Stochastic finite cell method for structural mechanics

• Published in: Computational mechanics Vol. 68; no. 1; pp. 185 - 210
• Main Author: Zakian, Pooya
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2021; Springer; Springer Nature B.V
• Subjects: Accuracy; Analysis; CAD; Civil engineering; Classical and Continuum Physics; Computational Science and Engineering; Computer aided design; Decomposition; Domains; Engineering; Fields (mathematics); Finite element analysis; Finite element method; Fredholm equations; Integral equations; Mathematical analysis; Mechanics; Mechanics (physics); Mesh generation; Methods; Monte Carlo simulation; Numerical analysis; Original Paper; Polynomials; Stochastic processes; Theoretical and Applied Mechanics; Karhunen-Loève expansion; Finite cell method; Polynomial chaos expansion; Fredholm integral equation; Stochastic finite cell method; Computational stochastic mechanics
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-021-02026-0

Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel computational framework, for uncertainty quantification of structures. For this purpose, stochastic finite cell method (SFCM) is developed as a new efficient method, including the features of finite cell method, for computational stochastic mechanics considering complicated geometries arising from computer-aided design (CAD). Firstly, finite cell method is formulated for solving the Fredholm integral equation of the second kind used for Karhunen-Loève expansion in order to decompose the random field within a physical domain having arbitrary boundaries. Then, the SFCM is formulated based on Karhunen-Loève and polynomial chaos expansions for the stochastic analysis. Several numerical examples consisting of benchmark problems are provided to demonstrate the efficiency, accuracy and capability of the proposed SFCM.