Fluid-structure interactions with geometrically nonlinear deformations

A numerical method for simulating fluid-structure interaction problems involving large, geometrically nonlinear deformations is presented. In this method, a proven computational fluid dynamics solver based on a higher-order immersed boundary method is coupled with a geometrically nonlinear structural finite element solver. The finite element solver employs the mixed interpolation of tensorial components formulation for shell elements. The implementation of the finite element solver and validation results for geometrically nonlinear test problems are discussed. Details of the coupling approach used to transfer loads and displacements between the fluid dynamic and finite element solvers are also presented. The fully-coupled fluid-structure interaction method is then applied to problems with large, geometrically nonlinear deformations, such as a cylinder with a flexible trailing filament, a hyperelastic bending tower, a compliant disk in a viscous flow, and a waving flag.