Complex oscillations including chaotic motions have been identified in off-shore and submerged mooring systems characterized by nonlinear fluid-structure interactions and restoring forces. In this paper, a means of controlling these nonlinear oscillations is addressed. When applied, the controller is able to drive the system to periodic oscillations of arbitrary periodicity. The controller applies a perturbation to the nonlinear system at prescribed time intervals to guide a trajectory towards a stable, periodic oscillatory state. The controller utilizes the pole placement method, a state feedback rule designed to render the system asymptotically stable. An outline of the proposed method is presented and applied to the fluid-structure interaction system and several examples of the controlled system are given. The effects of random noise in the excitation force are also investigated and the subsequent influence on the controller identified. A means of extending the controller design is explored to provide adequate control in the presence of moderate noise levels. Meanwhile, in the presence of over powering noise or system measurements that are not well defined, certain filtering and estimation techniques are investigated for their applicability. In particular, the Iterated Kalman Filter is investigated as a nonlinear state estimator of the nonlinear oscillations in these off-shore compliant structures. It is seen that although the inclusion of the nonlinearities is theoretically problematic, in practice, by applying the estimator in a judicious manner and then implementing the linear controllers outlined above, the system is able to estimate and control the nonlinear systems over a wide area of pseudo-stochastic regimes. / Graduation date: 2006

The heart is a complex organ and much is still unknown about its mechanical function. In order to use simulations to study heart mechanics, fluid and solid components and their interaction should be incorporated into any numerical model. Many previous studies have focused on myocardium motion or blood flow separately, while neglecting their interaction. Previous fluid-structure interaction (FSI) simulations of heart mechanics have made simplifying assumptions about their solid models, which prevented them from accurately predicting the stress-stain behaviour of the myocardium. In this work, a numerical model of the canine left ventricle (LV) is presented, which serves to address the limitations of previous studies. A canine LV myocardium material model was developed for use in conjunction with a commercial finite element code. The material model was modified from its original form to make it suitable for use in simulations. Further, numerical constraints were imposed when calculating the material parameter values, to ensure that the model would be strictly convex. An initial geometry and non-zero stress state are required to start cardiac cycle simulations. These were generated by the static inflation of a passive LV model to an end-diastolic pressure. Comparisons with previous measurements verified that the calculated geometry was representative of end diastole. Stresses calculated at the specified end diastolic pressure showed complex spatial variations, illustrating the superiority of the present approach over a specification of an arbitrary stress distribution to an end-diastolic geometry. In the third part of this study, FSI simulations of the mechanics of the LV were performed over the cardiac cycle. Calculated LV cavity pressures agreed well with previous measurements during most of the cardiac cycle, but deviated from them during rapid filling, which resulted in non-physiological backflow. This study is the first one to present a detailed analysis of the temporal and spatial variations of the properties of both the solid and the fluid components of the canine LV. The observed development of non-uniform pressure distributions in the LV cavity confirms the advantage of performing FSI simulations rather than imposing a uniform fluid pressure on the inner surface of the myocardium during solid-only simulations.

The heart is a complex organ and much is still unknown about its mechanical function. In order to use simulations to study heart mechanics, fluid and solid components and their interaction should be incorporated into any numerical model. Many previous studies have focused on myocardium motion or blood flow separately, while neglecting their interaction. Previous fluid-structure interaction (FSI) simulations of heart mechanics have made simplifying assumptions about their solid models, which prevented them from accurately predicting the stress-stain behaviour of the myocardium. In this work, a numerical model of the canine left ventricle (LV) is presented, which serves to address the limitations of previous studies. A canine LV myocardium material model was developed for use in conjunction with a commercial finite element code. The material model was modified from its original form to make it suitable for use in simulations. Further, numerical constraints were imposed when calculating the material parameter values, to ensure that the model would be strictly convex. An initial geometry and non-zero stress state are required to start cardiac cycle simulations. These were generated by the static inflation of a passive LV model to an end-diastolic pressure. Comparisons with previous measurements verified that the calculated geometry was representative of end diastole. Stresses calculated at the specified end diastolic pressure showed complex spatial variations, illustrating the superiority of the present approach over a specification of an arbitrary stress distribution to an end-diastolic geometry. In the third part of this study, FSI simulations of the mechanics of the LV were performed over the cardiac cycle. Calculated LV cavity pressures agreed well with previous measurements during most of the cardiac cycle, but deviated from them during rapid filling, which resulted in non-physiological backflow. This study is the first one to present a detailed analysis of the temporal and spatial variations of the properties of both the solid and the fluid components of the canine LV. The observed development of non-uniform pressure distributions in the LV cavity confirms the advantage of performing FSI simulations rather than imposing a uniform fluid pressure on the inner surface of the myocardium during solid-only simulations.

