CN113792456B - Metal roof service life prediction method based on wind load spectrum fatigue simulation - Google Patents
Metal roof service life prediction method based on wind load spectrum fatigue simulation Download PDFInfo
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Abstract
The invention discloses a metal roof life prediction method based on wind load spectrum fatigue simulation, which comprises estimating fatigue wind distribution according to meteorological wind speed data, and calculating a weibull distribution model of wind speed; constructing a pulsating wind load model by combining the average wind vertical characteristic, turbulence intensity, wind speed power spectral density and wind pressure coefficient parameters; correcting the pulsating wind load model by using real-time monitoring data; constructing a wind-induced fatigue load spectrum of a specific building roof; converting wind speed into pulsating wind load through a pulsating wind load model, and calculating the cycle number of each load to obtain a wind induced fatigue load spectrum; performing fatigue simulation on the metal roof under the action of different cyclic loads by a finite element simulation method; and predicting the service life of the metal roof by utilizing a miner damage superposition principle. The invention solves the problem that the data such as the wind pressure, the wind speed and the like are difficult to acquire in the accelerated life test.
Description
Technical Field
The invention relates to the technical field of structural fatigue damage, in particular to a metal roof life prediction method based on wind load spectrum fatigue simulation.
Background
The metal roofing system is widely applied to roofing enclosure systems of buildings such as railway stations, stadiums, airport terminal buildings and the like by virtue of the advantages of high strength, unique modeling, light weight, flexible design, simple and convenient construction and the like. However, as the metal roof is exposed to a complex weather environment throughout the year, the metal roof can be subjected to fatigue deformation under the action of alternating wind load, rain and snow load and temperature load, and the wind uncovering resistance performance is degraded, so that the metal roof can deform, crack, lift the roof and other accidents under the action of lower than the designed wind speed, and severe economic loss and casualties are caused.
In the prior art, a wind tunnel experiment or an anti-wind uncovering experiment is focused on a roof, the wind tunnel experiment can explore the wind pressure distribution rule of the roof configuration of a specific building, but the adopted scaling model has deviation from a real object, and can not simulate all conditions of the wind load action of a metal roof; the wind-break resistance test explores the wind-break resistance of the metal roof, the fatigue life of the roof is not researched, and the cost is high. In addition, a part of the prior art focuses on researching the performance degradation of an object based on a data driving mode, and analyzes the state trend according to the acquired data of the sensor, so that the method is flexible, but most of the prior art is applied to the performance degradation evaluation of mechanical equipment, and no effective method for predicting the fatigue life of a large-span metal roof exists.
Disclosure of Invention
The invention aims to provide a metal roof life prediction method based on wind load spectrum fatigue simulation, so as to solve the problems.
The invention solves the technical problems by adopting the following technical scheme:
a metal roof life prediction method based on wind load spectrum fatigue simulation comprises the following steps:
s1: estimating fatigue wind distribution according to meteorological wind speed data, and calculating a weibull distribution model of wind speed;
s2: building a pulsating wind load model; constructing a pulsating wind load model by combining the average wind vertical characteristic, turbulence intensity, wind speed power spectral density and wind pressure coefficient parameters;
s3: correcting the pulsating wind load model by using real-time monitoring data to enable the pulsating wind load model to approach the wind pressure load of the roof of the specific building; the real-time monitoring data is derived from wind speed-wind pressure data monitored by a sensor network on a large-span metal roof for a long time, and a least square method is used for fitting a functional relation to correct a pulsating wind load model;
s4: constructing a wind-induced fatigue load spectrum of a specific building roof; converting the wind speed into a pulsating wind load through a pulsating wind load model, and calculating the cycle times of each load by combining the load probability density and the cycle period, thereby obtaining a wind-induced fatigue load spectrum;
s5: performing fatigue simulation on the metal roof under the action of different cyclic loads by a finite element simulation method;
s6: and predicting the service life of the metal roof by utilizing a miner damage superposition principle.
Preferably, the expression of the wind speed Weibull distribution model is:
wherein v represents the average wind speed, k is a proportional parameter, c is a shape parameter, p wb (v, k, c) is a wind speed probability density function, e is a base of natural logarithm; parameters in the Weibull distribution model are estimated as follows:
where v is the average wind speed, σ is the standard deviation of wind speed,is a gamma distribution function, t represents a time parameter; the average wind speed was replaced by wind levels and the distribution of the short-term average wind at each wind level was plotted with the Weibull distribution.
