CN102567633A - Shore bridge structure wind vibration fatigue reliability forecasting method based on probability accumulated damage - Google Patents

Abstract

A shore bridge structure wind vibration fatigue reliability forecasting method based on probability accumulated damage comprises the following steps of 1 adopting a harmonic superposition method to simulate wind load time domain wave forms endured by a shore bridge structure and accorded with Davenport power spectrum characteristics; 2 enabling the wind load to act on a finite element model of the shore bridge structure and calculating a stress response time interval of a fatigued calculation point of the shore bridge structure; 3 adopting a rain flow counting method to process the stress response time interval so as to obtain the fatigue statistics characteristics of amplitude stress spectral; and 4 adopting a probability theory method to forecast the wind vibration fatigue reliability of the shore bridge structure in a certain serving period through a probability accumulated damage model. The shore bridge structure wind vibration fatigue reliability forecasting method has the advantages of being applicable to the complex shore bridge structure, wide in application scope, high in computational accuracy, and capable of calculating the fatigue reliability of a wind resisting structure under any random wind load effects.

Description

Based on the bank bridge construction wind of the probability accumulated damage tired fiduciary level forecasting procedure of shaking

Technical field

The wind that the present invention relates to a kind of bank bridge construction tired fiduciary level forecasting procedure of shaking specifically is a kind of bank bridge construction wind based on the probability accumulated damage tired fiduciary level forecasting procedure of shaking.

Background technology

Bank bridge crane works in the seashore throughout the year, and sail-center is high, and front face area is big, and wind load effect long-term, that be interrupted causes bank bridge metal construction to produce Cumulative Fatigue Damage.The wind of the bank bridge construction tired fiduciary level forecasting procedure of shaking is a major issue in bank bridge construction design and the working service; Its design difficulty is the experiment on fatigue properties data of lack of materials and the probability model of Cumulative Fatigue Damage, and is difficult to forecast the tired fiduciary level under the bank bridge construction wind action.

For addressing the above problem, people such as Ou Jinping are in last delivered " the probability Cumulative Fatigue Damage of wind induced structural vibration " of " vibration engineering journal " 1993,6 (2): 164-168.This article is that a kind of statistical distribution rule based on fatigue lifetime is set up the reliability degree calculation method of overhead water tower in certain length of service with the stress response statistic of random seismic response analysis method calculating overhead water tower one degree of freedom modeling in frequency domain.Yet this computing method only are suitable for the forecast of the tired fiduciary level of simple wind resisting structure, and forecast precision is low.In addition, this method according to the statistical distribution rule of fatigue lifetime the probability nature of Cumulative Fatigue Damage can not be described directly.

Summary of the invention

The objective of the invention is to overcome deficiency of the prior art; A kind of bank bridge construction wind based on the probability accumulated damage tired fiduciary level forecasting procedure of shaking is provided; Can adopt the stress response time-histories of Finite Element Method at the tired calculation level of the complicated bank bridge construction of calculated in time domain; Can significantly improve computational accuracy, and based on the tired fiduciary level of probability cumulative damage theory forecast structure in a certain length of service.

For achieving the above object, the present invention provides a kind of bank bridge construction wind based on the probability accumulated damage tired fiduciary level forecasting procedure of shaking, and may further comprise the steps:

The first step adopts the suffered wind load time domain waveform that meets the Davenport power spectrum characteristic of harmonic wave method of superposition simulation bank bridge construction;

In second step,, calculate the stress response time-histories of the tired calculation level of bank bridge construction with the finite element model of wind action in the bank bridge construction;

In the 3rd step, adopt rain flow method to handle the stress response time-histories, thereby obtain the tired statistical nature of luffing stress spectrum;

In the 4th step,, adopt the wind of probability theory method forecast bank bridge construction in a certain length of service tired fiduciary level of shaking through probability accumulated damage model.

