We consider the application of high-order spectral/hp finite element technology to the numerical solution of boundary-value problems arising in the fields of fluid and solid mechanics. For many problems in these areas, high-order finite element procedures offer many theoretical and practical computational advantages over the low-order finite element technologies that have come to dominate much of the academic research and commercial software of the last several decades. Most notably, we may avoid various forms of locking which, without suitable stabilization, often plague low-order least-squares finite element models of incompressible viscous fluids as well as weak-form Galerkin finite element models of elastic and inelastic structures. The research documented in this dissertation includes applications of spectral/hp finite element technology to an analysis of the roles played by the linearization and minimization operators in least-squares finite element models of nonlinear boundary value problems, a novel least-squares finite element model of the incompressible Navier-Stokes equations with improved local mass conservation, weak-form Galerkin finite element models of viscoelastic beams and a high-order seven parameter continuum shell element for the numerical simulation of the fully geometrically nonlinear mechanical response of isotropic, laminated composite and functionally graded elastic shell structures. In addition, we also present a simple and efficient sparse global finite element coefficient matrix assembly operator that may be readily parallelized for use on shared memory systems. We demonstrate, through the numerical simulation of carefully chosen benchmark problems, that the finite element formulations proposed in this study are efficient, reliable and insensitive to all forms of numerical locking and element geometric distortions.

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

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The thesis studies the relationship between inter-fiber forces present within a cellulose fiber web under varying external conditions. It particularly concentrates on the degree of fiber to fiber bonding and fiber entanglement as a function of moisture content. Finite element analysis of the fiber bonding is used in conjunction with the experimental results to analyze and explain the inter-fiber behaviors taking place within a sheet.

This thesis employs a finite element (FE) method for numerically simulating the mechanical response of constituents in a fiber-reinforced polymer (FRP) composite to indentation. Indentation refers to a procedure that subsumes a rigid indenter of specific geometry to impress the surface of a relatively softer material, with a view of estimating its mechanical properties. FE analyses are performed on a two-dimensional simplified microstructure of the FRP composite comprising perfectly bonded fiber, interphase and matrix sections. Indentation response of the constituents is first examined within the context of linearized elasticity. Time-dependent response of the polymer matrix is invoked by modeling the respective constituent section as a linear isotropic viscoelastic material. Furthermore, indentation responses to non-mechanical stimulus, like moisture absorption, is also simulated through a sequentially coupled analysis. A linear relationship describing the degradation of elastic moduli of the individual constituents with increasing moisture content has been assumed. The simulations subsume a point load idealization for the indentation load eventually substituted by indenter tips with conical and spherical profiles. Results from FE analyses in the form of load-displacement curves, displacement contours and stress contours are presented and discussed. With the application of concentrated load on linearly elastic constituents for a given/known degree of heterogenity in the FRP, simulations indicated the potential of indentation technique for determining interphase properties in addition to estimating the matrix-fiber interphase bond strength. Even with stiffer surrounding constituents, matrix characterization was rendered difficult. However, fiber properties were found to be determinable using the FE load-displacement data, when the load-displacement data from experimentation is made available. In the presence of a polymer (viscoelastic) matrix, the surrounding elastic constituents could be characterized for faster loading rates when viscoelastic effects are insignificant. Displacements were found to be greater in the presence of a polymer matrix and moisture content in comparison with a linearly elastic matrix and dry state. As one would expect, the use of different indenter tips resulted in varying responses. Conical tips resulted in greater displacements while concentrated load produced greater stresses. Further it was found that, despite the insignificant effects due to surrounding constituents, analytical (Flamant) solution for concentrated, normal force on a homogeneous, elastic half-plane becomes inapplicable in back calculating the elastic moduli of individual FRP constituents. This can be attributed to the finite domain and the associated boundary conditions in the problem of interest.

