Laminated composite plates have become an important and proven structural material in aerospace and ocean vehicles. However, because of the inherent orthotropy of laminated composite materials the analysis of these structures is complex and usually cannot be adequately performed using classical methods. In this dissertation the formulation of the fully coupled fluid-structure interaction of a laminated composite plate and its surrounding fluid medium is presented. The solution technique involves the finite element method for modeling the structural response and the boundary element method for modeling the acoustic field. The model incorporates the Mindlin plate theory which includes five degrees of freedom. An improved integration technique is demonstrated which significantly reduces the approximation error. Storage requirements are reduced by grouping complex numbers. Finally the fully coupled fluid-structure interaction involving laminated composite plates is modeled using the combined FEM-BEM approach demonstrating the usefulness and the significance of the method. / Ph. D.

Nonlinear free-surface flows generated by the motion of a surface-piercing body in an ideal fluid are studied. A numerical scheme employing a mixed Eulerian-Lagrangian approach and involving time stepping is used to simulate the flow. At each time step, the boundary value problem is solved using the Complex Boundary Element Method. The numerical performance of the method is studied by considering cases where the exact solution is known. Computational results for the impulsive wavemaker problem and the wedge entry problem for wedges of half-angles up to 15 degrees are presented. The obtained results are found to be in good agreement with existing analytical and numerical solutions. / Master of Science

A variation of the boundary element method is developed to determine the distribution of frictional heat and the ensuing surface or subsurface temperature rise caused by frictional heating between sliding solids. The theoretical model consists of two semi-infinite substrates each coated with a film of arbitrary thickness and thermal properties. A three dimensional transient analysis is developed which involves the thermal coupling of the two sliding solids at the true contact areas. The boundary element solution is based on a moving Green's function which naturally incorporates the combined conduction and convection effects due to sliding. Results are presented to display some of the important numerical characteristics of the boundary element solution method. Results are also presented that show the sensitivity of surface temperature rise to contact area evolvement, geometry and subdivision. The effects of surface film thickness and thermal properties on surface temperature rise are presented for a range of Peelet numbers. Lastly, a comparison of theoretical predictions and experimental measurements for surface temperature rise of a graphite epoxy ball loaded against a rotating sapphire disk is presented. / Master of Science

Numerical methods and specifically the finite element method have improved significantly since their introduction in the 60's. These advances were mainly in: 1) introducing higher-order elements, 2) developing effective solution schemes, 3) developing sophisticated means of modeling the constitutive behavior of geotechnical materials, and 4) introducing iteration techniques to model material non-linearity. This thesis, on the other hand, deals with the topic of modeling the boundary conditions of the finite element problem. Typically, the boundary conditions will be approximated by specifying displacement constraints. such as restraining the bottom boundary of the finite element mesh against displacements in the horizontal and vertical directions (x- and y-directions). Where bedrock or dense residual soils underlie the soft foundation soil at a relatively shallow depth, this is a good assumption. However. when soft soil is encountered for large depths, the assumption of zero movement constraints for a mesh boundary at a shallower depth than the actual bedrock will result in a serious underestimation of stresses and displacements. By coupling boundary elements to the finite elements and using them to model the infinite extent of the foundation soil, a more realistic answer is obtained. Employing the coupled boundary element - finite element method, four cases were analyzed and the results compared to values of the pure finite element method. The results show that the coupled method indeed yielded higher stress- and displacement-values, indicating that the pure finite element method underestimates stresses and displacements when modeling very deep soils. / Master of Science

