The objective of this study was the development of a procedure in GT STRUDL to design reinforced concrete flat plate systems based on the results of finite element analysis. The current state-of-practice of reinforced concrete flat plate design was reviewed, including the ACI direct design and equivalent frame techniques, the yield line method, and the strip design method. The principles of these methods along with a critical evaluation of their applicability and limitations were presented as motivation for a finite element based design procedure. Additionally, the current state-of-the-art of flat plate design based on finite element results was presented, along with various flat plate modeling techniques. Design methodologies studied included the Wood and Armer approach, based on element stress resultants, and the resultant force approach, based on element forces. A flat plate design procedure based on the element force approach was embodied in the DESIGN SLAB command, which was implemented in GT STRUDL. The DESIGN SLAB command provides the user the ability to design a slab section by specifying a cut definition and several optional design parameters. The procedure determines all nodes and elements along the cut, computes the resultant moment design envelope acting on the cross-section, and designs the slab for flexure in accordance with provisions of ACI 318-02. Design examples presented include single-panel flat plate systems with various support conditions as well as multi-panel systems with regular and irregular column spacing. These examples allowed for critical comparison with results from experimental studies and currently applied design methods in order to determine the applicability of the implemented procedure. The DESIGN SLAB command was shown to produce design moments in agreement with experimental data as well as conventional design techniques for regular configurations. The examples additionally showed that when cuts were not oriented orthogonally to the directions of principle bending, resulting designs based on element forces could significantly under-reinforce the cross-section due to significant torsional effects.

It is well documented that the mechanical response of polycrystalline metals depends on the metal's microstructure, for example the dependence of yield strength on grain size (Hall-Petch effect). Local continuum approaches do not address the sensitivity of deformation to microstructural features, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. In this work, a crystal plasticity model is developed that predicts a dependence of yield strength on grain size without grain size explicitly entering into the constitutive equations. The grain size dependence in the model is the result of non-local effects of geometrically necessary dislocations (GNDs), i.e. GNDs harden both the material at a point and the surrounding material. The conventional FeFp kinematics for single crystals have been augmented based on a geometric argument that accounts for the grain orientations in a polycrystal. The augmented kinematics allows an initial GND state at grain boundaries and an evolving GND state due to sub-grain formation within the grain to be determined in a consistent manner. Numerically, these non-local affects are captured using a non-local integral approach rather than a conventional gradient approach. The non-local crystal plasticity model is used to simulate the tensile behavior in copper polycrystals with grain sizes ranging from 14 to 244 micron. The simulation results show a grain size dependence on the polycrystal's yield strength, which are qualitatively in good agreement with the experimental data. However, the Hall-Petch exponent predicted by the simulations is more like d-1 rather than d-0.5. The effects of different simulation parameters including grain shape and misorientation distribution did not greatly affect the Hall-Petch exponent. The simulation results indicate that the Hall-Petch exponent is sensitive to the grain boundary strength: the Hall-Petch exponent decreases as grain boundary strength decreases. The intragrain misorientations predicted by the non-local model were compared with experiments on polycrystalline nickel. Experimentally, the intragrain misorientations were tracked by electron back scatter diffraction (EBSD) at various strain levels from the same location. On average, the simulation results predicted enough misorientation throughout the sample. However, the model did not correctly predict the spatial details of the intragrain misorientation.

Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand for water that stresses existing water resources. Coastal aquifers provide a source of water for coastal populations and are generally part of a larger system where freshwater aquifers are hydraulically connected with a saline surface-water body. They are characterized by salinity variations in space and time, sharp freshwater/saltwater interfaces which can lead to dramatic density differences, and complex groundwater chemistry. Mismanagement of coastal aquifers can lead to saltwater intrusion, the displacement of fresh water by saline water in the freshwater regions of the aquifers, making them unusable as a freshwater source. Saltwater intrusion is of significant interest to water resource managers and efficient simulators are needed to assist them. Numerical simulation of saltwater intrusion requires solving a system of flow and transport equations coupled through a density equation of state. The scale of the problem domain, irregular geometry and heterogeneity can require significant computational resources. Also, modeling sharp transition zones and accurate flow velocities pose numerical challenges. Discontinuous Galerkin (DG) finite element methods (FEM) have been shown to be well suited for modeling flow and transport in porous media but a fully coupled DG formulation has not been applied to the variable density flow and transport model. DG methods have many desirable characteristics in the areas of numerical stability, mesh and polynomial approximation adaptivity and the use of non-conforming meshes. These properties are especially desirable when working with complex geometries over large scales and when coupling multi-physics models (e.g. surface water and groundwater flow models). In this dissertation, we investigate a new combined local discontinuous Galerkin (LDG) and non-symmetric, interior penalty Galerkin (NIPG) formulation for the non-linear coupled flow and solute transport equations that model saltwater intrusion. Our main goal is the formulation and numerical implementation of a robust, efficient, tightly-coupled combined LDG/NIPG formulation within the Department of Defense (DoD) Proteus Computational Mechanics Toolkit modeling framework. We conduct an extensive and systematic code and model verification (using established benchmark problems and proven convergence rates) and model validation (using experimental data) to verify accomplishment of this goal. Lastly, we analyze the accuracy and conservation properties of the numerical model. More specifically, we derive an a priori error estimate for the coupled system and conduct a flow/transport model compatibility analysis to prove conservation properties. / text

This work focuses on the development of a reliable numerical model for investigating the bone-conduction of sound in the human head. The main challenge of the problem is the lack of fundamental knowledge regarding the transmission of acoustic energy through non-airborne pathways to the cochlea. I employed a fully coupled model based on the acoustic/elastic interaction problem with a detailed resolution of the cochlea region and its interface with the skull and the air pathways. The problem was simulated via hp-finite element approximation, employing a hybrid mesh (tetrahedral, prismatic and pyramidal elements) to better capture the geometrical features of the head. The numerical results thus obtained provide an insight into this fundamental, long standing research problem. / text

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Grinding is a commonly used finishing process to produce components of desired shape, size and dimensional accuracy. The ultimate goal is to have the maximum workpiece quality, minimum machining time and high economic efficiency by making a selective adaptation of the possible process strategy and chosen parameter selection. The focus of this study arose from a limitation that challenges the grinding industry. The production rate of the ground parts is generally constrained by surface topography and subsurface damage appearing as residual tensile stress, localized burns, and phase transformation induced micro and macro-cracking. This motivates the need for a reliable numerical modelling to simulate the grinding process. The numerical model sought should be able to predict not only the required grinding residual stresses but also the deformation history. The objective of this thesis is to build up a reliable finite element model for grinding-induced residual stress analysis and thus to explore thoroughly the mechanisms in terms of grinding conditions. The variations of the residual stresses and strains at integration points have been examined, and the effects of the friction coefficient (µ), Peclet number (Pe), non dimensional heat transfer coefficient (H) and different magnitudes of input heat flux (Q) on both the microstructure and the residual stress state are analyzed. Finally, based on the new findings in this research, a more comprehensive methodology is suggested for further study.

In this graduation thesis it is deduced deformation and tightness of leg’s receiver as well as skin and soft tissues’ at contact place. By using the finite elements method with digital ANSYS 5.5.1 programmable packet it was made leg��s prothesis receiver and stump soft tissues’ model. Two models were analysed: linear and non-linear. By making the non-linear system calculation it is measured non-linear features of leg’s prothesis receiver material and stump skin soft tissues’. Results of analyses showed that the size of maximum deformation is 1,3 less then in case of linear system, maximum stress decreases 1,2 times. Consequently for exact contact calculation it is needed to use non-linear model.

Nonlinear parametric response of a flexible cantilever beam is simulated. In the simulations, lateral response of the beam due to an imposed axial harmonic base displacement excitation is calculated. The response frequency is approximately half the input frequency. The transient simulations include the assumption of damping proportional to the square of the velocity along the beam. Velocity-squared damping is realistic for situations in which fluid forces resisting the structural motion are significant. The commercial finite element software, ANSYS, is used to perform the simulations. A flexible method is developed and implemented in this work, based on the ANSYS Parametric Design Language, for including the quadratic damping assumption in the analysis. Variation of steady state response amplitude is examined for a range of quadratic damping coefficients over a range of axial base excitation frequencies. Further, a definition of phase angle of the response with the respect to the input is proposed for these nonlinear cases in which the input frequency is an integer multiple of the response frequency. The response phase with respect to excitation is studied over a range of damping coefficients and excitation frequencies. In addition, numerical solutions of nonlinear dynamic systems obtained from the implicit finite element method and the explicit dynamics finite element method are compared. The nonlinear dynamic systems considered are a flexible beam subjected to axial base excitation and also lateral excitations. The studies comparing explicit and implicit method results include cases of stress-stiffening and large deflections.

