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

Abstract

A method for predicting wind-induced fatigue reliability of quay bridge structures based on probability cumulative damage includes the following steps: the first step is to use the harmonic superposition method to simulate the wind load time-domain waveforms of quay bridge structures that conform to the characteristics of the Davenport power spectrum; In the second step, the wind load is applied to the finite element model of the quay bridge structure, and the stress response time history of the fatigue calculation point of the quay bridge structure is calculated; in the third step, the stress response time history is processed by the rainflow counting method, thereby obtaining the variable amplitude The fatigue statistical characteristics of the stress spectrum; the fourth step, through the probability cumulative damage model, the probability theory method is used to predict the wind-induced fatigue reliability of the quay bridge structure within a certain service period. The invention has the advantages of being applicable to complex quay bridge structures, having a wide application range, high calculation accuracy and being able to calculate the fatigue reliability of the wind-resistant structure under any random wind load.

Description

Wind-induced fatigue reliability prediction method for quay bridge structure based on probability cumulative damage

technical field

The invention relates to a wind-induced fatigue reliability prediction method for a quay bridge structure, in particular to a method for predicting the wind-induced fatigue reliability of a quay bridge structure based on probability cumulative damage.

Background technique

The quay crane works on the seaside all the year round, the center of the wind force is high, and the windward area is large. The long-term and intermittent effect of the wind load causes fatigue and cumulative damage to the metal structure of the quay. The wind-induced fatigue reliability prediction method of the quay bridge structure is an important issue in the design and maintenance of the quay bridge structure. Fatigue reliability under wind loads.

In order to solve the above problems, Ou Jinping and others published "Probabilistic Fatigue Accumulative Damage of Structural Wind Vibration" in "Journal of Vibration Engineering" 1993, 6(2): 164-168. In this paper, the random vibration analysis method is used to calculate the stress response statistics of the single degree of freedom model of the elevated water tower in the frequency domain, which is a method for calculating the reliability of the elevated water tower within a certain service period based on the statistical distribution of fatigue life. However, this calculation method is only suitable for the prediction of fatigue reliability of simple wind-resistant structures, and the prediction accuracy is low. In addition, the statistical distribution of fatigue life based on this method cannot directly describe the probability characteristics of fatigue cumulative damage.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art and provide a wind-induced fatigue reliability prediction method for quay bridge structures based on probability cumulative damage, which can use the finite element method to calculate the stress of complex quay bridge structure fatigue calculation points in the time domain The response time history can greatly improve the calculation accuracy, and predict the fatigue reliability of the structure within a certain service period based on the probability cumulative damage theory.

In order to achieve the above object, the present invention provides a wind-induced fatigue reliability prediction method for quay bridge structures based on probability cumulative damage, comprising the following steps:

The first step is to use the harmonic superposition method to simulate the time-domain waveform of the wind load on the quay bridge structure that conforms to the characteristics of the Davenport power spectrum;

In the second step, the wind load is applied to the finite element model of the quay bridge structure, and the stress response time history of the fatigue calculation point of the quay bridge structure is calculated;

The third step is to use the rainflow counting method to process the stress response time history, so as to obtain the fatigue statistical characteristics of the variable amplitude stress spectrum;

The fourth step is to use the probability theory method to predict the wind-induced fatigue reliability of the quay bridge structure within a certain service period through the probability cumulative damage model.

According to the wind-induced fatigue reliability prediction method of the quay bridge structure based on the probability cumulative damage described in the preferred embodiment of the present invention, the first step of wind load time domain waveform simulation further includes the following steps:

First, according to the random vibration theory, the wind speed power spectral density matrix S(ω) of each wind load action point of the quay bridge structure conforming to the Davenport power spectrum characteristics is established, and then the time domain waveform of the fluctuating wind speed is calculated according to the waveform superposition method of the following formula:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; \&Delta;\&omega;</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; jm</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; no</span>}$

H_jm(ω)为S(ω)的Cholesky分解矩阵H(ω)中的元素。Among them, n is the number of wind load action points, v _j (t) is the fluctuating wind speed at the jth wind load action point, N is a sufficiently large positive integer, and φ _ml is a uniform distribution in the interval [0, 2π) With a random phase, Δω is defined as ω _u and ω _d are the upper and lower limits of the frequency band of interest, respectively, ω _ml is the double index frequency,

H _jm (ω) is an element in the Cholesky decomposition matrix H(ω) of S(ω).

