PSI - Issue 64

Fadi Oudah et al. / Procedia Structural Integrity 64 (2024) 1983–1989 Fadi Oudah/ Structural Integrity Procedia 00 (2019) 000 – 000

1985

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employed. Notably, the EOLE method (Li and Der-Kiureghian, 1993), which is a spectral representation of the OLE method, has been demonstrated to yield low error rates with fewer terms in the truncation process during field generation, and thus, is frequently used in structural engineering applications. 3. Random Finite Element Simulation (RFE) General purpose FE software packages like ABAQUS, ANASYS, and LS-DYNA have limited functionalities to perform random finite element (RFE) analysis of civil structures. Some of the developed functionalities of these software include the use of stochastic fields for buckling analysis and stochastic generation of material properties for limited element and material types. Supplemental computer scripts and coding are typically necessary to perform RFE analysis using existing software. Hassan and Oudah (2024) have developed a user-friendly computer interface called RF-DYNA for generating RFE models of concrete and geotechnical structures using LS-DYNA developed FE models. The software is user-friendly and has been used in engineering practice in Canada to build distributions of resistance models for reliability and risk assessments. The random field generator in RF-DYNA utilizes the EOLE mathematical formulation. In the EOLE method, the lognormal random field realizations, ̂ ( , ) , are represented as the exponential transformation of the realizations of a Gaussian random field, ̂( , ) , as expressed in Eq. (1). Here, represents a vector of a spatial coordinates, and corresponds to an independent identifier linked to a set of standard normal variables. ̂ ( , ) = exp⁡{ ̂( , )} (1) The generation of ̂( , ) is expressed in Eq. (2). It is a function of the mean of a lognormally distributed field, , standard deviation of a lognormally distributed field, σ , correlation function, and the number of standard random variables, . ̂( , ) = ⁡ +⁡σ ⁡∑ ξ √ ( θ ) ⁡ i T ⁡ Y,Y i = 1 (2) where, Y,Y i is the ℎ vector of the covariance matrix, is the ℎ greatest eigenvector of the standard normal field ( ℎ out of ), ( ) is the ℎ randomly generated standard normal variable ( ℎ out of ), is the ℎ greatest eigenvalue of the standard normal field ( ℎ out of ). σ and are obtained using Eq. (3) and (4), respectively. σ =⁡√ln(1+ 2 2 ) (3) = ln( )− 1 2 σ 2 (4) is determined based on an assumed correlation function to determine the correlation between two points ( ) and ( ) , , as expressed in Eq. (5), and the coordinates of the geometric centroids of the RFE model ( , , ). A squared exponential function is commonly used to determine as shown in Eq. (6), were the correlation lengths, , , and are defined in a three-dimensional space. . ( , ) = ⁡ (5) =∏ exp(− ( ( ) − ( ) ) 2 2 − ( ( ) − ( ) ) 2 2 − ( ( ) − ( ) ) 2 a 2 ) =1 (6) Nataf transformation is used to convert the correlation values of a lognormally distributed random field to a standard normal distribution (Eq. (7)) (Nataf, 1962), where, ′ ⁡ is the correlation for the standard normal field between two