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Digital light Projection based Additive Manufacturing (AM) enables fabrication of complex three-dimensional (3D) geometries for applications ranging from rapid prototyping jet parts to scaffolds for cell cultures. Despite the ability in producing complex, three-dimensional architectures, the state of art DLP AM systems is limited to a single homogenous photo-polymer and it requires a large volume of resin bath to begin with. Extensible Multi-material Stereolithography (EMSL) is a novel high-resolution projection stereolithography system capable of manufacturing hybrid 3D objects. This system provides new capabilities, allowing more flexible design criteria through the incorporation of multiple feedstock materials throughout the structure. With EMSL manufacturing ability, multi-material programmable negative Poissons ratio honeycomb reentrant structures are realized. Researchers have been studying auxetic structures over decades, the mechanical property control of auxetic structure mainly relies on geometry design in previous studies. Now with the help of EMSL system, other design variables associated with auxetic structures, such as material properties of local structural members, are added into design process. The additional variables are then proved to have significant effects on the material properties of the auxetic structures. The ability to accurately manufacture multi-material digital design will not only allow for novel mechanical and material researches in laboratory, but also extend the additive manufacturing technology to numerous future applications with characteristics such as multiple electrical, electromechanical and biological properties. The design and optimization of EMSL system realizes novel structures have not been producible, therefore it will stimulate new possibilities for future additive manufacturing development. / Master of Science

As finite element discretizations ever grow in size to address real-world problems, there is an increasing need for fast algorithms. Nowadays there are many GPU/CPU parallel approaches to solve such problems. Multigrid methods can be used to solve large-scale problems, or even better they can be used to precondition the conjugate gradient method, yielding better results in general. Capabilities of multigrid algorithms rely on the effectiveness of the inter-grid transfer operators. In this thesis we focus on the aggregation approach, discussing how different aggregation strategies affect the convergence rate. Based on these discussions, we propose an alternative parallel aggregation algorithm to improve convergence. We also provide numerous experimental results that compare different aggregation approaches, multigrid methods, and conjugate gradient iteration counts, showing that our proposed algorithm performs better in serial and parallel. / Modeling real-world problems incurs a high computational cost because these mathematical models involve large-scale data manipulation. Thus we need fast and efficient algorithms. Nowadays there are many high-performance approaches for these problems. One such method is called the Multigrid algorithm. This approach models a physical domain using a hierarchy of grids, and so the effectiveness of these approaches relies on how well data can be transferred from grid to grid. In this thesis, we focus on the aggregation approach, which clusters a grid’s vertices according to its connections. We also provide an alternative parallel aggregation algorithm to give a faster solution. We show numerous experimental results that compare different aggregation approaches and multigrid methods, showing that our proposed algorithm performs better in serial and parallel than other popular implementations.

Small-deflection plate equations are presented in terms of the midplane plate deformations and the temperature distribution within the plate, which is assumed independent of the plate deformation. The plate boundary conditions are presented in a general form and are suitable for solutions involving either fixed, free, or hinged edge conditions. The temperature distribution within the plate is assumed to be governed by Poisson's equation and a specified temperature distribution over the surfaces of the plate. Solutions for the temperature distribution are given in terms of a power series with respect to the plate thickness coordinate, the coefficients of which are dependent on the midplane temperature distribution and the midplane temperature gradient in the plate thickness direction. Out-of-plane plate deformations are discussed for plates with fixed edges. Discussions of plate deformations are also presented in which the temperature distributions result from constant heat generation within the plate and from radiation absorption. / Master of Science

This Thesis deals with the determination of Young's modulus and Poisson's ratio from the measurement of small strains (10-3 - 10-5 ) in triaxial tests on the overconsolidated Miocene clay from Moravia (Brno Tegel). The tests were performed in a hydraulic triaxial chamber, fitted with submersible local LVDT sensors, which were fixed directly on the sample. The tests were carried out on undisturbed samples of standard height and diameter (76x38 mm). There were three types of tests - isotropic loading probe, axial loading probe and shear test to the failure. The measured data were analyzed and the results were discussed. The research part of the Thesis briefly describes previous works on stiffness of Brno Tegel and also some works on stiffness of similar material to Brno Tegel - London Clay.

