CN102127932A - Method for judging cause of dynamic destruction of single-layer network shell structure under earthquake action - Google Patents

Abstract

The invention discloses a method for judging cause of dynamic destruction of a single-layer network shell structure under the action of an earthquake, comprising the following steps of: (1) completing incremental step equilibrium iteration; (2) substituting a rod piece rod end force obtained when each time incremental step is finished into an unstability judging equation of an ISO (international standardization organization) round steel pipe to judge whether a structural rod piece is unstable or not; (3) if the structural rod piece is not unstable, simulating the rod piece according to the method in the step (1) to calculate thrusts at the two ends of the rod piece, if the structural rod piece is unstable, simulating the rod piece according to a Marshall model; (4) judging the unstability type of the rod piece; and (5) determining that dynamic destruction is caused as the dynamic bearing capacity of the structure and the earthquake action can not be balanced when the nonlinear dynamic equilibrium equation set of the structure can not be converged after iteration for 15 times. By adopting the invention, the process of unstable-straightening and plastic hinge forming-disappearing which can be repeatedly experienced by the rod piece under the action of the earthquake can be simulated.

Description

The power destruction origin cause of formation determination methods of single-layer lattice shell structure under geological process

Technical field

The present invention relates to a kind of spatial mesh structure, relate in particular to the power destruction origin cause of formation determination methods of single-layer lattice shell structure under geological process.

Background technology

The single-layer lattice shell structure is the space structures that is made of according to certain how much rules a large amount of rod members, latticed shell structure experiences the loading-unloading process repeatedly under the dynamic load function, cause rod member may experience unstability-stretching, plastic hinge formation-disappearance process repeatedly, the rod member mechanical property is in the dynamic change, cause the bearing capacity of structure also to be in the dynamic change, therefore will obtain the real-time accurately dynamic response of single-layer lattice shell structure and must set up the rod member computation model that to simulate the real-time mechanical property of rod member.Present many scholars adopt general finite element program to set up structural model, and the dynamic response characteristics of single-layer lattice shell structure are studied.Document 1 (model peak, money is loud and clear, Xing Ji is intelligent etc. severe earthquake action lower peripheral surface net shell dynamic strength damage study [J]. and Harbin Institute of Technology's journal, 2004,36 (6): 722-725.) dynamic strength of research individual layer sphere net case structure is destroyed, document 2 (Shen Shizhao, Zhi Xudong. the failure mechanism [J] of sphere net case structure under macroseism. the civil engineering journal, 2005,38 (1): 11-20) two kinds of dynamic failure patterns of proposition individual layer sphere net case structure, document 3 (Wang Xiaoke, the model peak, Zhi Xudong etc. the failure mechanism research [J] of individual layer cylindrical reticulated shell under macroseism. civil engineering journal, 2006,39 (11): the 26-32) failure mechanism of research individual layer cylindrical reticulated shell structure, document 4 (Zhi Xudong, Wu Jinmei, Fan Feng etc. consider the inefficacy research [J] of material damage accumulation individual layer cylindrical reticulated shell under macroseism. the Computational Mechanics journal, 2008,25 (6): 770-775) by of the influence of parametrization Calculation and Study material damage to individual layer cylindrical reticulated shell structure power destruction.When single-layer lattice shell structural dynamic response overall process was become more meticulous simulation, there were two problems in the beam element in the employing common finite element software when simulating rod member: the accuracy problem of (1) element stiffness matrix.Common finite element software adopts the material constitutive at Gauss point place to concern the computing unit stiffness matrix, and rod member can obtain bar element stiffness matrix accurately if be in elastic stage.The general end cross-sectional of single-layer lattice shell structural member at first enters plasticity, the Gauss point of common finite element software unit is not all in the end, unit, what calculated this moment is still the Flexible element stiffness matrix, produces the plastic constitutive relation computing unit stiffness matrix that plastic strain time side utilizes the point place until go out Gauss point place by the elastic stiffness matrix computations.Rod member plastic zone difference is owing to historical different its material plastic constitutive relation differences of loading, and the very long part of rod member still is in elasticity, still adopts the plastic constitutive relation computing unit stiffness matrix at Gauss point place also unreasonable.(2) problem of modelling of rod member unstable phenomenon.If a rod member adopts a beam element simulation, then can't simulate the rod member unstable phenomenon, the reduction of rod member bearing capacity is caused by material yield fully, rod member can bear the active force that surpasses the unstability critical load far away, cause calculating very large plastic strain, the structural bearing capacity that obtains is much larger than actual conditions.If adopt the mechanical property after rod member of a plurality of beam element simulations then can't accurately be simulated the rod member unstability, can not simulate the plastic hinge that may appear at cross section, rod end and rod member middle part, what beam elements rod member is divided and can be simulated the rod member unstable phenomenon more exactly and also be difficult to determine.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art, provide a kind of can the simulated earthquake effect under the rod member unstability that may experience repeatedly-stretching and plastic hinge formations-disappearance process, the power destruction origin cause of formation determination methods of single-layer lattice shell structure under geological process of accurately definite rod member and structural bearing capacity dynamic changing process.

