Title: A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact,
Abstract: A unified fluid-structure interaction (FSI) formulation is presented for
solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the
generalized-alpha scheme are used for the spatial and temporal discretization.
The membrane discretization is based on curvilinear surface elements that can
describe large deformations and rotations, and also provide a straightforward
description for contact. The fluid is described by the incompressible
Navier-Stokes equations, and its discretization is based on stabilized
Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming
sharp interface discretization, and the resulting non-linear FE equations are
solved monolithically within the Newton-Raphson scheme. An arbitrary
Lagrangian-Eulerian formulation is used for the fluid in order to account for
the mesh motion around the structure. The formulation is very general and
admits diverse applications that include contact at free surfaces. This is
demonstrated by two analytical and three numerical examples exhibiting strong
coupling between fluid and structure. The examples include balloon inflation,
droplet rolling and flapping flags. They span a Reynolds-number range from
0.001 to 2000. One of the examples considers the extension to rotation-free
shells using isogeometric FE.