A review of the finite cell method for nonlinear structural analysis of complex CAD and image-based geometric models

TL;DR

This paper reviews the finite cell method (FCM), highlighting its advantages in handling complex geometries in nonlinear structural analysis without extensive meshing, and showcases recent applications in structural mechanics and beyond.

Contribution

It provides a comprehensive overview of FCM's recent developments, including extensions to nonlinear elasticity and applications to complex CAD and image-based models.

Findings

FCM effectively analyzes complex geometries without detailed meshing.

The method extends straightforwardly to nonlinear elasticity.

Applications include vibration analysis and nonlinear compression testing.

Abstract

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.