A calculation method and system for earthquake resistance of crane structure

Abstract

The present invention discloses a calculation method for the earthquake resistance of a crane structure, comprising: applying a unit pulse load to a crane model according to the modal analysis result, generating key node response values ​​and establishing a coefficient matrix; analyzing the vibration attenuation law of a single degree of freedom system, and providing an improved coefficient matrix time domain explicit expression; simulating an artificial earthquake time history, performing random earthquake response analysis according to the coefficient matrix and the improved coefficient matrix time domain explicit expression, and generating earthquake response analysis results of the crane key nodes. The calculation method for the earthquake resistance of a crane structure provided by the present invention has high accuracy, reduces calculation cost, and improves calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of crane structure seismic analysis, and in particular to a crane structure seismic calculation method, system, computer medium and computer. Background Art

[0002] During the construction of a nuclear power plant, the seismic performance of the nuclear power plant infrastructure and its ancillary equipment must be considered to ensure that when the nuclear power plant encounters extreme safety earthquake vibrations, the pressure boundary is intact, the reactor can be safely shut down and maintained, and the release of radioactive materials is within the permitted range.

[0003] Cranes are special lifting equipment for nuclear power plants. According to the "Design Criteria for Special Cranes for Nuclear Power Plants", cranes need to meet the following standards under seismic loads:

[0004] The crane can keep the load from falling under the conditions of rated load plus the load caused by a safe shutdown earthquake (SSE), the trolley and the carriage can remain on their respective tracks, without scratching the buildings and without parts falling; the trolley track, trolley track and bridge frame will not be deformed after the earthquake.

[0005] Theoretical research on structural seismic resistance has gone through three stages of development: static stage, response spectrum theory stage and dynamic analysis stage. Dynamic analysis includes time history analysis method (complete method) and frequency domain analysis method. In actual numerical analysis, time history analysis method usually adopts step-by-step analysis method, including central difference method, piecewise analysis method, Newmark-β method and many other methods. In the process of seismic analysis, time history analysis comprehensively considers the seismic intensity, spectrum characteristics, duration of strong earthquakes, etc., and can accurately calculate the linear and nonlinear dynamic response of the structure under a certain earthquake load. However, the disadvantage of this method is that it consumes a lot of computing resources and has low efficiency.

[0006] At present, with the continuous improvement of computing power, the structural seismic analysis method has undergone a development process from static to dynamic. At present, the domestic crane seismic analysis mainly uses the response spectrum method and is verified by a small amount of time-history analysis results. However, due to the weak statistical significance of a small number of earthquake time-history analysis results, some scholars have introduced random simulation methods in the seismic analysis of cranes. Although this type of method is accurate, it is relatively complicated.

[0007] Therefore, there is an urgent need for a calculation method for the earthquake resistance of crane structures that can avoid affecting the accuracy, reduce the calculation cost, and improve the calculation efficiency. Summary of the invention

[0008] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a calculation method and system for the seismic resistance of crane structures, which analyzes the vibration attenuation law of single-degree-of-freedom systems, improves the coefficient matrix, and gives an improved coefficient matrix time-domain explicit expression. Compared with the original method, the improved coefficient matrix time-domain explicit expression is effective and has higher computational efficiency.

[0009] In order to solve the above technical problems, the present invention provides a calculation method for the earthquake resistance of a crane structure, comprising:

[0010] Step S1: establishing a crane model according to the crane data, and then performing modal analysis on the crane model to generate modal analysis results;

[0011] Step S2: According to the modal analysis results, a unit pulse load is applied to the crane model to generate key node response values ​​and establish a coefficient matrix;

[0012] Analyze the vibration attenuation law of single degree of freedom system and give the time domain explicit expression of improved coefficient matrix;

[0013] Step S3: simulate the artificial earthquake time history, perform random earthquake response analysis according to the coefficient matrix and the improved coefficient matrix time domain explicit expression, and generate earthquake response analysis results of the key nodes of the crane.

[0014] As a preferred embodiment of the present invention, in step S1, the method further comprises: after performing modal analysis on the structure included in the crane model, setting a minimum time step that is the same as the time step of the modal superposition method.

[0015] As a preferred embodiment of the present invention, in step S2, the method further comprises the following steps:

[0016] Step S20: Obtain the time domain explicit format based on the Wilson-θ method and generate displacement, velocity and acceleration equations:

[0017]

[0018] Among them, U i+1 is the structural response characteristic displacement, is the structural response characteristic speed, is the structural response characteristic acceleration, P i , P i+1 is the earthquake excitation, L is the inertial force direction vector, where:

[0019]

[0020] M is the mass matrix of the system, C is the damping matrix, K is the stiffness matrix, and the damping matrix C uses the Rayleigh damping model: θ is the coefficient; △t is the time step;

[0021] Step S21: Generate a matrix form of displacement, velocity and acceleration according to the displacement, velocity and acceleration formula:

[0022]

[0023] As a preferred embodiment of the present invention, in step S2, the method further comprises the following steps:

[0024] Step S22: According to the matrix form of displacement, velocity and acceleration, let:

[0025]

[0026] Then we get the recursive calculation formula:

[0027] V i+1 =TV i +Q1P i +Q2P i+1 i = (0, 1, ..., l-1);

[0028] Step S23: By t i-1 The recursive calculation formula at the moment is used to obtain V i :

[0029] V i =TV i-1 +Q1P i-1 +Q2P i i=(1, 2, ..., l),

[0030] Then, when V0=0, the time t is generated. i =Δt response V i The expression:

[0031] V1=Q1P0+Q2P1 (i=1)

[0032] V i =T i-1 Q1P0+T i-2 Q3P1+…+T 0 Q3P i-1 +Q2P i (2≤i≤l)

[0033] Among them, Q3 = TQ2 + Q1;

[0034] Step S24: Using A i，0 , A i，1 , …, A i，i Represent P0, P1, ..., P i The coefficient matrix before, then the moment

[0035] ti =Δt response V i The expression is:

[0036] V i =A i，0 P0+A i，1 P1+…+A i，i P i i=(1, 2, ..., l),

[0037] In this way, the explicit expression of the structural response in time domain and the corresponding coefficient matrix are obtained.