According to the described bank bridge construction wind based on the probability accumulated damage of the preferred embodiment of the present invention tired fiduciary level forecasting procedure of shaking, its first step wind load time domain waveform simulation further may further comprise the steps:

At first, set up the wind speed power spectrum density matrix S (ω) of each the wind action point of bank bridge construction meet the Davenport power spectrum characteristic, calculate the time domain waveform of the wind speed of pulsing then according to the waveform method of superposition of following formula according to random vibration theory:

$v_j\left(t\right)=2\sqrt{\mathrm{\Δ\ω}}\underset{m=1}{\overset{j}{\mathrm{\Σ}}}\underset{l=1}{\overset{N}{\mathrm{\Σ}}}\left|H_{\mathrm{jm}}\left({\mathrm{\ω}}_{\mathrm{ml}}\right)\right|\cos ({\mathrm{\ω}}_{\mathrm{ml}}t+{\mathrm{\φ}}_{\mathrm{ml}})j=\mathrm{1,2}\·\·\·n$

Wherein, n is the application point number of wind load, v _j(t) be the pulsation wind speed of j wind action point, N is an abundant big positive integer, φ _MlFor be uniformly distributed in the interval [0,2 π) random phase, Δ ω is defined as ω _uAnd ω _dBe respectively the upper and lower bound of band of interest, ω _MlBe two index frequencies,

H _Jm(ω) be element among the Cholesky split-matrix H (ω) of S (ω).

Afterwards, adopt, calculate the wind load time domain waveform based on the Bernoulli's theorem in the fluid mechanics

$P\left(t\right)=\frac{\mathrm{\γ}}{2g}{\mathrm{\μ}}_{s}A{[\stackrel{\‾}{v}+v\left(t\right)]}^2$

Wherein, γ is an air unit weight, and g is an acceleration of gravity, μ _sWith A be respectively the build coefficient of structure and effective wind area,

It is mean wind speed.

According to the described bank bridge construction wind of the preferred embodiment of the present invention tired fiduciary level forecasting procedure of shaking based on the probability accumulated damage; Its finite element model is the finite element model of the complicated bank bridge construction of employing finite element software foundation, and it comprises beam element, bar unit and lumped mass unit.

According to the described bank bridge construction wind of the preferred embodiment of the present invention tired fiduciary level forecasting procedure of shaking based on the probability accumulated damage; The statistical study of its 3rd step luffing stress spectrum; The luffing stress spectrum that is based on the tired calculation level of rain flow method opposite bank bridge construction is added up; Obtain the cycle index of different stress amplitudes and different mean stresses, as the shake input of tired fiduciary level forecast algorithm of wind.

According to the described bank bridge construction wind of the preferred embodiment of the present invention tired fiduciary level forecasting procedure of shaking based on the probability accumulated damage; Its 4th step probability accumulated damage model; Regard the fatigue failure of bank bridge as random occurrence; Set up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K, confirm the regularity of distribution of fatigue of materials intensity K, based on the tired fiduciary level of probability theory method forecast bank bridge in a certain military service cycle through experimental technique.Specifically according to the D and the K of the tired calculation level of computes:

$D=\mathrm{\Σ}{\left(\frac{{\mathrm{\σ}}_{\mathrm{ai}}{\mathrm{\σ}}_b}{{\mathrm{\σ}}_b-{\mathrm{\σ}}_{\mathrm{mi}}}\right)}^m{n}_i$ $K={\left(\frac{{\mathrm{\σ}}_{\mathrm{aj}}{\mathrm{\σ}}_b}{{\mathrm{\σ}}_b-{\mathrm{\σ}}_{\mathrm{mj}}}\right)}^m{N}_j$

