Many technologically important problems are coupled in nature. For example, blood flow in deformable arteries, flow past (flexible) tall buildings, coupled deformation-diffusion, degradation, etc. It is, in general, not possible to solve these problems analytically, and one needs to resort to numerical solutions. An important ingredient of a numerical framework for solving these problems is the coupling algorithm, which couples individual solvers of the subsystems that form the coupled system, to obtain the coupled response. A popular coupling algorithm widely employed in numerical simulations of such coupled problems is the conventional staggered scheme (CSS). However, there is no systematic study on the stability characteristics of the CSS. The stability of coupling algorithms is of utmost importance, and assessment of the stability on real problems is not feasible given the computational costs involved. The main aim of this thesis, is to address this issue - assess the accuracy and stability characteristics of CSS using various canonical problems. In this thesis we show that the stability of CSS depends on the relative sizes of the domain, disparity in material properties, and the time step.

The present study aims to explore dynamical behavior of the fluid-elastic instability of a circular cylinder in shear flow by numerical simulations. The theoretical model comprises two groups of transient conservation equations of mass and momentum and the governing equations are solved numerically with an iterative SIMPLEC(Semi-Implicit Method for Pressure-Linked Equations Consistent) algorithm to determine the flow property and to analysis structure stress simultaneously. Additionally, the TFI (Transfinite interpolation) computation procedure is applied to characterize the behavior of fluid-structure interaction. The predictions are in reasonable agreement with literature showing the validity of the present theoretical model. The numerical results indicate that there is a transverse force acting from high velocity side toward the low velocity side in shear flow. The magnitude of this transverse force increases with the shear parameter. The Strouhal number slightly increases as the shear parameter increases for all Reynolds number. As the pattern of the approach flow changes from the uniform to shear flow, the front stagnation point shifts to high velocity side, and the base pressure increase. The magnitude of the shift of front stagnation point is linear with the shear parameter. Furthermore, this study appraises the amplitude and orbit of fluid elastic vibration of a circular cylinder in shear flow, and shows the effects of the spring constant and damping factor on fluid elastic vibration of the cylinder. In addition, various effects including shear parameter and mass ratio on the critical velocity of the fluid elastic vibration also has been examined detail.

Atherosclerosis is a disease of the cardiovascular system where a stenosis may develop in an artery which is an abnormal narrowing in the blood vessel that adversely affects the blood flow. Due to the constriction of the blood vessel, the flow is disturbed, forming a jet and recirculation downstream of the stenosis. Dynamic pressure fluctuations on the inner wall of the blood vessel leads to the vibration of the vessel structure and acoustic energy is propagated through the surrounding tissue that can be detected on the skin surface. Acoustic energy radiating from the interaction of blood flow and stenotic blood vessel carries valuable information from a diagnostic perspective. In this study, a constricted blood flow is modeled by using ADINA finite element analysis software together with the blood vessel in the form of a thin cylindrical shell with an idealized blunt constriction. The flow is considered as incompressible and Newtonian. Water properties at indoor temperature are used for the fluid model. The diameter of the modeled vessel is 6.4 mm with 87% area reduction at the throat of the stenosis. The flow is investigated for Reynolds numbers 1000 and 2000. The problem is handled in three parts which are rigid wall Computational Fluid Dynamics (CFD) solution, structural analysis of fluid filled cylindrical shell, and Fluid Structure Interaction (FSI) solutions of fluid flow and vessel structure. The pressure fluctuations and consequential vessel wall vibrations display broadband spectral content over a range of several hundred Hz with strong fluid-structural coupling. Maximum dynamic pressure and vibration amplitudes are observed around the reattachment point of the flow near the exit of the stenosis and this effect gradually decreases along downstream of flow. Results obtained by the numerical simulations are compared with relevant studies in the literature and it is concluded that ADINA can be used to investigate these types of problems involving high frequency pressure fluctuations of the fluid and the resulting vibratory motion of the surrounding blood vessel structure.