[0038]

[0039]

[0040] As a preferred embodiment of the present invention, in step S24, the method further comprises the following steps:

[0041] Step S240: A i，0 , A i，1 , …, A i，i It is only related to the structural parameters and reflects the influence of the structural parameters on the random response.

[0042] Wherein, i=(1, 2, ..., 1);

[0043] Step S241: Set time t i =Δt response V i The expression is:

[0044] V i =B i R i i=(1, 2, ..., l),

[0045] In this way, an explicit expression of the structural response in time domain is obtained.

[0046] As a preferred embodiment of the present invention, in step S3, the method further comprises the following steps:

[0047] Step S31: Calculate the response result of the structure included in the crane model under the unit pulse and generate a coefficient matrix;

[0048] Step S32: Preliminary calculation of the default point according to the integral target ratio;

[0049] Step S33: forming a preliminary improved coefficient matrix;

[0050] Step S34: Calculate V using the coefficient matrix obtained in S31 i , using the improved coefficient matrix obtained by S33 and the default points obtained by S32 to calculate the structural response And calculate V i and The relative error of

[0051] Step S35: Determine whether the relative error meets the preset accuracy requirement;

[0052] Step S36: If yes, then output a reusable improved coefficient matrix for structural response calculation; if no, then move the default point back and reform the improved coefficient matrix, and return to step S34.

[0053] As a preferred embodiment of the present invention, in step S34, the method further comprises the following steps:

[0054] Step S341: Calculate the structural response before and after the default point position

[0055]

[0056]

[0057] Where, P is the load;

[0058] Step S342: Calculate V i and The relative error is:

[0059]

[0060] Among them, j that meets the relative error is determined as the final default point k.

[0061] As a preferred embodiment of the present invention, in step S2, the method further comprises the following steps:

[0062] Step S25: Generate the relative displacement, relative velocity and absolute acceleration response spectrum under earthquake action according to Duhamel integration:

[0063] SD(ζ,ω n )=max|U|

[0064]

[0065] Among them, ζ is the damping, ω n is the natural frequency, U is the acceleration, velocity and displacement vector in a linear elastic single degree of freedom system, is the absolute acceleration, is the ground acceleration;

[0066] Step S26: Generate a response spectrum calculation result according to the relative displacement, relative velocity and absolute acceleration response spectrum, and generate a time domain calculation result according to the improved coefficient matrix time domain display expression;

[0067] Step S27: Calculate the average relative error based on the response spectrum calculation results and the time domain calculation results.

[0068] The present invention also provides a calculation system for earthquake resistance of crane structure, comprising:

[0069] A model building module, used for building a crane model according to the crane data, and then performing modal analysis on the crane model to generate modal analysis results;

[0070] The time domain calculation module is used to apply unit pulse load to the crane model according to the modal analysis results, generate key node response values ​​and establish coefficient matrices, analyze the vibration attenuation law of the single degree of freedom system, and provide an improved coefficient matrix time domain explicit expression;

[0071] The result analysis module is used to simulate the artificial earthquake time history, perform random earthquake response analysis based on the coefficient matrix and the improved coefficient time domain explicit expression, and generate the earthquake response analysis results of the key nodes of the crane.

[0072] The present invention also provides a computer medium, on which a computer program is stored, and the computer program is executed by a processor to implement the above-mentioned calculation method for earthquake resistance of a crane structure.

[0073] The present invention also provides a computer, comprising the above-mentioned computer medium.

[0074] The above technical solution of the present invention has the following advantages compared with the prior art:

[0075] 1. By analyzing the vibration attenuation law of single-degree-of-freedom structures with different periods, an improved time-domain explicit expression of the coefficient matrix is ​​proposed. The accuracy and efficiency of the calculation results of the improved time-domain explicit expression of the coefficient matrix compared with the original method are verified through examples. The comparison results show that the shorter the natural vibration period of the structure, the larger the part that can be calculated by default; the calculation speed of the improved time-domain explicit expression of the coefficient matrix increases with the increase of the structural damping ratio.

[0076] 2. When using simulated earthquakes to analyze the bridge crane model, the improved coefficient matrix time-domain explicit expression replaces the earthquake time history with lower computational cost than the modal superposition method, and the calculation results of the key node positions are slightly different from the modal superposition method results. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0078] Figure 1 It is a schematic diagram of the crane geometric model provided by an example of the present invention.

[0079] Figure 2 It is a schematic diagram of the mesh division result of the crane model provided by the example of the present invention.

[0080] Figure 3 It is a schematic diagram of the Wilson-θ method provided in an example of the present invention.

[0081] Figure 4 is a schematic diagram of the displacement, velocity and acceleration response time history curves of different periodic degrees of freedom systems under unit pulse load provided by an example of the present invention; wherein, Figure 4 a is a schematic diagram of the displacement time history curve. Figure 4 b is a schematic diagram of the velocity time history curve. Figure 4 c is a schematic diagram of the acceleration time history curve.

[0082] Figure 5 Schematic diagram of the relationship between the displacement response of different periods and the cumulative integral value of the area enclosed by the time axis over time provided by an example of the present invention; wherein, Figure 5 a is the relationship between the integral value of the displacement response curve at different periods and the time. Figure 5 b is the relationship between the integral cumulative integral value of the speed response curve of different cycles and time. Figure 5 c is the relationship between the integral cumulative integral value of the acceleration response curve of different periods and time.

