Dmytro Pivovarov

TL;DR: In this article, an alternative Gauss integration rule was proposed to stabilize the stochastic finite element method (SFEM) by truncating the probability density function for the random variable, resulting in higher accuracy for the standard deviation in the homogenized stress at the macro scale.

TL;DR: In this paper, the authors compare large-scale non-simplified and non-ergodic models with simplified, parametric, ergodic, and sometimes periodic models and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions.

TL;DR: A fuzzy FEM representation is proposed which requires only the modal value and support of the fuzzy input parameters and is completely independent of the membership function’s shape, which allows for severe dimension reduction of the non-deterministic problem if the accurate spectral simulation technique is used.

TL;DR: This work introduces a SFEM modification involving global basis functions in both the physical and the stochastic domain and addresses two very important questions, namely the treatment of the Gibbs phenomenon in the case of physical-stochastic trigonometric basis functions and the evaluation of the eigenvectors for the Stochastic problem which are suitable for further basis reduction.

TL;DR: The stochastic version of the FEM is applied to the homogenization of magneto-elastic heterogeneous materials with random microstructure to capture accurately the discontinuities appearing at matrix-inclusion interfaces.