In order to achieve the above object, the technical solution used in the present invention is:

The power destruction origin cause of formation determination methods of single-layer lattice shell structure under geological process, it may further comprise the steps:

(1) finishes the incremental step equilibrium iteration;

Solution procedure is as follows:

Step 101: adopt Newmark time integral method to find the solution structural nonlinear power balance equation group, each iteration obtains the displacement increment Δ u of rod end;

Step 102: establish the rod member two ends and be numbered I, J, I holds the weighing apparatus equation level with both hands and is

$F_{\mathrm{iI}}=\underset{J=1}{\overset{2}{\mathrm{\Σ}}}\underset{j=1}{\overset{6}{\mathrm{\Σ}}}{K}_{\mathrm{iI\; jJ}}^e(u_{\mathrm{jJ}}-u_{\mathrm{jJ}}^p)$

In the formula, F _IIBe I end section force component;

Be the matrix in block form in the unitary elasticity stiffness matrix, the lateral displacement of rod member adopts 4 order polynomial interpolating functions to represent when calculating rod member elastic stiffness matrix, rotation displacement is the derived function of lateral displacement interpolating function to length coordinate, axial displacement adopts 2 order polynomial interpolating functions to represent, torsional displacement adopts the linear interpolation function representation; u _JJBe the J end node displacement component that adds up by the displacement increment in the step 101 and obtain,

The plastic displacement component of J end node when finishing for previous iteration;

Step 103: the yield surface function phi of calculating the I end _IFor

${\mathrm{\Φ}}_I={\left(\frac{N_{\mathrm{xI}}-{\mathrm{\α}}_{\mathrm{NxI}}}{N_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{xI}}-{\mathrm{\α}}_{\mathrm{MxI}}}{M_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{yI}}-{\mathrm{\α}}_{\mathrm{MyI}}}{M_{\mathrm{yu}}}\right)}^2+{\left(\frac{M_{\mathrm{zI}}-{\mathrm{\α}}_{\mathrm{MzI}}}{M_{\mathrm{zu}}}\right)}^2-1$

In the formula, N _XuAxle power value when surrendered by a masterpiece time spent arbitrary section total cross-section for rod member; M _XuTorque value when the arbitrary section total cross-section is surrendered when only being subjected to torsional interaction for rod member; M _YuMoment of flexure value when only being subjected to moment of flexure effect around the y axle during surrender of arbitrary section total cross-section for rod member; M _ZuMoment of flexure value when only being subjected to moment of flexure effect around the z axle during surrender of arbitrary section total cross-section for rod member; N _XIBe axle power; M _YI, M _ZIBe respectively the moment of flexure of I end section around 2 main shafts; M _XIMoment of torsion for the I end section; α _NxI, α _MxI, α _MyI, α _MzIBe back stress component, Φ _I〉=0 expression I end total cross-section surrender forms plastic hinge;

Step 104: calculate the current iteration rod end plastic displacement increment in step

$\mathrm{\Δ}{u}_I^p=\mathrm{\Δ}{\mathrm{\λ}}_I\frac{{\∂\mathrm{\Φ}}_I}{\∂S_I}$

In the formula, Δ λ _IBe factor of proportionality; S _I=F _I-α _I, α _IBe I end section back stress vector; F _IBe I end rod end force vector.

Step 105: check whether structural nonlinear power balance equation group iteration restrains, if convergence, then this incremental time step calculates and finishes; If iteration does not restrain, then the incremental time step is reduced half and repeat step 101-105;

Whether the unstability discriminant equation of the rod member rod end power substitution ISO round steel pipe that is obtained by step 102 during (2) with each incremental time EOS to judge structural member unstability takes place;

(3) if judge structural member unstability does not take place, then continuing to simulate this rod member according to the method for step 1, to calculate the two ends of rod member stressed, if judge that unstability has taken place structural member, then according to this rod member of Marshall modeling;

(4) rod member unstability type is judged: if rod end yield surface equation Φ 〉=0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is first kind of unstability type, and the change of rod member slenderness ratio caused the rod member unstability greatly after described first kind of unstability type produced the plastic zone or form plastic hinge for the rod end cross section; If rod end yield surface equation Φ＜0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is second kind of unstability type, described second kind of unstability type is that the rod end cross section does not produce the plastic zone as yet or forms plastic hinge, and rod member reaches unstability critical condition unstability takes place because of bearing the effect of larger axis power;

(5) when the structural nonlinear power balance equation group in the step (1) does not still restrain through 15 iteration, then the dynamic bearing capacity of decision structure and geological process can not be kept balance and power destruction takes place, the power destruction origin cause of formation of single-layer lattice shell structure under geological process judged: if when destroying in the structure type of unstability rod member be first kind, then the power destruction of single-layer lattice shell structure is concentrated by the rod end plastic hinge and is occurred causing structure partial to become mechanism causing; If when destroying in the structure type of unstability rod member be second kind, then the structural bearing capacity that caused by the rod member unstability of the power destruction of single-layer lattice shell structure descends and causes; If the rod member of two kinds of unstability types all exists in structure when destroying, then the power destruction of single-layer lattice shell structure causes that by the unstability rod member structural bearing capacity reduction makes structure partial form mechanism with the rod end plastic hinge and causes jointly.

The invention has the beneficial effects as follows:

Adopt the inventive method can the simulated earthquake effect under rod member unstability that may experience repeatedly-stretching and plastic hinge formation-disappearance process.Application this method is carried out the dynamic response analysis to latticed shell structure and can accurately be obtained rod member changes of mechanical properties process, and the dynamic changing process of the structural bearing capacity that causes thus, thereby and can determine accurately to cause that dynamic bearing capacity of structure and geological process can't keep the origin cause of formation that balance causes structural dynamic to destroy.

