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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-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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Correspondence to Pooya Zakian.

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Zakian, P. Stochastic finite cell method for structural mechanics. Comput Mech 68, 185–210 (2021).

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  • Stochastic finite cell method
  • Finite cell method
  • Karhunen-Loève expansion
  • Polynomial chaos expansion
  • Fredholm integral equation
  • Computational stochastic mechanics