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The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM and a macroscopic FEM. The spatial variation of inclusion shape is modeled using KarhunenLoeve expansion with exponential-type covariance kernels. The characteristic function on a 2-D unit cell and the homogenized diffusion tensor are calculated using the spectral stochastic BEM. The macroscale diffusion problems are solved using the stochastic FEM with the polynomial chaos (PC) expansion. Through numerical tests, the expected value and the standard deviation of the concentration in macroscale problems and their distribution are investigated. | The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM and a macroscopic FEM. The spatial variation of inclusion shape is modeled using KarhunenLoeve expansion with exponential-type covariance kernels. The characteristic function on a 2-D unit cell and the homogenized diffusion tensor are calculated using the spectral stochastic BEM. The macroscale diffusion problems are solved using the stochastic FEM with the polynomial chaos (PC) expansion. Through numerical tests, the expected value and the standard deviation of the concentration in macroscale problems and their distribution are investigated. | ||
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Revision as of 11:53, 1 July 2024
Abstract
The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM and a macroscopic FEM. The spatial variation of inclusion shape is modeled using KarhunenLoeve expansion with exponential-type covariance kernels. The characteristic function on a 2-D unit cell and the homogenized diffusion tensor are calculated using the spectral stochastic BEM. The macroscale diffusion problems are solved using the stochastic FEM with the polynomial chaos (PC) expansion. Through numerical tests, the expected value and the standard deviation of the concentration in macroscale problems and their distribution are investigated.
Full Paper
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Published on 01/07/24
Accepted on 01/07/24
Submitted on 01/07/24
Volume Structural Mechanics, Dynamics and Engineering, 2024
DOI: 10.23967/wccm.2024.076
Licence: CC BY-NC-SA license
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