[0083] Figure 6 It is a flow chart of the preliminary calculation of the default point provided by the example of the present invention.

[0084] Figure 7 is a schematic diagram of the relationship between the response time and the cumulative integral ratio provided by the example of the present invention; wherein, Figure 7 a is the displacement cumulative integral ratio, Figure 7 b is the proportion of speed cumulative points, Figure 7 c is the percentage of the cumulative integral of acceleration.

[0085] Figure 8 It is a flowchart of calculating the time-domain explicit expression of the improved coefficient matrix provided by an example of the present invention.

[0086] Fig. 9is a schematic diagram of the relationship between the new response time course and the cumulative integral ratio provided by the example of the present invention; wherein, Fig. 9 a is the displacement cumulative integral ratio, Fig. 9 b is the proportion of speed cumulative points, Fig. 9 c is the percentage of the cumulative integral of acceleration.

[0087] Fig.10 is a schematic diagram of the seismic wave acceleration time history provided by an example of the present invention; wherein, Fig.10 a is the acceleration time history, Fig.10 b is the velocity time course, Fig.10 c is the displacement time history.

[0088] Fig.11 is a schematic diagram of the positional relationship of different periodic default points in a time step provided by an example of the present invention; wherein, Fig.11 a is the default point position in the displacement time history, Fig.11 b is the default point position in the velocity time history, Fig.11 c is the default point position in the acceleration time history.

[0089] Fig.12 It is a schematic diagram comparing the time-domain explicit expression of the improved coefficient matrix provided by the example of the present invention and the response spectrum calculation result of the time-domain explicit method; Fig.12 a is the displacement response spectrum curve, Fig.12 b is the velocity response spectrum curve, Fig.12 c is the acceleration response spectrum curve.

[0090] Fig.13 is a schematic diagram of relative errors of responses of different damping ratios provided by an example of the present invention; Fig.13 a is the relative error of Damp=5% displacement time history, Fig.13 b is the relative error of speed history of Damp=5%, Fig.13 c is the relative error of Damp=5% acceleration time history, Fig.13 d is the relative error of Damp = 10% displacement time history, Fig.13 e is the relative error of speed history with Damp = 10%, Fig.13 f is the relative error of Damp=10% acceleration time history, Fig.13 g is the relative error of displacement time history of Damp = 20%, Fig.13 h is Damp = 20% speed time relative error, Fig.13 i is the relative error of Damp=20% acceleration time.

[0091] Fig.14 It is a schematic diagram of the module connection of a calculation system for the earthquake resistance of a crane structure provided by an example of the present invention.

[0092] Fig.15It is a flow chart of the steps and methods for earthquake-resistant crane structure provided by an example of the present invention. DETAILED DESCRIPTION

[0093] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0094] Earthquake is a serious natural disaster. In the process of understanding and fighting earthquakes, various seismic analysis theories are applied in practice. At present, the time history analysis method is more accurate than other methods. The time domain explicit method constructs the coefficient matrix by calculating the response of the structure under the unit pulse load, and calculates the structural response by applying the actual load with the same time step as the unit pulse load. Due to the damping and suppression effect of damping on vibration, the response value of the structure under the unit pulse load will gradually decrease over time. The arrangement characteristics of its coefficient matrix are obvious: starting from the main diagonal elements of each row of the matrix, the oscillation decreases and converges to 0 in the direction of the first element of the row. The part of the coefficient matrix that contributes more to the structural response is concentrated in the beginning of the unit pulse response time history, and the unit pulse response time history corresponding to the part of the coefficient matrix that contributes less to the structural response oscillates around 0. In actual calculations, there is still room for optimization of the part that contributes less to the structural response. To address this problem, this application analyzes the response law of a single-degree-of-freedom system under a unit pulse load, derives a time-domain explicit coefficient matrix in the Wilson-θ integral format, and provides a calculation method for the seismic resistance of a crane structure based on the Wilson-θ method with an improved coefficient matrix in the time domain.

[0095] refer to Figure 1-Figure 14 As shown, an embodiment of the present invention provides a method for calculating the earthquake resistance of a crane structure, the method comprising the following steps:

[0096] S1: Building a crane model based on crane data, wherein the crane model includes: geometric model building, model material definition and finite element model building.

[0097] Specifically, in order to make the analysis results accurate and effective, the geometric model of the bridge crane is simplified as follows during the modeling process, which specifically includes the following steps:

[0098] Simplify the geometric features that have little effect on the analysis results and are prone to singularity in the analysis to improve the quality of meshing and the efficiency of finite element analysis, and then use concentrated load or distributed mass models to replace the geometric features of auxiliary structures on the bridge, such as electrical cabinets, sliding wire brackets, etc.

[0099] The fixed connections of the crane's bridge main and end beams and the continuous welds of each bridge welding plate are simulated in the form of common nodes.

[0100] Ignore the operating mechanisms of the crane's trolley and crane trolley, and retain the characteristics of the wheel mechanism.

[0101] The geometric features of the crane's lifting device and hoisting mechanism are replaced with rod units and concentrated loads, which are loaded into the crane's hook position.

[0102] According to the crane drawing data, a simplified crane model is established. Figure 1 shown.

[0103] In the actual implementation process, after the crane model is established, the corresponding structural material data is added to the model. For example, the present application refers to the use of low-alloy high-strength structural steel.

[0104] In some embodiments, the grid division directly affects the accuracy of the analysis results and the speed of the analysis. Selecting a suitable unit type according to the structural characteristics can effectively improve the analysis efficiency and accuracy. Therefore, in this application, after the crane model is established, the method further includes the following steps:

[0105] Select the matching unit type according to the structural characteristics of the crane and perform mesh division.

