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.

In this thesis we study efficient parallel iterative solution algorithms for multi-physics problems. In particular, we consider fluid structure interaction (FSI) problems, a type of multi-physics problem in which a fluid and a deformable solid interact. All computations were performed in Oomph-Lib, a finite element library for the simulation of multi-physics problems. In Oomph-Lib, the constituent problems in a multi-physics problem are coupled monolithically, and the resulting system of non-linear equations solved with Newton's method. This requires the solution of sequences of large, sparse linear systems, for which optimal solvers are essential. The linear systems arising from the monolithic discretisation of multi-physics problems are natural candidates for solution with block-preconditioned Krylov subspace methods.We developed a generic framework for the implementation of block preconditioners within Oomph-Lib. Furthermore the framework is parallelised to facilitate the efficient solution of very large problems. This framework enables the reuse of all of Oomph-Lib's existing linear algebra infrastructure and preconditioners (including block preconditioners). We will demonstrate that a wide range of block preconditioners can be seamlessly implemented in this framework, leading to optimal iterative solvers with good parallel scaling.We concentrate on the development of an effective preconditioner for a FSI problem formulated in an arbitrary Lagrangian Eulerian (ALE) framework with pseudo-solid node updates (for the deforming fluid mesh). We begin by considering the pseudo-solid subsidiary problem; the deformation of a solid governed by equations of large displacement elasticity, subject to a prescribed boundary displacement imposed with Lagrange multiplier. We present a robust, optimal, augmented-Lagrangian type preconditioner for the resulting saddle-point linear system and prove analytically tight bounds for the spectrum of the preconditioned operator with respect to the discrete problem size.This pseudo-solid preconditioner is incorporated into a block preconditioner for the full FSI problem. One key feature of the FSI preconditioner is that existing optimal single physics preconditioners (such as the well known Navier-Stokes Least Squares Commutator preconditioner) can be employed to approximately solve the linear systems associated with the constituent sub-problems. We evaluate its performance on selected 2D and 3D problems. The preconditioner is optimal for most problems considered. In cases when sub-optimality is detected, we explain the reasons for such behavior and suggest potential improvements.

Les buts principaux recherchés de la présente thèse visent au développement et à l’expertise d’une méthodologie de simulation numérique des problèmes d’interactions fluides-structures. Afin de cerner progressivement le problème étudié, nous nous sommes intéressés en premier lieu à la simulation numérique des écoulements autour d’obstacles solides, plus particulièrement au phénomène d’éclatements tourbillonnaires dans la zone de sillage d’obstacles de différentes formes. Nous avons utilisé la méthode des éléments finis en adoptant la technique de stabilisation GLS (Galerkin Least-Square). Pour le traitement de la turbulence, nous avons opté pour la méthode LES (Large-Eddy Simulation) en utilisant le filtre de Smagorinsky. En deuxième phase, nous nous sommes intéressés aux écoulements en milieux déformables. Nous avons entrepris la formulation ALE (Arbitrairement Lagrangienne Eulérienne) en considérant un maillage déformable. Pour la mise à jour de la grille du maillage dynamique, nous avons utilisé une approche pseudo-élastique. Afin d’expertiser la méthodologie mise en oeuvre, nous avons choisi d’aborder le problème des ballottements à la surface libre de réservoirs partiellement remplis de liquide. En dernière partie, nous nous sommes intéressés au comportement vibratoire d’un corps solide sous l’effet d’un écoulement de fluide. Par l’utilisation d’un algorithme de couplage totalement implicite basé sur la méthode de Gauss-Seidel par Bloc, nous avons abordé le phénomène des instabilités aéroélastiques des ponts à haubans. Pour la validation du modèle numérique traitant les interactions fluides-structures par les données expérimentales, nous nous sommes intéressés au comportement vibratoire d’une maquette sectionnelle d’un tablier de pont réel sous l’effet d’un vent soufflant uniforme. / The main goals sought by this thesis target the development and expertise of a methodology for numerical simulation of fluid-structure interactions problems. In order to identify the studied problem progressively, we are interested primarily in numerical simulation of flows around bluff bodies, especially the phenomenon of vortex shedding in the wake zone of a bluff body of different shapes. We used the finite element method by adopting the stabilized GLS (Galerkin Least-Square) technique. For the treatment of turbulence, we opted the LES (Large-Eddy Simulation) method using the Smagorinsky filter. In the second phase, we were interested in flows in deformable media. We undertook the ALE (Arbitrary Lagrangian Eulerian) formulation by considering a deformable mesh. To update the grid of the dynamic mesh, we used a pseudo-elastic approach. To appraise the implemented methodology, we decided to approach the problem of sloshing at the free surface of a tank partially filled with liquid. In the final part, we were interested in vibration behavior of a solid body under the effect of fluid flow. By using a fully implicit coupling algorithm based on a relaxed Bloc Gauss-Seidel method, we studied the phenomenon of aeroelastic instability of cable-stayed bridges. To validate the numerical model treating fluid-structure interactions by experimental data, we investigated the vibration behavior of a real deck sectional model under the effect of a uniform wind.