Wherein, σ _bBe the strength degree of material, m is and material, stress ratio, the relevant constant of load mode, σ _AiAnd σ _MiBe respectively asymmetric stresses round-robin stress amplitude and mean stress, n _iAnd N _iBe respectively the actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress.Regard the fatigue failure of bank bridge as random occurrence, under different stress levels, carry out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K, K obeys logarithm normal distribution through statistical study

lnK～N(μ _k，σ _k)；

According to the described bank bridge construction wind based on the probability accumulated damage of the preferred embodiment of the present invention tired fiduciary level forecasting procedure of shaking, above-mentioned probability accumulated damage model is calculated as follows the reliability R of structure in certain length of service:

$R=P(\ln D<\ln K)=\mathrm{\&phi;}\left[\frac{{\mathrm{\&mu;}}_k-\ln D}{{\mathrm{\&sigma;}}_k}\right]$

Wherein, φ is a Standard Normal Distribution.

The present invention adopts the time domain waveform of the suffered wind load of harmonic wave method of superposition simulation bank bridge construction; Utilize ripe finite element software to calculate the stress response time-histories of the tired calculation level of bank bridge construction; The cycle index of different stress amplitudes and mean stress in the employing rain flow method statistics luffing stress spectrum; Regard the fatigue failure of bank bridge construction as random occurrence; Set up the probability model of Cumulative Fatigue Damage and fatigue strength, based on the wind of probability theory method forecast bank bridge construction in a certain length of service tired fiduciary level of shaking.Method of the present invention can be calculated the tired fiduciary level of wind resisting structure under any random wind.Simultaneously, adopt commercial finite element software to set up the finite element model of complicated bank bridge construction, the bank bridge construction finite element model of setting up like this not only can adapt to complicated bank bridge construction, can also reflect the dynamics of bank bridge construction, significantly improves computational accuracy.Therefore, compared with prior art, beneficial effect of the present invention is: be applicable to complicated bank bridge construction, the scope of application is extensive, computational accuracy is high and can calculate the tired fiduciary level of wind resisting structure under any random wind.

Description of drawings

Fig. 1 is the shake process flow diagram of tired fiduciary level forecasting procedure of the bank bridge construction wind that the present invention is based on the probability accumulated damage;

Fig. 2 is that bank bridge construction geometric model reaches and the load point synoptic diagram in the embodiment of the invention;

Fig. 3 is the stress response time-histories synoptic diagram of tired calculation level in the embodiment of the invention.

Embodiment

Below in conjunction with accompanying drawing and enumerate embodiment and specify the present invention.Following embodiment provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment being to implement under the prerequisite with technical scheme of the present invention.

See also Fig. 1, a kind of bank bridge construction wind based on the probability accumulated damage tired fiduciary level forecasting procedure of shaking may further comprise the steps:

S11: adopt the suffered wind load time domain waveform that meets the Davenport power spectrum characteristic of harmonic wave method of superposition simulation bank bridge construction.

This step further may further comprise the steps:

At first, set up the wind speed power spectrum density matrix S (ω) of each the wind action point of bank bridge construction meet the Davenport power spectrum characteristic, calculate the time domain waveform of the wind speed of pulsing then according to the waveform method of superposition of following formula according to random vibration theory:

$v_j\left(t\right)=2\sqrt{\mathrm{\&Delta;\&omega;}}\underset{m=1}{\overset{j}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{N}{\mathrm{\&Sigma;}}}\left|H_{\mathrm{jm}}\left({\mathrm{\&omega;}}_{\mathrm{ml}}\right)\right|\cos ({\mathrm{\&omega;}}_{\mathrm{ml}}t+{\mathrm{\&phi;}}_{\mathrm{ml}})j=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;n$

Wherein, n is the application point number of wind load, v _j(t) be the pulsation wind speed of j wind action point, N is an abundant big positive integer, φ _MlFor be uniformly distributed in the interval [0,2 π) random phase, Δ ω is defined as

ω _uAnd ω _dBe respectively the upper and lower bound of band of interest, ω _MlBe two index frequencies,

H _Jm(ω) be element among the Cholesky split-matrix H (ω) of S (ω).

