Full-life power design method for steel-concrete composite beam bridge under action of automobile load

Abstract

The invention discloses a full-life power design method for a steel-concrete composite beam bridge under the action of an automobile load, and relates to the technical field of bridge life evaluation. The method comprises the following steps: establishing a bridge finite element model according to a design drawing, simulating a random traffic flow, performing nonlinear time-history analysis by taking a contact position of a midspan section web and a lower flange plate as a stress attention part, selecting equivalent stress amplitude and a stress cycle index as random vectors, determining a probability density distribution function, selecting an initial point set, and reforming the point set. And determining a bridge fatigue damage performance function, solving to obtain a time-varying probability density function considering uncertainty, calculating reliability, and obtaining a bridge reliability curve graph under the automobile load according to the reliability under continuous time. By establishing a bridge finite element model, bridge nonlinear dynamic time history analysis under the consideration of vehicle action uncertainty is carried out, the structural reliability of a bridge along with the change of the service life under the action of an automobile load can be quickly and accurately calculated, and the service life prediction of the bridge is realized.

Description

Technical Field

[0001] The invention relates to the technical field of bridge life assessment, in particular to a full-life dynamic design method for a steel-concrete composite beam bridge under automobile load. Background Art

[0002] Steel-concrete composite beam bridges are widely used in medium and small span bridges on highways and urban roads because they make full use of the excellent tensile properties of steel and the excellent compressive properties of concrete. However, due to the increasing traffic volume on highways and cities, steel-concrete composite beam bridges are subject to the increasing cycle of automobile loads, making steel beams more prone to fatigue problems, resulting in insufficient bridge durability and affecting the life of the structure. However, traditional design methods cannot fully consider the stress accumulation effect caused by traffic volume, resulting in the inability to accurately predict the fatigue life of the bridge. Therefore, the fatigue life design of steel-concrete composite beam bridges has become a key issue in the field of bridge design.

[0003] At present, the life assessment of steel-concrete composite beam bridges faces many difficulties, especially when considering future changes in traffic volume. The existing fatigue life assessment model lacks sufficient predictive ability for the growth trend of traffic flow, resulting in the bridge being unable to meet long-term durability requirements in actual use. The uncertainty of future traffic loads and its impact on fatigue life have not been fully studied. Therefore, a more comprehensive and dynamic life assessment method is needed to improve the accuracy of the design.

[0004] In summary, given that traditional design methods do not take changes in traffic volume into consideration sufficiently, it is difficult to effectively calculate the life of steel-concrete composite beam bridges under accumulated traffic volume. Therefore, there is an urgent need for an efficient and reliable full-life dynamic design method for steel-concrete composite beam bridges under automobile loads, so as to extend the full life of steel-concrete composite beam bridges in design. Summary of the invention

[0005] In order to address the shortcomings of the background technology, the present invention provides a full-life dynamic design method for a steel-concrete composite beam bridge under automobile loads. By establishing a finite element model of the bridge, a nonlinear dynamic time-history analysis of the steel-concrete composite beam bridge considering the uncertainty of vehicle action is carried out. The structural reliability of the bridge under automobile loads that changes with the service life can be quickly and accurately calculated, thereby realizing the life prediction of the bridge and providing a basis for full-life dynamic design.

[0006] To achieve the above object, the present invention adopts the following technical scheme: a full-life dynamic design method for a steel-concrete composite beam bridge under automobile load, comprising the following steps:

[0007] Step 1: Create a finite element model of the bridge

[0008] According to the design drawings of the steel-concrete composite beam bridge, a bridge finite element model considering material, boundary and geometric nonlinearity is established;

[0009] Step 2: Simulate random traffic flow

[0010] The random traffic flow simulation is carried out with the fleet. According to the demand, the traffic volume in the future years is considered and the number of fleets in a day is C N , the number of vehicles V and the distance between vehicles d in a convoy are fitted as log-normal distributions, the weight of each vehicle G in a convoy is fitted as normal distributions, the corresponding random numbers are generated in the interval [0,1], and random sampling is performed for the log-normal distribution and the normal distribution respectively;

[0011] Step 3: Select the random vectors contained in the system and determine their probability density distribution function

