Fluid-Structure Interaction with Application to Structural Vibration and Blood Flow in Arteries
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The problem of interaction between fluids and structures is of practical significance in many fields of engineering. This interaction has to be taken into account in analyzing floating objects, ship sloshing, fluid containers subject to earthquake, flutter of airplane wings, suspended bridge subject to wind, submerged structures such as submarines, dam-reservoir systems, and blood flow through arteries. Such problems are known as the fluid-structure interaction (FSI) problems, where a structural domain interacts with an internal or surrounding fluid. A comprehensive study of these problems still remains a challenging task because of the coupling between the two domains and the existence of strong nonlinearity. For most FSI problems, constructing a complete mathematical model is the most difficult part because of different descriptions of motions used for fluids and solids. Most studies involving FSI embrace many simplifying assumptions to make the problem tractable. In this dissertation, finite element formulations are presented to study two types of representative FSI problems. First, we investigate the effect of the fluid region on the free vibration of beam and plate structures; in particular, natural frequencies and mode shapes of the beams and plates when they are surrounded by a fluid medium are determined. In these problems, we assume that the strains and rotations are considered to be infinitesimally small. Finite element models are constructed for both structural and fluid domains. To connect these two regions, the solid-fluid interface conditions, using the concept of an added mass, are used to construct a finite element model of the problems. Then, we focus on the transient response of plates in the presence of a fluid medium, wherein we consider the geometric nonlinearity with small strains and moderate rotations. Second, we study the effect of arterial walls on the blood flow through large arteries. Although we make several assumptions to simplify the development and formulate the finite element model, we obtain a reasonable amount of useful knowledge from this exercise. The problem is nonlinear due to the Navier-Stokes equations governing the fluid domain, even without considering the geometric nonlinearity of the arterial wall. The existence of first derivatives of primary variables, such as volume flow rate, cross-sectional area and pressure, in the obtained system of differential equations allows us to take the advantage of least-squares formulation to construct a corresponding finite element model.
Blood flow through arteries
Soltani, Helnaz (2016). Fluid-Structure Interaction with Application to Structural Vibration and Blood Flow in Arteries. Doctoral dissertation, Texas A & M University. Available electronically from