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Dynamic structure reliability evaluation method based on uncertain random variables

A technology of random variables and dynamic structures, applied in random CAD, special data processing applications, instruments, etc.

Active Publication Date: 2020-12-18
BEIHANG UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

At present, no one has applied uncertain random variables to the reliability analysis of dynamic structures. Aiming at the problem of the implicit limit state function of dynamic structures, the present invention combines the uniform design experiment (Uniform design experiment) proposed by Fang Kaitai and Wang Yuan with the classic two The sub-polynomial response surface function realizes the simulation fitting of the limit state function, and then calculates the reliability and reliability index based on uncertain random variables

Method used

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  • Dynamic structure reliability evaluation method based on uncertain random variables
  • Dynamic structure reliability evaluation method based on uncertain random variables
  • Dynamic structure reliability evaluation method based on uncertain random variables

Examples

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Embodiment 1

[0095] Under uniform load p = ρb 0 h 0 and a corroded bending beam of concentrated force F as figure 2 shown. The length of the curved beam is L=5m, and its section is rectangular, where b 0 =0.18m is the section width, h 0 =0.035m is the section height, ρ is the density of the curved beam. Assume the corrosion depth d of the corroded curved beam c has a functional relationship d with time t c =kt,k=2.5×10 -4 m / year, so the formulas for the length and width of the section of the beam are respectively b(t)=b 0 -2kt, h(t)=h 0 -2kt. When the maximum bending moment M of the bending beam is greater than the ultimate bending moment M u (t) is regarded as failure, and the expression of the limit state function is obtained as follows:

[0096]

[0097] In the formula, σ e is the yield stress, which obeys random normal distribution, while F and ρ obey uncertain linear distribution, namely: and σ e , F and ρ are independent of each other. Table 1 lists the specific di...

Embodiment 2

[0141] Such as Figure 5 In the four-bar truss structure shown, the elastic modulus and cross-sectional area of ​​each bar are E=2.95×10 11 N / m 2 and A, both rods 1 and 2 have length L. Now exert a vertical downward (y-axis negative direction) time-varying force F on node 3 1 (t)=5(1+0.05t)×10 4 N, apply a time-varying force F horizontally to the right (positive direction of the x-axis) on node 2 2 (t)=5(1-0.05t)×10 4 N, where the unit of time t is hour. When the displacement of a node in the truss structure exceeds the limit threshold D max =0.328×10 -3 m is considered invalid. Assume that the rod length L obeys a random normal distribution, and the cross-sectional area A obeys an uncertain normal distribution, namely: And L and A are independent of each other. Table 4 lists the specific distribution parameters of random variables and uncertain variables.

[0142] The concrete distribution parameter of random variable and uncertain variable of table 4 embodiment 2 ...

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Abstract

The invention provides a dynamic structure reliability evaluation method based on an uncertain random variable. The method comprises the following steps: 1, determining a design variable of a dynamicstructure; using a quadratic polynomial response surface function for approximating real response, and a test is arranged through uniform test design; 2, determining an undetermined coefficient by adopting a least square method, and if the coefficient is judged to be unreasonable, carrying out uniform test design again; 3, determining the type and distribution function of a variable, constructinga limit state function according to the response surface function and a limit threshold, and writing a corresponding uncertain random variable; 4, obtaining a process function by solving an uncertainty measure or solving an equation; 5, based on the process function, solving the opportunity measure to obtain the reliability of the dynamic structure; 6, calculating the mean value of the uncertain random variables; 7, calculating the variance of the uncertain random variable; and 8, solving a reliability index of the dynamic structure according to the mean value and the variance. The reliabilityanalysis method disclosed by the invention is scientific and good in manufacturability, and has a wide application value.

Description

technical field [0001] The invention relates to a dynamic structural reliability evaluation method based on uncertain random variables, belonging to the technical field of structural reliability analysis. Background technique [0002] The reliability of dynamic structures has always been an important attribute, and how to accurately evaluate the reliability of dynamic structures has received more and more attention. Among them, selecting an appropriate measure for uncertainty quantification (Uncertainty quantification) is the basic problem of all reliability engineering related work. Generally speaking, there are two types of uncertainty in the reliability analysis process: one is the inherent uncertainty caused by the inherent randomness of the physical world (Inherent randomness), and the other is the uncertainty caused by the lack of sufficient data. Uncertainty (Epistemicuncertainty). [0003] The traditional reliability measurement of dynamic structure is realized thr...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/20G06F111/08G06F119/02
CPCG06F30/20G06F2111/08G06F2119/02Y02T90/00
Inventor 张建国周霜游令非
Owner BEIHANG UNIV
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