X-SFEM, a computational technique based on X-FEM to deal with random shapes
DOI:
https://doi.org/10.13052/REMN%20%2016/2007/Keywords:
computational stochastic mechanics, X-FEM, level set, stochastic finite element, random geometryAbstract
We propose a new method to deal with random geometries. It is an extension to the stochastic context of the eXtended Finite Element Method. This method lies on two majors points: the implicit description of geometry by the level set technique and the use of the partition of unity method for the enrichment of the finite element approximation space. This new technique leads by a direct calculus on a fixed finite element mesh to a solution which is explicit in terms of the basic random variables describing the geometry. We present here the basis of this approach and several examples to illustrate its performances.
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