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Spline-based finite element methods in the simulation of deformable sloshing tanks

The structural design of liquid storage tanks is sufficient for conventional load cases. Nevertheless, extraordinary loads like seismic excitations in combination with minor material defects can lead to a complete failure of the structure.
The challenges of numerical simulation of seismic effects on sloshing fluids in flexible tanks can be summarized as follows: An accurate consideration of the interaction between fluid and surface of the structure is essential; on the structural side, the numerical representation of curved shell structured has to be geometrically exact; and finally, a suitable consideration of the free-surface flow is needed, including its influence on load changes on the structure.
For the solution of the surface-coupled problem in the presented work a staggered approach is applied, successively calling the single-field solvers FEAFA and XNS. The in-house finite element code FEAFA solves the elastodynamic problem. The in-house code XNS is a finite element code based on the Deforming Spatial Domain/Stabilized Space-Time (DSD/SST) method, taking the unsteady character of the problem as well as the deformable computational domain resulting from both the free-surface motion and the deforming structure into account. Expecting minor and homogeneous surface motion, the free-surface flow is evaluated on boundary-conforming meshes with an interface-tracking scheme. The Elastic Mesh Update Method transfers the resulting surface displacements of both structural deformation and free-surface motion to the CFD grid.
The analysis of tank structures is extremely sensitive to the geometrical approximation, especially if shell elements are used. As a possible remedy, spline-based methods, such as the isogeometric analysis, can offer geometrically exact representation. Following this strategy, spline-based methods are integrated into the existing partitioned approach to reduce inaccuracies in the overall analysis. The extensions include modifications not only in the solution strategies for structural and fluid mechanics as well as the free-surface problem, but also in the projection routines.

Author(s):

Stefanie Elgeti    
Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University
Germany

Norbert Hosters    
Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University
Germany

Atanas Stavrev    
Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University
Germany

Marek Behr    
Chair for Computational Analysis of Technical Systems (CATS), RWTH Aachen University
Germany