[0012] The contact position between the web and the lower flange of the span section is taken as the stress focus point. The random traffic flow is loaded into the bridge finite element model, and nonlinear time history analysis is performed to obtain a stress time history sample for one day: σ={σ i T i}, i = 1, 2, ..., m, m represents the amount of data for linear time history analysis, and the peaks and valleys of the stress time history sample σ are found in chronological order to obtain the peak and valley set: σ a =(σ a,s ), s = 1, 2, ..., z, z represents the number of peaks and valleys;

[0013] The equivalent stress amplitude β1 and the stress cycle number β2 of the stress focus area are selected as random vectors, where:

[0014] Equivalent stress amplitude Stress cycle number

[0015] Calculate the mean and standard deviation of the equivalent stress amplitude, and its distribution should conform to the normal distribution, as shown below:

[0016]

[0017] The distribution of the number of stress cycles should also conform to the normal distribution, as shown below:

[0018]

[0019] In the formula, and represent the mean and standard deviation of the equivalent stress amplitude, and represent the mean and standard deviation of the stress cycle number, respectively, and Φ represents the normal distribution function;

[0020] Step 4: Select the initial point set

[0021] In the geometric space [0,1] 2 In , the Sobol sequence is used to select uniform point sets, which are expressed as follows:

[0022] ρ Basic =(x q,1 ,x q,2 ), q=1,2,...,n

[0023] Make an inverse function change to the uniform point set according to the marginal probability distribution, that is, take:

[0024]

[0025] Then the initial point set is obtained as:

[0026]

[0027] Where n represents the number of partitions of the single-dimensional parameter space, n>10, x q,1 and x q,2 The probability point vectors representing the equivalent stress amplitude and the number of stress cycles respectively;

[0028] Step 5: Point set reorganization

[0029] The first step is to reorganize and adjust the positions of each point in the initial point set, which is expressed as follows:

[0030]

[0031] Then the point set at this time is:

[0032]

[0033] In the formula, I(·) is the indicative function,

[0034] The second step is to reorganize the distribution space Ω of the equivalent stress amplitude β1 and the stress cycle number β2. β In the point set ρ n1 Perform Voronoi set subdivision and obtain q =(β′ q,1 ,β′ q,2 ) as the core of n subdomains It is expressed as follows:

[0035]

[0036] Where β=(β1,β2)∈Ω β Represents the distribution space Ω β , ||·||2 represents the Euclid distance;

[0037] Calculate the probability P of each subdivision unit q , calculated as follows:

[0038]

[0039] According to the following formula for the point set ρ n1 Make adjustments:

[0040]

[0041] The adjusted point set is:

[0042]

[0043] Point set ρ n2 Perform Voronoi set subdivision again and obtain q ″=(β q ″ ,1 ,β q ″ ,2 ) as the core of n subdomains And calculate the probability P of each subdivision unit q ′, calculated as follows:

[0044]

[0045] Where p(β) represents the joint probability distribution density, p(β) = f1(β1)·f2(β2);

[0046] Step 6: Determine the bridge fatigue damage function

[0047] The fatigue damage function of the steel-concrete composite beam bridge is expressed as:

[0048]

[0049] In the formula, t represents the service life of the bridge, C is the constant of the relationship between steel fatigue life and stress amplitude, and M is the index of fatigue life;

[0050] Step 7: Solve the probability equation to obtain the time-varying probability density function

[0051] There are n time-varying probability densities in total, and the time-varying probability density evolution equation is as follows:

[0052]

[0053] The (h~t) plane is discretized, where h is the value of the fatigue damage function H(t) after time t, and the discretization is expressed as:

[0054] h=h l , t=t k, l=0,1,2,...,L, k=0,1,2,...,K

[0055] In the formula, h l = l·Δh,t k = k·Δt, Δh and Δt are discrete steps of space and time respectively, and L and K are corresponding discrete quantities respectively;

[0056] The p q (h,t) at the discretized grid point p q (h l ,t k ) is recorded as

[0057] According to the TVD format, the probability equation is discretized into n iterative equations, which are expressed as follows:

[0058]

[0059] The boundary points are treated with periodic boundary conditions, where:

[0060]

[0061] Flux limiter ψ(r + ,r - ) is in the following format:

[0062]

[0063] Among them, u(·) is a unit cross-order function;

[0064] The initial value of:

[0065]

[0066] Where δ(·) is the Dirac delta function;

[0067] The calculated Fitting to curve p HΒ (h,β q ,t), then the time-varying probability density function considering the uncertainty of equivalent stress amplitude and stress cycle number is:

[0068] Step 8: Obtain the reliability curve of the bridge structure under vehicle load

[0069] Through the time-varying probability density function p H (h, t) draws a probability density surface diagram of the bridge structure with fatigue damage function H(t) and time t as variables. When H(t)>0, the steel-concrete composite beam bridge is considered to be reliable, and the reliability R(t) is calculated according to the following formula:

[0070]

[0071] Where Pr{H(t)>0} represents the probability that the fatigue damage function H(t)>0. Finally, the bridge reliability curve is drawn according to the reliability R(t) at continuous time t.