In this thesis the impact of inverted cones on a liquid surface is studied. It is known that with the right combination of velocity, geometry, and surface treatment, a cavity of air can be formed behind an impacting body and extended for a considerable distance. Other investigators have shown that the time and depth of the cone when this cavity collapses and seals follows a different power law for flat objects such as disks, then it does for slender objects such as cylinders. Intuitively it can be expected that a more slender body will have less drag and that the streamlined shape will not push the fluid out of it's way at impact to the same extent as a more blunt body, therefore forming a smaller cavity behind it. With a smaller initial cavity, the time and depth of it's eventual collapse can be expected to be less than that of a much more blunt object, such as a flat disk. To study this, a numerical model has been developed to simulate cones with the same base radius but different angles impacting on a liquid surface over a range of velocities, showing how the seal depth, time at cavity seal, and drag forces change. In order to ensure the numerical model is accurate, it is compared with experimental data including high speed video and measurements made of the force with time. It is expected that the results will fall inside the power law exponents reported by other authors for very blunt objects such as disks on one end of the spectrum, and long slender cylinders on the other. Furthermore, we expect that the drag force exerted on the cones will become lower as the L/D of the cone is increased. / Master of Science

Knowledge of the indoor propagation of sound has many important applications including acoustic prediction in homes, office buildings, stores, and schools, and the design of concert halls, auditoriums, classrooms, and factories. At low frequencies, interior acoustics are analyzed with the wave equation, but significant computational expense imposes an upper frequency limit. Thus, energy methods are often sought for high frequency analysis. However, conventional energy methods are significantly limited by vast simplifications or computational costs. Therefore, new improvements are still being sought. The basis of this dissertation is a recently developed mathematical model for interior acoustics known as the acoustic diffusion model. The model extends statistical methods in high frequency acoustics to predict the spatial distribution of acoustic energy in the volume over time as a diffusion process. Previously, solutions to the acoustic diffusion model have been limited to one dimensional (1-D) analytical solutions and to the use of the finite element method (FEM). This dissertation focuses on a new, efficient method for solving the acoustic diffusion model based on a boundary element method (BEM) solution using the Laplace transform. First, a Laplace domain solution to the diffusion model is obtained using the BEM. Then, a numerical inverse Laplace transform is used to efficiently compute the time domain response. The diffusion boundary element-Laplace transform solution (BE-LTS) is validated through comparisons with Sabine theory, ray tracing, and a diffusion FEM solution. All methods demonstrate excellent agreement for three increasingly complex acoustic volumes and the computational efficiency of the BE-LTS is exposed. Structural coupling is then incorporated in the diffusion BE-LTS using two methods. First, a simple transmission coefficient separating two acoustic volumes is implemented. Second, a structural power flow model represents the coupling partition separating acoustic volumes. The validation of these methods is successfully performed in an example through comparisons with statistical theory, a diffusion FEM solution, ray tracing, and experimental data. Finally, the diffusion model and the BE-LTS are shown to possess capabilities beyond that of room acoustics. The acoustic transmission through a heat exchanger, acoustic foam, and mufflers is successfully modeled using the diffusion BE-LTS and compared to experimental data. / Ph. D.

Soil-structure interaction problems involve the solution of boundary value problems consisting of two domains: A near field finite domain representing the structure and adjacent soil, and a semi-infinite far-field domain representing the soil distant from the structure. Currently, the most used numerical method for solving such problems, the finite element method, considers only the near field, and neglects the effects of the far field. Depending on the domain size considered, this results in significant errors in the computed displacements and stress compared to closed form solutions. This research develops a numerical method in which both the near and far-field are considered. In this numerical procedure, the far field is assumed to be a homogenous elastic half-plane is modeled using boundary elements based on the Melan fundamental solution. A technique, called the substructure method, for coupling the boundary element method with finite element method is developed. Unlike other coupling techniques, the substructure method preserves the bandedness and symmetry of the system of equations resulting from the finite element method. The substructure method is implemented into a computer for program BEFEC for solving linear elastic and elasto-plastic plane strain problems. The proposed coupling technique is also incorporated into an existing finite element program SOILSTRUCT to perform soil-structure interaction analysis on U-frame lock structures. A series of analyses performed on the elastic strip footing problem indicate that significant errors occur in the predicted displacements and stresses when the effects of the the far field are ignored. These errors are unaffected by the boundary conditions assumed or the type of finite element used. The analyses demonstrated that the displacements and stresses obtained using the coupled BEM-FEM solution agree well with closed form solutions. Results of the soil-structure interaction analyses performed on U-frame lock structures indicates that neglecting the effects of the far field domain results in a significant underprediciton of the vertical displacements. These analyses also showed that there are significant differences in the computed shear stress and lateral pressures when the effects of the far field are considered. Results of the bearing capacity analyses of strip footing on elasto-plastic soils indicate that when the effects of the far field are taken into consideration, initial yield takes place at a higher load level. This in turn results is smaller plastic deformations as compared to the case when the far field is ignored. These analyses also shown that taking into consideration the far field results in significant differences in the computed stresses. These differences are diminished when the effects of self-weight are taken into consideration. The analyses performed on the Rankine earth pressure problem indicate that while the far field does not significantly affect the computed Rankine forces or lateral pressure distribution, much larger wall movements are required to reach both the active or passive States. / Ph. D.