After that, the time domain waveform of wind load is calculated by using Bernoulli's theorem based on fluid mechanics

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; A</span>}{<span\; class="notranslate">\; [</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

是平均风速。Among them, γ is the air bulk density, g is the acceleration of gravity, μ _s and A are the shape coefficient and effective wind receiving area of the structure respectively,

is the average wind speed.

According to the wind-induced fatigue reliability prediction method of quay bridge structure based on probability cumulative damage described in the preferred embodiment of the present invention, its finite element model is a finite element model of complex quay bridge structure established by finite element software, which includes beam elements , rod element and lumped mass element.

According to the wind-induced fatigue reliability prediction method of the quay bridge structure based on the probability cumulative damage described in the preferred embodiment of the present invention, the statistical analysis of the third step of the variable amplitude stress spectrum is based on the fatigue calculation of the quay bridge structure by the rainflow counting method The variable-amplitude stress spectrum of each point is counted, and the number of cycles of different stress amplitudes and different average stresses is obtained, which is used as the input of the wind-induced fatigue reliability prediction algorithm.

According to the wind-induced fatigue reliability prediction method of the quay bridge structure based on the probability cumulative damage described in the preferred embodiment of the present invention, the fourth step of the probabilistic cumulative damage model is to regard the fatigue failure of the quay bridge as a random event and establish the fatigue cumulative damage The calculation formula of the random variable D and the random variable K of the fatigue strength of the material, the distribution law of the fatigue strength K of the material is determined by the experimental method, and the fatigue reliability of the quay bridge in a certain service period is predicted based on the method of probability theory. Specifically, D and K of the fatigue calculation point are calculated according to the following formula:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; ai</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$ $\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; aj</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; mj</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

Among them, σ _b is the strength limit of the material, m is a constant related to the material, stress ratio, and loading mode, σ _ai and σ _mi are the stress amplitude and mean stress of the asymmetric stress cycle, respectively, and _ni and _Ni are some The actual number of cycles and the number of failure cycles for each stress cycle. The fatigue failure of the quay bridge is regarded as a random event, and the sample value of the fatigue strength K of the material is obtained by fatigue experiments under different stress levels, and the distribution law of K is established through statistical analysis, and K obeys the logarithmic normal distribution

lnK～N(μ _k ，σ _k );

According to the wind-induced fatigue reliability prediction method of the quay bridge structure based on the probability cumulative damage described in the preferred embodiment of the present invention, the above-mentioned probability cumulative damage model calculates the reliability R of the structure within a certain service period according to the following formula:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; ]</span>$

where φ is the standard normal distribution function.

The invention uses the harmonic superposition method to simulate the time-domain waveform of the wind load on the quay bridge structure, uses mature finite element software to calculate the stress response time history of the quay bridge structure fatigue calculation point, and uses the rainflow counting method to count the variable amplitude stress spectrum. The number of cycles of different stress amplitudes and average stresses, the fatigue failure of the quay bridge structure is regarded as a random event, the probability model of fatigue cumulative damage and fatigue strength is established, and the wind damage of the quay bridge structure within a certain service period is predicted based on the probability theory method. vibration fatigue reliability. The method of the invention can calculate the fatigue reliability of the wind-resistant structure under any random wind load. At the same time, commercial finite element software is used to establish the finite element model of the complex quay bridge structure. The finite element model of the quay bridge structure can not only adapt to the complex quay bridge structure, but also reflect the dynamic characteristics of the quay bridge structure, greatly improving the calculation accuracy . Therefore, compared with the prior art, the beneficial effect of the present invention is that it is suitable for complex quay bridge structures, has a wide application range, high calculation accuracy, and can calculate the fatigue reliability of wind-resistant structures under any random wind load.

Description of drawings

Fig. 1 is the flow chart of the wind-induced fatigue reliability prediction method of the quay bridge structure based on the probability cumulative damage of the present invention;

Fig. 2 is a schematic diagram of the geometric model of the quay bridge structure and the point of action of the load in the embodiment of the present invention;

Fig. 3 is a schematic diagram of the stress response time history of the fatigue calculation point in the embodiment of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and examples. The following examples are implemented on the premise of the technical solutions of the present invention, and detailed implementation methods and specific operation processes are provided, but the protection scope of the present invention is not limited to the following examples.