Description of drawings

Fig. 1 is a Marshall model envelope;

Fig. 2 is a unstability rod member position view among the embodiment 1;

Fig. 3 is a structural strain energy time-histories schematic diagram among the embodiment 1;

Fig. 4 is unstability rod member position view during 1.69s among the embodiment 1;

Fig. 5 is a unstability rod member position view when destroying among the embodiment 1;

Fig. 6 is No. 373 bar axle power time-histories figure among the embodiment 1;

Fig. 7 is rod end plastic hinge distribution map during 6.04s among the embodiment 2;

Fig. 8 is a rod end plastic hinge distribution map when destroying among the embodiment 2;

Fig. 9 is unstability rod member number change figure among the embodiment 3;

Figure 10 is rod end plastic hinge number change figure among the embodiment 3;

Figure 11 is unstability rod member and the distribution of rod end plastic hinge when latticed shell structure destroys among the embodiment 3.

The specific embodiment

Describe the present invention below in conjunction with specific embodiment.

The power destruction origin cause of formation determination methods of single-layer lattice shell structure of the present invention under geological process, it is characterized in that it may further comprise the steps: (1) finishes the incremental step equilibrium iteration;

Solution procedure is as follows:

Step 101: adopt Newmark time integral method to find the solution structural nonlinear power balance equation group, each iteration obtains the displacement increment Δ u of rod end;

Step 102: establish the rod member two ends and be numbered I, J, I holds the weighing apparatus equation level with both hands and is

$F_{\mathrm{iI}}=\underset{J=1}{\overset{2}{\mathrm{\Σ}}}\underset{j=1}{\overset{6}{\mathrm{\Σ}}}{K}_{\mathrm{iI\; jJ}}^e(u_{\mathrm{jJ}}-u_{\mathrm{jJ}}^p)$

In the formula, F _IIBe I end section force component;

Be the matrix in block form in the unitary elasticity stiffness matrix, the lateral displacement of rod member adopts 4 order polynomial interpolating functions to represent when calculating rod member elastic stiffness matrix, rotation displacement is the derived function of lateral displacement interpolating function to length coordinate, axial displacement adopts 2 order polynomial interpolating functions to represent, torsional displacement adopts the linear interpolation function representation; u _JJBe the J end node displacement component that adds up by the displacement increment in the step 101 and obtain,

The plastic displacement component of J end node when finishing for previous iteration;

Step 103: the yield surface function phi of calculating the I end _IFor

${\mathrm{\Φ}}_I={\left(\frac{N_{\mathrm{xI}}-{\mathrm{\α}}_{\mathrm{NxI}}}{N_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{xI}}-{\mathrm{\α}}_{\mathrm{MxI}}}{M_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{yI}}-{\mathrm{\α}}_{\mathrm{MyI}}}{M_{\mathrm{yu}}}\right)}^2+{\left(\frac{M_{\mathrm{zI}}-{\mathrm{\α}}_{\mathrm{MzI}}}{M_{\mathrm{zu}}}\right)}^2-1$

In the formula, N _XuAxle power value when surrendered by a masterpiece time spent arbitrary section total cross-section for rod member; M _XuTorque value when the arbitrary section total cross-section is surrendered when only being subjected to torsional interaction for rod member; M _YuMoment of flexure value when only being subjected to moment of flexure effect around the y axle during surrender of arbitrary section total cross-section for rod member; M _ZuMoment of flexure value when only being subjected to moment of flexure effect around the z axle during surrender of arbitrary section total cross-section for rod member; N _XIBe axle power; M _YI, M _ZIBe respectively the moment of flexure of I end section around 2 main shafts; M _XIMoment of torsion for the I end section; α _NxI, α _MxI, α _MyI, α _MzIBe back stress component, Φ _I〉=0 expression I end total cross-section surrender forms plastic hinge;

Step 104: calculate the current iteration rod end plastic displacement increment in step

$\mathrm{\Δ}{u}_I^p=\mathrm{\Δ}{\mathrm{\λ}}_I\frac{{\∂\mathrm{\Φ}}_I}{\∂S_I}$

In the formula, Δ λ _IBe factor of proportionality; S _I=F _I-α _I, α _IBe I end section back stress vector; F _IBe I end rod end force vector;

Step 105: check whether structural nonlinear power balance equation group iteration restrains, if convergence, then this incremental time step calculates and finishes; If iteration does not restrain, then the incremental time step is reduced half and repeat step 101-105;

Whether the unstability discriminant equation of the rod member rod end power substitution ISO round steel pipe that is obtained by step 102 during (2) with each incremental time EOS to judge structural member unstability takes place;

(3) if judge structural member unstability does not take place, then continuing to simulate this rod member according to the method for step 1, to calculate the two ends of rod member stressed, if judge that unstability has taken place structural member, then according to this rod member of Marshall modeling;

(4) rod member unstability type is judged: if rod end yield surface equation Φ 〉=0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is first kind of unstability type, and the change of rod member slenderness ratio caused the rod member unstability greatly after described first kind of unstability type produced the plastic zone or form plastic hinge for the rod end cross section; If rod end yield surface equation Φ＜0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is second kind of unstability type, described second kind of unstability type is that the rod end cross section does not produce the plastic zone as yet or forms plastic hinge, and rod member reaches unstability critical condition unstability takes place because of bearing the effect of larger axis power;