[0106] In the actual implementation process, the webs, flange plates and diaphragms of the main beams and end beams of the reference crane model in this application are much larger in their length and width directions than in their thickness dimensions, and shell units are used; the relatively complex geometric shapes of the crane model, such as the tracks, drums and supports, use locally encrypted solid units; the wire rope slings of the crane model use rod units; the hoisting weight of the crane model acts on the typical working position as a concentrated load; the lifting mechanism, electrical equipment, trolley running mechanism and car running mechanism of the crane model use a distributed mass method to ensure that the model quality is consistent with the quality in the crane drawing data.

[0107] The positions of singular points in the grid are adjusted, the grid is re-divided, and then the wheel-rail constraints are set to generate the finite element model of the crane.

[0108] In the actual implementation process, the existing "Overhead Crane Manufacturing Specifications" provides a typical four-wheel overhead crane seismic analysis model. The bridge structure adopts a simply supported beam mechanical model. The wheel numbers of the trolley and the trolley are referenced. Figure 2 The wheel-rail freedom constraints of the crane are set according to the actual working conditions, as shown in the following table of the wheel-rail freedom constraints of the crane:

[0109]

[0110] Perform modal analysis on the crane model and generate modal analysis results.

[0111] Specifically, in step S1, after performing modal analysis on the structure included in the crane model, a minimum time step is set that is the same as the time step of the modal superposition method. Specifically, the method further includes the following steps:

[0112] Use modal coordinate y i The linear combination of represents the node displacement {u}:

[0113]

[0114] Among them, {φ i} is the i-th order mode, and n is the number of extracted modes.

[0115] Then the coupled motion equations of the structure contained in the crane model are simplified to an equivalent single degree of freedom system.

[0116] The time-history analysis method is used to calculate the seismic response of the equivalent single-degree-of-freedom system, and then multiple vibration modes are superimposed to generate the total dynamic response of the structure.

[0117] In the actual implementation process, refer to the following formula: For a linear structure, its kinetic equilibrium equation is:

[0118]

[0119] Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the system, respectively. The damping matrix C uses the Rayleigh Damping model:

[0120] C=α0M+α1K

[0121] α0, α1 are proportional coefficients; {u} is the acceleration, velocity and displacement vector of the system;

[0122] is the earthquake acceleration.

[0123] Substitute the node displacement {u} into the dynamic equilibrium equation and multiply it by a typical modal vibration shape {φ i} T ,have to:

[0124]

[0125] Among them, {φ j} T [K]{φ i}=0 i≠j and {φ j} T [M]{φ i}=0 i≠j, and then we get

[0126]

[0127] Specifically, in the above formula and j The coefficients are as follows:

[0128] Normalize using the mass matrix to get The coefficients are: {φ j} T [M]{φ j}=1;

[0129] The coefficient is {φ j} T [C]{φ j}=2ζ j ω j , where ξ j is the critical damping ratio of the j-th mode; ω j is the natural frequency of the j-th mode;

[0130] y j The coefficients are: Here, j represents any mode.

[0131] Step S2: See Fig.15 ,According to the modal analysis results, a unit pulse load is applied to the crane model, the key node response values ​​are generated and the coefficient matrix is ​​established.

[0132] Specifically, in step S2, the coefficient matrix is ​​constructed by calculating the response of the structure under the unit pulse load, and the structural response is calculated by applying the actual load with the same time step as the unit pulse load. Due to the damping and suppression effect of damping on vibration, the response value of the structure under the unit pulse load will gradually decrease over time; the arrangement characteristics of the coefficient matrix are obvious: starting from the main diagonal elements of each row of the matrix, the oscillation decreases toward the first element of the row and converges to 0. The part of the coefficient matrix that contributes more to the structural response is concentrated in the beginning of the unit pulse response time history, and the unit pulse response time history corresponding to the part of the coefficient matrix that contributes less to the structural response oscillates around 0.

[0133] In the actual implementation process, based on the time domain explicit expression of the Wilson-θ method, in a linear elastic single-degree-of-freedom system considering only earthquake action, the dynamic equation of the structure can be expressed as:

[0134]

[0135] Among them, M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the system respectively;

[0136] The damping matrix C uses the Rayleigh Damping model: C = α0M + α1K; α0, α1 are proportional coefficients, U is the acceleration, velocity and displacement vector of the system, L is the direction vector of the inertial force, is the earthquake acceleration.

[0137] Wilson-θ method is based on the linear acceleration assumption. The basic idea is to assume that acceleration In the time period [t, t+θΔt], the acceleration changes linearly. Available from: Indicates that the parameter θ ≥ 1, and then linear interpolation is used to calculate the motion of the structure at time t + Δt. The schematic diagram of the Wilson-θ method is shown in the figure. Figure 3 As shown. For example, when θ≥1.37, the Wilson-θ method has a stable solution. In practical applications, θ=1.4 is generally taken.

[0138] At present, the existing time domain explicit format based on Wilson-θ method, displacement, velocity and acceleration are:

[0139]

[0140] Among them, U i+1 , P i , P i+1 is the structural response characteristic displacement, velocity and acceleration and seismic excitation at the i-th moment, where:

[0141]

[0142] L is the inertial force pointing vector; θ is the coefficient; Δt is the time step;

[0143] It can be expressed in matrix form as:

[0144]

[0145] The time domain explicit method adopts a completely separated processing method to reduce the dimension of the random vibration problem. This method can establish an explicit expression of the dynamic response for any degree of freedom and any time. Through the explicit expression, the response characteristics of the key nodes can be directly calculated. The coefficient matrix corresponding to the response at each time can be established by the explicit expression, which has good calculation accuracy and efficiency. Therefore, this application refers to the time domain explicit format of the existing Wilson-θ method, supplements the coefficient matrix derivation method under the Wilson-θ integral format, and according to the above matrix, makes:

