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.
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Zakian, P. Stochastic finite cell method for structural mechanics. Comput Mech 68, 185–210 (2021). https://doi.org/10.1007/s00466-021-02026-0
- Stochastic finite cell method
- Finite cell method
- Karhunen-Loève expansion
- Polynomial chaos expansion
- Fredholm integral equation
- Computational stochastic mechanics