(5) when the structural nonlinear power balance equation group in the step (1) does not still restrain through 15 iteration, can think that then the dynamic bearing capacity of structure and geological process can not keep balance and power destruction takes place.The power destruction origin cause of formation of single-layer lattice shell structure under geological process judged: if when destroying in the structure type of unstability rod member be first kind, then the power destruction of single-layer lattice shell structure is concentrated by the rod end plastic hinge and is occurred causing structure partial to become mechanism causing; If when destroying in the structure type of unstability rod member be second kind, then the structural bearing capacity that caused by the rod member unstability of the power destruction of single-layer lattice shell structure descends and causes; If the rod member of two kinds of unstability types all exists in structure when destroying, then the power destruction of single-layer lattice shell structure causes that by the unstability rod member structural bearing capacity reduction makes structure partial form mechanism with the rod end plastic hinge and causes jointly.

The unstability discriminant equation of the round steel pipe in the described step (2) is an International Standards Organization according to the unstability discriminant equation of stressed round steel pipe between a large amount of Test Summary clearancens (see ISO 10721-1.Steel structures.materials and design[S] .1997.ISO10721-1. " steel work: material and design " [S] .1997.)

$I(f_c,f_{b1},f_{b2})=\frac{f_c}{F_c}+\frac{1}{F_b}\sqrt{{\left(\frac{c_{m1}{f}_{b1}}{1-\frac{f_c}{F_{e1}}}\right)}^2+{\left(\frac{c_{m2}{\mathrm{<figure-callout\; id="2"\; label="f\; b"\; filenames="HDA0000044474320000025.png"\; state="\{\{state\}\}">f</figure-callout>}}_b}{1-\frac{f_c}{F_{e2}}}\right)}^2}---\left(1\right)$

In the formula, f _c=P/A is an axial compression stress, and P, A are respectively a power and rod member cross-sectional area; f _B1, f _B2Be respectively maximum stress in bend, f around 2 main shafts _B1=M ₁/ W _e, f _B2=M ₂/ W _e, W _eBe the elasticity module of anti-bending section; c _M1, c _M2Be respectively the Moment at End reduction coefficient, c _M1=c _M2=0.85; F _E1, F _E2Be respectively the Euler buckling critical stress of 2 main shafts,

L ₁, L ₂Be the unbraced length of rod member in 2 main shaft plane, k ₁, k ₂Be the calculated length coefficient in 2 main shaft plane, i is a radius of gyration; F _c, F _bBe respectively axial pressure characteristic value and flexural stress characteristic value

$F_c=\left\{\begin{array}{cc}(1.0-0.28{\mathrm{\&lambda;}}^2)F_{\mathrm{yc}}& \mathrm{\&lambda;}\&le;1.34\\ \frac{0.89282978}{{\mathrm{\&lambda;}}^2}{F}_{\mathrm{yc}}& \mathrm{\&lambda;}>1.34\end{array}\right.---\left(2\right)$

$F_b=\left\{\begin{array}{cc}\frac{W_p}{W_e}{\mathrm{\&sigma;}}_s& \frac{{\mathrm{\&sigma;}}_{s}D}{\mathrm{Et}}\&le;0.051\\ (1.133386-2.58\frac{{\mathrm{\&sigma;}}_{s}D}{\mathrm{Et}})\frac{W_p}{W_e}{\mathrm{\&sigma;}}_s& 0.0517<\frac{{\mathrm{\&sigma;}}_{s}D}{\mathrm{Et}}\&le;0.103\\ (0.945198-0.76\frac{{\mathrm{\&sigma;}}_{s}D}{\mathrm{Et}})\frac{W_p}{W_e}{\mathrm{\&sigma;}}_s& 0.1034<\frac{{\mathrm{\&sigma;}}_{s}D}{\mathrm{Et}}\&le;\frac{120{\mathrm{\&sigma;}}_s}{E}\end{array}\right.---\left(3\right)$

In the formula, F _YcBe local buckling's stress characteristics value

$F_{\mathrm{yc}}=\left\{\begin{array}{cc}{\mathrm{\&sigma;}}_s& \frac{5{\mathrm{\&sigma;}}_{s}D}{3\mathrm{Et}}\&le;0.170\\ (1.04654873-0.27381606\frac{5{\mathrm{\&sigma;}}_{s}D}{3\mathrm{Et}}){\mathrm{\&sigma;}}_s& 0.170<\frac{5{\mathrm{\&sigma;}}_{s}D}{3\mathrm{Et}}\&le;1.911\\ \frac{0.6\mathrm{Et}}{D}& \frac{5{\mathrm{\&sigma;}}_{s}D}{3\mathrm{Et}}>1.911\end{array}\right.---\left(4\right)$

In the formula, σ _sBe material yield intensity; T, D are respectively the wall thickness and the diameter of round steel pipe; λ=max (λ ₁, λ ₂); W _p=[D ³-(D-2t) ³]/6.