[0146]

[0147] It can be written as a recursive calculation formula:

[0148] V i+1 =TV i +Q1P i +Q2P i+1 i=(0,1,…,l-1)

[0149] Similarly, V i It can also be obtained by i-1 The recursive calculation formula of the time is obtained:

[0150] V i =TV i-1 +Q1P i-1 +Q2P i i=(1,2,…,l)

[0151] Assuming V0 = 0, we can deduce the time t i =Δt response V i The expression is:

[0152]

[0153] Among them, Q3 = TQ2 + Q1;

[0154] If you use A i,0 ,A i,1 ,…,A i,i Respectively represent P0, P1, ..., P i The previous coefficient matrix can be expressed as: V i =A i, 0P0+A i,1 P1+…+A i,i P i i=(1,2,…,l). It can be seen that the time domain explicit method can be used to calculate the response of a single degree of freedom structure. The corresponding structural response can be obtained by multiplying the coefficient matrix with the load time history.

[0155] l means load step, and the value range needs to be determined according to the load duration and step length. For example, a 20S load duration has a time step interval of 0.02s, which is reflected in i as 1, 2, 3...l-2, l-1, l, and corresponds to the load duration (unit / s) as 0.02, 0.04, 0.06...19.96, 19.98, 20.

[0156] Among them, A i,0 ,A i,1 ,…,A i,i It is only related to the structural parameters and reflects the influence of the structural parameters on the random response, so it is:

[0157]

[0158] It can be seen from this that to find the time-history response of the structure under different loads, we only need to change the load R i , the coefficient matrix B i After being obtained for the first time, it can be reused in the subsequent calculation of the structural time-history response under other loads; i Corresponding system

[0159] Number matrix, A i,0 ,A i,1 ,…,A i,i The calculation process is a recursive process, which can be used to i-1 The corresponding coefficient matrix A i-1,0 ,A i-1,1 ,…,A i-1,i-1 It is expressed as:

[0160]

[0161] The coefficient matrix recursive relationship of , the coefficient matrix corresponding to the response at each moment refers to the following table:

[0162]

[0163] As can be seen from the above table, in order to obtain the coefficient matrix corresponding to the response at each moment, it is only necessary to calculate the two columns of the matrix corresponding to P0 and P1, namely A i,0 and A i,1 (i=1,2,…,l).

[0164] For example, taking a single degree of freedom system with unit mass and arbitrary natural vibration period as an example, when P0=1, excitation P1, P2, ..., P l When both are 0, it is equivalent to applying a half-triangular unit pulse load to the structure at time t0, and the corresponding response of the structure at each time is V i =A i,0 (i=1,2,…,l); when P1=1, P0,P2,…,P l When all are 0, that is, a full triangle unit pulse load is applied to the structure at time t1, the structure responds to V at each time. i =A i,1 (i=1,2,…,l).

[0165] The coefficient matrix constructed using the unit pulse load reflects the attenuation law of the response. The load R i The size of only affects the amplitude of the structure's response at each moment. The time domain explicit method converts the corresponding load R of all nodes at past moments into iIt acts on the structure independently and lasts until the current moment. The structural response at the current moment is the result of the superposition of the load duration results at the past moments and the load action at the current moment.

[0166] In actual use, the design is often carried out with reference to the standards in the building seismic design code. The industry default rule for selecting the load duration is "Technical Code for Concrete Structures of High-Rise Buildings JGJ3-2010 4.3.5 (2)". "Code for Seismic Design of Building Structures GB 50011-2010 5.1.2" also has similar provisions. The original text of JGJ3-2010 4.3.5 (2) is as follows: The duration of the earthquake wave should not be less than 5 times the basic natural vibration period of the building structure and 15s, and the time interval of the earthquake wave can be 0.01s or 0.02s.

[0167] S3. Simulate the artificial earthquake time history, perform random earthquake response analysis based on the coefficient matrix and the improved coefficient matrix time domain explicit expression, and generate the earthquake response analysis results of the key nodes of the crane.

[0168] Specifically, the earthquake simulation method includes the following steps:

[0169] According to the selected preset seismic wave, the seismic motion simulation is performed and the seismic motion peak value is adjusted:

[0170]

[0171] in, is the time history curve of seismic acceleration after adjustment, a(t) is the time history curve of seismic acceleration before adjustment, is the adjusted peak acceleration of the earthquake, A max is the peak acceleration of the earthquake before adjustment.

[0172] Specifically, the principle for selecting seismic waves is: seismic motion is a random vibration, and the frequency spectrum, amplitude and duration of different seismic motions are usually different. In engineering practice, the seismic motion time history used for seismic analysis mainly comes from the following two sources: 1. Existing earthquake records; 2. Artificially simulated earthquakes.

[0173] The Gaussian stationary random process is generated using the trigonometric series superposition method:

[0174]

[0175] Among them, M is the total number of samples, N ω is the number of segments of circular frequency, φ k,m is a random number that follows a uniform distribution in the interval [0,2π]; ω k is the circular frequency of the kth harmonic component, in rad / s;

[0176] Ak is the amplitude of the kth harmonic component, expressed as:

[0177]

[0178] Where Δω is the circular frequency interval of the harmonic components, ω max is the upper frequency limit of the cutoff circle, ω min is the lower limit of the cut-off circle frequency.

[0179] The power spectrum function of the Gaussian stationary random process is S(ω), and the rate spectrum density function is S(ω k ) adopts Kanai-Tajimi model (Kanai Kiyoshi model), the specific expression is:

[0180]

[0181] Among them, ξ g is the damping ratio of foundation soil, ω g is the dominant frequency of foundation soil, and S0 is the spectral intensity factor.

[0182] According to the Gaussian stationary random process and the uniform adjustment function g(t), a non-stationary random process is obtained, and then earthquake simulation is carried out.