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Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches. These devices typically consist of a metallic membrane which is activated by a time-periodic electrostatic force and makes periodic contact with a contact pad. The increase in switch capacitance at contact causes the RF signal to be deflected and the switch thus closes. Membrane motion is damped by the surrounding gas, typically air or nitrogen. As the switch opens and closes, the flow transitions between the continuum and rarefied regimes. Furthermore, creep is a critical physical mechanism responsible for the failure in these devices, especially those operating at high RF power. Simultaneous and accurate modeling of all these different physics is required to understand the dynamical membrane response in these devices and to estimate device lifetime and to improve MEMS reliability. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this work, we develop a single unified finite volume method based numerical framework to study this multi-physics problem in RF MEMS. Our objective required us to develop structural solvers, fluid flow solvers, and electrostatic solvers using the finite volume method, and efficient mechanisms to couple these different solvers. A particular focus is the development of flow solvers which work efficiently across continuum and rarefied regimes. A number of novel contributions have been made in this process. Structural solvers based on a fully implicit finite volume method have been developed for the first time. Furthermore, strongly implicit fluid flow solvers have also been developed that are valid for both continuum and rarefied flow regimes and which show an order of magnitude speed-up over conventional algorithms on serial platforms. On parallel platforms, the solution techniques developed in this thesis are shown to be significantly more scalable than existing algorithms. The numerical methods developed are used to compute the static and dynamic response of MEMS. Our results indicate that our numerical framework can become a computationally efficient tool to model the dynamics of RF MEMS switches under electrostatic actuation and gas damping. / text

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Large structures exposed to the environment such as the collinear omni and large panel communication antennas in this research suffer damage from cyclic wind, rain, hail, ice load and impacts from birds and stones. Stresses from self-weight, ice loading and wind gusts will produce deformations of the structure that will lead to performance deterioration of the antenna. In order to avoid such a case, it is important to understand the static, dynamic and aerodynamic behavior of these structures and thus optimization can be achieved. In this research the current fluid-structure interaction methods are used to model, simulate and analyze these communication antennas in order to assess whether failure would occur under service loads. The FEA models developed are verified against analytical models and/or experiments. Different antenna configurations are compared based on their capacity to minimize vibration effects, stress-induced deformations and aerodynamic loading effects.

The demand for artificial heart valve replacements is increasing as a result of birth defects, ageing and disease. Collaboration between engineers, biologists and mathematicians is necessary to handle problems related to biocompatibility and fluid dynamics. As a result of the increased demand for artificial heart valves, many new designs have been developed recently. A method to test those designs is to use mathematical modeling. This method has a relatively low-cost and can be used as a preliminary tool before expensive prototypes are created. This research analyzes the use of the numerical modeling software LS-DYNA for large-displacement fluid-structure interaction. It is a preliminary study aimed at the analysis of heart valve dynamics. In particular, a channel with flap model is created in LS-DYNA. The model's physics, convergence and ability to handle large deformations is investigated.

A monolithic approach to aero-structural analysis and optimization has been developed and implemented. In contrast to a partitioned approach which uses individual fluid and structural solvers to solve their respective systems separately, the monolithic approach solves a fully-coupled system simultaneously, enforcing solution compatibility across the sub-system interfaces at each iteration. In this work, a three-field formulation is used, consisting of fluid, structural, and fluid mesh-movement sub-systems. The performance of the monolithic approach is characterized using 1-D unsteady and 2-D steady analysis problems, and compared with a partitioned approach. Four steady model aero-structural optimization problems are also investigated. Gradients of the objective function are computed using the discrete-adjoint and flow-sensitivity (direct) methods. In each case, the monolithic approach is shown to be a promising option for efficient aero-structural analysis and optimization, though the implementation requires additional development of coupling sub-matrices when compared to a partitioned approach.