[0072] Furthermore, the step 2 specifically includes:

[0073] The fitted lognormal and normal distributions are expressed as follows:

[0074]

[0075] When randomly selecting, generate the corresponding random number p in the interval [0,1] α ,but:

[0076] x α =exp(μ α +σ α p α ), α=1,2,4

[0077] x α =μ α +σ α p α , α=3

[0078] In the formula, μ α and σ α , α=1,2,3,4, respectively represent the corresponding mean and standard deviation.

[0079] Furthermore, in step 3, the data peak and valley judgment condition of the stress time history sample σ is: if σ i >σ i-1 And σ i >σ i+1 Time i is the stress peak, if σ i <σ i-1 And σ i <σ i+1 Time i The stress valley.

[0080] Furthermore, in step 7, in order to maintain the stability of the numerical solution,

[0081] Compared with the prior art, the invention has the following beneficial effects: by establishing a bridge finite element model that takes into account material, boundary and geometric nonlinearity, the invention selects random vehicle flows, and carries out nonlinear dynamic time history analysis of steel-concrete composite beam bridges under uncertainty of vehicle action, and by using data calculation and analysis technology, the invention realizes life prediction of the bridge, and has the following advantages:

[0082] 1. High accuracy of life assessment: By using random traffic flow for finite element analysis, the stress time history data of the bridge structure is obtained. Combining the uncertainty of the equivalent stress amplitude and the number of stress cycles, a fatigue life prediction model based on future traffic flow is constructed, which converts the static assumptions of traditional fatigue life design into dynamic probabilistic analysis, and achieves high-precision assessment of the fatigue life of bridges under complex traffic loads, promoting the transition of bridge fatigue life design from empirical to accurate reliability calculation based on the evolution of stress distribution and probability density;

[0083] 2. High efficiency of life design: By simply performing finite element analysis on random traffic flow, the stress data of bridge structures under different traffic flows can be generated in batches to form a distribution model of equivalent stress amplitude and stress cycle number. Subsequently, the fatigue life reliability of the remaining service years of the bridge structure can be quickly calculated by simply updating the function through the SN curve model, which significantly improves the efficiency of fatigue life assessment and simplifies the complex fatigue life prediction process into an easy-to-operate standardized process.

[0084] 3. Intelligent design method: The use of parametric programming technology and ready-made data packages can realize automatic calculation of all formulas, avoiding tedious and complicated calculation processes, helping to realize intelligent calculation methods, greatly improving the accuracy and reliability of fatigue life assessment results, and ensuring that the fatigue life assessment results of bridge structures have a high level of accuracy and credibility under different traffic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flow chart of the method of the present invention;

[0086] Figure 2 is a Voronoi set decomposition diagram in the embodiment;

[0087] Figure 3 is a probability density surface diagram of the bridge structure in the embodiment;

[0088] Figure 4 is a bridge reliability curve diagram in the embodiment. DETAILED DESCRIPTION

[0089] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0090] A full-life dynamic design method for steel-concrete composite beam bridges under vehicle loads, the process combines Figure 1 As shown, the following steps are included:

[0091] Step 1: Create a finite element model of the bridge

[0092] According to the design drawings of the steel-concrete composite beam bridge, a finite element model of the bridge considering material, boundary and geometric nonlinearity was established using finite element simulation software;

[0093] Step 2: Simulate random traffic flow

[0094] The random traffic flow simulation is carried out with the fleet. According to the demand, the traffic volume in the future years is considered and the number of fleets in a day is C N (If the front vehicle gets off the bridge and the rear vehicle has not yet gotten on the bridge, it is considered as the same convoy), the number of vehicles V and the distance between vehicles d in a convoy are fitted as log-normal distributions, and the weight G of each vehicle in a convoy is fitted as normal distribution, which is expressed as follows:

[0095]

[0096] Randomly select the number of fleets C in a day N , the number of vehicles V in a convoy, the weight of each vehicle G, and the distance between vehicles d.