Developing lifelike vocal fold models is challenging due to various associatedbiomechanical complexities. Nevertheless, the development and analysis of improved vocal foldmodels is worthwhile since they are valuable tools for gaining insight into human vocal foldvibratory, aerodynamic, and acoustic response characteristics. This thesis seeks to contribute tothe development of computational and physical vocal fold modeling in two ways. First is byintroducing a method of obtaining internal deformation fields within vibrating synthetic vocal foldmodels; second is by presenting an optimization algorithm coupled with a computational vocalfold model to optimize geometry and stiffness of a synthetic vocal fold model to achieve morerealistic vibration patterns.The method for tracking the internal deformation of self-oscillating vocal fold models isbased on MR imaging. Silicone models scaled to four times life-size to lower the flow-inducedvibration frequency were imbedded with fiducial markers in a coronal plane. Candidate markermaterials were tested using static specimens, and two materials, cupric sulfate and glass, werechosen for testing in the vibrating VF models. The vibrating models were imaged using a gatedMRI protocol wherein MRI acquisition was triggered using the subglottal pressure signal. Twodimensionalimage slices at different phases during self-oscillation were captured, and in eachphase the fiducial markers were clearly visible. The process was also demonstrated using a threedimensionalscan at two phases. The benefit of averaging to increase signal-to-noise ratio wasexplored. The results demonstrate the ability to use MRI to acquire quantitative deformation datathat could be used, for example, to validate computational models of flow-induced VF vibrationand quantify deformation fields encountered by cells in bioreactor studies.A low fidelity, two-dimensional, finite element model of VF flow-induced vibration wascoupled with a custom MATLAB-based genetic algorithm optimizer. The objective was to achievea closed quotient within the normal human physiological range. The results showed that changesin geometry and stiffness would lead to a model that exhibited the desired characteristics. Aphysical model based on optimized parameters was then fabricated and the closed quotient wastested. The physical model successfully vibrated with nonzero closed quotient as predicted by thecomputational model.

This thesis deals with dynamic behavior of swirl turbine vibrating in a liquid. Primarily is studied decrease of natural frequencies of rotor due the interaction with fluid environment, namely for different levels of submerged rotor in fluid. After that follows the detection of natural frequencies of swirl turbine in operating speed. The problem is solved by computational modeling in ANSYS system. For this solution is used acoustic elements method. The results are compared with experiment.

This master thesis is focused on usage of monitoring pulse wave propagation in aortic system in a field of diagnostic abdominal aortic aneurysm (AAA). There is a description of cardio-vascular system and its pathology in a form of AAA. A summarization of temporary diagnostic method was created and some new methods were proposed. This new methods presume monitoring of pulse wave propagation. Fluid structure interaction (FSI) analyses of pulse wave propagation were performed on simplified models of geometry which representing specific sections of aorta. The goal of these analyses was to prove usage of FSI method in a future development of proposed diagnostic methods.

The purpose of this study was to develop a robust fluid-structure-interaction (FSI) technology that can accurately model non-linear flutter responses for sub- and transonic fluid flow. The Euler equation set governs the fluid domain, which was spatially discretised by a vertex-centred edge-based finite volume method. A dual-timestepping method was employed for the purpose of temporal discretisation. Three upwind schemes were compared in terms of accuracy, efficiency and robustness, viz. Roe, HLLC (Harten-Lax-Van Leer with contact) and AUSM+-up Advection Up-stream Splitting Method). For this purpose, a second order unstructured MUSCL (Monotonic Upstream-centred Scheme for Conservation Laws) scheme, with van Albada limiter, was employed. The non-linear solid domain was resolved by a quadratic modal reduced order model (ROM), which was compared to a semi-analytical and linear modal ROM. The ROM equations were solved by a fourth order Runge-Kutta method. The fluid and solid were strongly coupled in a partitioned fashion with the information being passed at solver sub-iteration level. The developed FSI technology was verified and validated by applying it to test cases found in literature. It was demonstrated that accurate results may be obtained, with the HLLC upwind scheme offering the best balance between accuracy and robustness. Further, the quadratic ROM offered significantly improved accuracy when compared to the linear method. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