Preferably, the pulsating wind load model building method comprises the following steps:
s21, constructing a turbulent wind mathematical model:
wherein ,the average wind speed of turbulent wind is represented by f which is frequency, and I represents turbulence intensity;
s22, static pressure load modeling:
the wind pressure distribution of the building surface is calculated based on an RNGk-epsilon model, the wind pressure coefficient is used for representing the rule and the size of the wind pressure distribution, and the wind pressure coefficient is defined as follows:
the relation between the calculated wind load and the wind speed is shown in the following formula, delta P represents the negative wind pressure generated by the wind load, and P 0 Representing the static pressure of the static air under the metal roof plate, known in conjunction with the bernoulli equation:
wherein p represents the pressure of the metal roof surface measuring point, p H Represents the static pressure of the reference point, v H Reference point wind speed, ρ is air density;
s23, modeling of pulsating wind load:
the expression of the pulsating wind speed is brought into the relation between the load and the wind speed, the pulsating wind is further simplified to be seen as harmonic vibration with single frequency, and the pulsation period is obtained according to the power spectral density of the wind speed; the expression of the wind load constructed in this way is:
wherein ,representing the average wind pressure.
Preferably, the method for correcting the pulsating wind load model by using the least square fitting function relation comprises the following steps:
obtaining wind speed-wind pressure data of the building surface, and obtaining the building surface by least square fitting and I* Then use +.> and I* Replacing corresponding parameters in the wind load expression to correct the model;
the mathematical model after correction is:
for the point set { v i (i=0, 1, …, m) } a linear independent basis function, m being the number of data sets, +.>Is the coefficient before the corresponding basis function.
Preferably, the fatigue load spectrum is constructed according to the wind speed distribution rule:
calculating the short-time average wind distribution under different wind levels, obtaining wind speed spectrums under different wind levels in a discrete mode, and obtaining a wind pressure load spectrum according to the wind speed and load relation; the cyclic load spectrum under different wind levels is constructed, the load spectrum of one year is counted according to weather data, and the calculation formula is shown as follows:
i represents different cyclic loads, u represents wind level, m u Representing the annual statistics of different wind levels, n iu The number of cycles at different loads at different wind levels is indicated.
Preferably, the fatigue simulation method of the metal roof comprises the following steps:
importing a metal roof model into finite element analysis software COMSOL, setting material properties, defining boundary conditions according to actual conditions, setting a load as symmetrical circulation, and defining load circulation amplitude and steps of fatigue simulation loading; calculating stress cloud graph distribution of the roof board in one period through COMSOL, and calculating fatigue life under each load cycle through SWT fatigue model, wherein a display equation of life calculation is as follows:
the above formula is sigma f Fatigue strength coefficient, b is fatigue strength index, ε f For the fatigue ductility coefficient, q is the fatigue ductility index.
Preferably, the metal roof life calculating method comprises the following steps:
the service life of the metal roof can be calculated according to the fatigue wind spectrum through the P-N curve; drawing a P-N curve, calculating to obtain the fatigue life of the metal roof board under different load cycles, and drawing under a double logarithmic coordinate; the life calculation formula of the metal roof is as follows:
wherein ,Ni For actual cycle times, N fi For cycle of life, D 1 D is the damage amount of one year c Is the total damage of the metal roof under the action of different load cycles.
Preferably, the P-N curve is obtained under a symmetrical cycle, however, the actual wind load is an asymmetric pulsating cycle, the load cycle of the metal panel is equivalently converted by using a black lattice fatigue curve, and the asymmetric cycle is converted into a symmetric constant-amplitude cycle, and the method comprises the following steps of:
the black lattice fatigue curve is a parabola passing through symmetrical cyclic limit and ultimate strength, and the equation is:
for points above the black lattice fatigue curve, the equivalent transformation is performed with a curve parallel to the black lattice fatigue line and passing through the point, and the formula is as follows:
wherein ,σ-1 Is symmetrical cycle fatigue limit sigma b Is the intensity limit sigma 0 Is the limit of pulsation cycle, (sigma ')' a ,σ' m ) Is the point coordinate, sigma, above the black lattice fatigue curve a 、σ m Is the vertical and horizontal axes of the black lattice fatigue curve.
The beneficial effects are that:
the invention provides a metal roof life prediction method based on wind load spectrum fatigue simulation, which corrects a pulsating wind load model according to data acquired by a sensor network, so that the established model is more approximate to the actual situation than a wind tunnel experiment and a wind lift resistance experiment. Under the condition that monitoring data of a metal roof plate fatigue damage stage are not available, fatigue simulation is carried out on the metal roof plate under different loads by a finite element simulation method, so that the residual life of the roof plate is predicted, the problem that data such as acceleration life experiments, long-term monitoring wind pressure and wind speed are difficult to obtain is solved, a method is provided for life prediction of a metal roof maintenance system, improvement of a metal roof health management system is facilitated, and the modernization level of health management of the metal roof system is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a load cycle equivalent transformation diagram of the black lattice fatigue diagram of the present invention.