[0097] For lognormal distribution and normal distribution, generate the corresponding random number p in the interval [0,1] respectively. α ,but:

[0098] x α =exp(μ α +σ α p α ), α=1,2,4

[0099] x α =μ α +σ α p α , α=3

[0100] In the formula, μ α and σ α , α=1,2,3,4, respectively representing the mean and standard deviation of the corresponding traffic flow data;

[0101] Step 3: Select the random vectors contained in the system and determine their probability density distribution function

[0102] The contact position between the cross-section web and the lower flange plate is taken as the stress focus position of the steel-concrete composite beam bridge. The random traffic flow obtained in step 2 is loaded into the bridge finite element model established in step 1, and a nonlinear time history analysis is performed to obtain a one-day stress time history sample, which is expressed as follows:

[0103] σ={σ i T i},i=1,2,...,m

[0104] Where m represents the amount of data for linear time history analysis.

[0105] Find the peaks and valleys of the stress time history sample σ in chronological order. If σ i >σ i-1 And σ i >σ i+1 Time i is the stress peak, if σ i <σ i-1 And σ i <σ i+1 Time i is the stress valley, and the peak-valley set is obtained, which is expressed as follows:

[0106] σ a =(σ a,s ), s=1,2,...,z

[0107] Where z represents the number of peaks and valleys.

[0108] The equivalent stress amplitude β1 and the stress cycle number β2 of the stress focus area are selected as random vectors, where:

[0109] Equivalent stress amplitude:

[0110]

[0111] Number of stress cycles:

[0112]

[0113] Calculate the mean and standard deviation of the equivalent stress amplitude, and its distribution should conform to the normal distribution, as shown below:

[0114]

[0115] The distribution of the number of stress cycles should also conform to the normal distribution, as shown below:

[0116]

[0117] In the formula, and represent the mean and standard deviation of the equivalent stress amplitude, and represent the mean and standard deviation of the stress cycle number, respectively, and Φ represents the normal distribution function;

[0118] Step 4: Select the initial point set

[0119] In the geometric space [0,1] 2 In , the Sobol sequence is used to select uniform point sets, which are expressed as follows:

[0120] ρ Basic =(x q,1 ,x q,2 ), q=1,2,...,n

[0121] Make an inverse function change to the uniform point set according to the marginal probability distribution, that is, take:

[0122]

[0123] Then the initial point set is obtained as:

[0124]

[0125] Where n represents the number of partitions of the single-dimensional parameter space, n>10, x q,1 and x q,2 The probability point vectors representing the equivalent stress amplitude and the number of stress cycles respectively;

[0126] Step 5: Point set reorganization

[0127] The first step is to reorganize and adjust the positions of each point in the initial point set, which is expressed as follows:

[0128]

[0129] Then the point set at this time is:

[0130]

[0131] Where I(·) is the indicative function, expressed as follows:

[0132]

[0133] The second step is to reorganize the distribution space Ω of the equivalent stress amplitude β1 and the stress cycle number β2. β In the point set ρ n1 Perform Voronoi set subdivision and obtain q =(β′ q,1 ,β′ q,2 ) as the core of n subdomains It is expressed as follows:

[0134]

[0135] Where β=(β1,β2)∈Ω β Represents the distribution space Ω β , ||·||2 represents the Euclid distance.

[0136] Calculate the probability P of each subdivision unit q , calculated as follows:

[0137]

[0138] According to the following formula for the point set ρ n1 Make adjustments:

[0139]

[0140] The adjusted point set is:

[0141]

[0142] Point set ρ n2 Perform Voronoi set subdivision again and obtain q ″=(β q ″ ,1 ,β q ″ ,2 ) as the core of n subdomains And calculate the probability P of each subdivision unit q ′, calculated as follows:

[0143]

[0144] Where p(β) represents the joint probability distribution density, p(β) = f1(β1)·f2(β2);

[0145] Step 6: Determine the bridge fatigue damage function

[0146] The fatigue damage function of the steel-concrete composite beam bridge is expressed as:

[0147]