As I (f _c, f _B1, f _B2) 〉=1.0 o'clock rod member unstability.When axial pressure is also little if rod member bears very big moment of flexure, also I (f may take place _c, f _B1, f _B2) 〉=1.0, this will produce pseudo-unstability judges, therefore also need introduce the intensity equation

$S(f_c,f_{b1},f_{b2})=\frac{f_c}{F_{\mathrm{yc}}}+\frac{1}{F_b}\sqrt{f_{b1}^2+{\mathrm{<figure-callout\; id="2"\; label="f\; b"\; filenames="HDA0000044474320000025.png"\; state="\{\{state\}\}">f</figure-callout>}}_b^2}---\left(5\right)$

Like this, the unstability criterion of space-load round steel pipe is

$\left\{\begin{array}{c}I(f_c,f_{b1},f_{b2})\&GreaterEqual;1.0\\ S(f_c,f_{b1},f_{b2})\&le;1.0\end{array}\right.---\left(6\right)$

As I (f _c, f _B1, f _B2)=1.0 and S (f _c, f _B1, f _B2)≤1.0 o'clock, the space-load round steel pipe is in the unstability critical condition, axially critical load

P _cr＝f _cA (7)

Marshall model in the described step (3) (is seen P W Marshall, W E Gates, S Anagnostopoulos.Inelastic dynamic analysis of tubular offshore structures[A] .In:proceedings of ninth annual offshore technology conference[C] .Houston, the Elasto-Plastic Dynamic Analysis of U S A:1977.235-246. round steel pipe offshore structure, the 9th offshore engineering technical conference, the Houston, the U.S. .235-246. in 1977) for having model now.The essence of Marshall model is the hysteresis envelope of elastoplasticity rod member as shown in Figure 1: (1) A-F is the elasticity tension stage; (2) F-F ' is the strengthening segment after the tension surrender; (3) A-B is the elasticity pressurized stage; (4) B-D is a rod member unstability after-stage; (5) D-F is the rod member tension stage.If the unstability after-stage on envelope (as B ', C ', D ' point) unloading, then the unloading path of rod member is that unloading point points to the line segment that F is ordered, the i.e. line segment of envelope inside.The distortion of rod member can only occur in the envelope or envelope on.When the rod member cross section under tension produced the plastic zone, envelope was along the transverse axis translation, and translation distance is identical with the plastic strain of generation.Coefficient gamma among Fig. 1=0.02; κ=0.28; β=0.02; ζ=min (1.0,5.8 (t/D) ^0.7/ 0.95); α=0.03+0.004L/D; L is a rod member length, and E is a modulus of elasticity, and A is the rod member cross-sectional area.The elastic limit load

P _y＝0.95σ _sA (8)

Embodiment 1

Be that 40m, ratio of rise to span are that 1/3 Kiewitt type individual layer sphere net case structure is an example with the span, rod member adopts Φ 114 * 3.0, Φ 127 * 3.5, Φ 140 * 4.5 3 kind of round steel pipe, applies 2.0kN/m ²Area load, material is Q235.Input three-dimensional El Centro ripple, degree of will speed up peak value transfers to 620gal.

Adopt method step of the present invention (1) to step (5):

(1) finishes the incremental step equilibrium iteration;

Solution procedure is as follows:

Step 101: adopt Newmark time integral method to find the solution structural nonlinear power balance equation group, each iteration obtains the displacement increment Δ u of rod end;

Step 102: establish the rod member two ends and be numbered I, J, I holds the weighing apparatus equation level with both hands and is

$F_{\mathrm{iI}}=\underset{J=1}{\overset{2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{6}{\mathrm{\&Sigma;}}}{K}_{\mathrm{iI\; jJ}}^e(u_{\mathrm{jJ}}-u_{\mathrm{jJ}}^p)$

In the formula, F _IIBe I end section force component;

Be the matrix in block form in the unitary elasticity stiffness matrix, the lateral displacement of rod member adopts 4 order polynomial interpolating functions to represent when calculating rod member elastic stiffness matrix, rotation displacement is the derived function of lateral displacement interpolating function to length coordinate, axial displacement adopts 2 order polynomial interpolating functions to represent, torsional displacement adopts the linear interpolation function representation; u _JJBe the J end node displacement component that adds up by the displacement increment in the step 101 and obtain,

The plastic displacement component of J end node when finishing for previous iteration;

Step 103: the yield surface function phi of calculating the I end _IFor

${\mathrm{\&Phi;}}_I={\left(\frac{N_{\mathrm{xI}}-{\mathrm{\&alpha;}}_{\mathrm{NxI}}}{N_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{xI}}-{\mathrm{\&alpha;}}_{\mathrm{MxI}}}{M_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{yI}}-{\mathrm{\&alpha;}}_{\mathrm{MyI}}}{M_{\mathrm{yu}}}\right)}^2+{\left(\frac{M_{\mathrm{zI}}-{\mathrm{\&alpha;}}_{\mathrm{MzI}}}{M_{\mathrm{zu}}}\right)}^2-1$

In the formula, N _XuAxle power value when surrendered by a masterpiece time spent arbitrary section total cross-section for rod member; M _XuTorque value when the arbitrary section total cross-section is surrendered when only being subjected to torsional interaction for rod member; M _YuMoment of flexure value when only being subjected to moment of flexure effect around the y axle during surrender of arbitrary section total cross-section for rod member; M _ZuMoment of flexure value when only being subjected to moment of flexure effect around the z axle during surrender of arbitrary section total cross-section for rod member; N _XIBe axle power; M _YI, M _ZIBe respectively the moment of flexure of I end section around 2 main shafts; M _XIMoment of torsion for the I end section; α _NxI, α _MxI, α _MyI, α _MzIBe back stress component, Φ _I〉=0 expression I end total cross-section surrender forms plastic hinge;

Step 104: calculate the current iteration rod end plastic displacement increment in step

$\mathrm{\&Delta;}{u}_I^p=\mathrm{\&Delta;}{\mathrm{\&lambda;}}_I\frac{{\&PartialD;\mathrm{\&Phi;}}_I}{\&PartialD;S_I}$

In the formula, Δ λ _IBe factor of proportionality; S _I=F _I-α _I, α _IBe I end section back stress vector; F _IBe I end rod end force vector.

