Keywords: fluid-structure interaction, hybrid element, plates, shells.

Plates and shells constitute important components of complex structures and are of great significance to modern construction engineering, aerospace and aircraft structures, nuclear power plant components, naval structures to name a few. In the most of industrial applications, these structures are in contact with fluid media. The forces generated by violent fluid-structure contacts can be very high; they are stochastic in nature and thus difficult to describe. They do, however, often constitute the design loading for the structure. Hydrodynamic pressure is generated by the vibrating structure, and this pressure will modify the structural deformation, which, in turn, will modify the hydrodynamic pressure that caused them. This is tightly coupled elasto-dynamic problem in which the structure and fluid form a single system. Solution of this type of problems is obviously complex and technically challenging.

This paper outlines the development of a computational model in order to analyze the dynamic responses of coupled fluid-structure systems e.g. the liquid containers, a set of parallel or radial plates. The mathematical model is developed using a hybrid fluid-solid element, which is a combination of the finite element method and Sanders' shell theory. This theory is an extension of that expounded by Lakis and Paidoussis [1,2]. The membrane and bending displacement components are modelled using bilinear polynomials and an exponential function, respectively, which represent a general form of exact solution of the equations of motion.

The mass and stiffness matrices are then determined by exact analytical integration in order to establish the structural dynamic equations. The velocity potential and Bernoulli's equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the structural shape function developed is integrated over the structure-fluid interface to assess the virtual added mass, stiffness and damping due to the fluid. Detailed equations can be found in [3,4] A number of examples is presented in the dynamic analysis of both plate and shell structures in air or subjected to stationary or flowing fluid forces. The effect of various physical and geometrical parameters on the dynamic responses of various structures e.g. 'n' parallel or radial plates, open and closed rectangular reservoirs, and cylindrical shells have been explored in this work. The results are in satisfactorily agreement with those of experiments and other theories.

1

A.A. Lakis, M.P. Paidoussis, "Free vibration of cylindrical shells partially filled with liquid", Journal of Sound and Vibration, 19(1), 1-15, 1971. doi:10.1016/0022-460X(71)90417-2

2

A.A. Lakis, M.P. Paidoussis, "Dynamic analysis of axially non-uniform thin cylindrical shells", Journal of Mechanical Engineering Science, 14(1), 49-71, 1972. doi:10.1243/JMES_JOUR_1972_014_009_02

3

Y. Kerboua, A.A. Lakis, M. Thomas, L. Marcouiller, "Comportement dynamique des plaques rectangulaires submergées", École Polytechnique of Montréal, EPM-RT-2005-05, 2005.

4

Y. Kerboua, A.A. Lakis, M. Thomas, L. Marcouiller, "Critical velocity of potential flow in interaction with a system of plates", École Polytechnique of Montréal, Canada, EPM-RT-2009-05, 2009.

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