Please refer to Figure 1, a wind-induced fatigue reliability prediction method for quay bridge structures based on probability cumulative damage, including the following steps:

S11: Using the harmonic superposition method to simulate the time-domain waveform of the wind load on the quay bridge structure that conforms to the Davenport power spectrum characteristics.

This step further comprises the steps of:

First, according to the random vibration theory, the wind speed power spectral density matrix S(ω) of each wind load action point of the quay bridge structure conforming to the Davenport power spectrum characteristics is established, and then the time domain waveform of the fluctuating wind speed is calculated according to the waveform superposition method of the following formula:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; \&Delta;\&omega;</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; jm</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; ml</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; no</span>}$

ω_u和ω_d分别为感兴趣频带的上限和下限，ω_ml为双索引频率，

H_jm(ω)为S(ω)的Cholesky分解矩阵H(ω)中的元素。Among them, n is the number of wind load action points, v _j (t) is the fluctuating wind speed at the jth wind load action point, N is a sufficiently large positive integer, and φ _ml is a uniform distribution in the interval [0, 2π) With a random phase, Δω is defined as

ω _u and ω _d are the upper and lower limits of the frequency band of interest, respectively, ω _ml is the double index frequency,

H _jm (ω) is an element in the Cholesky decomposition matrix H(ω) of S(ω).

After that, the time domain waveform of wind load is calculated by using Bernoulli's theorem based on fluid mechanics

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; A</span>}{<span\; class="notranslate">\; [</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

是平均风速。Among them, γ is the air bulk density, g is the acceleration of gravity, μ _s and A are the shape coefficient and effective wind receiving area of the structure respectively,

is the average wind speed.

S12: The wind load is applied to the finite element model of the quay bridge structure, and the stress response time history of the fatigue calculation point of the quay bridge structure is calculated.

The finite element model is a finite element model of the complex quay bridge structure established by commercial finite element software, which mainly includes beam elements, bar elements and lumped mass elements. The finite element model of the quay bridge structure established in this way reflects the dynamic characteristics of the quay bridge structure, is suitable for complex quay bridge structures, and has high calculation accuracy. The wind load acts on the finite element model of the quay bridge structure, and the stress response time history of the fatigue calculation point of the quay bridge structure is obtained by using the finite element method.

S13: The rainflow counting method is used to process the stress response time history, so as to obtain the fatigue statistical characteristics of the variable-amplitude stress spectrum.

This step counts the variable-amplitude stress spectrum of the fatigue calculation point of the quay bridge structure based on the rainflow counting method, and obtains the cycle times of different stress amplitudes and different average stresses, which are used as the input of the wind-induced fatigue reliability prediction algorithm.

S14: Through the probabilistic cumulative damage model, the probability theory method is used to predict the wind-induced fatigue reliability of the quay bridge structure within a certain service period.

In this step, the probabilistic cumulative damage model first regards the fatigue failure of the quay bridge as a random event, establishes the calculation formula of the fatigue cumulative damage random variable D and the material fatigue strength random variable K, and determines the distribution law of the material fatigue strength K through experiments , based on the probability theory method to predict the fatigue reliability of the quay crane in a certain service period. Specifically, D and K of the fatigue calculation point are calculated according to the following formula:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; ai</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$ $\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; aj</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; mj</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

Among them, σ _b is the strength limit of the material, m is a constant related to the material, stress ratio, and loading mode, σ _ai and σ _mi are the stress amplitude and mean stress of the asymmetric stress cycle, respectively, and _ni and _Ni are some The actual number of cycles and the number of failure cycles for each stress cycle. The fatigue failure of the quay bridge is regarded as a random event, and the sample value of the fatigue strength K of the material is obtained by fatigue experiments under different stress levels, and the distribution law of K is established through statistical analysis, and K obeys the logarithmic normal distribution

lnK～N(μ _k ，σ _k );

Afterwards, the probability cumulative damage model calculates the reliability R of the structure in a certain service period according to the following formula:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; ]</span>$

where φ is the standard normal distribution function.

