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A review of the finite cell method for nonlinear structural analysis of complex CAD and image-based geometric models. (arXiv:1807.01285v1 [math.NA])
来源于:arXiv
The finite cell method (FCM) belongs to the class of immersed boundary
methods, and combines the fictitious domain approach with high-order
approximation, adaptive integration and weak imposition of unfitted Dirichlet
boundary conditions. For the analysis of complex geometries, it circumvents
expensive and potentially error-prone meshing procedures, while maintaining
high rates of convergence. The present contribution provides an overview of
recent accomplishments in the FCM with applications in structural mechanics.
First, we review the basic components of the technology using the p- and
B-spline versions of the FCM. Second, we illustrate the typical solution
behavior for linear elasticity in 1D. Third, we show that it is straightforward
to extend the FCM to nonlinear elasticity. We also outline that the FCM can be
extended to applications beyond structural mechanics, such as transport
processes in porous media. Finally, we demonstrate the benefits of the FCM with
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