CN112214825A - Selection method for input seismic waves with complex structure and shock resistance vulnerability - Google Patents

Selection method for input seismic waves with complex structure and shock resistance vulnerability Download PDF

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CN112214825A
CN112214825A CN202011219886.0A CN202011219886A CN112214825A CN 112214825 A CN112214825 A CN 112214825A CN 202011219886 A CN202011219886 A CN 202011219886A CN 112214825 A CN112214825 A CN 112214825A
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seismic waves
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谢皓宇
郑万山
刘怀林
高文军
刘海明
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China Merchants Chongqing Communications Research and Design Institute Co Ltd
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Abstract

The invention discloses a selection method of input seismic waves of complex structure anti-seismic vulnerability, which comprises the steps of carrying out modal analysis on a target structure; the target structure is equivalent to a two-degree-of-freedom model, and the initial stiffness corresponding to the two double-fold hysteresis structure models is calculated; determining the reduction rigidity and the yield displacement; calculating the probability density distribution condition of the maximum displacement response and calculating the information entropy E corresponding to the seismic wavesiThe diversity and the discrete type of the set of input seismic waves can be rapidly evaluated by utilizing the information entropy of the seismic wave set response probability density distribution, and then the appropriate seismic waves are selected as the input seismic wave set for analyzing and calculating the anti-seismic vulnerability of the complex structure, so that the blank of the determination rule of the input seismic waves of the anti-seismic vulnerability of the complex structure is filled, and a reliable basis is provided for the selection of the input seismic waves for calculating the anti-seismic vulnerability of the structure by using time-course dynamic analysis.