As explosive blasts continue to cause casualties in both civil and military environments, there is a need for increased understanding of the mechanisms of blast trauma at the organ level and a need for a more detailed predictive methodology. A fundamental understanding of blast injury will lead to the development of improved protective equipment and ultimately reduce the severity of injury. Models capable of predicting injury to varied blast loading will also reduce the emphasis on animal blast testing. To provide some historical context, this research was begun shortly after the U.S. led invasion of Iraq, and came to a close while there continues to be daily loss of life from blast injuries in the Middle East, as well as continued threats of terrorism throughout the world. In addition to industrial accidents, it is clear that blast injury is far more than just a military concern. Simplified finite element models of the human and sheep thoraces were created in order to provide practical and flexible models for the prediction of primary blast injury in simple and complex blast environments, and subsequently for the development of improved protective equipment. The models were created based on actual human and sheep geometries and published material properties. The fluid-structure interaction of the models compared well with experimental blast studies carried out during the course of the research, as shown by comparing actual and predicted overpressures in the free field and at the thorax. By comparing the models to published experimental data from simple blasts, trends in the results were verified and peak lung pressure was proposed as a trauma criterion. Local extent of injury in the lung is correlated to the peak pressure measured in each finite element, categorized as no injury (< 60 kPa), trace (60-100 kPa), slight (100-140 kPa), moderate (140-240 kPa) and severe (> 240 kPa). The calculation of the mean value of the peak lung pressures of all of the finite elements allows for an overall estimate of the injury level, with 35 kPa predicting threshold damage, 129 kPa for one percent lethality, and 186 kPa for fifty percent lethality. The simple blast results also compared well to the predictions of two previously validated mathematical models. Variation of predicted injury within a given loading severity was 15%, which is comparable to the model by Stuhmiller that had a variation of 20%. The model by Axelsson had very little variation (1.4%), but the differences between levels of severity were quite small, and often difficult to decipher. In addition to predicting consistent levels of injury, the finite element models were able to provide insight into the trauma mechanism, map the extent of injury through the lungs, and validate a local injury criterion. The models were then applied to predict injury under complex blast loading by subjecting the human finite element torso to a threshold level blast while located at varying distances from a wall or a corner. The results compared well to the validated mathematical models, showing a sharp increase in injury severity as the model approached the reflecting surface. When directly against the wall, the mean of the peak lung pressure values was 57 kPa, and in the corner, the mean value reached 69 kPa. Although these values did not reach the level representing one percent lethality, they do represent a significant increase in injury above threshold as a direct result of the surrounding geometry. Once again, the finite element models correctly showed injury trends and lung injury patterns reported in experiments. The models predicted the level of injury and were able to predict the time varying pattern of injury, which is something existing models cannot do. Having designed the models from physical principals, and having validated the models against published results, they can now be used in the continued development of protective equipment. Acknowledging that this model was the first iteration, the author believes that improvements in material properties, mesh refinement, and the investigation of other possible parameters for the prediction of injury will lead to substantial advances in the understanding of primary blast injury.

