FINITE ELEMENT APPROXIMATION OF FLUID STRUCTURE INTERACTION (FSI) OPTIMIZATION IN ARBITRARY LAGRANGIAN-EULERIAN COORDINATES

Advanced composite materials such as Carbon Fiber Reinforced Plastics (CFRP) are being applied to many aircraft structures in order to improve performance and reduce weight. Most composites have strong, stiff fibers in a matrix which is weaker and less stiff. However; aircraft wings can break due to Fluid-Structure Interaction (FSI) oscillations or material fatigue. This paper focuses on the analysis of a non-linear fluid-structure interaction problem and its solution in the finite element software package DOpElib: the deal. II based optimization library. The principal aim of this research is to explore and understand the behaviour of the fluid-structure interaction during the impact of a deformable material (e.g. an aircraft wing) on air Here we briefly describe the analysis of incompressible Navier-Stokes and Elastodynamic equations in the arbitrary Lagrangian-Eulerian (ALE) frameworks in order to numerically simulate the FSI effect on a double wedge airfoil. Since analytical solutions are only available in special cases, the equation needs to be solved by numerical methods. This coupled problem is defined in a monolithic framework and ftactional-step-theta time stepping scheme are implemented. Spatial discretization is based on a Galerkin finite element scheme. The non-linear system is solved by a Newton method. The implementation using the software library package DOpElib and deal. II serves for the computation of different fluid-structure configurations.