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.