CN102567633B - 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-induced fatigue reliability forecasting method of accumulated damage of probability

Technical field

The present invention relates to a kind of wind-induced fatigue reliability forecasting method of bank bridge construction, specifically a kind of bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability.

Background technology

Bank bridge crane works in seashore throughout the year, and sail-center is high, and front face area is large, and wind load effect that is long-term, that be interrupted causes bank bridge metal construction to produce Cumulative Fatigue Damage.The wind-induced fatigue reliability forecasting method of bank bridge construction is a major issue in the design of bank bridge construction and 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 the Fatigue Reliability under forecast bank bridge construction wind action.

For solving the problem, the people such as Ou Jinping have delivered " Probabilistic Fatigue Damage Accumulation of wind induced structural vibration " on " vibration engineering journal " 1993,6 (2): 164-168.This article random seismic response analysis method calculates the stress response statistic of overhead water tower one degree of freedom modeling in frequency domain, is that a kind of Statistical Distribution based on fatigue lifetime sets up the reliability degree calculation method of overhead water tower in certain length of service.But this computing method are suitable only for the forecast of simple wind resisting structure Fatigue Reliability, and forecast precision is low.In addition, the method the probability nature of Cumulative Fatigue Damage can not directly be described according to the Statistical Distribution of fatigue lifetime.

Summary of the invention

The object of the invention is to overcome deficiency of the prior art, a kind of bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability is provided, Finite Element Method can be adopted in the stress response time-histories of calculated in time domain complicated bank bridge construction fatigue mechanisms point, significantly can improve computational accuracy, and based on the Fatigue Reliability of accumulated damage of probability Theoretical Prediction structure in a certain length of service.

For achieving the above object, the invention provides a kind of bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability, comprising the following steps:

The first step, adopts the wind load time domain waveform meeting Davenport power spectrum characteristic suffered by harmony superposition simulation bank bridge construction;

Second step, by the finite element model of wind action in bank bridge construction, calculates the stress response time-histories of bank bridge construction fatigue mechanisms point;

3rd step, adopts rain flow method process stress response time-histories, thus obtains the fatigue statisic feature of luffing stress spectra;

4th step, by accumulated damage of probability model, adopts the wind-induced fatigue fiduciary level of probability theory method forecast bank bridge construction in a certain length of service.

According to the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability described in present pre-ferred embodiments, the simulation of its first step wind load time domain waveform is further comprising the steps:

First, set up the power spectral density of the wind speed matrix S (ω) meeting each wind action point of bank bridge construction of Davenport power spectrum characteristic according to random vibration theory, then calculate the time domain waveform of fluctuating wind speed according to the addition of waveforms method of following formula:

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

Wherein, n is the application point number of wind load, v _j(t) for the fluctuating wind speed of a jth wind action point, N be a fully large positive integer, φ _mlfor be uniformly distributed in 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 _mlfor two index frequency, h _jm(ω) be the element in the Cholesky split-matrix H (ω) of S (ω).

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

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

Wherein, γ is air unit weight, and g is acceleration of gravity, μ _sthe Shape Coefficient of structure and effective wind area respectively with A, it is mean wind speed.

According to the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability described in present pre-ferred embodiments, its finite element model is the finite element model of the complicated bank bridge construction adopting finite element software to set up, and it comprises beam element, bar unit and lumped mass unit.

According to the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability described in present pre-ferred embodiments, the statistical study of its 3rd step luffing stress spectra, add up based on the luffing stress spectra of the fatigue mechanisms point of rain flow method opposite bank bridge construction, obtain the cycle index of different stress amplitude and different mean stress, as the input of wind-induced fatigue fiduciary level prediction algorithm.

According to the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability described in present pre-ferred embodiments, its the 4th step accumulated damage of probability model, the fatigue failure of bank bridge is regarded as random occurrence, set up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K, the regularity of distribution of method determination fatigue of materials intensity K by experiment, based on the Fatigue Reliability of probability theory method forecast bank bridge within a certain military service cycle.Concrete D and K calculating fatigue mechanisms point according to the following formula:

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

Wherein, σ _bbe the strength degree of material, m is the constant relevant with material, stress ratio, load mode, σ _aiand σ _mistress amplitude and the mean stress of asymmetric stresses circulation respectively, n _iand N _ibe respectively actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress.The fatigue failure of bank bridge is regarded as random occurrence, under different stress level, carries out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K by statistical study, K obeys logarithm normal distribution

lnK～N(μ _k，σ _k)；

According to the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability described in present pre-ferred embodiments, above-mentioned accumulated damage of probability model is calculated as follows the fiduciary level 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 Standard Normal Distribution.