Soft biological tissues, being live and due to their physiological structures, display considerably complex mechanical behaviors. For a better understanding and use in various applications, first study to be carried out is the tests made particularly as in vivo. An indenter test device developed for this purpose in the METU, Department of Mechanical Engineering, Biomechanics Laboratory is operational. In this study, in order to carry out precise and dependable tests, initially, various tests and improvements were conducted on the device and the software controlling the device. At the end of this study, displacement and load measurement accuracies and precisions were improved. Better algorithms for filtering the noisy data were prepared. Some test protocols within the software were improved and new protocols were annexed. To be able to conduct more dependable tests a new connection system was attached to the device. In order to study the anisotropic behavior of soft tissues ellipsoid tips were designed and produced. In the second phase of the study, tests on medial forearm were carried out. In these tests, hysteresis, relaxation and creep behaviors displaying the viscoelastic v properties of the soft biological tissues were observed. In addition to viscoelastic behaviors, preconditioning (Mullin&amp / #8217 / s) effect and anisotropic response were examined. By using the results of the relaxation and creep tests, parameters of the Prony series capable of modelling these data were determined. With this study, some important conclusions regarding the soft biological tissues were drawn and thus the behaviors of the soft biological tissues were better understood. Besides, the difficulties inherent to in-vivo tests were recognized and actions to reduce these difficulties were explained. Finally, clean experimental data, to be used in the computer simulations, were obtained.

Soft biological tissue material models in the literature are frequently limited to integer order constitutive relations where the order of differentiation of stress and/or strain is integer-valued. However, it has been demonstrated that fractional calculus theory applied in soft tissue material model formulation yields more accurate and reliable soft tissue material models. In this study, firstly a fractional order (where the order of differentation of stress in the constitutive relation is non-integer-valued) linear viscoelastic material model for soft tissues is fitted to force-displacement-time indentation test data and compared with two different integer order linear viscoelastic material models by using MATLAB&reg / optimization toolbox. After the superiority of the fractional order material model compared to integer order material models has been shown, the linear fractional order material model is extended to its nonlinear counterpart in finite deformation regime. The material model developed is assumed to be isotropic and homogeneous. v A user-subroutine is developed for the material model formulated to implement it into the commercial finite element software Msc.Marc 2010. The user-subroutine developed is verified by performing a small strain finite element analysis and comparing the results obtained with linear viscoelastic counterpart of the model on MATLAB&reg / . Finally, the unknown coefficients of the fractional order material model are identified by employing the inverse finite element method. A material parameter set with an amount of accuracy is determined and the material model with the parameters identified is capable of simulating the three different indentation test protocols, i.e., &ldquo / relaxation&rdquo / , &ldquo / creep&rdquo / and &ldquo / cyclic loading&rdquo / protocols with a good accuracy.

In der Aufbau und Verbindungstechnik von mikroelektronischen Komponenten finden vermehrt polymere Werkstoffe Einzug. Zum Beispiel wird klassisches Metalllot durch elektrisch leitfähige Klebstoffe ersetzt, beziehungsweise werden zur Fixierung von oberflächenkontaktierten elektronischen Bauelementen schnell härtende Epoxidharzklebstoffe eingesetzt. Insbesondere im automobilen Einsatzbereich werden hohe Anforderungen an die Funktionszuverlässigkeit an die elektronischen Komponenten gesetzt. Große Temperaturschwankungen sowie unterschiedlichste mechanische Lastfälle wirken auf die Elektronik ein. Die vorliegende Arbeit behandelt die Beschreibung des viskoelastischen Materialverhaltens am Beispiel eines Epoxidharzklebstoffs zur Fixierung mikroelektronischer Bauelemente in einem ausgedehnten Temperatur- und Zeitbereich. Es werden unterschiedliche experimentelle Vorgehensweisen zur Ermittlung des Relaxationsverhaltens diskutiert und eine für den großen Temperaturbereich optimierte Zeit-Temperaturverschiebung präsentiert. Die experimentellen Ergebnisse des Relaxationsverhaltens werden mittels einer Vielparameteranpassung unter Zuhilfenahme genetischer Algorithmen in ein Materialmodell übertragen. Zur Beschreibung des dreidimensionalen viskoelastischen Stoffverhaltens wird neben dem E-Modul auch die Poissonzahl mit unterschiedlichen Messmethoden in Abhängigkeit von Temperatur und Zeit untersucht. Insbesondere die berührungslose Messung von Längs- und Querdehnung im Zugrelaxationsversuch und anschließender Auswertung mittels Grauwertkorrelation wird als zielführend bewertet. Es wird ein Funktionsansatz vorgestellt, mit dem sich die Poissonzahl in Abhängigkeit von Temperatur und Zeit beschreiben lässt. Damit lässt sich das Relaxationsverhalten für sowohl den Schub- als auch dem Kompressionsmodul darstellen. Dies erhöht die Aussagegenauigkeit von numerischen Beanspruchungsanalysen und verbessert somit auch die Präzision der darauf basierenden von Lebensdauerprognosen.

Thesis (Ph. D.)--Institute of Paper Chemistry, 1960. / Includes bibliographical references (p. 164-165).