<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>

{{  :pfem:grafico1.png?nolink&512  }} Figure 1 - Cantilever beam under point load: linear analysis. Vibration amplitude.

{{  :pfem:grafico2.png?nolink&512  }} 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>

{{  :pfem:barragem.png?nolink&512  }} Figure 3 - Dam collapse. Velocity field over time.

{{ youtube>yh1YkCFj3EQ?large }}{{ youtube>GisXhld6OKY?large }}

{{  :pfem:barragem2.png?nolink&512  }} Figure 4 - Dam collapse with a rigid obstacle.

{{ youtube>rGfUWwaXBnE?large }}

{{  :pfem:slosh.png?nolink&512  }} 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>

{{  :pfem:fsi.png?nolink&512  }} Figure 6 - Water tank with a high flexible wall. Pressure field and tension.

{{ youtube>vCXHBzJXnLI?large }}

{{  :pfem:fsi2.png?nolink&512  }} Figure 7 - Beam under a lateral wave. Pressure field and tension.

{{ youtube>Q-kI01eE1b0?large }}

The full text in Portuguese can be downloaded at [[http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23042018-103653/pt-br.php|http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23042018-103653/pt-br.php]]

Authors:

Giovane Avancini

Rodolfo A. K. Sanches