The present invention adopts harmony superposition to simulate the time domain waveform of wind load suffered by bank bridge construction, ripe finite element software is utilized to calculate the stress response time-histories of bank bridge construction fatigue mechanisms point, adopt the cycle index of different stress amplitude and mean stress in rain flow method statistics luffing stress spectra, the fatigue failure of bank bridge construction is regarded as random occurrence, set up the probability model of Cumulative Fatigue Damage and fatigue strength, based on the wind-induced fatigue fiduciary level of probability theory method forecast bank bridge construction in a certain length of service.Method of the present invention can calculate the Fatigue Reliability of wind resisting structure under any random wind.Meanwhile, adopt business finite element software to set up the finite element model of complicated bank bridge construction, the bank bridge construction finite element model set up like this can not only adapt to complicated bank bridge construction, can also reflect the dynamics of bank bridge construction, significantly improve computational accuracy.Therefore, compared with prior art, beneficial effect of the present invention is: be applicable to complicated bank bridge construction, applied widely, computational accuracy is high and the Fatigue Reliability of wind resisting structure under can calculating any random wind.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the bank bridge construction wind-induced fatigue reliability forecasting method that the present invention is based on accumulated damage of probability;

Fig. 2 be in the embodiment of the present invention bank bridge construction geometric model and and load point schematic diagram;

Fig. 3 is the stress response time-histories schematic diagram of fatigue mechanisms point in the embodiment of the present invention.

Embodiment

Enumerate embodiment illustrate the present invention below in conjunction with accompanying drawing.Following embodiment is implemented under premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Refer to Fig. 1, a kind of bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability, comprises the following steps:

S11: adopt the wind load time domain waveform meeting Davenport power spectrum characteristic suffered by harmony superposition simulation bank bridge construction.

This step is further comprising the steps:

First, set up the power spectral density of the wind speed matrix S (ω) meeting each wind action point of bank bridge construction of Davenport power spectrum characteristic according to random vibration theory, then calculate the time domain waveform of fluctuating wind speed according to the addition of waveforms method of following formula:

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

Wherein, n is the application point number of wind load, v _j(t) for the fluctuating wind speed of a jth wind action point, N be a fully large positive integer, φ _mlfor be uniformly distributed in 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 _mlfor two index frequency, h _jm(ω) be the element in the Cholesky split-matrix H (ω) of S (ω).

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

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

Wherein, γ is air unit weight, and g is acceleration of gravity, μ _sthe Shape Coefficient of structure and effective wind area respectively with A, it is mean wind speed.

S12: by the finite element model of wind action in bank bridge construction, calculates the stress response time-histories of bank bridge construction fatigue mechanisms point.

Finite element model is the finite element model of the complicated bank bridge construction adopting business finite element software to set up, and it mainly comprises beam element, bar unit and lumped mass unit.The bank bridge construction finite element model of such foundation reflects the dynamics of bank bridge construction, be applicable to complicated bank bridge construction, and computational accuracy is higher.By the finite element model of wind action in bank bridge construction, Finite Element Method is adopted namely to obtain the stress response time-histories of bank bridge construction fatigue mechanisms point.

S13: adopt rain flow method process stress response time-histories, thus obtain the fatigue statisic feature of luffing stress spectra.

This step is added up based on the luffing stress spectra of the fatigue mechanisms point of rain flow method opposite bank bridge construction, obtains the cycle index of different stress amplitude and different mean stress, as the input of wind-induced fatigue fiduciary level prediction algorithm.

S14: by accumulated damage of probability model, adopts the wind-induced fatigue fiduciary level of probability theory method forecast bank bridge construction in a certain length of service.