Step 105: check whether structural nonlinear power balance equation group iteration restrains, if convergence, then this incremental time step calculates and finishes; If iteration does not restrain, then the incremental time step is reduced half and repeat step 101-105.

Whether the unstability discriminant equation of the rod member rod end power substitution ISO round steel pipe that is obtained by step 102 during (2) with each incremental time EOS to judge structural member unstability takes place;

(3) if judge structural member unstability does not take place, then continuing to simulate this rod member according to the method for step 1, to calculate the two ends of rod member stressed, if judge that unstability has taken place structural member, then according to this rod member of Marshall modeling;

(4) rod member unstability type is judged: if rod end yield surface equation Φ 〉=0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is first kind of unstability type, and the change of rod member slenderness ratio caused the rod member unstability greatly after described first kind of unstability type produced the plastic zone or form plastic hinge for the rod end cross section; If rod end yield surface equation Φ＜0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is second kind of unstability type, described second kind of unstability type is that the rod end cross section does not produce the plastic zone as yet or forms plastic hinge, and rod member reaches unstability critical condition unstability takes place because of bearing the effect of larger axis power;

(5) when the structural nonlinear power balance equation group in the step (1) does not still restrain through 15 iteration, can think that then the dynamic bearing capacity of structure and geological process can not keep balance and power destruction takes place.The power destruction origin cause of formation of single-layer lattice shell structure under geological process judged: if when destroying in the structure type of unstability rod member be first kind, then the power destruction of single-layer lattice shell structure is concentrated by the rod end plastic hinge and is occurred causing structure partial to become mechanism causing; If when destroying in the structure type of unstability rod member be second kind, then the structural bearing capacity that caused by the rod member unstability of the power destruction of single-layer lattice shell structure descends and causes; If the rod member of two kinds of unstability types all exists in structure when destroying, then the power destruction of single-layer lattice shell structure causes that by the unstability rod member structural bearing capacity reduction makes structure partial form mechanism with the rod end plastic hinge and causes jointly.

Judgement shows, 8 whole unstabilitys of radial bars between 0.92s～0.93s in the structure centre ring, as shown in Figure 2.Rod member unstability type is second kind.Unstability rod member bearing capacity reduces rapidly, causes that structural internal force heavily distributes.0.94s the time center ring unstability also takes place to rod member, unstability rod member quantity increases sharply, structural bearing capacity reduces, and can't continue to bear geological process and destroy.Structural strain can time-histories as shown in Figure 3, geological process strengthens between 0.90s～0.92s, strain energy increases suddenly.Can see in the steep increasing process of strain energy that by partial enlarged drawing minor fluctuations is arranged twice, this is to cause because of the rod member unstability discharges strain energy.Discharge the process of destroying because of the rod member unstability corresponding to structure 0.94s strain energy is suddenly a large amount of between～0.95s.

The earthquake acceleration peak value is reduced to 350gal.Adopt method step of the present invention (1) to judge to step (5) and show that rod member unstability type still is second kind, a lot of rod members experience unstability-stretching process repeatedly, and unstability rod member quantity is in the dynamic change, and structural bearing capacity is also in dynamic change.As shown in Figure 4, the unstability rod member is 32 during 1.69s, though this moment, the unstability rod member was more, geological process is not very strong, and structural bearing capacity and geological process still can be kept balance, and this rear section rod member is straightened.1.78s the time geological process strengthen, structure can't be kept dynamic equilibrium because of bearing capacity and geological process and destroy, the distribution of unstability rod member as shown in Figure 5 during destruction.

Comparison diagram 4 and Fig. 5 as can be known, whether structure is destroyed depends on whether structural bearing capacity and geological process can keep dynamic equilibrium, rather than the quantity of unstability rod member.

Fig. 6 is the axle power time-history curves of No. 373 bars (Figure 10), rod member generation unstability when the axial pressure in the rod member reaches 164kN, and the axle power in the rod member just reduces rapidly, and No. 373 bar has experienced the unstability process twice.

Set up ratio of rise to span and be respectively five kinds of individual layer sphere net case structural models commonly used of 1/4,1/5,1/6,1/7 and carry out Parametric Analysis, span is all got 40m, and the input peak accelerator is the three-dimensional El Centro ripple of 900gal, gets 12s when holding.During destruction in the structure quantity of the quantity of unstability rod member and plastic hinge as shown in table 1.

The quantity of unstability bar and rod end plastic hinge in individual layer sphere net case when table 1 destroys

As can be seen from Table 1, the unstability type of individual layer sphere net case structure compression member is second kind under the geological process.Ratio of rise to span is big more, during destruction in the structure quantity of unstability rod member many more.So as seen, it is the reason that individual layer sphere net case structural dynamic destroys that the rod member unstability causes structural bearing capacity to descend.