[0183] Specifically, the formula of the uniform adjustment function g(t) is:

[0184]

[0185] In some embodiments, when the time domain explicit method is used for actual analysis, the part of the coefficient matrix that contributes more to the structural response is concentrated in the beginning of the unit impulse response time history. Under the influence of structural damping, the unit impulse response time history gradually decreases with time, and the part of the corresponding coefficient matrix contributes less to the structural response calculation result. By selecting the part of the unit impulse response time history that contributes more to the structural response and ignoring the part of the unit impulse response time history that oscillates around 0 to construct the coefficient matrix, the calculation accuracy can be guaranteed while improving the calculation efficiency of the time domain explicit method.

[0186] For example, for multiple single-degree-of-freedom systems with unit mass, damping ratio ζ = 0.05, calculation time t = 40s, and natural vibration period of 1 to 6 (s), the response time history curve under unit pulse load is as follows: Figure 4 The displacement time history curve is shown in Figure 4 As shown in a, the initial displacement condition is 0, the long period (low frequency) amplitude is large and the vibration decays slowly, while the short period (high frequency) amplitude is small and the vibration decays quickly; the velocity time history curve is as follows Figure 4 As shown in b, the initial velocity condition is 0, the amplitudes of long and short periods are similar, but the vibration attenuation speed slows down as the period becomes longer; the acceleration time history curve is shown in Figure 4 As shown in c, the initial acceleration condition is -1, the long-period vibration has a small amplitude and a slow decay speed, while the short-period vibration has a large amplitude and a fast decay speed.

[0187] It can be seen from this that the common change law of the displacement, velocity and acceleration time-history curves is that the shorter the natural vibration period, the faster the amplitude decays; the main part of the response is concentrated in the front part of the time history, and the main part moves backward with the increase of the period; therefore, the main part of the response can be selected according to the change law of the response and the ratio of the area of ​​the cumulative integral of the absolute value of the response on the time axis to the total area.

[0188] refer to Figure 5 As shown in the figure, the relationship between the cumulative integral value of the area enclosed by the displacement response of different periods and the time axis and time is as follows Figure 5 As shown in a, for a single cumulative integral curve, the cumulative integral value curve of the area enclosed by the displacement response time history curve and the time axis increases with time; for multiple curves, compared with short periods, the initial value of the cumulative integral value change rate of the long period is larger, and the rate of change to 0 is slower. Figure 5 As shown in b, the growth law of the single curve of the velocity time history cumulative integral and the displacement time history cumulative integral value is the same. For multiple curves, the initial value of the change rate of the long and short cycles is similar compared with that of the short cycle, and the rate at which the long cycle changes to 0 is slow. Figure 5 As shown in Figure c, the growth law of the cumulative integral of the acceleration time history is the same as the growth law of the single curve of the displacement and velocity time history, but the maximum cumulative integral value is basically the same; for multiple curves, compared with the short period, the initial value of the short period is larger than that of the long period, and the rate at which the long period changes to 0 is slower.

[0189] In summary, for displacement, velocity and acceleration time histories, the short-period cumulative integral increases to the maximum value faster and takes less time. Therefore, compared with the long-period and short-period time histories, the short-period can omit more parts.

[0190] Therefore, taking a unit mass single degree of freedom system with a damping ratio of ζ = 0.05, a stiffness of 40, an initial displacement and velocity of 0, and an acceleration of 1 as an example, a unit pulse load is applied to the structure, the time step is 0.01s, and the integration time is 40s. Figure 6 The process shown calculates the default point position, including the steps:

[0191] S320, calculating the response of the structure under a unit pulse load;

[0192] S321. Calculate the total area A enclosed by the response curve and the time axis max ;

[0193] S322, assigning a default point i;

[0194] S323, calculate the area A enclosed by the response curve to the default point i and the time axisi ;

[0195] S324, judgment A i / A max ≥99% whether it is true, if not, the default point i is moved back and the process returns to step S322;

[0196] S325. Preliminarily determine the default point position i.

[0197] refer to Figure 7 As shown in , for the displacement, velocity and acceleration time history responses, when the area cumulative integral accounts for 99% of the part used to construct the coefficient matrix, as shown in Figure 7 As shown in a, the default point is 15.74s for the time point, and the defaultable part accounts for 60.65% of the displacement response curve; the relationship between the velocity cumulative integral ratio is as follows Figure 7 As shown in b, the default point is 14.65s for the time point, and the defaultable part accounts for 63.4% of the speed response curve; the proportion of the acceleration cumulative integral is as follows Figure 7 As shown in c, the default point is 14.61s for the time point, and the defaultable part accounts for 63.5% of the speed response curve.

[0198] It can be seen that for the time-history responses of displacement, velocity and acceleration, it is feasible to use the ratio of the cumulative integral value of the area enclosed by the response and the time axis to the maximum integral value as the basis for selecting the main part of the response. Compared with the original method, the improved time-domain explicit expression of the coefficient matrix in this application can improve the calculation efficiency under the condition of equivalent calculation accuracy.

[0199] Therefore, the coefficient matrix after default is shown in the following table:

[0200]

[0201] When the default coefficient matrix is ​​used for response calculation, the t at the end of the time history is l-1 and t l The amount of calculation at each moment is the same; for the non-default part, the calculation result is the same as the original coefficient matrix, and for the default part, due to the default of t l and t l-1 The calculation results only affect the initial time t1 and t2. For loads P0, P1 and P2, the calculation results only affect the initial time t1 and t2. l-1 and t l The response result accounts for 5 / (n 2 +3n / 2) n=1,2,...,l, the sum of the calculation amount is 5 / (n 2 +n / 2) n=1,2,...,l.