In this step, first the fatigue failure of bank bridge is regarded as random occurrence by accumulated damage of probability model, set up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K, the regularity of distribution of method determination fatigue of materials intensity K by experiment, based on the Fatigue Reliability of probability theory method forecast bank bridge within a certain military service cycle.Concrete D and K calculating fatigue mechanisms point according to the following formula:

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

Wherein, σ _bbe the strength degree of material, m is the constant relevant with material, stress ratio, load mode, σ _aiand σ _mistress amplitude and the mean stress of asymmetric stresses circulation respectively, n _iand N _ibe respectively actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress.The fatigue failure of bank bridge is regarded as random occurrence, under different stress level, carries out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K by statistical study, K obeys logarithm normal distribution

lnK～N(μ _k，σ _k)；

Afterwards, accumulated damage of probability model is calculated as follows the fiduciary level 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 Standard Normal Distribution.

For understanding technical scheme of the present invention better, below provide an embodiment: certain type bank bridge construction during operation, in suffered wind load, mean wind speed is 30m/s, and fluctuating wind speed meets Davenport power spectrum characteristic, uses the inventive method to forecast its fiduciary level using 10 years.

(1) time domain waveform of simulated wind load

As shown in Figure 1, be the geometric model of certain type bank bridge construction.False wind load action is on the discrete node shown in Fig. 1, fluctuating wind meets Davenport power spectrum characteristic, set up the power spectral density of the wind speed matrix S (ω) of each wind action point of bank bridge construction, when mean wind speed equals 30m/s, according to harmony superposition simulated wind pressure time-histories.Consider the natural mode of vibration of bank bridge, during 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 fatigue mechanisms point

NASTRAN software is adopted to set up the finite element model of the bridge construction of bank shown in Fig. 1, because bank bridge metal construction size is very large, and the sectional dimension of primary structure is relative to much smaller its length, so mainly adopt beam element, bar unit and lumped mass unit in model, totally 923 nodes, 978 unit.Blast time-histories is acted on the load point shown in Fig. 1, using No. 479 nodes of No. 403 on hound between on ladder frame rear pole No. 948 node, doorframe between node and doorframe on triatic stay as fatigue mechanisms point, Finite Element Method is adopted to obtain the stress response time-histories of fatigue mechanisms point as shown in Figure 2.

In the present embodiment, it should be noted that, the node numbering of the present embodiment is without optimization process, though have 923 nodes, node numbering is not from 1 to 923 serial numbers.Therefore, the node numbering of the present embodiment has more than and is limited to 1 to No. 923.

(3) rain flow method process stress response time-histories

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

(4) Fatigue Reliability of bank bridge construction is forecast

Bank bridge is manufactured by steel Q345, and its material constant is m=7.806, σ _b=597.4MPa, the distribution parameter being obtained the fatigue strength stochastic variable of Q345 material in addition by the fatigue experiment data under different stress level is μ _k=55.3946, σ _k=0.32916.Suppose that bank bridge works 6300 hours every year, the accumulated damage calculated in this case between each fatigue mechanisms points such as bank bridge construction 403,479 and 948 10 years is respectively 1.52 × 10 ²³, 4.55 × 10 ²¹with 6.70 × 10 ²².Can see, total damage of No. 403 nodes between 10 years rear door frames on hound is maximum, and the life-span is the shortest.So after bank bridge work for 10 years, its fiduciary level is

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

The present invention adopts harmony superposition to simulate the time domain waveform of wind load suffered by bank bridge construction, ripe finite element software is utilized to calculate the stress response time-histories of bank bridge construction fatigue mechanisms point, adopt the cycle index of different stress amplitude and mean stress in rain flow method statistics luffing stress spectra, the fatigue failure of bank bridge construction is regarded as random occurrence, set up the probability model of Cumulative Fatigue Damage and fatigue strength, based on the wind-induced fatigue fiduciary level of probability theory method forecast bank bridge construction in a certain length of service.Method of the present invention can calculate the Fatigue Reliability of wind resisting structure under any random wind.Meanwhile, adopt business finite element software to set up the finite element model of complicated bank bridge construction, the bank bridge construction finite element model set up like this can not only adapt to complicated bank bridge construction, can also reflect the dynamics of bank bridge construction, significantly improve computational accuracy.Therefore, compared with prior art, beneficial effect of the present invention is: be applicable to complicated bank bridge construction, applied widely, computational accuracy is high and the Fatigue Reliability of wind resisting structure under can calculating any random wind.

The above, it is only better embodiment of the present invention, not any pro forma restriction is done to the present invention, any content not departing from technical solution of the present invention, the any simple modification done above embodiment according to technical spirit of the present invention, equivalent variations and modification, all belong to the scope of technical solution of the present invention.

