The sloshing analysis of liquid storage tanks by the finite element method is basically categorized into two approaches, Lagrangian approach and Eulerian approach. In the Lagragian approach, the behavior of the fluid is expressed in terms of the displacements at nodal points. The advantage of the Lagragian method is that the computer code can be easily developed to modify an existing structural analysis code. The disadvantage is that some spurious modes are included in the vibration modes. The Lagrangian method is widely used in two- and three-dimensional problems. On the other hand, it has not been reported its applicability to the axisymmetric problem. This paper presents the applicability of the Lagragian method to the axisymmetric sloshing problem. The eigenvalue of an elemental stiffness matrix is analyzed in order to investigate the characteristics of the rotational stiffness to the compressibility of the fluid. As a result, this method is found to be difficult to apply to the axisymmetric problem if the equation of motion is directly solved using time integration. However, it gives the highly precise response solutions if the only sloshing modes are taken out and the modal analysis technique is used.
Lagrangian Finite Element Formulation to Axisymmetric Liquid Sloshing
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Yoshida, S, Sekine, K, Tsuchida, T, & Iwata, K. "Lagrangian Finite Element Formulation to Axisymmetric Liquid Sloshing." Proceedings of the ASME 2011 Pressure Vessels and Piping Conference. Volume 4: Fluid-Structure Interaction. Baltimore, Maryland, USA. July 17–21, 2011. pp. 391-398. ASME. https://doi.org/10.1115/PVP2011-57450
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