Afterwards, adopt, calculate the wind load time domain waveform based on the Bernoulli's theorem in the fluid mechanics

$P\left(t\right)=\frac{\mathrm{\&gamma;}}{2g}{\mathrm{\&mu;}}_{s}A{[\stackrel{\&OverBar;}{v}+v\left(t\right)]}^2$

Wherein, γ is an air unit weight, and g is an acceleration of gravity, μ _sWith A be respectively the build coefficient of structure and effective wind area,

It is mean wind speed.

S12:, calculate the stress response time-histories of the tired calculation level of bank bridge construction with the finite element model of wind action in the bank bridge construction.

Finite element model is the finite element model of the complicated bank bridge construction of the commercial finite element software foundation of employing, and it mainly comprises beam element, bar unit and lumped mass unit.The bank bridge construction finite element model of setting up has like this reflected the dynamics of bank bridge construction, be applicable to complicated bank bridge construction, and computational accuracy is higher.With the finite element model of wind action, adopt Finite Element Method promptly to obtain the stress response time-histories of the tired calculation level of bank bridge construction in the bank bridge construction.

S13: adopt rain flow method to handle the stress response time-histories, thereby obtain the tired statistical nature of luffing stress spectrum.

This step is added up based on the luffing stress of the tired calculation level of rain flow method opposite bank bridge construction spectrum, obtains the cycle index of different stress amplitudes and different mean stresses, as the shake input of tired fiduciary level forecast algorithm of wind.

S14:, adopt the wind of probability theory method forecast bank bridge construction in a certain length of service tired fiduciary level of shaking through probability accumulated damage model.

In this step; Probability accumulated damage model is at first regarded the fatigue failure of bank bridge as random occurrence; Set up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K; Confirm the regularity of distribution of fatigue of materials intensity K through experimental technique, based on the tired fiduciary level of probability theory method forecast bank bridge in a certain military service cycle.Specifically according to the D and the K of the tired calculation level of computes:

$D=\mathrm{\&Sigma;}{\left(\frac{{\mathrm{\&sigma;}}_{\mathrm{ai}}{\mathrm{\&sigma;}}_b}{{\mathrm{\&sigma;}}_b-{\mathrm{\&sigma;}}_{\mathrm{mi}}}\right)}^m{n}_i$ $K={\left(\frac{{\mathrm{\&sigma;}}_{\mathrm{aj}}{\mathrm{\&sigma;}}_b}{{\mathrm{\&sigma;}}_b-{\mathrm{\&sigma;}}_{\mathrm{mj}}}\right)}^m{N}_j$

Wherein, σ _bBe the strength degree of material, m is and material, stress ratio, the relevant constant of load mode, σ _AiAnd σ _MiBe respectively asymmetric stresses round-robin stress amplitude and mean stress, n _iAnd N _iBe respectively the actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress.Regard the fatigue failure of bank bridge as random occurrence, under different stress levels, carry out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K, K obeys logarithm normal distribution through statistical study

lnK～N(μ _k，σ _k)；

Afterwards, probability accumulated damage model is calculated as follows the reliability R of structure in certain length of service:

$R=P(\ln D<\ln K)=\mathrm{\&phi;}\left[\frac{{\mathrm{\&mu;}}_k-\ln D}{{\mathrm{\&sigma;}}_k}\right]$

Wherein, φ is a Standard Normal Distribution.

For understanding technical scheme of the present invention better; An embodiment below is provided: certain type bank bridge construction during operation; Mean wind speed is 30m/s in the suffered wind load, and the pulsation wind speed meets the Davenport power spectrum characteristic, and it uses the fiduciary level in 10 years the forecast of utilization the inventive method.