[0202] And from the coefficient matrix after default, it can be seen that to improve the coefficient matrix for response calculation, it is necessary to calculate the response results step by step, that is, for the first default position at time t j Structural response before j=(2,3,…,l) The calculation formula is as follows:

[0203]

[0204] Structural response at and after the default point The calculation formula is as follows:

[0205]

[0206] Then calculate V i and Relative error ε:

[0207]

[0208] If the accuracy requirement is not met, the default point is moved back, and the response and relative error are calculated again. The above process is repeated until the response calculation result of the time domain explicit expression of the improved coefficient matrix is ​​sufficiently close to the calculation result of the time domain explicit method, that is, the iteration is stopped when the two curves are sufficiently correlated. In this paper, ε=0.05 is taken, and the coefficient matrix obtained at this time can be used for subsequent response calculation. The above method implementation process reference Figure 8 shown.

[0209] Therefore, Figure 7 For example, in Figure 8 After the process calculation is completed, the percentage and relative error of the defaultable parts are shown in the following table:

[0210] Response type Now you can default some percentages Maximum relative error ε Displacement 30.13％ 2.79％ speed 31.6％ 4.21％ Acceleration 30.2％ 2.73％

[0211] Among them, the relationship between the new response time and the cumulative integral ratio is as follows: Fig. 9 As shown in the figure, it can be seen that after the relative error is used to control the default point position, the default part now accounts for about 30%. At the same time, the relative error between the original method and the improved coefficient matrix time domain explicit expression is controlled within 5%, which has good calculation accuracy.

[0212] In some embodiments, the method of the present application is compared with other methods:

[0213] Seismic waves are taken from the ground acceleration time history records occurring in a certain area, where the seismic wave acceleration time history is as follows Fig.10 The velocity and displacement time histories shown are obtained by integrating the acceleration time histories;

[0214] Take the earthquake acceleration time wave 10-50s, and the response spectrum period range is T n,min =0.02s, Tn,max =6s cycle interval ΔT n =0.02s, the structural mass is 1, the structural damping ratios are selected as ζ=0.05, ζ=0.1 and ζ=0.2 respectively, the time step of the time history analysis is 0.01s, the analysis duration is 35s, the number of time steps is 3500, and the calculation duration is shown in the following table:

[0215]

[0216] It can be seen that the construction time of the coefficient matrix with different damping ratios is similar, and the average time is 1.87s, which is faster than the average time of 2.53s for the construction of the improved coefficient matrix. This is because the construction of the improved coefficient matrix requires calculation of the default point position; the calculation time of the time domain explicit method with different damping ratios is similar, and the average time is 40s. However, the calculation time of the time domain explicit expression of the improved coefficient matrix is ​​significantly reduced as the damping ratio increases. This is because as the damping ratio of the structure increases, the structure's vibration reduction and suppression effect is enhanced, such as Fig.11 As shown in the figure, as the damping ratio increases, the position of the default point in the time step moves forward significantly, the default part increases, and the amount of calculation decreases. It can be seen that the default coefficient time-domain explicit method can improve the calculation efficiency compared with the original time-domain explicit method.

[0217] refer to Fig.12 As shown in Figure 2, it is a comparison between the time-domain explicit expression of the improved coefficient matrix and the response spectrum calculation results of the time-domain explicit method. Fig.12 a. Fig.12 b and Fig.12 c are the relative displacement response spectrum, relative velocity response spectrum and absolute acceleration response spectrum respectively. It can be seen that the calculation results of the improved coefficient matrix time domain explicit expression are highly consistent with the calculation results of the response spectrum of the time domain explicit method when the damping ratios are ζ=0.05, ζ=0.1 and ζ=0.2 respectively. Fig.13 for Fig.12 The relative error of the time history curve in the corresponding time domain direction in the frequency domain period 0 to 6s.

[0218] From the relative errors of displacement, velocity and acceleration, it can be seen that when the area cumulative integral ratio is used as the basis for selecting the main part of the structural response under unit pulse load, and the relative error is used as the calculation accuracy control condition, the average relative error of the response calculation result of the original method in the default calculation part of the explicit expression when the coefficient matrix is ​​improved can be expressed as follows:

[0219]

[0220] The calculation is shown in the following table:

[0221]

[0222] It can be seen that as the structural damping ratio increases, the position of the default point in the time domain continues to move forward, the part that can be calculated by default continues to increase, and the corresponding average relative error gradually decreases, and the relative error is within 5%. Therefore, the calculation results of the improved coefficient matrix time domain explicit expression response are quite accurate compared with the calculation results of the original method.

[0223] refer to Fig.14 As shown, in some embodiments, the present invention further provides a calculation system for earthquake resistance of crane structure, comprising:

[0224] The model building module 20 is used to perform modal analysis on the crane model and generate modal analysis results; the crane model includes: geometric model building, model material definition and finite element model building;

[0225] The time domain calculation module 22 is used to apply a unit pulse load to the crane model according to the modal analysis results, generate key node response values ​​and establish a coefficient matrix; analyze the vibration attenuation law of the single degree of freedom system, and provide an improved coefficient matrix time domain explicit expression;

[0226] The result analysis module 23 is used to simulate the artificial earthquake time history, perform random earthquake response analysis based on the coefficient matrix and the improved coefficient time domain explicit method, and generate earthquake response analysis results of the key nodes of the crane.

[0227] In some embodiments, the present invention further provides a computer medium having a computer program stored thereon, and the computer program is executed by a processor to implement the calculation method for earthquake resistance of a crane structure.

[0228] In some embodiments, the present invention also provides a computer, comprising the computer medium.

