Nowadays, fluid-structure interaction problems are a great challenge of different fields in engineering and applied sciences. Wind flow and structural motion may lead to aeroelastic instabilities on constructions such as long-span bridges, high-rise buildings and light-weight roof structures. Biomechanical applications are interested in the study of blood flow through large arteries, where membrane deformations interact with incompressible fluids. In the structural part of this work, a new methodology for the analysis of geometrically nonlinear orthotropic membrane and rotation-free shell...