For a better understanding of the technical scheme of the present invention, an embodiment is provided below: a certain type of quay bridge structure is during work, and the average wind speed in the wind load is 30m/s, and the fluctuating wind speed meets the Davenport power spectrum feature, using the method of the present invention Forecast its 10-year reliability.

(1) Time domain waveform of simulated wind load

As shown in Figure 1, it is the geometric model of a certain type of quay bridge structure. Assuming that the wind load acts on the discrete nodes shown in Figure 1, and the fluctuating wind conforms to the Davenport power spectrum characteristics, the wind speed power spectral density matrix S(ω) of each wind load action point of the quay bridge structure is established. When the average wind speed is equal to 30m/s When , the wind pressure time history is simulated according to the harmonic superposition method. Considering the natural mode of the quay bridge, when simulating the time history of wind pressure, the time step is 0.1s, and the total time length is 600s.

(2) Finite element modeling and stress response time domain analysis of fatigue calculation points

NASTRAN software is used to establish the finite element model of the quay bridge structure shown in Figure 1. Because the metal structure of the quay bridge is very large, and the cross-sectional size of the main structure is much smaller than its length, the model mainly uses beam elements, Rod elements and lumped mass elements, a total of 923 nodes, 978 elements. The time history of wind pressure acts on the load point shown in Figure 1, taking the No. 948 node on the rear brace of the ladder frame, the No. 403 node on the diagonal brace between the door frames and the No. 479 node on the horizontal brace between the door frames. No. 1 node is used as the fatigue calculation point, and the stress response time history of the fatigue calculation point shown in Figure 2 is obtained by using the finite element method.

In this embodiment, it should be noted that the node numbers in this embodiment are not optimized. Although there are 923 nodes in total, the node numbers are not sequentially numbered from 1 to 923. Therefore, the node numbers in this embodiment are not limited to numbers 1 to 923.

(3) Rainflow counting method to deal with stress response time history

The stress response time history of each calculation point is analyzed by rainflow counting method, and the frequency diagrams of stress amplitude and average stress of each stress response time history are obtained.

(4) Predict the fatigue reliability of the quay bridge structure

The quay bridge is made of steel Q345, and its material constant is m=7.806, σ _b ＝597.4MPa. In addition, the distribution parameters of the fatigue strength random variable of Q345 material are obtained from the fatigue experimental data under different stress levels as μ _k ＝55.3946, σ _k = 0.32916. Assuming that the quay crane works for 6300 hours per year, in this case, the accumulated damages of the quay crane structure 403, 479 and 948 and other fatigue calculation points in 10 years are 1.52×10 ²³ , 4.55×10 ²¹ and 6.70×10 ²² respectively. It can be seen that after 10 years, the joint No. 403 on the diagonal brace between the door frames has the largest total damage and the shortest life span. So after 10 years of operation of the quay bridge, its reliability is

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 52.9433</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.5202</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 0.57903</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.7513</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.23</span>}$

The invention uses the harmonic superposition method to simulate the time-domain waveform of the wind load on the quay bridge structure, uses mature finite element software to calculate the stress response time history of the quay bridge structure fatigue calculation point, and uses the rainflow counting method to count the variable amplitude stress spectrum. The number of cycles of different stress amplitudes and average stresses, the fatigue failure of the quay bridge structure is regarded as a random event, the probability model of fatigue cumulative damage and fatigue strength is established, and the wind damage of the quay bridge structure within a certain service period is predicted based on the probability theory method. vibration fatigue reliability. The method of the invention can calculate the fatigue reliability of the wind-resistant structure under any random wind load. At the same time, commercial finite element software is used to establish the finite element model of the complex quay bridge structure. The finite element model of the quay bridge structure can not only adapt to the complex quay bridge structure, but also reflect the dynamic characteristics of the quay bridge structure, greatly improving the calculation accuracy . Therefore, compared with the prior art, the beneficial effect of the present invention is that it is suitable for complex quay bridge structures, has a wide application range, high calculation accuracy, and can calculate the fatigue reliability of wind-resistant structures under any random wind load.

