A review of the finite cell method for nonlinear structural analysis of complex CAD and image-based geometric models
For researchers in computational mechanics, this review consolidates progress on a method that simplifies analysis of complex geometries, though it is incremental as it surveys existing work.
This review paper summarizes recent advances in the finite cell method (FCM) for nonlinear structural analysis of complex geometries, demonstrating its ability to avoid expensive meshing while maintaining high convergence rates. Applications include vibration analysis of a ship propeller and nonlinear compression of a CT-based metal foam.
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 two application examples, i.e. the vibration analysis of a ship propeller described by T-spline CAD surfaces and the nonlinear compression test of a CT-based metal foam.