Stochastic finite cell method for structural mechanics

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-Loeve expansion in order to decompose the random field within a physical domain having arbitrary boundaries. Then, the SFCM is formulated based on Karhunen-Loeve 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.