The above is only a preferred implementation example of the present invention, and is not intended to limit the present invention in any form, any content that does not deviate from the technical solution of the present invention, any simple modification made to the above implementation examples according to the technical essence of the present invention , equivalent changes and modifications all belong to the scope of the technical solution of the present invention.

Claims (6)

1. A wind-induced fatigue reliability prediction method for quay bridge structures based on probability cumulative damage, characterized in that it comprises the following steps: The first step is to use the harmonic superposition method to simulate the time-domain waveform of the wind load on the quay bridge structure that conforms to the characteristics of the Davenport power spectrum; In the second step, the wind load is applied to the finite element model of the quay bridge structure, and the stress response time history of the fatigue calculation point of the quay bridge structure is calculated; The third step is to use the rainflow counting method to process the stress response time history, so as to obtain the fatigue statistical characteristics of the variable amplitude stress spectrum; The fourth step is to use the probability theory method to predict the wind-induced fatigue reliability of the quay bridge structure within a certain service period through the probability cumulative damage model. 2. the quay bridge structure wind-induced fatigue reliability prediction method based on probability cumulative damage according to claim 1, is characterized in that, the wind load time domain waveform simulation described in the first step further comprises the following steps: First, according to the random vibration theory, the wind speed power spectral density matrix S(ω) of each wind load action point of the quay bridge structure conforming to the Davenport power spectrum characteristics is established, and then the time domain waveform of the fluctuating wind speed is calculated according to the waveform superposition method of the following formula: Among them, n is the number of wind load action points, v _j (t) is the fluctuating wind speed at the jth wind load action point, N is a sufficiently large positive integer, and φ _ml is a uniform distribution in the interval [0, 2π) With a random phase, Δω is defined as ω _u and ω _d are the upper and lower limits of the frequency band of interest, respectively, ω _ml is the double index frequency,

H _jm (ω) is an element in the Cholesky decomposition matrix H(ω) of S(ω). After that, the time domain waveform of wind load is calculated by using Bernoulli's theorem based on fluid mechanics

Among them, γ is the air bulk density, g is the acceleration of gravity, μ _s and A are the shape coefficient and effective wind receiving area of the structure respectively,

is the average wind speed. 3. the quay bridge structure wind-induced fatigue reliability prediction method based on probability cumulative damage according to claim 1, is characterized in that, described finite element model is the finite element model of the complex quay bridge structure that adopts finite element software to set up , which includes beam elements, rod elements, and lumped mass elements. 4. the wind-induced fatigue reliability prediction method of quay bridge structure based on probability cumulative damage according to claim 1, is characterized in that, the statistical analysis of the variable-amplitude stress spectrum described in the third step is based on the rainflow counting method on the bank The variable-amplitude stress spectrum of the fatigue calculation points of the bridge structure is counted to obtain the cycle times of different stress amplitudes and different average stresses, which are used as the input of the wind-induced fatigue reliability prediction algorithm. 5. the wind-induced fatigue reliability prediction method of quay bridge structure based on probability cumulative damage according to claim 1, is characterized in that, the probability cumulative damage model described in the 4th step regards the fatigue failure of quay bridge as a random event In order to establish the calculation formulas of fatigue cumulative damage random variable D and material fatigue strength random variable K, the distribution law of material fatigue strength K is determined by experimental methods, and the fatigue reliability of quay cranes in a certain service period is predicted based on probability theory. Specifically, D and K of the fatigue calculation point are calculated according to the following formula:

Among them, σ _b is the strength limit of the material, m is a constant related to the material, stress ratio, and loading mode, σ _ai and σ _mi are the stress amplitude and mean stress of the asymmetric stress cycle, respectively, and _ni and _Ni are some The actual number of cycles and the number of failure cycles for each stress cycle. The fatigue failure of the quay bridge is regarded as a random event, and the sample value of the fatigue strength K of the material is obtained by fatigue experiments under different stress levels, and the distribution law of K is established through statistical analysis, and K obeys the logarithmic normal distribution lnK～N(μ _k , σ _k ). 6. The wind-induced fatigue reliability prediction method of quay bridge structures based on probability cumulative damage according to claim 5, wherein the probability cumulative damage model calculates the reliability R of the structure in a certain service period according to the following formula:

where φ is the standard normal distribution function. the

Images