"We develop a selfconsistent solution of the Schroedinger and Poisson equations in semiconductor heterostructures with arbitrary doping profiles and layer geometries. An algorithm for this nonlinear problem is presented in a multiband k.P framework for the electronic band structure using the finite element method. The discretized functional integrals associated with the Schroedinger and Poisson equations are used in a variational approach. The finite element formulation allows us to evaluate functional derivatives needed to linearize Poisson’s equation in a natural manner. Illustrative examples are presented using a number of heterostructures including single quantum wells, an asymmetric double quantum well, p-i-n-i superlattices and trilayer superlattices."

In this paper, the numerical simulation for nano-indentation is performed to measure time-dependent behavior of polymeric films. The possibility to extract the relaxed shear modulus of the polymer is evaluated using a rigid ball indenter. The viscoelastic behavior of the polymer was represented by the standard model. The effects of Poisson’s ratio are also discussed. / Singapore-MIT Alliance (SMA)

Soft materials have attracted much scientific and technical interest in recent years. In this thesis, attention has been placed on the underpinning relations between molecular structure and properties of one type of soft matter - main chain liquid crystalline elastomers (MCLCEs), which may have application as shape memory or as auxetic materials. In this work, a number of siloxane-based MCLCEs and their linear polymer analogues (MCLCPs) with chemical variations were synthesized and examined. Among these chemical variations, rigid p-phenylene transverse rod and flat-shaped anthraquinone (AQ) mesogenic monomers were specifically incorporated. Thermal and X-ray analysis found a smectic C phase in most of our MCLCEs, which was induced by the strong self-segregation of siloxane spacers, hydrocarbon spacers and mesogenic rods. The smectic C mesophase of the parent LCE was not grossly affected by terphenyl transverse rods. Mechanical studies of MCLCEs indicated the typical three-region stress-strain curve and a polydomain-to-monodomain transition. Strain recovery experiments of MCLCEs showed a significant dependence of strain retentions on the initial strains but not on the chemical variations, such as the crosslinker content and the lateral substituents on mesogenic rods. The MCLCE with p-phenylene transverse rod showed a highly ordered smectic A mesophase at room temperature with high stiffness. Mechanical properties of MCLCEs with AQ monomers exhibit a strong dependence on the specific combination of hydrocarbon spacer and siloxane spacer, which also strongly affect the formation of ð-ð stacking between AQ units. Poisson s ratio measurement over a wide strain range found distinct trends of Poisson s ratio as a function of the crosslinker content as well as terphenyl transverse rod loadings in its parent MCLCEs.

In this thesis, least-squares based finite element models (LSFEM) for the Poisson equation and Navier-Stokes equation are presented. The least-squares method is simple, general and reliable. Least-squares formulations offer several computational and theoretical advantages. The resulting coefficient matrix is symmetric and positive-definite. Using these formulations, the choice of approximating space is not subject to any compatibility condition. The Poisson equation is cast as a set of first order equations involving gradient of the primary variable as auxiliary variables for the mixed least-square finite element model. Equal order C0 continuous approximation functions is used for primary and auxiliary variables. Least-squares principle was directly applied to develop another model which requires C1continous approximation functions for the primary variable. Each developed model is compared with the conventional model to verify its performance. Penalty based least-squares formulation was implemented to develop a finite element for the Navier Stokes equations. The continuity equation is treated as a constraint on the velocity field and the constraint is enforced using the penalty method. Velocity gradients are introduced as auxiliary variables to get the first order equivalent system. Both the primary and auxiliary variables are interpolated using equal order C0 continuous, p-version approximation functions. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.

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.