(1) time domain waveform of simulation wind load

As shown in Figure 1, be the geometric model of certain type bank bridge construction.The false wind load action is on discrete node shown in Figure 1; Fluctuating wind meets the Davenport power spectrum characteristic; Set up the wind speed power spectrum density matrix S (ω) of each wind action point of bank bridge construction, when mean wind speed equals 30m/s, according to harmonic wave method of superposition simulated wind pressure time-histories.Consider the natural mode of vibration of bank bridge, during the simulated wind pressure time-histories, getting time step is 0.1s, T.T. length be 600s.

(2) the stress response time-domain analysis of finite element modeling and tired calculation level

Adopt NASTRAN software to set up the finite element model of bank bridge construction shown in Figure 1; Because of bank bridge metal construction size very big; And it is much little that the sectional dimension of primary structure is wanted with respect to its length; So main beam element, bar unit and the lumped mass unit of adopting in the model, totally 923 nodes, 978 unit.The blast time-histories is acted on the load point shown in Figure 1; As tired calculation level, adopt Finite Element Method to obtain the stress response time-histories of tired calculation level as shown in Figure 2 with No. 479 nodes on the triatic stay between No. 403 nodes on the hound between No. 948 nodes on the ladder frame rear pole, doorframe and doorframe.

In the present embodiment, need to prove that the node numbering of present embodiment is without optimization process, though have 923 nodes, node numbering is not from 1 to 923 serial number.Therefore, the node numbering of present embodiment has more than and is limited to 1 to No. 923.

(3) rain flow method is handled the stress response time-histories

Adopt rain flow method to analyze the stress response time-histories of each calculation level, obtain the frequency diagram of the stress amplitude and the mean stress of each stress response time-histories.

(4) the tired fiduciary level of forecast bank bridge construction

The bank bridge is made by steel Q345, and its material constant is m=7.806, σ _b=597.4MPa is μ by the distribution parameter that the fatigue experiment data under the different stress levels obtain the fatigue strength stochastic variable of Q345 material in addition _k=55.3946, σ _k=0.32916.Suppose the annual work of bank bridge 6300 hours, the accumulated damage that calculates in this case in the period of each tired calculation level 10 such as bank bridge construction 403,479 and 948 is respectively 1.52 * 10 ²³, 4.55 * 10 ²¹With 6.70 * 10 ²²Can see, total damage maximum of No. 403 nodes on the hound between doorframe after 10 years, the life-span is the shortest.So the work of bank bridge is after 10 years, its fiduciary level does

$R=\mathrm{\&phi;}\left[\frac{52.9433-\ln (1.5202\&times;{10}^{22})}{0.57903}\right]=\mathrm{\&phi;}(-0.7513)=0.23$

The present invention adopts the time domain waveform of the suffered wind load of harmonic wave method of superposition simulation bank bridge construction; Utilize ripe finite element software to calculate the stress response time-histories of the tired calculation level of bank bridge construction; The cycle index of different stress amplitudes and mean stress in the employing rain flow method statistics luffing stress spectrum; Regard the fatigue failure of bank bridge construction as random occurrence; Set up the probability model of Cumulative Fatigue Damage and fatigue strength, based on the wind of probability theory method forecast bank bridge construction in a certain length of service tired fiduciary level of shaking.Method of the present invention can be calculated the tired fiduciary level of wind resisting structure under any random wind.Simultaneously, adopt commercial finite element software to set up the finite element model of complicated bank bridge construction, the bank bridge construction finite element model of setting up like this not only can adapt to complicated bank bridge construction, can also reflect the dynamics of bank bridge construction, significantly improves computational accuracy.Therefore, compared with prior art, beneficial effect of the present invention is: be applicable to complicated bank bridge construction, the scope of application is extensive, computational accuracy is high and can calculate the tired fiduciary level of wind resisting structure under any random wind.

The above; It only is preferable embodiment of the present invention; Be not that the present invention is done any pro forma restriction; Any content that does not break away from technical scheme of the present invention according to any simple modification, equivalent variations and the modification that technical spirit of the present invention is done above embodiment, all belongs to the scope of technical scheme of the present invention.

