Dimensionally reduced, nonlinear dragged solids: Theory and finite elements for rigid and shell-like bodies

This article describes a dimensional reduction technique that can be employed to study the dynamics of three-dimensional bodies by linking them with surrogate structural models that simplify the governing equations. The main idea of these approximation is to tie the two types of bodies in such a way that the external loads are supported by the three-dimensional body, whereas the kinematics and the equilibrium are enforced through the reduced structure. By this choice, the expensive numerical discretizations of three-dimensional continuum models can be replaced by computationally cheaper structural elements without losing relevant geometrical features and keeping all the details of the applied loading, a key feature for modeling accurately the interfaces between structures and continua. In particular, these situations frequently appear in fluid/structure interaction problems, where the results of this article should be of most interest.

Automated summary

This article presents a technique for dimension reduction that allows the study of dynamics for three-dimensional bodies by connecting them with simplified structural models. The main idea is to link the two types of bodies in a way that the three-dimensional body supports external loads, while kinematics and equilibrium are handled by the reduced structure. This approach enables the replacement of expensive numerical discretizations with computationally cheaper structural elements, without sacrificing relevant geometrical features, making it especially useful for fluid/structure interaction problems.