[0148] In the formula, t represents the service life of the bridge (years), C is the constant of the relationship between the fatigue life of steel and the stress amplitude, and M is the index of fatigue life, which is selected according to the design of the bridge;

[0149] Step 7: Solve the probability equation to obtain the time-varying probability density function

[0150] There are n time-varying probability densities in total, and the time-varying probability density evolution equation is as follows:

[0151]

[0152] The (h~t) plane is discretized, where h is the value of the fatigue damage function H(t) after time t, and the discretization is expressed as:

[0153] h=h l , t=t k , l=0,1,2,...,L, k=0,1,2,...,K

[0154] In the formula, h l = l·Δh,t k =k·Δt, Δh and Δt are discrete steps in space and time respectively, and L and K are corresponding discrete quantities respectively.

[0155] For the sake of simplicity, p q (h,t) at the discretized grid point p q (h l ,t k ) is recorded as

[0156] According to the TVD format, the probability equation is discretized into n iterative equations, which are expressed as follows:

[0157]

[0158] The boundary points are processed using periodic boundary conditions to ensure the stability of the numerical solution. in:

[0159]

[0160] Flux limiter ψ(r + ,r - ) is in the following format:

[0161]

[0162] Where u(·) is a unit cross-order function.

[0163] The initial value of:

[0164]

[0165] Where δ(·) is the Dirac delta function.

[0166] The calculated Fitting to curve p HΒ (h,βq ,t), then the time-varying probability density function considering the uncertainty of equivalent stress amplitude and stress cycle number is:

[0167] Step 8: Obtain the reliability curve of the bridge structure under vehicle load

[0168] Through the time-varying probability density function p H (h, t) draws a probability density surface diagram of the bridge structure with fatigue damage function H(t) and time t as variables. When H(t)>0, the steel-concrete composite beam bridge is considered to be reliable, and the reliability R(t) is calculated according to the following formula:

[0169]

[0170] Where Pr{H(t)>0} represents the probability that the fatigue damage function H(t)>0. Finally, the bridge reliability curve can be drawn according to the reliability R(t) at continuous time t.

[0171] Example

[0172] This embodiment is implemented for the PM123-PM126 continuous steel-concrete composite beam bridges of Harbin East Third Ring Expressway. The actual operation according to the method of the present invention is as follows:

[0173] S1. Based on the design drawings of the bridge, a finite element model of the bridge was established using finite element simulation software, which took into account material, boundary and geometric nonlinearity;

[0174] S2. According to the traffic volume, obtain the number of convoys in one day C N The probability distribution of the number of vehicles V, the weight of each vehicle G, and the distance between vehicles d in a convoy is as follows:

[0175]

[0176] To select the number of teams C on the first day N1 For example, generate a random number p1=0.824 in the interval [0,1], then:

[0177] C N1 =exp(4.60+0.824×0.30)≈127

[0178] Select the vehicle information of the convoy, take the first convoy as an example, and obtain V=13, the weight G of each vehicle and the distance d between vehicles, as shown in Table 1:

[0179] Table 1 Fleet information

[0180] Vehicle number 1 2 3 4 5 6 7 Vehicle weight 2.31 2.62 1.93 2.17 1.83 1.94 2.57 Distance between vehicles 13.17 18.71 22.35 18.38 22.88 30.03 16.55 Vehicle number 8 9 10 11 12 13 Vehicle weight 1.43 1.67 1.87 2.22 2.41 2.51 Distance between vehicles 10.83 26.96 18.80 29.16 28.33 22.39

[0181] S3. Take the contact position between the web and the lower flange plate of the cross-section as the bridge stress focus point, load the random traffic flow obtained in step 2 into the bridge finite element model established in step 1, perform nonlinear time history analysis, and obtain stress time history samples. Take the loading of a fleet as an example, as shown in Table 2:

[0182] Table 2 Stress time history samples

[0183]

[0184]

[0185] Extract the peaks and valleys in the data, as shown in Table 3:

[0186] Table 3 Peak and valley data samples of stress time history analysis

[0187]

[0188]

[0189] Calculate the equivalent stress amplitude, as shown in Table 4:

[0190] Table 4 Equivalent stress amplitude of a fleet

[0191]

[0192] The number of stress cycles of the bottom plate in the mid-span section under the convoy load is 33 times.

