1. Reference problem

This test case, based on the model in article [bib1], aims to test the correct consideration of a free surface in a fluid-structure calculation coupled with the DYNA_NON_LINE operator.

1.1. Geometry

We consider a parallelepipedic reservoir, filled with water, whose external walls are undeformable. This rigid tank has a deformable internal plate, named \(\Gamma\). It is embedded at its base at the bottom of the tank, its vertical sides being free. This flexible wall extends beyond the free surface by a height of \(\mathrm{12,9}\mathrm{cm}\):

1.2. Material properties

The fluid (water) contained in the tank has the following characteristics:

density:	\({\rho }_{f}=1000\mathrm{kg}/{m}^{3}\)
speed of sound:	\(c=1500m/s\)

The deformable wall is linear elastic (duralumin):

density:	\({\rho }_{s}=2787\mathrm{kg}/{m}^{3}\)
Young’s modulus:	\(E=\mathrm{62,43}\mathrm{GPa}\)
Poisson’s ratio:	\(\nu =\mathrm{0,35}\)

1.3. Boundary conditions and loading

1.3.1. Dirichlet conditions

The load defined here is of the type of displacement imposed on a surface. More precisely, it is considered that the bottom of the tank can only move in direction \(x\).

In this direction \(x\), the system will be stressed by imposing on the bottom of the tank a sinusoidal displacement in time, with a frequency \(\mathrm{1,7704}\mathrm{Hz}\) and an amplitude \(\mathrm{0,001}m\).

This imposed displacement can be assimilated to a single-support type of stress applied by the base of the reservoir (seismic application).

1.3.2. Neumann conditions

Superimposed on the Dirichlet surface condition previously defined, the model is also subjected to the gravity field (imposed volume force).

Finally, the upper surface of the fluid domain is characterized by free surface conditions.