<font 12pt/inherit;;inherit;;inherit>This work introduces a formulation, under Lagrangian description, for the solution of solid, incompressible fluid dynamics and fluid-structure interaction (FSI). In FSI problems, the structure usually presents large displacements thus making mandatory a geometric non-linear analysis. Considering it, we adopt a position based formulation of the finite element method (FEM) which has been shown to be very robust when applied to large displacement solid dynamics. Some results are presented below:</font>
Figure 1 - Cantilever beam under point load: linear analysis. Vibration amplitude.
Figure 2 - Fixed beam under point load: non linear analysis. Comparison between linear and non linear vibration amplitude.
<font 12pt/inherit;;inherit;;inherit>For the fluid mechanics problem it is well known that a Lagrangian description eliminates the convective terms from the Navier-Stokes equations and thus, no stabilization technique is required. However, the difficulty is then transferred to the need of efficient re-meshing, mesh quality and external boundary identification techniques, since the fluid presents no resistance to shear stresses and may deform indefinitely. In this sense, we employ a combination of finite element and particle methods in which the particle interaction forces are computed by mean of a finite element mesh which is re-constructed at every time step. Free surface flows are simulated by a boundary recognition technique enabling large domain distortions or even the particles separation from the main domain, representing for instance a water drop. A few examples solved in this work are shown below.</font>
Figure 3 - Dam collapse. Velocity field over time.
Figure 4 - Dam collapse with a rigid obstacle.
Figure 5 - Sloshing of a viscous fluid. Pressure field evolution.
<font 12pt/inherit;;inherit;;inherit>Finally, the fluid-structure coupling is simplified due to the Lagrangian description adopted for both materials, with no need for extra adaptive mesh-moving technique for the fluid computational domain to follow the structure motion. The coupling is perfomed using a strong partitioned technique and the contact between both fluid and solid is detected using a ghost particles technique. We present two examples of FSI problem.</font>
Figure 6 - Water tank with a high flexible wall. Pressure field and tension.
Figure 7 - Beam under a lateral wave. Pressure field and tension.
The full text in Portuguese can be downloaded at http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23042018-103653/pt-br.php
Authors:
Giovane Avancini
Rodolfo A. K. Sanches