[0193] The information of other fleets is processed by the above method, and the equivalent stress amplitude and stress cycle number are fitted with normal function to obtain:

[0194]

[0195] S4, in the geometric space [0,1] 2 In the above example, we use the Sobol sequence to select a uniform point set, taking n as 49, and obtain the probability point vector x q,1 and x q,2 The uniform point set is shown in Table 5 and Table 6:

[0196] Table 5x q,1 Uniform point set

[0197]

[0198]

[0199] Table 6x q,2 Uniform point set

[0200] 0.5 0.25 0.75 0.375 0.875 0.125 0.625 0.3125 0.8125 0.0625 0.5625 0.1875 0.6875 0.4375 0.9375 0.46875 0.96875 0.21875 0.71875 0.09375 0.59375 0.34375 0.84375 0.15625 0.65625 0.40625 0.90625 0.28125 0.78125 0.03125 0.53125 0.265625 0.765625 0.015625 0.515625 0.140625 0.640625 0.390625 0.890625 0.078125 0.578125 0.328125 0.828125 0.453125 0.953125 0.203125 0.703125 0.234375 0.734375

[0201] According to the inverse of the normal function:

[0202]

[0203] According to the inverse of the normal function:

[0204]

[0205] Calculate the equivalent stress amplitude and stress cycle number under each probability in the above table, and obtain the equivalent stress amplitude point set and stress cycle number point set, as shown in Table 7 and Table 8:

[0206] Table 7 Equivalent stress amplitude point set

[0207] 52.31124 65.90532 38.71716 45.88918 75.49609 58.73330 29.12639 34.43114 62.16234 83.23086 49.14070 42.46014 70.19134 55.48178 21.39162 25.74723 57.09196 72.66721 44.20404 50.73087 89.85389 63.98343 36.66275 31.95527 60.41844 78.87525 47.53052 40.63905 67.95973 53.89161 14.76859 18.53331 54.68485 69.04987 41.56057 48.33878 80.88640 61.28199 33.22921 37.70893 64.93003 95.72177 51.52166 45.05296 74.02816 57.90799 27.52390 23.73608 56.28370

[0208] Table 8 Stress cycle number point set

[0209] 5124 5470 4778 4961 5714 5287 4534 4669 5375 5911 5043 4873 5579 5205 4337 4448 5246 5642 4918 5084 6080 5421 4726 4606 5330 5800 5002 4827 5522 5164 4168 4264 5184 5550 4850 5023 5851 5352 4638 4752 5445 6229 5104 4939 5677 5266 4493 4397 5225

[0210] S5. Reorganize according to the following formula:

[0211]

[0212] The new point set after the first step of reorganization is obtained, as shown in Table 9 and Table 10:

[0213] Table 9 Equivalent stress amplitude point set after the first step of reorganization

[0214] 52.31124 66.89262 39.03902 46.02463 76.79257 59.68997 29.86026 34.90378 63.11767 85.26484 49.20593 42.67741 71.26754 55.41655 19.35764 25.51509 57.52389 72.93732 43.81826 50.24558 90.03808 64.32806 36.35606 31.68516 60.80422 79.10739 47.09859 40.29442 68.26642 53.34271 5.57755 14.58440 54.37690 69.71870 41.50481 48.15794 81.84247 61.94507 33.35494 37.72986 65.58346 99.04493 51.27977 44.93251 74.76222 58.59785 27.82991 22.78001 56.46454

[0215] Table 10 Stress cycle number point set after the first step of reforming

[0216] 5124 4786 5495 4964 5747 4501 5284 4879 5606 4285 5203 4642 5369 5045 5963 5098 6314 4718 5430 4442 5257 4936 5695 4599 5340 5018 5876 4849 5567 4164 5177 4818 5530 3934 5150 4553 5312 4991 5806 4372 5230 4908 5649 5071 6084 4681 5399 4753 5462

[0217] Use the existing Voronoi set meshing data package to perform Voronoi set meshing on the above two-dimensional plane, combined with Figure 2 shown.