Description

Selection method for input seismic waves with complex structure and shock resistance vulnerability
Technical Field
The invention relates to the technical field of seismic wave selection, and particularly discloses a selection method for inputting seismic waves with complex-structure anti-seismic vulnerability.
Background
The damage of earthquake to the structures including key buildings, bridges and the like not only causes huge economic loss, but also brings difficulty to rescue and reconstruction after earthquake. In order to have an accurate assessment of the seismic performance of new and existing structures, the concept of seismic vulnerability is often chosen as the most common approach. The method of anti-seismic vulnerability uses a large amount of input seismic waves to excite a finite element model of the structure, defines the damage standard, and calculates the probability that the response exceeds the damage standard so as to represent the anti-seismic performance of the structure. However, neither incremental dynamics, banding, or cloud mapping in vulnerability make any requirements or reasonable provisions for the selection of input seismic waves. When time-course dynamic analysis is performed on a nonlinear finite element model of a complex structure, the time cost is extremely high, and in addition, the vulnerability analysis is usually that hundreds of seismic waves are input, if the input seismic waves are similar to each other in nature, the value of the result of the vulnerability analysis is considered to be reduced.
Disclosure of Invention
In view of the above, the present invention provides a method for selecting an input seismic wave with a complex structure anti-seismic vulnerability, so as to solve the problem of a decrease in the value of an analysis result due to similar properties of the input seismic wave in the existing anti-seismic vulnerability analysis process.
In order to achieve the purpose, the invention provides the following technical scheme:
a selection method of input seismic waves with complex structure anti-seismic vulnerability specifically comprises the following steps:
s1: performing modal analysis on the target structure;
s2: equating the target structure to a two-degree-of-freedom model, wherein each degree of freedom corresponds to a double-fold hysteresis structure model, and calculating the initial stiffness corresponding to the double-fold hysteresis model;
s3: determining the reduction rigidity and the yield displacement of the double-fold line hysteresis structure model;
s4: applying a plurality of groups of seismic waves to the double-fold line hysteresis structure model, calculating structure response and dividing displacement intervals to obtain the maximum displacement probability density distribution condition corresponding to each group of seismic waves;
s5, respectively calculating the information entropy E of each group of seismic waves according to the probability density distribution conditioniTaking the information entropy EiThe minimum group of seismic waves is used as input seismic waves for analyzing the earthquake-resistant vulnerability of the complex structure, and the information entropy EiThe calculation formula of (2) is as follows:
Figure BDA0002761627960000021
wherein: r represents the number of the maximum displacement intervals corresponding to the ith group of seismic waves, PijAnd representing the response occurrence probability of the jth maximum displacement interval corresponding to the ith group of seismic waves.
Further, the step S1 of performing modal analysis on the target structure specifically includes the following steps:
s101: establishing a finite element model of a target structure;
s102: modal analysis is carried out on a finite element model of the target structure through finite element analysis software to obtain modal circular frequency omega of the first two orders of the finite element model of the target structure1And ω2
Further, the step S2 is to make the target structure equivalent to a two-degree-of-freedom model, where each degree of freedom corresponds to a bi-fold hysteresis structure model, and calculating the initial stiffness of the corresponding bi-fold hysteresis model specifically includes the following steps:
s201: establishing a two-particle two-degree-of-freedom system of a target structure, wherein each degree of freedom corresponds to a double-fold hysteresis structure model;
s202: solving a motion equation of free vibration of the two double-fold hysteresis models to obtain the natural vibration frequency of the two-particle two-degree-of-freedom system;
s203: and enabling the natural vibration frequency to be equal to the modal circular frequencies of the first two orders of the finite element model of the target structure, and calculating to obtain the initial stiffness k corresponding to the two double-fold hysteresis structure models1And k2
Figure BDA0002761627960000022
Wherein m represents the mass of each particle in the two-particle two-degree-of-freedom system, and k1Representing the initial stiffness, k, between two particles2Representing the initial stiffness between the mass point and the ground.
Further, in step S3, the reduction stiffness is 0.1 times of the initial stiffness, and the value range of the yield displacement is 10 to 50 cm.
Further, in step S4, the method for obtaining the maximum displacement probability density distribution corresponding to each group of seismic waves includes the following steps:
s401: selecting p groups of seismic waves, wherein each group of seismic waves comprises q earthquakes, and applying all the earthquakes to a double-fold line hysteresis structure model of the target structure;
s402: respectively calculating the maximum displacement structural response corresponding to each earthquake to obtain p groups of maximum displacement response sets, wherein each group of maximum displacement response set comprises q maximum displacement response values;
s403: sorting the q maximum displacement response values in each group from small to large, and taking the maximum displacement response value q with the maximum valuemaxAnd equally dividing the maximum displacement response value into R displacement intervals, wherein the interval displacement value corresponding to each displacement interval is R, and the number R of the obtained displacement intervals is as follows:
Figure BDA0002761627960000031
s404: and respectively calculating the proportion of the maximum displacement response value in each displacement interval to obtain the maximum displacement probability density distribution condition of the maximum displacement response set.
Further, in step S403, the range displacement value r corresponding to each displacement range is an integer ranging from 1 cm to 5 cm.
The working principle and the beneficial effects of the scheme are as follows: the method comprises the steps of performing modal analysis on a target structure, establishing a two-particle two-degree-of-freedom system aiming at modal characteristics of the target structure, enabling the target structure to be equivalent to a double-fold hysteresis structure model, applying a plurality of groups of seismic waves to the model, obtaining information entropies of maximum displacement response sets corresponding to each group of seismic waves, comparing the information entropies of the groups, rapidly judging the diversity and the discrete types of maximum displacement response values in the maximum displacement response sets corresponding to an input seismic wave set, and selecting proper seismic waves as input seismic wave sets for analyzing and calculating the seismic vulnerability of the complex structure.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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FIG. 1 is a flow chart of a selection method of input seismic waves for complex structure seismic vulnerability in accordance with the present invention.
Fig. 2 is a flowchart of step S1 in fig. 1.
Fig. 3 is a flowchart of step S2 in fig. 1.
Fig. 4 is a flowchart of step S4 in fig. 1.
Detailed Description
The following is further detailed by way of specific embodiments:
examples
