Simplified spectral stochastic finite element formulations for uncertainty quantification of engineering structures. (December 2020) - Yazdani, Abbas
Abstract: In general, the structure inputs including loading and physical specifications can be deterministic or stochastic and uncertainties can be modeled using a random variable, random field, or a stochastic process. A well-known method developed to analyze structures with uncertainties is the spectral stochastic finite element method (SSFEM). To improve the efficiency of SSFEM, this paper has developed three simplified formulations to separately solve problems involving stochastic loading and constant material properties, stochastic loading and random material properties and stochastic loading and stochastic material properties the main feature of which is that they need fewer finite element (FE) analyses to assess the statistical specifications of the response. To examine their accuracy and efficiency, three practical engineering problems: 1) Euler-Bernoulli beam, 2) square solid and 3) modeling the corrosion effect in a concrete structure were solved and the results were compared with those of the Monte Carlo simulation (MCS). To see if the proposed formulations can be used in structural reliability analyses, a limit state function (LSF) was defined for each problem and the results were compared with those of the corresponding MCS; their significant efficiency and enough potential was, thus, confirmed.