Embodiment 2

Be that 15m, length 21m, ratio of rise to span are that 1/2 three-way grid individual layer cylindrical reticulated shell structure is an example with the span, rod member adopts Φ 114 * 3.0, Φ 127 * 3.5, Φ 140 * 4.5 3 kind of round steel pipe, applies 1.0kN/m ²Area load, material is Q235, input three-dimensional El Centro ripple is got 12s when holding, for destructive process degree of the will speed up peak value of model configuration transfers to 620gal.

Adopting method step of the present invention (1) to judge to step (5) shows, the rod end cross section of rod member at first produces the plastic zone under the geological process, along with many rod member rod ends of the increase cross section of load forms plastic hinge, the rod end cross section can not bear bigger bending moment to be out of shape with shearing and increase sharply.If this moment, geological process was strengthened then structure generation redistribution of internal force, the internal force increment that has produced the plastic hinge rod member is born by other rod members of conode, so just may cause adjacent rod member end cross-sectional also to form plastic hinge, therefore plastic hinge is often concentrated in the Rod end cross section of conode and is produced, and causes structure partial to become mechanism.6.04s the time produce 43 rod end plastic hinges, as shown in Figure 7, solid rim represent the rod end plastic hinge, open circle is represented generation plastic zone, rod end cross section but is not formed plastic hinge.If this moment, geological process weakened then the rod end plastic hinge can disappear because of unloading, in the residual plastic strain in rod end cross section.The quantity of rod end plastic hinge and position constantly change under the geological process, and therefore structural bearing capacity is in the dynamic change.6.13s the time structure can't keep dynamic equilibrium because of bearing capacity and geological process and destroy, have 26 rod end plastic hinges in the structure this moment, as shown in Figure 8.

Comparison diagram 7 and Fig. 8 equally as can be known, whether structure is destroyed depends on whether structural bearing capacity and geological process can keep dynamic equilibrium, rather than the quantity of plastic hinge.

Set up ratio of rise to span and be respectively four kinds of individual layer cylindrical reticulated shell structure models commonly used of 1/2,1/3,1/4,1/5 and carry out Parametric Analysis, length is all got 21m, and span is all got 15m, and the input peak accelerator is the three-dimensional El Centro ripple of 900gal, gets 12s when holding.During destruction in the structure quantity of the quantity of unstability rod member and plastic hinge as shown in table 2.

The quantity of unstability bar and rod end plastic hinge in individual layer sphere net case when table 2 destroys

As can be seen from Table 2, the unstability type of individual layer cylindrical reticulated shell structure compression member is first kind under the geological process.Ratio of rise to span is more little, during destruction in the structure quantity of rod end plastic hinge many more.Therefore as seen, the rod end plastic hinge is concentrated and is occurred causing structure partial to become the reason that mechanism is a structural dynamic destruction.

Embodiment 3

With long 48m, wide 30m, the unidirectional brace orthogonal spatial type individual layer paraboloid latticed shell structure of ratio of rise to span 1/3 is an example, rod member adopts Φ 114 * 4.0, Φ 121 * 4.0, Φ 146 * 6.0 and Φ 152 * 6.0 4 kind of round steel pipe, applies 1.0kN/m ²Area load, material is Q235, input three-dimensional El Centro ripple is got 12s when holding, for destructive process degree of the will speed up peak value of model configuration transfers to 620gal.

Adopt method step of the present invention (1) to judge and show that unstability rod member and rod end plastic hinge all occur in a large number under the geological process, have the rod member of two kinds of unstability types in the structure to step (5).Unstability rod member quantity, rod end plastic hinge quantity in time change curve respectively as Fig. 9, shown in Figure 10.Structural member experiences unstability-stretching process and plastic hinge formation-disappearance process repeatedly in the geological process process, the existence of unstability rod member causes structural bearing capacity to descend, the existence of rod end plastic hinge makes structure partial become mechanism, and both actings in conjunction cause structure to issue lively power destruction in geological process.Unstability rod member and rod end plastic hinge distribute as shown in figure 11 during structural deterioration.

Embodiment 4

Setting up ratio of rise to span is respectively two kinds of individual layer paraboloid latticed shell structure models commonly used of 1/3,1/4,1/5,1/6 and carries out Parametric Analysis, length is all got 48m, span is all got 30m, and the input peak accelerator is the three-dimensional El Centro ripple of 900gal, gets 12s when holding.Adopt method step of the present invention (1) to step (5) to judge and show, during destruction in the structure quantity of the quantity of unstability rod member and plastic hinge as shown in table 3.

The quantity of unstability bar and rod end plastic hinge in individual layer paraboloid net shell when table 3 destroys

As can be seen from Table 3, the rod member that has two kinds of unstability types under the geological process in the individual layer paraboloid latticed shell structure.Along with the change of ratio of rise to span is big, during destruction in the structure quantity of unstability rod member become many, and the quantity of rod end plastic hinge tails off.The power destruction of individual layer paraboloid latticed shell structure under geological process causes that by the unstability rod member structural bearing capacity reduction makes structure partial form mechanism with the rod end plastic hinge and causes jointly.