FIG. 3 is a diagram of a monitoring sensor profile according to the present invention.
FIG. 4 is a graph showing probability density distribution of short-term 10s average wind speed at different average wind speeds according to the present invention.
FIG. 5 is a graph showing the power spectral density function of different average wind speeds according to the present invention.
FIG. 6 is a graph of wind speed versus turbulence intensity for the present invention.
FIG. 7 is a graph of wind speed versus wind load for the present invention.
FIG. 8 is a probability density for seven-stage short-term average wind speeds according to the present invention.
FIG. 9 shows the number of cycles per load intensity of the present invention.
Fig. 10 is a view showing the structure and partial assembly of the metal roof plate according to the present invention.
FIG. 11 is a fatigue cloud and P-N graph of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The prior art has the following problems: limitations of wind tunnel and anti-wind-break experiments: the two experiments are simulation of natural wind, and deviation exists between a scaling model adopted by the wind tunnel experiment and a real object, so that the influence of the load on the real object cannot be completely and truly reflected; the wind uncovering resistance experiment has high cost, the wind uncovering resistance of the roof is researched, and the service life of the roof is not predicted. According to the invention, the wind-induced fatigue load spectrum is constructed by using measured wind speed and other data, so that the wind-induced fatigue load spectrum approximates to the wind pressure load on a specific building roof, a region with larger wind pressure on the roof is explored, and fatigue simulation is further carried out on the region and the residual life is predicted.
The prior art has the following problems: building a wind load model from an energy perspective does not take into account the effects of building modeling. In contrast, according to the invention, the wind load model parameters are corrected by using the least square method through the data such as wind pressure, wind speed, wind direction, metal roof plate stress and the like acquired by the sensors built on the metal roof plate, so that the built wind load model simultaneously considers the influences of wind speed, wind direction and roof modeling, and the model accuracy is higher.
The prior art has the following problems: the accelerated life test has high cost, and long-term real-time monitoring of wind pressure, stress and deformation data is difficult to obtain. On the basis of constructing a wind load spectrum of the metal roof board, the fatigue life of the roof board is calculated by using a finite element simulation method, the fatigue life corresponding to each load cycle is determined, the life of the metal roof board is predicted by using a miner damage superposition principle, the problem that the accelerated life experiment cost is high, and long-term real-time monitoring of wind pressure, stress and deformation data is difficult to acquire is solved.
Referring to fig. 1, the invention discloses a metal roof life prediction method based on wind load spectrum fatigue simulation, which comprises the following steps:
s1: estimating fatigue wind distribution according to meteorological wind speed data, and calculating a weibull distribution model of wind speed;
s2: and (5) establishing a pulsating wind load model. The construction of the pulsating wind load model needs to consider a mathematical model and a static pressure load model of turbulent wind, the average wind vertical characteristic, the turbulent flow intensity and the wind speed power spectrum density are all manifestations of the turbulent flow characteristic, the wind pressure coefficient can manifest the rule and the size of wind pressure distribution, and the pulsating wind load model is constructed by combining the parameters.
S3: and correcting the pulsating wind load model by using the real-time monitoring data to enable the model to approach the wind pressure load of the roof of the specific building. The real-time monitoring data is derived from wind speed-wind pressure data monitored by a sensor network on a large-span metal roof for a long time, and a least square method is used for fitting a functional relation to correct a model.
S4: constructing wind-induced fatigue load spectrum of the roof of the specific building. Discretizing the wind speed distribution in the first step, converting the wind speed into a pulsating wind load through a pulsating wind load model, and calculating the circulation times of each load by combining the load probability density and the circulation period, thereby obtaining a wind load spectrum.
S5: and carrying out fatigue simulation on the metal roof system under the action of different cyclic loads by using a finite element simulation method.
S6: and predicting the service life of the metal roof by utilizing a miner damage superposition principle.
1. Wind speed Weibull distribution model based on meteorological data
The distribution characteristics of wind estimate the distribution of the fatigue wind on the same day according to the meteorological data on the same day, and further the fatigue wind speed spectrum of one year is counted. Weibull distribution expression is:
wherein v represents the average wind speed, k is a proportional parameter, c is a shape parameter, p wb (v, k, c) is a wind speed probability density function, e is a base of natural logarithm; parameters in the Weibull distribution model are estimated as follows:
where v is the average wind speed, σ is the standard deviation of wind speed,is a gamma distribution function, t represents a time parameter; the average wind speed was replaced by wind levels and the distribution of the short-term average wind at each wind level was plotted with the Weibull distribution.
2. Pulsating wind load modeling
2.1 mathematical modeling of turbulent wind
Turbulence characteristics are important factors causing fatigue damage and resistance degradation of buildings, and turbulent wind is generally considered as superposition of average wind field and pulsating wind by common researches.
