Non-intrusive random finite element method for plate structure stochastic analysis
A non-invasive, plate-structured technology, applied in special data processing applications, complex mathematical operations, instruments, etc., to solve problems such as computational efficiency, accuracy, and applicability limitations, high computational costs, and a large number of samples
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Embodiment 1
[0027] Consider the elastic modulus Gaussian random field, where the random field mean is 2.184×10 11 Pa, the standard deviation σ is 2.184×10 10 Pa, the autocovariance function is: Cov(x 1 ,y 1 ; x 2 ,y 2 ) = σ 2 exp(-|x 1 -x 2 | / d x )exp(-|y 1 -y 2 | / d y ), where (x 1 ,y 1 ) and (x 2 ,y 2 ) is any two space points of the plate, d x and d y is the correlation length of the plate structure random field. Consider a random Kirchhoff thin plate, where the length is 2m, the width is 1m, the thickness is 0.01m, and the Poisson's ratio is 0.3. Such as figure 2 As shown, the boundary condition of the plate structure is simply supported on four sides. The loading situation is a concentrated excitation of 100 N applied at the center of the plate.
[0028] The deflection of the stochastic Kirchhoff thin plate obtained based on the present invention and the probability density function of the von Mises stress response are as follows image 3 As shown, where the corr...
Embodiment 2
[0033]Consider a random Mindlin plate with length 1m, width 1m, modulus of elasticity 100GPa, and Poisson's ratio 0.3. There are two types of boundary conditions: four-sided simple support and four-sided fixed support, among which the four-sided fixed support boundary condition is as follows Figure 5 shown. 10 load cases 4 Uniform excitation of Pa. The plate thickness is a Gaussian random field, where the average value of the random field is 1mm, and the autocovariance function is:
[0034] Cov(x 1 ,y 1 ; x 2 ,y 2 ) = σ 2 exp{-[(x 1 -x 2 ) / d x ] 2}exp{-[(y 1 -y 2 ) / d y ] 2}.
[0035] The probability density curves of the deflection response of the four-sided simply supported random Mindlin medium plate under different thickness variation coefficients are as follows: Image 6 shown. For a Gaussian-distributed input thickness random field, the output deflection response of the linear elastic plate structure is non-Gaussian-distributed. As the coefficient of v...
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