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Au cours de cette thèse, nous avons développé un outil numérique, basé sur une formulation intégrale en éléments de frontière, qui permet une analyse classique du comportement d'une fissure 3D soumise à des sollicitations mécaniques complexes. Cet outil industriel est destiné à être intégré dans un code de calcul à usage industriel. Dans le but d'appréhender l'impact de la microstructure sur le comportement en fissuration fragile, nous nous sommes intéressés aux modèles de comportement non local. Nous avons commencé par adopter le modèle de comportement élastique non local de Eringen, qui permet de décrire plus finement le comportement élastique au voisinage de la fissure en prenant en compte les interactions à longue distance au sein du matériau. Cette modélisation du comportement conduit, contrairement à l'approche classique, à un un champ de contrainte fini sur le front de la fissure et localement maximal en avant du front. Ces résultats montrent qu'il est possible de prévoir la stabilité et la direction de propagation de la fissure à l'aide d'un critère plus simple et plus naturel, basé sur les variations du champ de contrainte au voisinage du front de la fissure. La stratégie numérique adoptée permet de traiter indifféremment des cas de fissure en traction, compression, cisaillement ou sollicitation mixte. L'intérêt de l'approche non-locale étant clairement démontré, nous avons considéré la version améliorée du modèle de Eringen telle que proposée par Polizzotto. Cette modélisation est la plus appropriée pour les milieux finis et requiert une mise en oeuvre numérique particulière. Les bases d'une méthodologie numérique, initiée par R. Kouitat ont été établies. Cette méthode est fondée sur un couplage des éléments de frontière avec une méthode de collocation par points d'équations aux dérivées partielles. Les premiers résultats obtenus dans ce cadre sont très encourageants et montrent qu'il sera effectivement possible de traiter le phénomène irréversible de fissuration de la même façon que les problèmes de plasticité / In this thesis, we have developed a numerical tool, based on a classical boundary elements method, which allows a conventional analysis of a stationary crack in a 3D specimen under complex mechanical loading. In order to assess the impact of the microstructure on the brittle fracture, we were interested in non local models of behavior. First, we have adopted the non local elastic model due to Eringen. This refined constitutive equation allows to account for long range interactions in the description of the elastic behavior in the vicinity of the crack front. Unlike the traditional approach, this type of model leads to a finite stress field at the crack front. Moreover, the stress is locally maximal ahead of the front. These interesting results indicate that it is possible to predict the stability and direction of crack propagation in a simple and more naturel way by using stress based criteria. The implemented numerical strategy can handle cases of crack in tension or compression, under shear stress or mixed loadings. Having clearly highlighted the interest of non local models, we have adopted the improved version of Eringen elastic model as proposed by Polizzotto. This elastic model is applicable to finite domains and requires a specific numerical treatment. The basis of such a numerical strategy initiated by R. Kouitat has been established. The method couples the conventional boundary element method with local point interpolation of a strong form differential equation. Promising results are obtained and show that with such modeling of material behavior, it is possible to describe the irreversible process of fracturing in a similar way as plasticity