2.1.1 mean wind vertical Properties
The average wind speed of the wind field increases along with the increase of the altitude, and the altitude distribution of the wind speed adopts an exponential rate distribution description method, wherein the expression is as follows:
v (z) is the average wind speed at z height from the ground, v 10 Is 10m highThe average wind speed at the altitude (reference point height), a, is the surface roughness index.
2.1.2 pulsating wind Properties
Turbulence intensity is a key parameter describing the turbulence characteristics of natural wind, and is defined as the ratio of the average amplitude of the pulsating component of wind to the average wind speed, and the turbulence intensity is expressed by I: i=σ/v. σ represents the standard deviation of the pulsating wind and v represents the average wind speed.
The power spectral density of wind speed is a main digital characteristic of the turbulence characteristic of natural wind, the contribution of pulsating wind under each frequency can be accurately described in a frequency domain, and the expression mode of a power spectral density function is as follows:
where G (f) is a power spectral density function, f is frequency,representing the variance of the wind speed fluctuations. It can be seen that pulsating wind is superposition of wind fields at various frequencies, and the usual power spectral density function is a continuous spectral density function proposed by Von Karman, namely +.> wherein Sm (f) L is the turbulence integral scale, which is a measure of the average size of turbulence vortices in the gas stream, as a function of spectral density.
2.2 turbulent wind math model
The pulsating wind is superposition of wind fields under different frequency spectrums, however, because the wind speed has certain contingency, the uniform formula is used for describing the change of the wind fields in the time domain, the qualitative analysis can only be carried out on the characteristics of the pulsating wind in the size and the frequency domain, the wind fields are simplified into circulation under single frequency so as to construct wind load, the corresponding average wind speed field is regarded as circulation under single frequency corresponding to the abscissa of the wind load, and no loss is caused from the energy. The turbulent wind mathematical model constructed in this way is as follows:
wherein ,for turbulent wind average wind speed, f is frequency and I represents turbulence intensity.
2.3 static pressure load modeling
The wind pressure distribution of the building surface is calculated based on an RNGk-epsilon model, the wind pressure coefficient is used for representing the rule and the size of the wind pressure distribution, and the wind pressure coefficient is defined as follows:
the relation between the calculated wind load and the wind speed is shown in the following formula, delta P represents the negative wind pressure generated by the wind load, and P 0 Representing the static pressure of the static air under the metal roof plate, known in conjunction with the bernoulli equation:
wherein p represents the pressure of the metal roof surface measuring point, p H Represents the static pressure of the reference point, v H Reference point wind speed, ρ is the air density.
2.4 pulsating wind load modeling
For construction of the pulsating wind load, the theory should bring the expression of the pulsating wind speed into the relation between the load and the wind speed, but the complex form of the load is inconvenient for subsequent research due to the excessively complex summation of the series, the simplified expression is selected here, the pulsating wind is further simplified, the pulsating wind is regarded as harmonic vibration with single frequency, and the pulsation period is obtained according to the power spectrum density of the wind speed. The expression of the wind load constructed in this way is:
wherein ,representing the average wind pressure.
3. Wind load model correction
There are many model correction methods, including: least squares, maximum likelihood, bayesian, neural network, and the like. The invention adopts the least square method correction with wide application.
3.1 parameters to be modified
The wind load model constructed above is obtained based on energy conservation, and the model does not consider the influence of building configuration on wind pressure distribution, so that the related parameters need to be corrected according to the actual measurement data of the specific building roof. When the metal roof has different configurations, the wind pressure distribution, the wind pressure coefficient and the turbulence intensity are different, namely the average wind pressure in the modelWind pressure coefficient C p The turbulence intensity I is related to the configuration of the roof panel. In order to consider the building configuration factor, the wind speed-wind pressure data of the building surface is needed to be obtained, and the +.> and I* Then use +.> and I* Replacing corresponding parameters in the wind load expression to correct the model;
3.2 data processing method
Three methods are available for acquiring wind pressure data on a metal roof, namely, a wind tunnel experimental method is adopted, numerical wind tunnel simulation is adopted, and a real-time online monitoring system is built. The third method is adopted in the patent, numerical simulation is carried out aiming at the wind pressure distribution rule of the target building roof, a dangerous area is determined on the basis, and a wind speed-wind pressure distributed sensor network is distributed in the dangerous area for real-time monitoring. The collected data is free from interference anomaly data, which needs to be rejected before data processing, and Laida rule (3 sigma rule) is used herein.