Fig. 1 is a flowchart of a preferred embodiment of a method for selecting input seismic waves for earthquake vulnerability of a complex structure according to the present invention, which specifically includes the following steps:
s1: and performing modal analysis on the target structure.
And carrying out modal analysis on the finite element model of the target structure by establishing the finite element model of the target structure so as to obtain the vibration characteristic of the target structure.
Referring to fig. 2, the step S1 of performing modal analysis on the target structure specifically includes the following steps:
s101: and establishing a finite element model of the target structure.
S102: modal analysis is carried out on a finite element model of the target structure through finite element analysis software to obtain modal circular frequency omega of the first two orders of the finite element model of the target structure1And ω2
S2: an initial stiffness is calculated.
And (3) equating the target structure to a two-degree-of-freedom model, wherein each degree of freedom corresponds to a double-fold hysteresis structure model, and calculating the initial rigidity of the corresponding double-fold hysteresis model.
Referring to fig. 3, the step S2 of calculating the initial stiffness of the target structure specifically includes the following steps:
s201: and establishing a two-particle two-degree-of-freedom system of the target structure, wherein each degree of freedom corresponds to a double-fold hysteresis structure model.
In the two-mass point two-degree-of-freedom system, mass point M1Sum particle M2Mass of (2) is M, defining mass point M1Sum particle M2Has an initial stiffness of k1Particle M2Initial stiffness to ground is k2Then, the mass matrix M of the two-particle two-degree-of-freedom system can be expressed as:
Figure BDA0002761627960000041
its initial stiffness matrix K can be expressed as:
Figure BDA0002761627960000042
s202: and solving a motion equation of free vibration of the two double-fold hysteresis models to obtain the natural vibration frequency of the two-particle two-degree-of-freedom system.
Specifically, the motion equation of the free vibration of the double-fold hysteresis model is as follows:
||K-ω2M||=0 (3)
wherein ω is the natural frequency of the two-particle two-degree-of-freedom system.
Substituting the above formula (1) and formula (2) into formula (3), the motion equation of the free vibration of the double-fold hysteresis model can be further obtained as follows:
Figure BDA0002761627960000051
let ω in equation (4)2Then the following equation can be derived by developing equation (4):
β2+(-2k1-k2)β+k1k2=0 (5)
solving the formula (5) to obtain the natural vibration frequency omega of the two-particle two-degree-of-freedom system as follows:
Figure BDA0002761627960000052
s203: enabling the natural vibration frequency omega and the modal circular frequency omega of the first two orders of the finite element model of the target structure1And ω2Equal, i.e.:
Figure BDA0002761627960000053
solving the formula (7) to obtain the initial stiffness k corresponding to the two double-fold hysteresis structure models1And k2Comprises the following steps:
Figure BDA0002761627960000054
s3: and determining the reduction rigidity and yield displacement of the double-fold hysteresis structure model.
Specifically, the initial stiffness k of the double-fold hysteresis structure obtained according to the formula (8)1And k2The reduction stiffness was 0.1 times the initial stiffness, and the stiffness after reduction was 0.1k each1And 0.1k2The value range of the yield displacement is 10-50cm, and the specific value can be determined by engineers according to the nonlinear characteristic of the finite element model, and can also be determined according to the displacement corresponding to the state of entering a plastic hinge in the bridge or building structure model.
S4: and determining the probability density distribution condition of the maximum displacement response.
Applying a plurality of groups of seismic waves to a double-fold hysteresis structure model of a target structure, respectively calculating the maximum displacement response of the target structure, obtaining a maximum displacement response set, dividing a maximum displacement interval, and determining the maximum displacement probability density distribution condition corresponding to each group of seismic waves.
Referring to fig. 4, the step S4 of determining the probability density distribution of the maximum displacement response specifically includes the following steps:
s401: selecting p groups of seismic waves from a seismic database, wherein each group of seismic waves comprises q earthquakes, and applying all the selected earthquakes to the double-fold hysteresis structure model of the target structure.
S402: the maximum displacement structural response corresponding to each earthquake is calculated, in the embodiment, the displacement of the mass point above is used as the index for analyzing the diversity and discrete type of the input earthquake wave set, that is, the mass point M is used1And taking the displacement generated under each earthquake action as a maximum displacement response value. Therefore, p groups of maximum displacement response sets can be obtained after all earthquakes are applied to the target structure, and each group of maximum displacement response set comprises q maximum displacement response values.
S403: sorting the q maximum displacement response values in each group of maximum displacement response sets from small to large, and taking the maximum displacement response value q with the maximum valuemaxAnd equally dividing the maximum displacement into R displacement intervals, wherein the displacement value of the interval corresponding to each interval is R, and the number R of the obtained displacement intervals is as follows:
Figure BDA0002761627960000061
the value of the interval displacement value r is any integer ranging from 1 cm to 5 cm.
S404: and respectively calculating the proportion of the number of the maximum displacement response values in each displacement interval to the number of the large displacement response values of all groups in the maximum displacement response set in which the maximum displacement response values are positioned, and obtaining the maximum displacement probability density distribution condition of the group of the maximum displacement response sets.
S5, respectively calculating the information entropy E of p groups of seismic waves according to the probability density distribution conditioniThe entropy E of the informationiThe calculation formula of (2) is as follows:
Figure BDA0002761627960000062
wherein: pijAnd representing the response occurrence probability of the jth maximum displacement interval in the maximum displacement response set corresponding to the ith group of seismic waves.
Information entropy E corresponding to p groups of seismic waves obtained by calculationiMaking a comparison, the information entropy EiThe smaller the value of (A), the larger the probability difference of the maximum displacement response value in each displacement interval is, and the larger the property difference between the earthquakes corresponding to the maximum displacement response set is, so that the information-taking entropy E isiThe smallest set of seismic waves is used as input seismic waves for analyzing the seismic vulnerability of the complex structure.
The invention utilizes the information entropy of seismic wave set response probability density distribution to quickly evaluate the diversity and the discrete type of the set of input seismic waves, further selects proper seismic waves as the input seismic wave set for analyzing and calculating the anti-seismic vulnerability of the complex structure, fills the blank of the determination rule of the input seismic waves of the anti-seismic vulnerability of the complex structure, and provides reliable basis for the selection of the input seismic waves for calculating the anti-seismic vulnerability of the structure by using time-course dynamic analysis.
The foregoing is merely an example of the present invention and common general knowledge of known specific structures and features of the embodiments is not described herein in any greater detail. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the present invention.