Claims (1)

1. the power destruction origin cause of formation determination methods of single-layer lattice shell structure under geological process is characterized in that it may further comprise the steps:

(1) finishes the incremental step equilibrium iteration;

Solution procedure is as follows:

Step 101: adopt Newmark time integral method to find the solution structural nonlinear power balance equation group, each iteration obtains the displacement increment Δ u of rod end;

Step 102: establish the rod member two ends and be numbered I, J, I holds the weighing apparatus equation level with both hands and is

$F_{\mathrm{iI}}=\underset{J=1}{\overset{2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{6}{\mathrm{\&Sigma;}}}{K}_{\mathrm{iI\; jJ}}^e(u_{\mathrm{jJ}}-u_{\mathrm{jJ}}^p)$

In the formula, F _IIBe I end section force component;

Be the matrix in block form in the unitary elasticity stiffness matrix, the lateral displacement of rod member adopts 4 order polynomial interpolating functions to represent when calculating rod member elastic stiffness matrix, rotation displacement is the derived function of lateral displacement interpolating function to length coordinate, axial displacement adopts 2 order polynomial interpolating functions to represent, torsional displacement adopts the linear interpolation function representation; u _JJBe the J end node displacement component that adds up by the displacement increment in the step 101 and obtain,

The plastic displacement component of J end node when finishing for previous iteration;

Step 103: the yield surface function phi of calculating the I end _IFor

${\mathrm{\&Phi;}}_I={\left(\frac{N_{\mathrm{xI}}-{\mathrm{\&alpha;}}_{\mathrm{NxI}}}{N_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{xI}}-{\mathrm{\&alpha;}}_{\mathrm{MxI}}}{M_{\mathrm{xu}}}\right)}^2+{\left(\frac{M_{\mathrm{yI}}-{\mathrm{\&alpha;}}_{\mathrm{MyI}}}{M_{\mathrm{yu}}}\right)}^2+{\left(\frac{M_{\mathrm{zI}}-{\mathrm{\&alpha;}}_{\mathrm{MzI}}}{M_{\mathrm{zu}}}\right)}^2-1$

In the formula, N _XuAxle power value when surrendered by a masterpiece time spent arbitrary section total cross-section for rod member; M _XuTorque value when the arbitrary section total cross-section is surrendered when only being subjected to torsional interaction for rod member; M _YuMoment of flexure value when only being subjected to moment of flexure effect around the y axle during surrender of arbitrary section total cross-section for rod member; M _ZuMoment of flexure value when only being subjected to moment of flexure effect around the z axle during surrender of arbitrary section total cross-section for rod member; N _XIBe axle power; M _YI, M _ZIBe respectively the moment of flexure of I end section around 2 main shafts; M _XIMoment of torsion for the I end section; α _NxI, α _MxI, α _MyI, α _MzIBe back stress component, Φ _I〉=0 expression I end total cross-section surrender forms plastic hinge;

Step 104: calculate the current iteration rod end plastic displacement increment in step

$\mathrm{\&Delta;}{u}_I^p=\mathrm{\&Delta;}{\mathrm{\&lambda;}}_I\frac{{\&PartialD;\mathrm{\&Phi;}}_I}{\&PartialD;S_I}$

In the formula, Δ λ _IBe factor of proportionality; S _I=F _I-α _I, α _IBe I end section back stress vector; F _IBe I end rod end force vector;

Step 105: check whether structural nonlinear power balance equation group iteration restrains, if convergence, then this incremental time step calculates and finishes; If iteration does not restrain, then the incremental time step is reduced half and repeat step 101-105;

Whether the unstability discriminant equation of the rod member rod end power substitution ISO round steel pipe that is obtained by step 102 during (2) with each incremental time EOS to judge structural member unstability takes place;

(3) if judge structural member unstability does not take place, then continuing to simulate this rod member according to the method for step 1, to calculate the two ends of rod member stressed, if judge that unstability has taken place structural member, then according to this rod member of Marshall modeling;

(4) rod member unstability type is judged: if rod end yield surface equation Φ 〉=0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is first kind of unstability type, and the change of rod member slenderness ratio caused the rod member unstability greatly after described first kind of unstability type produced the plastic zone or form plastic hinge for the rod end cross section; If rod end yield surface equation Φ＜0 when satisfying the unstability discriminant equation of round steel pipe, then rod member is second kind of unstability type, described second kind of unstability type is that the rod end cross section does not produce the plastic zone as yet or forms plastic hinge, and rod member reaches unstability critical condition unstability takes place because of bearing the effect of larger axis power;

(5) when the structural nonlinear power balance equation group in the step (1) does not still restrain through 15 iteration, then the dynamic bearing capacity of decision structure and geological process can not be kept balance and power destruction takes place, the power destruction origin cause of formation of single-layer lattice shell structure under geological process judged: if when destroying in the structure type of unstability rod member be first kind, then the power destruction of single-layer lattice shell structure is concentrated by the rod end plastic hinge and is occurred causing structure partial to become mechanism causing; If when destroying in the structure type of unstability rod member be second kind, then the structural bearing capacity that caused by the rod member unstability of the power destruction of single-layer lattice shell structure descends and causes; If the rod member of two kinds of unstability types all exists in structure when destroying, then the power destruction of single-layer lattice shell structure causes that by the unstability rod member structural bearing capacity reduction makes structure partial form mechanism with the rod end plastic hinge and causes jointly.

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