For average wind pressureAt the same average wind speed, there are a plurality of wind pressure values, and the average wind pressure value is taken as the average wind pressure value at the wind speed for least square fitting (the wind pressure coefficient data is selected to be the same). For turbulence intensity I, since the turbulence intensity is not directly measured, it can be calculated from wind speed data: and calculating the average value and standard deviation of the wind speed in the proper time period by taking the proper time period as an interval, then calculating the turbulence intensity at the average wind speed according to a calculation formula of the turbulence intensity I, and finally fitting a functional relation between the turbulence intensity and the average wind speed by a least square method.
3.3 principle of least squares
The least square method comprises the following steps: assume that there is m+1 sets of data (v i ,p i ) (i=0, 1, …, m), if a curve is defined
So that
True, then p * (v) For data (v) determined by least squares in family of curves i ,p i ) WhereinFor the point set { v i (i=0, 1, …, m) } a linear independent basis function.
Least squares fitting curve p * (v) I.e. solving coefficients by definitionThe method comprises the following steps:
A＝[φ 0 ,φ 1 ,…,φ n ]
p＝(p 0 ,p 1 ,…,p m ) T
c＝(c 0 ,c 1 ,…,c n ) (11)
due to
So that
C is therefore * The calculation formula is as follows:
A T Ac * ＝A T y
c * ＝(A T A) -1 A T y (14)
from this, p is obtained by fitting the data * (v) Similarly, I can be calculated * The modified mathematical model is:
for the point set { v i (i=0, 1, …, m) } a linear independent basis function, m being the number of data sets, +.>Is the coefficient before the corresponding basis function.
The corrected wind load model not only considers the influence of wind speed and wind direction, but also considers the influence of the metal roof configuration. Therefore, aiming at the building roof with the same target configuration, the model can be used for constructing the wind pressure distribution on the surface of the building roof, determining the area with the largest wind pressure, constructing a wind-induced fatigue load spectrum for the roof board of the area, and calculating the fatigue life, thereby determining the residual life of the metal roof.
4. Wind induced fatigue load spectrum
The construction of the pulsating wind load model intuitively defines the magnitude of wind load, meanwhile, the occurrence frequency of various wind loads is also the key for wind load damage research, and a fatigue load spectrum is constructed according to a wind speed distribution rule.
Calculating the short-time average wind distribution under different wind levels, obtaining wind speed spectrums under different wind levels in a discrete mode, and obtaining a wind pressure load spectrum according to the wind speed and load relation. The cyclic load spectrum under different wind levels is constructed, the load spectrum of one year is counted according to weather data, and the calculation formula is shown as follows:
i represents different cyclic loads, u represents wind level, m u Years representing different wind levelsCounting times, n iu The number of cycles at different loads at different wind levels is indicated.
5. Fatigue simulation of metal roof
5.1 finite element software setup
Importing a metal roof model into finite element analysis software COMSOL, setting material properties, defining boundary conditions according to actual conditions, setting a load as symmetrical circulation, and defining load circulation amplitude and steps of fatigue simulation loading; calculating stress cloud graph distribution of the roof board in one period through COMSOL, and calculating fatigue life under each load cycle through SWT fatigue model, wherein a display equation of life calculation is as follows:
the above formula is sigma f Fatigue strength coefficient, b is fatigue strength index, ε f For the fatigue ductility coefficient, a is the fatigue ductility index.
6. Metal roof service life calculation method
6.1 Black grid fatigue drawing
The P-N curve is an important curve for life analysis in engineering, and the life of the metal roof can be calculated according to the fatigue wind spectrum through the P-N curve. Drawing the P-N curve requires calculation to obtain the fatigue life of the metal roof board under different load cycles, and drawing the metal roof board under a double logarithmic coordinate. The P-N curve is obtained under symmetrical cycle, however, the actual wind load is asymmetric pulsation cycle, the load cycle of the metal panel is equivalently transformed by using the black lattice fatigue diagram, and the load cycle for loading test is equal-amplitude fatigue loading, and the actual wind load is asymmetric cycle, so that the black lattice fatigue diagram is needed to transform the asymmetric cycle into symmetric equal-amplitude cycle. The specific algorithm is as follows:
the black lattice fatigue curve is a parabolic curve passing through symmetrical cyclic limits and ultimate strength as shown in fig. 2, and the equation is:
for point a ' (σ ' above the black lattice fatigue curve ' a ,σ' m ) Equivalent transformation can be performed with a curve parallel to the black lattice fatigue line and passing through this point, as shown by the dotted line in fig. 2. The formula is as follows:
wherein ,σ-1 Is symmetrical cycle fatigue limit sigma b Is the intensity limit sigma 0 Is the limit of pulsation cycle, (sigma ')' a ,σ' m ) Is the point coordinate, sigma, above the black lattice fatigue curve a 、σ m Is the vertical and horizontal axes of the black lattice fatigue curve.