Claims (6)

1. A selection method of input seismic waves with complex structure anti-seismic vulnerability is characterized by comprising the following steps:
s1: performing modal analysis on the target structure;
s2: equating the target structure to a two-degree-of-freedom model, wherein each degree of freedom corresponds to a double-fold hysteresis structure model, and calculating the initial stiffness corresponding to the double-fold hysteresis model;
s3: determining the reduction rigidity and the yield displacement of the double-fold line hysteresis structure model;
s4: applying a plurality of groups of seismic waves to the double-fold line hysteresis structure model, calculating structure response and dividing displacement intervals to obtain the maximum displacement probability density distribution condition corresponding to each group of seismic waves;
s5, respectively calculating the information entropy E of each group of seismic waves according to the probability density distribution conditioniTaking the information entropy EiThe minimum group of seismic waves is used as input seismic waves for analyzing the earthquake-resistant vulnerability of the complex structure, and the information entropy EiThe calculation formula of (2) is as follows:
Figure FDA0002761627950000011
wherein: r represents the number of the maximum displacement intervals corresponding to the ith group of seismic waves, PijAnd representing the response occurrence probability of the jth maximum displacement interval corresponding to the ith group of seismic waves.
2. The method for selecting input seismic waves for resisting seismic vulnerability of complex structures according to claim 1, wherein the step of performing modal analysis on the target structure in step S1 specifically comprises the steps of:
s101: establishing a finite element model of a target structure;
s102: modal analysis is carried out on a finite element model of the target structure through finite element analysis software to obtain modal circular frequency omega of the first two orders of the finite element model of the target structure1And ω2
3. The method for selecting input seismic waves of a complex structure with earthquake resistance vulnerability according to claim 1, wherein the step S2 is equivalent to a bi-fold hysteresis structure model of the target structure, and calculating the initial stiffness of the bi-fold hysteresis structure model specifically comprises the following steps:
s201: establishing a two-particle two-degree-of-freedom system of a target structure, wherein each degree of freedom corresponds to a double-fold hysteresis structure model;
s202: solving a motion equation of free vibration of the two double-fold hysteresis models to obtain the natural vibration frequency of the two-particle two-degree-of-freedom system;
s203: and enabling the natural vibration frequency to be equal to the modal circular frequencies of the first two orders of the finite element model of the target structure, and calculating to obtain the initial stiffness k corresponding to the two double-fold hysteresis structure models1And k2
Figure FDA0002761627950000021
Wherein m represents the mass of each particle in the two-particle two-degree-of-freedom system, and k1Representing the initial stiffness, k, between two particles2Representing the initial stiffness between the mass point and the ground.
4. The method for selecting the input seismic waves with the complex structure anti-seismic vulnerability according to claim 1, wherein in step S3, the reduction stiffness is 0.1 times of the initial stiffness, and the value range of the yield displacement is 10-50 cm.
5. The method of claim 1, wherein the method comprises the steps of: in step S4, the method for obtaining the maximum displacement probability density distribution corresponding to each group of seismic waves includes the following steps:
s401: selecting p groups of seismic waves, wherein each group of seismic waves comprises q earthquakes, and applying all the earthquakes to a double-fold line hysteresis structure model of the target structure;
s402: respectively calculating the maximum displacement structural response corresponding to each earthquake to obtain p groups of maximum displacement response sets, wherein each group of maximum displacement response set comprises q maximum displacement response values;
s403: sorting the q maximum displacement response values in each group from small to large, and taking the maximum displacement response value q with the maximum valuemaxAnd equally dividing the total interval displacement into R displacement intervals, wherein the interval displacement value corresponding to each displacement interval is R, and the number R of the obtained displacement intervals is as follows:
Figure FDA0002761627950000022
s404: and respectively calculating the proportion of the maximum displacement response value in each displacement interval to obtain the maximum displacement probability density distribution condition of the maximum displacement response set.
6. The method for selecting the input seismic waves with the complex structure earthquake resistance and vulnerability according to claim 5, wherein in step S403, the value of the interval displacement value r corresponding to each displacement interval is an integer ranging from 1 cm to 5 cm.
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