Claims (5)

1., based on a bank bridge construction wind-induced fatigue reliability forecasting method for accumulated damage of probability, it is characterized in that, comprise the following steps:

The first step, adopts the wind load time domain waveform meeting Davenport power spectrum characteristic suffered by harmony superposition simulation bank bridge construction;

Second step, by the finite element model of wind action in bank bridge construction, calculates the stress response time-histories of bank bridge construction fatigue mechanisms point;

3rd step, adopts rain flow method process stress response time-histories, thus obtains the fatigue statisic feature of luffing stress spectra;

4th step, by accumulated damage of probability model, adopt the wind-induced fatigue fiduciary level of probability theory method forecast bank bridge construction in a certain length of service, described accumulated damage of probability model, the fatigue failure of bank bridge is regarded as random occurrence, set up the computing formula of Cumulative Fatigue Damage stochastic variable D and fatigue of materials intensity stochastic variable K, the regularity of distribution of method determination fatigue of materials intensity K by experiment, based on the Fatigue Reliability of probability theory method forecast bank bridge within a certain military service cycle, specifically calculate D and K of fatigue mechanisms point according to the following formula:

$\begin{array}{cc}D=\mathrm{\&Sigma;}{\left(\frac{{\mathrm{\&sigma;}}_{\mathrm{ai}}{\mathrm{\&sigma;}}_b}{{\mathrm{\&sigma;}}_b-{\mathrm{\&sigma;}}_{\mathrm{mi}}}\right)}^m{n}_i& K={\left(\frac{{\mathrm{\&sigma;}}_{\mathrm{ai}}{\mathrm{\&sigma;}}_b}{{\mathrm{\&sigma;}}_b-{\mathrm{\&sigma;}}_{\mathrm{mi}}}\right)}^m{N}_i\end{array}$

Wherein, σ _bbe the strength degree of material, m is the constant relevant with material, stress ratio, load mode, σ _aiand σ _mistress amplitude and the mean stress of asymmetric stresses circulation respectively, n _iand N _ibe respectively actual cycle number of times and the inefficacy cycle index of certain Cyclic Stress, the fatigue failure of bank bridge is regarded as random occurrence, under different stress level, carry out the sample value that fatigue experiment obtains fatigue of materials intensity K, set up the regularity of distribution of K by statistical study, K obeys logarithm normal distribution

lnK～N(μ _k,σ _k)。

2. the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability according to claim 1, is characterized in that, the wind load time domain waveform simulation described in the first step is further comprising the steps:

First, set up the power spectral density of the wind speed matrix S (ω) meeting each wind action point of bank bridge construction of Davenport power spectrum characteristic according to random vibration theory, then calculate the time domain waveform of fluctuating wind speed according to the addition of waveforms method of following formula:

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

Wherein, n is the application point number of wind load, v _j(t) for the fluctuating wind speed of a jth wind action point, N be a fully large positive integer, φ _mlfor be uniformly distributed in 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 _mlfor two index frequency, h _jm(ω) be the element in the Cholesky split-matrix H (ω) of S (ω).

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

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

Wherein, γ is air unit weight, and g is acceleration of gravity, μ _sthe Shape Coefficient of structure and effective wind area respectively with A, it is mean wind speed.

3. the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability according to claim 1, it is characterized in that, described finite element model is the finite element model of the complicated bank bridge construction adopting finite element software to set up, and it comprises beam element, bar unit and lumped mass unit.

4. the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability according to claim 1, it is characterized in that, the statistical study of the luffing stress spectra described in the 3rd step, add up based on the luffing stress spectra of the fatigue mechanisms point of rain flow method opposite bank bridge construction, obtain the cycle index of different stress amplitude and different mean stress, as the input of wind-induced fatigue fiduciary level prediction algorithm.

5. the bank bridge construction wind-induced fatigue reliability forecasting method based on accumulated damage of probability according to claim 1, it is characterized in that, accumulated damage of probability model is calculated as follows the fiduciary level R of structure in certain length of service:

$R=P(1\mathrm{nD}<\ln K)=\mathrm{\&phi;}\left[\frac{{\mathrm{\&mu;}}_k-\ln D}{{\mathrm{\&sigma;}}_k}\right]$

Wherein, φ is Standard Normal Distribution.