6.2 lifetime calculation formula
The simplest rule of thumb for damage accumulation is the Miner criterion. Assuming a cyclic loading of the plastic stress amplitude ofCorresponding fatigue life of N f1 ,N f2 ,N f3 …, cycle number N 1 ,N 2 ,N 3 … the life time at each stress amplitude is N actual cycles i Divided by life cycle number N fi . The annual load band damage accumulation formula obtains the annual damage amount as follows:
the amount of plastic deformation allowed in engineering is 10% of the using length of the material, and the critical value of the damage variable is set to be 0.1 according to related damage research, because the elastic modulus is reduced along with the accumulation of damage, the deformation of the metal roof is increased along with the reduction, and when the damage amount reaches 0.1, the deformation of the metal roof under the same load is increased by 11%. It is therefore not easy to understand why the metal roof is lifted by the negative wind pressure less than the design load. The damage amount of one year can be calculated according to the average fatigue wind load spectrum by the damage accumulation model:
the service life of the metal roof can be calculated by taking the data converted into symmetrical circulation into the following formula.
wherein ,Ni For actual cycle times, N fi For cycle of life, D 1 D is the damage amount of one year c Is the total damage of the metal roof under the action of different load cycles.
The invention provides a metal roof life prediction method based on wind load spectrum fatigue simulation. Firstly, calculating wind speed Weibull distribution of an area where a building is located according to long-term meteorological data; then analyzing and establishing a pulsating wind load model from the aspects of average wind vertical characteristic, turbulence intensity, wind speed power spectral density, wind pressure coefficient and the like according to the turbulence characteristic of wind; considering the influence of roof configuration on wind pressure distribution, correcting variables such as turbulence intensity, wind pressure coefficient and the like in a theoretical model by combining data such as wind pressure, wind speed and the like acquired by a distributed sensor network with a least square algorithm, so as to approximate the wind pressure load of an actual roof system; and converting the regional wind speed spectrum into a wind induced fatigue load spectrum according to the modified pulsating wind load model, performing fatigue simulation in finite element software, and finally predicting the service life of the metal roof by utilizing a miner damage superposition principle. The invention provides a new method for predicting the service life of the metal roof enclosure system, and the residual service life can be predicted by monitoring data in the roofing service process, so that the metal roof health management system is perfected.
Application example
A metal roof on-line monitoring system is built on a flat roof in Daxing area of Beijing city, the metal roof is an upright lockstitch metal roof, T-shaped supports are adopted between roof plates to be connected with sandalwood strips, and the roof plate ribs are clamped on plum blossom heads of the fixing seats. On the basis of numerical simulation, 15 sensor networks are arranged in a region with larger wind pressure distribution, wind pressure, stress and other data at monitoring points are respectively collected, and a weather station sensor is additionally arranged, so that weather data such as wind speed, wind direction, temperature and the like can be monitored in real time. The actual distribution of the monitoring sensors is shown in fig. 3, the system is put into operation at the end of 2019, and the data collected by the system in the section 2020, 1-6 months, is used for calculation.
1. Wind speed Weibull distribution model based on meteorological data
According to the recorded meteorological wind speed data, the weibull distribution is used for drawing the distribution of short-time average wind under each wind level, and the duration of the short-time average wind is selected to be 10s according to the energy concentration frequency range obtained by the power spectrum density function. By combining the weibull distribution expression and the parameter estimation formula, the weibull distribution model under different wind speeds can be obtained, the ratio of the short-time average wind speed under different average wind speeds is shown in fig. 4, and meanwhile, the probability density distribution of the short-time wind speed is the basis for constructing a fatigue wind spectrum.
2. Pulsating wind load model correction
The power spectral density of wind speed is a main digital characteristic of turbulence characteristics of natural wind, the contribution of each frequency of pulsating wind can be accurately described in a frequency domain, the power spectral density curves of different average wind speeds are shown in fig. 5, and the low-frequency region with the energy concentration range of 0.01-0.6 can be seen from fig. 5.
For turbulence intensity I: the average value and standard deviation of the wind speed in the period of time are calculated by taking ten minutes as an interval, then the turbulence intensity at the average wind speed is calculated according to a calculation formula of the turbulence intensity I, and finally a functional relation is fitted through a least square method, as shown in figure 6.
I＝0.73e -1.36v +0.2e -0.05v
For average wind pressureAt the same average wind speed, there are a plurality of wind pressure values, and the average wind pressure value is taken as the average wind pressure value at the wind speed for least square fitting. The table of the correspondence between the average wind speed and the average wind pressure is shown in table 1, and the fitted curve is shown in fig. 7.