[0229] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0230] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the earthquake resistance of a crane structure, characterized in that: The following steps are involved: Step S1: performing modal analysis on the crane model to generate modal analysis results; Step S2: According to the modal analysis results, a unit pulse load is applied to the crane model to generate key node response values ​​and establish a coefficient matrix; Analyze the vibration attenuation law of single degree of freedom system and give the time domain explicit expression of improved coefficient matrix; Step S3: simulating the artificial earthquake time history, performing random earthquake response analysis according to the coefficient matrix and the improved coefficient matrix time domain explicit expression, and generating earthquake response analysis results of the key nodes of the crane; Wherein, in step S2, providing the time-domain explicit expression of the improved coefficient matrix further includes the following steps: Step S20: Obtain the time domain explicit format based on the Wilson-θ method and generate displacement, velocity and acceleration equations: Among them, U i+1 is the structural response characteristic displacement, is the structural response characteristic speed, is the structural response characteristic acceleration, P i , P i+1 is the earthquake excitation, L is the inertial force direction vector, where: M is the mass matrix of the system, C is the damping matrix, K is the stiffness matrix, and the damping matrix C uses the Rayleigh damping model: θ is the coefficient; Δt is the time step; Step S21: Generate a matrix form of displacement, velocity and acceleration according to the displacement, velocity and acceleration formula: In step S2, the method further comprises the following steps: Step S22: According to the matrix form of displacement, velocity and acceleration, let: Then we get the recursive calculation formula: V i+1 =TV i +Q1P i +Q2P i+1 i=0,1,…,l-1, where l is the load step; Step S23: By t i-1 The recursive calculation formula at the moment is used to obtain V i : V i =TV i-1 +Q1P i-1 +Q2P i i=1,2,…,l, Then, when V0=0, the time t is generated. i =Δt response V i The expression is: V1=Q1P0+Q2P1 i=1 V i =T i-1 Q1P0+T i-2 Q3P1+…+T 0 Q3P i-1 +Q2P i 2≤i≤l Among them, Q3=TQ2+Q1, T i-1 , T i-2 , T 0 is the exponential power of T; Step S24: Using A i，0 , A i，1 , …, A i，i Represent P0, P1, ..., P i The coefficient matrix before, then at time t i =Δt response V i The expression is: V i =A i，0 P0+A i，1 P1+…+A i，i P i i = 1, 2, ..., l, so as to obtain the explicit expression of the structural response in the time domain and the corresponding coefficient matrix, Wherein, in step S24, the method further includes the following steps: Step S240: A i，0 , A i，1 , …, A i，i It is only related to the structural parameters and reflects the influence of the structural parameters on the random response. B i =[A i，0 A i，1 … A i，i ] R i =[P0 T P1 T … P i T ] T , where i = 1, 2, ..., l; Step S241: Set time t i =Δt corresponds to V i The expression is: V i =B i R i ,i=1,2,…,l, In this way, an explicit expression of the structural response in time domain is obtained; In step S3, the random seismic response analysis is performed according to the coefficient matrix and the improved coefficient matrix time domain explicit expression, and further includes the following steps: Step S31: Calculate the response result of the structure included in the crane model under the unit pulse and generate a coefficient matrix; Step S32: Preliminarily calculating the default point according to the integral target ratio; Step S33: forming a preliminary improved coefficient matrix; Step S34: Calculate V using the coefficient matrix obtained in S31 i , using the improved coefficient matrix obtained by S33 and the default points obtained by S32 to calculate the structural response And calculate V i and The relative error of Step S35: Determine whether the relative error meets the preset accuracy requirement; Step S36: If yes, output a reusable improved coefficient matrix for structural response calculation; if no, move the default point back and re-form the improved coefficient matrix, and return to step S34; Wherein, in step S32, the method further includes the following steps: S320, calculating the response of the structure under a unit pulse load; S321. Calculate the total area A enclosed by the response curve and the time axis max ; S322, assigning a default point i; S323, calculate the area A enclosed by the response curve to the default point i and the time axis i ; S324, judgment A i / A max ≥99% whether it is true, if not, the default point i is moved back and the process returns to step S322; S325, preliminarily determine the default point position i; The method further comprises the following steps: Step S341: Calculate the structural response before and after the default point position Where, P is the load; Step S342: Calculate V i and The relative error is: Among them, j that meets the relative error is determined as the final default point k.

2. A crane structure seismic calculation method according to claim 1, characterized in that: In step S1, the method further comprises: after performing modal analysis on the structure included in the crane model, setting a minimum time step that is the same as the time step of the modal superposition method.

3. The calculation method for earthquake resistance of crane structure according to claim 1, characterized in that: In step S2, the method further comprises the following steps: Step S25: Generate the relative displacement, relative velocity and absolute acceleration response spectrum under earthquake action according to Duhamel integral: SD(z,w n )=max|U| Among them, ζ is the damping, ω n is the natural frequency, are the acceleration, velocity and displacement vectors in a linear elastic single degree of freedom system, is the absolute acceleration, is the ground acceleration; Step S26: Generate a response spectrum calculation result according to the relative displacement, relative velocity and absolute acceleration response spectrum, and generate a time domain calculation result according to the improved coefficient matrix time domain display expression; Step S27: Calculate the average relative error based on the response spectrum calculation results and the time domain calculation results.

4. A calculation system for earthquake resistance of crane structure, characterized in that: A method for calculating the earthquake resistance of a crane structure according to any one of claims 1 to 3, comprising: Model building module, used to perform modal analysis on the crane model and generate modal analysis results; The time domain calculation module is used to apply unit pulse load to the crane model according to the modal analysis results, generate key node response values ​​and establish coefficient matrices, analyze the vibration attenuation law of the single degree of freedom system, and provide an improved coefficient matrix time domain explicit expression; The result analysis module is used to simulate the artificial earthquake time history, perform random earthquake response analysis based on the coefficient matrix and the improved coefficient time domain explicit method, and generate the earthquake response analysis results of the key nodes of the crane.

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