[0218] The point set is reorganized again according to the following formula:

[0219]

[0220] The adjusted point sets are obtained, as shown in Tables 11 and 12:

[0221] Table 11 Equivalent stress amplitude point set after the second step of reorganization

[0222] 51.63448 68.57567 38.95194 47.80046 77.09109 58.95699 29.01676 34.57870 62.58660 87.20887 51.09027 44.50082 72.29486 56.42300 19.06293 26.11898 56.29131 71.74580 44.48843 51.96925 91.10955 62.42482 35.96132 32.82740 60.32611 78.36153 46.15231 40.11659 70.24385 54.43809 6.95870 12.74537 55.60244 68.66560 40.25896 46.84912 83.20107 60.16380 31.86555 36.60566 65.14016 100.60537 52.03890 46.26107 74.13229 58.65285 27.66010 24.21912 56.74592

[0223] Table 12 Stress cycle number point set after the second step reformation

[0224] 5130 4809 5515 4993 5753 4499 5273 4887 5600 4286 5176 4667 5381 5020 5982 5111 6329 4689 5427 4467 5236 4921 5676 4611 5368 5031 5882 4847 5572 4175 5191 4844 5552 3942 5169 4566 5295 5009 5817 4349 5238 4912 5631 5077 6073 4658 5403 4770 5443

[0225] The adjusted point set is again divided into Voronoi sets, and the probability of each divided unit is calculated, as shown in Table 13:

[0226] Table 13 The probability of each subdivision unit being assigned

[0227] 0.0189 0.0252 0.0182 0.0272 0.0023 0.0262 0.0283 0.0361 0.0308 0.0251 0.0314 0.0251 0.0359 0.0326 0.0330 0.0056 0.0303 0.0216 0.0280 0.0309 0.0078 0.0270 0.0037 0.0104 0.0200 0.0029 0.0121 0.0040 0.0003 0.0181 0.0244 0.0162 0.0125 0.0422 0.0105 0.0159 0.0162 0.0177 0.0261 0.0338 0.0398 0.0004 0.0414 0.0287 0.0285 0.0036 0.0116 0.0025 0.0092

[0228] S6. The fatigue damage function of the steel-concrete composite beam bridge is expressed as:

[0229]

[0230] β q ″ ,1 and β q ″ ,2 These are the data in Table 11 and Table 12 respectively;

[0231] S7. The value range of t is [0,50], the value range of h is [-2,2], t is discretized into 200 parts, and h is discretized into 400 parts.

[0232] The finite difference method in TVD format is used to calculate the time-varying probability density evolution equation and obtain the time-varying probability density function of the numerical solution.

[0233] S8. Draw a probability density surface diagram of the bridge structure by numerically solving the time-varying probability density function, and combine it with Figure 3 shown.

[0234] pass Get the bridge reliability curve, combined with Figure 4 shown.

