Fluid-structure interaction physical processes are very complex, non linear in nature and can not be solved analytically. In fact experimental setups are essential to provide reliable data. However, these are generally associated with enormous costs, which is why the demand for numerical simulations as development tool is increasing rapidly. In this study, an Arbitrary Lagrangian-Eulerian (ALE) formulation is employed in a fully coupled monolithic way, considering the problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that more complicated constitutive relations (and more realistic for biomechanics applications) for the fluid as well as the structural part can be easily incorporated. The aim is to study the interaction of the elastic walls of the aneurysm with the geometrical shape of the implanted stent structure. This study can be seen as a basic step towards the understanding of the resulting complex flow phenomena so that in future aneurysm rupture shall be suppressed by an optimal setting for the implanted stent geometry. The optimization of fluid structure interaction problems are also investigated to set the benchmark.