To increase aerodynamic performance, the geometric porosity of a ringsail spacecraft parachute canopy is sometimes increased, beyond the "rings" and "sails" with hundreds of "ring gaps" and "sail slits." This creates extra computational challenges for fluid--structure interaction (FSI) modeling of clusters of such parachutes, beyond those created by the lightness of the canopy structure, geometric complexities of hundreds of gaps and slits, and the contact between the parachutes of the cluster. In FSI computation of parachutes with such "modified geometric porosity," the flow through the "windows" created by the removal of the panels and the wider gaps created by the removal of the sails cannot be accurately modeled with the Homogenized Modeling of Geometric Porosity (HMGP), which was introduced to deal with the hundreds of gaps and slits. The flow needs to be actually resolved. All these computational challenges need to be addressed simultaneously in FSI modeling of clusters of spacecraft parachutes with modified geometric porosity. The core numerical technology is the Stabilized Space--Time FSI (SSTFSI) technique, and the contact between the parachutes is handled with the Surface-Edge-Node Contact Tracking (SENCT) technique. In the computations reported here, in addition to the SSTFSI and SENCT techniques and HMGP, we use the special techniques we have developed for removing the numerical spinning component of the parachute motion and for restoring the mesh integrity without a remesh. We present results for 2- and 3-parachute clusters with two different payload models. We also present the FSI computations we carried out for a single, subscale modified-porosity parachute.

As explosive blasts continue to cause casualties in both civil and military environments, there is a need for increased understanding of the mechanisms of blast trauma at the organ level and a need for a more detailed predictive methodology. A fundamental understanding of blast injury will lead to the development of improved protective equipment and ultimately reduce the severity of injury. Models capable of predicting injury to varied blast loading will also reduce the emphasis on animal blast testing. To provide some historical context, this research was begun shortly after the U.S. led invasion of Iraq, and came to a close while there continues to be daily loss of life from blast injuries in the Middle East, as well as continued threats of terrorism throughout the world. In addition to industrial accidents, it is clear that blast injury is far more than just a military concern. Simplified finite element models of the human and sheep thoraces were created in order to provide practical and flexible models for the prediction of primary blast injury in simple and complex blast environments, and subsequently for the development of improved protective equipment. The models were created based on actual human and sheep geometries and published material properties. The fluid-structure interaction of the models compared well with experimental blast studies carried out during the course of the research, as shown by comparing actual and predicted overpressures in the free field and at the thorax. By comparing the models to published experimental data from simple blasts, trends in the results were verified and peak lung pressure was proposed as a trauma criterion. Local extent of injury in the lung is correlated to the peak pressure measured in each finite element, categorized as no injury (< 60 kPa), trace (60-100 kPa), slight (100-140 kPa), moderate (140-240 kPa) and severe (> 240 kPa). The calculation of the mean value of the peak lung pressures of all of the finite elements allows for an overall estimate of the injury level, with 35 kPa predicting threshold damage, 129 kPa for one percent lethality, and 186 kPa for fifty percent lethality. The simple blast results also compared well to the predictions of two previously validated mathematical models. Variation of predicted injury within a given loading severity was 15%, which is comparable to the model by Stuhmiller that had a variation of 20%. The model by Axelsson had very little variation (1.4%), but the differences between levels of severity were quite small, and often difficult to decipher. In addition to predicting consistent levels of injury, the finite element models were able to provide insight into the trauma mechanism, map the extent of injury through the lungs, and validate a local injury criterion. The models were then applied to predict injury under complex blast loading by subjecting the human finite element torso to a threshold level blast while located at varying distances from a wall or a corner. The results compared well to the validated mathematical models, showing a sharp increase in injury severity as the model approached the reflecting surface. When directly against the wall, the mean of the peak lung pressure values was 57 kPa, and in the corner, the mean value reached 69 kPa. Although these values did not reach the level representing one percent lethality, they do represent a significant increase in injury above threshold as a direct result of the surrounding geometry. Once again, the finite element models correctly showed injury trends and lung injury patterns reported in experiments. The models predicted the level of injury and were able to predict the time varying pattern of injury, which is something existing models cannot do. Having designed the models from physical principals, and having validated the models against published results, they can now be used in the continued development of protective equipment. Acknowledging that this model was the first iteration, the author believes that improvements in material properties, mesh refinement, and the investigation of other possible parameters for the prediction of injury will lead to substantial advances in the understanding of primary blast injury.

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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