[pt] É apresentado um modelo não-linear para estruturas unidimensionais em equilíbrio, onde não são feitas restrições de caráter geométrico. Este modelo é capaz de descrever movimentos que envolvam flexão, torção, cilhamento e extensão. As configurações de referência e deformada têm sua geometria descrita através da posição espacial de uma curva e da orientação de uma base ortonormal associada a cada ponto dessa curva. O uso dos ângulos de Euler na descrição das rotações, o que pode implicar em instabilidades numéricas, é evitado através do uso de uma nova parametrização para o problema. O problema de equilíbrio que envolve o comportamento não-linear de uma estrutura unidimensional é formulado de diferentes maneiras. São apresentados dois métodos numéricos para a solução desse problema. Um deles é baseado numa decomposição via lagrangeano aumentado e outro é um método de Newton não convencional. São discutidos detalhes acerca da implementação computacional desses métodos. A validade das formulações é atestada através de alguns exemplos numéricos. Em particular. São analisadas algumas aplicações relacionadas com operações de cabos umbilicais em prospecção petrolífera, que envolvem carregamentos estáticos complicados como aqueles ocasionados por flutuadores e pela atração gravitacional. / [en] It is presented a model of the static geometrically non-linear behavior of an elastic rod which considers flexion, torsion, shear and tension. The geometry of the body, in the reference and deformed configurations, is described given the position of the centerline and the geometry of a rigid frame attached to each point of the line. A particular parametrization that avoids the difficulties associated with the use of Euler angles is employed simplifying the numerical treatment. The equilibrium problem for a nonlinear rod is formulated in several different ways and two numerical methods for solution of these problems are presented. One is based on augmented Lagrangian splitting and the second is a non-standard Newton’s method. Details pertaining to the implementation of that method are discussed. A number of numerical simulations have been documented to demonstrate the robustness of the formulations. In particular, some applications in connection with Off shore pipe lines operations, which involves complicated static loading conditions that includes floaters and gravitational forces, are analysed.

[pt] Apresentamos uma formulação de um robô-manipulador como uma viga em rotação engastada num eixo fixo que tem uma parte rígida de comprimento variável e uma parte flexível, com uma carga no extremo livre. O movimento é decomposto em duas partes: um movimento global rígido e outro devido a deformações da viga em torno de uma configuração variável. Para possibilitar futuro controle na estrutura simplificamos o modelo supondo que a parte flexível da viga com respeito a um referencial móvel sofre apenas pequenas deformações. A contribuição principal da tese consiste no desenvolvimento de um código simbólico-numérico. A formulação da dinâmica, a partir do lagrangeano e das forças generalizadas é feita simbolicamente. As equações são discretizadas no espaço pelo método dos elementos finitos e as matrizes de massa, rigidez, amortecimento e as forças generalizadas são construídas simbolicamente por elemento e então montadas, sendo que todo este processo é automático. / [en] The formulation of a manipulator robot is presented as a rotating beam which is clamped in a fixed shaft and hás a stiff parto f variable length and a flexible part with na applied load at the free end. The motion is decomposed in two parts: a global rigid motion and another one due to beam deformations around a variable configuration. Looking forward to controlling the structure, the model is simplified with the assumption that the flexible part of beam suffers only small deformations with respect to a moving reference frame. The main contribution of this thesis consists in the development of a symbolic-numerical code. The dynamics formualtion obtained through the Lagrangean and generalized forces in computed symbolically. The equations are written in discrete form in PI2 using the finite element method and the mass steffness, damping and generalized forces matrices are symbolically constructed by element and then assembled, the whole process being automatic.