[0235] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0236] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A full-life dynamic design method for a steel-concrete composite beam bridge under vehicle loads, characterized by: The following steps are involved: Step 1: Create a finite element model of the bridge According to the design drawings of the steel-concrete composite beam bridge, a bridge finite element model considering material, boundary and geometric nonlinearity is established; Step 2: Simulate random traffic flow The random traffic flow simulation is carried out with the fleet. According to the demand, the traffic volume in the future years is considered and the number of fleets in a day is C N , the number of vehicles V and the distance between vehicles d in a convoy are fitted as log-normal distributions, the weight of each vehicle G in a convoy is fitted as normal distributions, the corresponding random numbers are generated in the interval [0,1], and random sampling is performed for the log-normal distribution and the normal distribution respectively; Step 3: Select the random vectors contained in the system and determine their probability density distribution function The contact position between the web and the lower flange of the span section is taken as the stress focus point. The random traffic flow is loaded into the bridge finite element model, and nonlinear time history analysis is performed to obtain a stress time history sample for one day: σ={σ i T i }, i = 1, 2, ..., m, m represents the amount of data for linear time history analysis, and the peaks and valleys of the stress time history sample σ are found in chronological order to obtain the peak and valley set: σ a =(σ a,s ), s = 1, 2, ..., z, z represents the number of peaks and valleys; The equivalent stress amplitude β1 and the stress cycle number β2 of the stress focus area are selected as random vectors, where: Equivalent stress amplitude Stress cycle number Calculate the mean and standard deviation of the equivalent stress amplitude, and its distribution should conform to the normal distribution, as shown below: The distribution of the number of stress cycles should also conform to the normal distribution, as shown below: In the formula, and represent the mean and standard deviation of the equivalent stress amplitude, and represent the mean and standard deviation of the stress cycle number, respectively, and Φ represents the normal distribution function; Step 4: Select the initial point set In the geometric space [0,1] 2 In , the Sobol sequence is used to select uniform point sets, which are expressed as follows: ρ Basic =(x q,1 ,x q,2 ),q=1,2,...,n Make an inverse function change to the uniform point set according to the marginal probability distribution, that is, take: Then the initial point set is obtained as: Where n represents the number of partitions of the single-dimensional parameter space, n>10, x q,1 and x q,2 The probability point vectors representing the equivalent stress amplitude and the number of stress cycles respectively; Step 5: Point set reorganization The first step is to reorganize and adjust the positions of each point in the initial point set, which is expressed as follows: Then the point set at this time is: In the formula, I(·) is the indicative function, The second step is to reorganize the distribution space Ω of the equivalent stress amplitude β1 and the stress cycle number β2. β In the point set ρ n1 Perform Voronoi set subdivision and obtain q =(β′ q,1 ,β′ q,2 ) as the core of n subdomains It is expressed as follows: Where β=(β1,β2)∈Ω β Represents the distribution space Ω β , ||·||2 represents the Euclid distance; Calculate the probability P of each subdivision unit q , calculated as follows: According to the following formula for the point set ρ n1 Make adjustments: The adjusted point set is: Point set ρ n2 Perform Voronoi set subdivision again and obtain q ″=(β q ″ ,1 ,β q ″ ,2 ) as the core of n subdomains And calculate the probability P of each subdivision unit q ′, calculated as follows: Where p(β) represents the joint probability distribution density, p(β) = f1(β1)·f2(β2); Step 6: Determine the bridge fatigue damage function The fatigue damage function of the steel-concrete composite beam bridge is expressed as: In the formula, t represents the service life of the bridge, C is the constant of the relationship between steel fatigue life and stress amplitude, and M is the index of fatigue life; Step 7: Solve the probability equation to obtain the time-varying probability density function There are n time-varying probability densities in total, and the time-varying probability density evolution equation is as follows: The (h~t) plane is discretized, where h is the value of the fatigue damage function H(t) after time t, and the discretization is expressed as: h=h l ,t=t k ,l=0,1,2,...,L,k=0,1,2,...,K In the formula, h l = l·Δh,t k = k·Δt, Δh and Δt are discrete steps of space and time respectively, and L and K are corresponding discrete quantities respectively; The p q (h,t) at the discretized grid point p q (h l ,t k ) is recorded as According to the TVD format, the probability equation is discretized into n iterative equations, which are expressed as follows: The boundary points are treated with periodic boundary conditions, where: λ=Δt / Δh Flux limiter ψ(r + ,r - ) is in the following format: Among them, u(·) is a unit cross-order function; The initial value of: Where δ(·) is the Dirac delta function; The calculated Fitting to curve p HΒ (h,β q ,t), then the time-varying probability density function considering the uncertainty of equivalent stress amplitude and stress cycle number is: Step 8: Obtain the reliability curve of the bridge structure under vehicle load Through the time-varying probability density function p H (h, t) draws a probability density surface diagram of the bridge structure with fatigue damage function H(t) and time t as variables. When H(t)>0, the steel-concrete composite beam bridge is considered to be reliable, and the reliability R(t) is calculated according to the following formula: Where Pr{H(t)>0} represents the probability that the fatigue damage function H(t)>0. Finally, the bridge reliability curve is drawn according to the reliability R(t) at continuous time t.

2. The full-life dynamic design method of a steel-concrete composite beam bridge under vehicle load according to claim 1, characterized in that: The step 2 specifically includes: The fitted lognormal and normal distributions are expressed as follows: When randomly selecting, generate the corresponding random number p in the interval [0,1] α ,but: x α =exp(μ α +s α p α ),α=1,2,4 x α =μ α +s α p α ,α=3 In the formula, μ α and σ α , α=1,2,3,4, respectively represent the corresponding mean and standard deviation.

3. The full-life dynamic design method of a steel-concrete composite beam bridge under vehicle load according to claim 1 is characterized by: In step 3, the data peak and valley judgment condition of the stress time history sample σ is: i >σ i-1 And σ i >σ i+1 Time i is the stress peak, if σ i <σ i-1 And σ i <σ i+1 Time i The stress valley.

4. The full-life dynamic design method for a steel-concrete composite beam bridge under vehicle load according to claim 1 is characterized by: In step 7, in order to keep the numerical solution stable,

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