Claims (6)

1. the bank bridge construction wind based on the probability accumulated damage tired fiduciary level forecasting procedure of shaking is characterized in that, may further comprise the steps:

The first step adopts the suffered wind load time domain waveform that meets the Davenport power spectrum characteristic of harmonic wave method of superposition simulation bank bridge construction;

In second step,, calculate the stress response time-histories of the tired calculation level of bank bridge construction with the finite element model of wind action in the bank bridge construction;

In the 3rd step, adopt rain flow method to handle the stress response time-histories, thereby obtain the tired statistical nature of luffing stress spectrum;

In the 4th step,, adopt the wind of probability theory method forecast bank bridge construction in a certain length of service tired fiduciary level of shaking through probability accumulated damage model.

2. the bank bridge construction wind based on the probability accumulated damage according to claim 1 tired fiduciary level forecasting procedure of shaking is characterized in that, the described wind load time domain waveform simulation of the first step further may further comprise the steps:

At first, set up the wind speed power spectrum density matrix S (ω) of each the wind action point of bank bridge construction meet the Davenport power spectrum characteristic, calculate the time domain waveform of the wind speed of pulsing then according to the waveform method of superposition of following formula according to random vibration theory:

Wherein, n is the application point number of wind load, v _j(t) be the pulsation wind speed of j wind action point, N is an abundant big positive integer, φ _MlFor be uniformly distributed in the interval [0,2 π) random phase, Δ ω is defined as ω _uAnd ω _dBe respectively the upper and lower bound of band of interest, ω _MlBe two index frequencies,

H _Jm(ω) be element among the Cholesky split-matrix H (ω) of S (ω).

Afterwards, adopt, calculate the wind load time domain waveform based on the Bernoulli's theorem in the fluid mechanics

Wherein, γ is an air unit weight, and g is an acceleration of gravity, μ _sWith A be respectively the build coefficient of structure and effective wind area,

It is mean wind speed.

3. the bank bridge construction wind based on the probability accumulated damage according to claim 1 tired fiduciary level forecasting procedure of shaking; It is characterized in that; Described finite element model is the finite element model of the complicated bank bridge construction of employing finite element software foundation, and it comprises beam element, bar unit and lumped mass unit.

4. the bank bridge construction wind based on the probability accumulated damage according to claim 1 tired fiduciary level forecasting procedure of shaking; It is characterized in that; The statistical study of described luffing stress spectrum of the 3rd step; The luffing stress spectrum that is based on the tired calculation level of rain flow method opposite bank bridge construction is added up, and obtains the cycle index of different stress amplitudes and different mean stresses, as the shake input of tired fiduciary level forecast algorithm of wind.

5. the bank bridge construction wind based on the probability accumulated damage according to claim 1 tired fiduciary level forecasting procedure of shaking; It is characterized in that; Described probability accumulated damage model of the 4th step is regarded the fatigue failure of bank bridge as random occurrence, sets up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K; Confirm the regularity of distribution of fatigue of materials intensity K through experimental technique, based on the tired fiduciary level of probability theory method forecast bank bridge in a certain military service cycle.Specifically according to the D and the K of the tired calculation level of computes:

Wherein, σ _bBe the strength degree of material, m is and material, stress ratio, the relevant constant of load mode, σ _AiAnd σ _MiBe respectively asymmetric stresses round-robin stress amplitude and mean stress, n _iAnd N _iBe respectively the actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress.Regard the fatigue failure of bank bridge as random occurrence, under different stress levels, carry out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K, K obeys logarithm normal distribution through statistical study

lnK～N(μ _k，σ _k)。

6. the bank bridge construction wind based on the probability accumulated damage according to claim 5 tired fiduciary level forecasting procedure of shaking is characterized in that probability accumulated damage model is calculated as follows the reliability R of structure in certain length of service:

Wherein, φ is a Standard Normal Distribution.

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