0043-B-Sloshing Water Frequencies
Casimir Katz | Casimir KatzB0 Classification
| Class | Numerical Verification Example |
|---|---|
| Type of structure | Plate or Shell Structure-Panel |
| Mechanics | Dynamics |
| Material law | Other Material Laws |
| Building material | General |
| Design type | Dynamic Design |
| Design code | - |
| Status |
published on 14-03-2024 |
B1 Problem description
A fluid with a free surface in a tank may move during an earthquake or other dynamic loading with certain frequencies. There are many possibilities to model this behaviour: From discrete particles, viscous fluids or just based on potential theory.
For the latter case a solution with classical FE-Software might be obtainable using the Lagrangian model of fluids.
The analytical reference solution for this 2D problem has been taken from [1]
A rectangular water tank with a width of L = 5.080 m and a water level of D = 1.905 m (L/D=8/3) is considered. Plain strain conditions have to be applied.
The assumed material constants of water are: a density of 1000 kg/m³ and a bulk modulus of 2000 N/m². Thus the Poisson ratio is 0.5 while the elasticity and shear modulus will vanish. A numerical solution will require to select material parameters close to these values triggering numerical problems with the so called "incompressibility". (Locking, spurious Escher-Modes etc.)
The boundary conditions are sliding support at the walls. The free surface requires a boundary condition with a stiffness of 10 kN/m² to simulate the pressure change if the water level is changing.
B5 References
[1] Konstantin Meskouris, Baudynamik: Modelle Methoden Praxisbeispiele, Ernst & Sohn, 1999, 3433013268.
[2] O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, Finite Element Methods Vol. 1: Basis & Fundamentals, Elsevier, 2000, 6th edition , 0 7506 6320 0.
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