}}^2\end{array}---\left(10\right)$

Same according to linear relation (8), when can obtain initiatively cable force control, by the average of the stochastic distribution of dynamic search internal force deviation and variance:

$\begin{array}{cc}{\mathrm{\μ}}_{\mathrm{ti}}=\underset{j=1}{\overset{b-s}{\mathrm{\Σ}}}{R}_{\mathrm{tij}}{\mathrm{\μ}}_{\mathrm{ej}}& {\mathrm{\σ}}_{\mathrm{ti}}^2=\underset{j=1}{\overset{b-s}{\mathrm{\Σ}}}{R}_{\mathrm{tij}}^2{\mathrm{\σ}}_{\mathrm{ej}}^2\end{array}---\left(11\right)$

By dynamic search bar internal force deviation statistics parameter under the accurate controlled condition of active rope internal force that formula (11) can be tried to achieve, and then the error effects (selecting different initiatively rope) under various stretch-draw forming scheme can be evaluated.

The embody rule embodiment annular cable-strut tensile structure three-dimensional plot of the rope bar pretension structure stretch-draw forming method for optimizing based on error sensitivity analysis of the present invention as shown in Figure 2.The embody rule embodiment annular cable-strut tensile structure sectional view of the rope bar pretension structure stretch-draw forming Scheme Optimum Seeking Methods based on error sensitivity analysis of the present invention and physical dimension are as shown in Figure 3.Outer radii is 100m, and inner radii is 70m, and long depression bar length is 20m, and short depression bar length is 14m, and total is divided into 24 symmetrical Pin, periphery joint constraint.The topological relation of known structure, the elastic modulus of rope is E _c=1.7 × 10 ¹¹pa, the elastic modulus E of bar _b=2.1 × 10 ¹¹pa.Table 5 is the design coordinate of 4 Controlling vertex of certain truss structure, and table 6 is sectional area and the initial prestress distribution of this system same class component.

The design coordinate at upper four reference mark of a certain Pin of table 5

The sectional area of each unit of table 6 (component) and structural initial pre stress

According to the permissible variation (table 1, table 2) of drag-line, pull bar in China's " Cable Structure technical regulation ", set up the stochastic mathematical models of rope pole length deviation, try to achieve sensitivity matrix S according to formula (5) and (10) _twith the statistical property value of pretension deviation, then try to achieve according to formula (8) and (11) further and adopt the three kinds of each rope of stretching plan (bar) prestress deviation statistics characteristics such as footpath rope (scheme 2), upper and lower footpath, simultaneous tension outer ring rope (scheme 3) on footpath rope (scheme 1) under stretch-draw outer ring, outer ring respectively, as shown in table 7.Can find: (1) strop (5,6) variance is maximum, mast (7,8) variance is minimum, and upper and lower footpath rope variance is placed in the middle, shows that all kinds of rod member error sensitivity differs, and strop is the strongest, and mast is the most weak, in living alone in upper and lower footpath; (2) adopt the stretching plan of part Suo Zuowei active stretching rope comparatively can significantly reduce pretension deviation by the former long assembling scheme of component, improve construction precision; (3) due to structural symmetry (not considering that dead load affects), scheme 2 has identical construction precision with scheme 1; (4) in scheme 3 owing to adopting upper and lower footpath, outer ring rope totally 48 initiatively stretching ropes, rope internal force precision improves further, but improves few relative to scheme 1 and scheme 2; (5) to sum up, scheme 1 (under stretch-draw outer ring footpath rope) or scheme 2 (on stretch-draw outer ring footpath rope) can be paid the utmost attention to according to practice of construction condition for this structure, effectively to ensure construction precision under control construction cost condition.

Table 7 various stretch-draw forming scheme tension force deviation statistics characteristic

The rope bar pretension structure stretch-draw forming method for optimizing analyzed based on error sensitivity provided by the present invention, by the error effects of the various arrangement and method for construction of assay thus the arrangement and method for construction that Select Error effect is low, easy construction, construction cost are low as the stretch-draw forming scheme of structure, for the scheme choice of such engineering provides theoretical direction.

Should be understood that, application of the present invention is not limited to above-mentioned citing, for those of ordinary skills, can be improved according to the above description or convert, and all these improve and convert the protection domain that all should belong to claims of the present invention.

Claims (1)

1., based on the rope bar pretension structure stretch-draw forming method for optimizing that error sensitivity is analyzed, it is characterized in that, comprise step:

A, to build the fundamental relation of pretension deviations and rod member length variation based on three large equations of space articulated structure, i.e. rod member error in length sensitivity analysis theory;

B, accurately can to control initiatively i.e. rustling sound internal force deviation based on active stretch-draw rustling sound internal force be under zero condition, derive all the other by the fundamental relation of dynamic search bar internal force deviation and rod member length variation, under trying to achieve various stretch-draw forming scheme, selects different initiatively stretching rope, by the internal force deviation of dynamic search bar;

C, join probability opinion method and mathematical statistics calculate various stretch-draw forming scheme by the evaluating of dynamic search bar internal force deviation, and then evaluate the error effects of different stretching plan.