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

Highlights

• A general mechanical theory for three-dimensional bodies with structure-like kinematics.

• An explicit form of the projection operation for loads on 3D bodies onto structures.

• A finite-element formulation of dragged bodies, 3D bodies that move like structures.

• Examples showing significant computational savings of dragged vs. standard bodies.

• Illustrations of how dragged bodies simplify contact/impact between shells.

Abstract

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.