We have developed a third-order shear and normal deformable plate/shell theory (TSNDT) incorporating all geometric nonlinearities and used it to analyze, by the finite element method (FEM), transient finite deformations of a sandwich beam with two face sheets and the core made of St. Venant-Kirchhoff materials.  A triangular cohesive zone model with stress based criterion for delamination initiation and energy based relation for complete separation is used to analyze delamination failure in a beam under mixed-mode loading. We have studied transient post-buckling deformations and delamination progression in an axially compressed and initially delaminated clamped-clamped sandwich beam.  The buckling load for transient deformations exceeds that for static deformations and the increase depends upon the loading rate.  This FE software for analyzing deformations of sandwich beam is coupled with that based on the boundary element method (BEM) for studying time-dependent deformations of water and the coupled software is used to analyze deformations of flexible curved hulls due to water slamming loads.  The water is assumed to be inviscid and incompressible and undergo irrotational deformations.  The Laplace equation for the velocity potential is numerically solved by the BEM with normal velocity and pressure assumed to be continuous across the interface between the hull and the water.  Challenging issues resolved in this work include finding the wetted surface of the hull, nonlinear deformations of the fluid due to convective part of acceleration, effects of geometric nonlinearities on hull\'s deformations, resolution of the jet tip, as well as the initiation and propagation of delamination between the face sheets and the core.  It is found that both delamination and geometric nonlinearities significantly affect the hydrodynamic pressure acting on the hull, and transverse shear deformations contribute more to the strain energy absorbed by the core than its transverse normal deformations.  <br />We have used the discontinuous basis functions to derive the Galerkin formulation of a nonlinear problem involving simple shearing deformations of a homogeneous and isotropic thermo-elasto-visco-plastic body with uniform deformations perturbed to simulate the effect of a defect.  The resulting coupled nonlinear ordinary differential equations are integrated with respect to time by using the package, LSODE (Livermore Solver for Ordinary Differential Equations).  Computed results showing localization of deformations into narrow regions are found to agree well with those found by the FEM, and spatial variations of the shear stress are smoother than those obtained by the FEM.<br /><br /> / Ph. D.

Interaction of fluctuating vortex shedding with blade vibration can lead to a new class of aeromechanical instability referred as Non-synchronous vibrations. Investigating a well-known case that shows similar NSV features such as a circular cylinder can develop the understanding of physics behind NSV. A common approach to further investigating the vortex induced vibration is to control the motion of the cylinder and allowing the response of the wake to the motion to be studied in isolation. It has been found very important to carefully match the experimental conditions between free and controlled vibration. Many of research in the field of vortex induced vibration apply a rigid cylinder mounted horizontally and moving transversely to the flow stream as a paradigm for understanding the physics behind this phenomenon. Regarding the difficulties of implementation of vertically moving cylinder in experimental study, vortex dynamic and lock-in behavior of eccentrically rotating cylinder is studied in this M.Sc. Thesis. The main focus of this research is to understand to what extend a general feature of free vortex-induced vibration can be observed in the case of eccentrically rotating cylinder. If the present case captures the essential characteristics of freely oscillating cylinder the results of the forced motion via eccentrically rotating cylinder can be applied to predict the motion of an elastically mounted body. To do so a CFD model is established to predict the response, vorticity structure in near wake, timing of vortex shedding and the range of lock-in region over specific parameter space of the introduced alternative case. A commercial CFD code, Ansys/CFX, was implemented to perform this numerical study. Existences of synchronization region, striking similarity in lift force coefficient and wake mode have been observed in the current study.

The presented research investigates the effects of shock wave boundary layer interaction on the unsteady pressure response of the surface of an oscillating structure. A simplified structure, a 2D prismatic bump, located in a straight channel is used to better understand the bending flutter phenomenon. Time-resolved measurements of the unsteady surface pressures and the instantaneous model geometry measurements are performed in order to study the effect of the shock wave on the aerodynamic load acting over the flexible generic bump. The bump is oscillated in a controlled manner with amplitude of ±0.5mm for four reduced frequencies ranging from k=0.123 to k=0.492. The experiments are performed for a transonic flow operating point characterized by an inlet Mach number of 0.69 and a total inlet pressure of 160 kPa, with an outlet Mach number and outlet static pressure of 0.79 and 106 kPa, respectively. The unsteady pressure measurements were performed using recessed mounted pressure transducers with Kulite fast response sensors. The presented results demonstrate that the shock wave induces a strong amplification of the unsteady pressure at the foot of the shock. This amplification was shown to decrease with the increase in reduced frequency, specifically between k=0.123 and k=0.246.