Unconstrained vector nonlinear dynamic shell formulation applied to Fluid Structure Interaction

Fluid Structure Interaction (FSI) is a well-developed subject and several authors constantly provide improvements in related solution processes. The aim of this paper is to present an improvement in the shell formulation regarding large displacement analysis applied to FSI problems, i.e., a new curved shell finite element based on positions and unconstrained vector mappings is coupled with a compressible 3D fluid flow Finite Element approach. This improvement is important when an initial simple fluid velocity field cannot replace embedded shell movements, or when the shell closure changes position in a way that large rotations are present. The proposed formulation does not use the concept of rotations, resulting in an algorithm that conserves linear and angular momentum for large rigid body displacements when using the well established Newmark time integrator. Other advantages of this formulation are the use of complete stress–strain relations and the possibility of solving thin or thick shells developing large displacements and small strains. Numerical examples are presented in order to validate the proposed shell formulation regarding FSI applications.