TABLE 1
The model of the final wind load is therefore:
I＝0.73e -1.36v +0.2e -0.05v
3. wind induced fatigue load spectrum
Taking seven-level wind as an example, the average wind speed is about 17m/s, and a corresponding load spectrum is constructed. The probability density of the seven-stage short-time average wind speed after discretization is shown in fig. 8, and the relationship between the wind speed and the wind pressure is given by a wind load model, so that the wind speed can directly correspond to the load, if the 10s average wind in one day is regarded as a load cycle period for the probability density, the total load cycle times in one day are determined, and the cycle times under each load intensity can be obtained through the probability density, and the result is shown in fig. 9.
For example, as shown in FIG. 8, the probability of a wind speed of 17m/s is 0.6 within 10s, and the wind load corresponding to the wind speed of 17m/s is about 450Pa according to the wind load model, the number of times of day of the wind load of 450Pa is about: 24×60×60++10×0.6=5184 times.
The cyclic load spectrum under different wind levels is constructed in the same way, the load spectrum of one year is counted according to weather data, a calculation formula is as follows, and the obtained load spectrum is shown in table 2.
TABLE 2
4. Fatigue simulation of metal roof
Fig. 10 (a) and fig. 10 (b) show partial assembly diagrams of a metal roof, the green part is locked on a plum blossom head support, the support is fixed on a purline, a finite element analysis software COMSOL is introduced into a model, the roof panel and the support are locked, boundary conditions are set to be fixed, the load is set to be symmetrical, the COMSOL calculates the stress cloud pattern distribution of the roof panel in one period, then the SWT fatigue model calculates the fatigue life under each load period, and the display equation, the fatigue model parameters and the material mechanical parameters of life calculation are shown in table 3.
TABLE 3 Table 3
Fatigue life was calculated at mid-point positions of roof panels under different load cycles and a P-N curve was plotted on a double logarithmic scale. The load cycle amplitude of fatigue simulation loading is 500 Pa-3500 Pa, under 1500Pa symmetrical cycle, the stress time-dependent change graph and the stress distribution cloud graph of the central position of the metal roof are shown in fig. 11 (a) and 11 (b), the fatigue life cloud graph is shown in fig. 11 (c), and the fatigue life of the part with strong stress level can be seen to be short. The P-N curve obtained in the same manner is shown in FIG. 11 (d).
5. Fatigue life calculation
Since the black lattice fatigue diagram is the real stress condition of the material, the actual wind load cycle is the pulsation cycle, the pulsation cycle is converted into the symmetrical cycle, and the plastic mechanical parameters of the metal roof are shown in table 4.
TABLE 4 Table 4
The correspondence between the load and the maximum stress of the roof panel (at the midpoint of the roof) is found here by simulation calculation:
σ max ＝9.5×10 4 P
wherein σmax Is the roof panel maximum stress and P is the wind load.
The pulsating wind load cycle is thus converted to a symmetrical cycle as shown in table 5:
TABLE 5
In Table 5Representing calculated wind load of wind load model, P i Represents the symmetrical circulating wind load obtained by conversion calculation, N fi The number of times of wind load application in one year is represented.
The data in table 5 is taken into the roof panel life calculation formula:
t=55.4 years. Typically, the roof enclosure system takes the load of 50 years or 100 years as a calculation standard, and does not represent that the metal roof can have a service life of 50 years.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A metal roof life prediction method based on wind load spectrum fatigue simulation is characterized by comprising the following steps:
s1: estimating fatigue wind distribution according to meteorological wind speed data, and calculating a weibull distribution model of wind speed;
s2: building a pulsating wind load model; constructing a pulsating wind load model by combining the average wind vertical characteristic, turbulence intensity, wind speed power spectral density and wind pressure coefficient parameters;
s3: correcting the pulsating wind load model by using real-time monitoring data to enable the pulsating wind load model to approach the wind pressure load of the roof of the specific building; the real-time monitoring data is derived from wind speed-wind pressure data monitored by a sensor network on a large-span metal roof for a long time, and a least square method is used for fitting a functional relation to correct a pulsating wind load model;
s4: constructing a wind-induced fatigue load spectrum of a specific building roof; converting the wind speed into a pulsating wind load through a pulsating wind load model, and calculating the cycle times of each load by combining the load probability density and the cycle period, thereby obtaining a wind-induced fatigue load spectrum;
s5: performing fatigue simulation on the metal roof under the action of different cyclic loads by a finite element simulation method;
s6: and predicting the service life of the metal roof by utilizing a miner damage superposition principle.
2. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 1, wherein the expression of a wind speed Weibull distribution model is as follows:
wherein v represents the average wind speed, k is a proportional parameter, c is a shape parameter, p wb (v, k, c) is a wind speed probability density function, e is a base of natural logarithm; parameters in the Weibull distribution model are estimated as follows:
where v is the average wind speed, σ is the standard deviation of wind speed,is a gamma distribution function, t represents a time parameter; the average wind speed was replaced by wind levels and the distribution of the short-term average wind at each wind level was plotted with the Weibull distribution.
3. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 2, wherein the method for building the pulsating wind load model comprises the following steps:
s21, constructing a turbulent wind mathematical model:
wherein ,the average wind speed of turbulent wind is represented by f which is frequency, and I represents turbulence intensity;
s22, static pressure load modeling:
the wind pressure distribution of the building surface is calculated based on an RNGk-epsilon model, the wind pressure coefficient is used for representing the rule and the size of the wind pressure distribution, and the wind pressure coefficient is defined as follows:
the relation between the calculated wind load and the wind speed is shown in the following formula, delta P represents the negative wind pressure generated by the wind load, and P 0 Representing the static pressure of the static air under the metal roof plate, known in conjunction with the bernoulli equation:
wherein p represents the pressure of the metal roof surface measuring point, p H Represents the static pressure of the reference point, v H Reference point wind speed, ρ is air density;
s23, modeling of pulsating wind load:
the expression of the pulsating wind speed is brought into the relation between the load and the wind speed, the pulsating wind is further simplified to be seen as harmonic vibration with single frequency, and the pulsation period is obtained according to the power spectral density of the wind speed; the expression of the wind load constructed in this way is:
wherein ,representing the average wind pressure.
4. A method for predicting metal roofing life based on fatigue simulation of wind load spectrum according to claim 3, wherein the method for correcting pulsating wind load model by using least square fitting function relation is as follows:
obtaining wind speed-wind pressure data of the building surface, and obtaining the building surface by least square fitting and I* Then use and I* Replacing corresponding parameters in the wind load expression to correct the model;
the mathematical model after correction is:
γ j (v)、for the point set { v i (i=0, 1, …, m) } a linear independent basis function, m being the number of data sets, +.>Is the coefficient before the corresponding basis function.
5. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 4, wherein the fatigue load spectrum is constructed according to a wind speed distribution rule:
calculating the short-time average wind distribution under different wind levels, obtaining wind speed spectrums under different wind levels in a discrete mode, and obtaining a wind pressure load spectrum according to the wind speed and load relation; the cyclic load spectrum under different wind levels is constructed, the load spectrum of one year is counted according to weather data, and the calculation formula is shown as follows:
i represents different cyclic loads, u represents wind level, m u Representing different wind levelsNumber of annual statistics of n iu The number of cycles at different loads at different wind levels is indicated.
6. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 5, wherein the method for simulating the fatigue of the metal roof is as follows:
importing a metal roof model into finite element analysis software COMSOL, setting material properties, defining boundary conditions according to actual conditions, setting a load as symmetrical circulation, and defining load circulation amplitude and steps of fatigue simulation loading; calculating stress cloud graph distribution of the roof board in one period through COMSOL, and calculating fatigue life under each load cycle through SWT fatigue model, wherein a display equation of life calculation is as follows:
the above formula is sigma f Fatigue strength coefficient, b is fatigue strength index, ε f For the fatigue ductility coefficient, q is the fatigue ductility index.
7. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 6, wherein the method for calculating the service life of the metal roof is as follows:
the service life of the metal roof can be calculated according to the fatigue wind spectrum through the P-N curve; drawing a P-N curve, calculating to obtain the fatigue life of the metal roof board under different load cycles, and drawing under a double logarithmic coordinate; the life calculation formula of the metal roof is as follows:
wherein ,Ni For actual cycle times, N fi For cycle of life, D 1 D is the damage amount of one year c For metal roofing with different load circulationAll damage amounts below.
8. The method for predicting the service life of the metal roof based on wind load spectrum fatigue simulation according to claim 7, wherein the P-N curve is obtained under a symmetrical cycle, the actual wind load is an asymmetric pulsating cycle, the load cycle of the metal panel is equivalently converted by using a black lattice fatigue curve, and the asymmetric cycle is converted into a symmetrical constant-amplitude cycle, and the method comprises the following steps:
the black lattice fatigue curve is a parabola passing through symmetrical cyclic limit and ultimate strength, and the equation is:
for points above the black lattice fatigue curve, the equivalent transformation is performed with a curve parallel to the black lattice fatigue line and passing through the point, and the formula is as follows:
wherein ,σ-1 Is symmetrical cycle fatigue limit sigma b Is the intensity limit sigma 0 Is the limit of pulsation cycle, (sigma ')' a ,σ' m ) Is the point coordinate, sigma, above the black lattice fatigue curve a 、σ m Is the vertical and horizontal axes of the black lattice fatigue curve.
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