The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.

Based on a previous empirical study of the effect of a residential demand response program in Sala, Sweden, this project  investigated the economic consequences of consumer behaviour change after a demand-based time of use distribution tariff was employed. The economic consequences of consumers were proven to be disadvantageous in terms of unit electricity price. Consumers could achieve more electricity bill saving through stabilising their electricity consumption during peak hours, and this way bring least compromising of their comfort level. In order to estimate the price elasticity of the studies demand response program, a new method of estimation price elasticity was proposed. With this method, the intensity of demand response of the demand response program was estimated in terms of price elasticity. Regression analysis was also applied to find out the price incentives of consumer behaviour change. And the results indicated that the rise in electricity supply charge hardly contributes to load reduction, while the demand-based tariff constituted an advantageous solution on load demand management. However stronger demand response still requires better communication with customers and more incentives other than the rise in distribution tariff.

Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes it applicable only to polycrystals with (single) crystal symmetry defined by a proper point group. In the present study we consider ODFs defined on the orthogonal group O(3) and extend the representation theorem of Man and Huang to cover pseudotensors and polycrystals with crystal symmetry defined by any improper point group. This extension is important because many materials, including common metals such as aluminum, copper, iron, have their group of crystal symmetry being an improper point group. We present the restrictions on texture coefficients imposed by crystal symmetry for all the 21 improper point groups and we illustrate the extended representation theorem by its application to elasticity.

No description available.

Mooney-Rivlin hyperelasticity equations are nonlinear coupled partial differential equations (PDEs) that are used to model various elastic materials. These models have been extended to account for fiber reinforced solids with applications in modeling biological materials. As such, it is important to obtain solutions to these physical systems. One approach is to study the admitted Lie symmetries of the PDE system, which allows one to seek invariant solutions by the invariant form method. Furthermore, knowledge of conservation laws for a PDE provides insight into conserved physical quantities, and can be used in the development of stable numerical methods. The current Thesis is dedicated to presenting the methodology of Lie symmetry and conservation law analysis, as well as applying it to fiber reinforced Mooney-Rivlin models. In particular, an outline of Lie symmetry and conservation law analysis is provided, and the partial differential equations describing the dynamics of a hyperelastic solid are presented. A detailed example of Lie symmetry and conservation law analysis is done for the PDE system describing plane strain in a Mooney-Rivlin solid. Lastly, Lie symmetries and conservation laws are studied in one and two dimensional models of fiber reinforced Mooney-Rivlin materials.

In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. / In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können.

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This thesis focuses on the investigation of behavior of thick and moderately thick laminates under transverse and horizontal loading for different boundary conditions and configurations. An efficient finite element solution is proposed for analyzing composite laminates. Based on a combination of composite theory and 3-D Elasticity Theory, a 3-D finite element program is developed in MATLAB for calculating the stresses, strains and deformations of composite laminates under transverse and/or horizontal loading for different boundary conditions. The applicability of the formulation to analysis of laminated rubber bearings is also examined in this study. Since it is very important to calculate the correct stress state when developing models for composite behavior, the 3-D Elasticity Theory is used in this research. Numerical results are presented for various problems with different lamination schemes, loading and boundary conditions. In order to verify the analysis and the numerical calculations, numerical solutions obtained in this study are compared with available closed form solutions in the literature, experiment results and a commercial finite element program, namely ANSYS. The results obtained using the present finite element is found to be in acceptable and good agreement with the closed form solutions in the literature for thick and moderately thick rectangular and square plates.

This dissertation measures the extent of relationship between production, processing and marketing channels of fig products in Turkey for the period 1971-2003. We first provide a detailed analysis of world and Turkish fig products market. We then estimate the own price and cross price elasticities of fig products in Turkey by using simultaneous systems. The results imply that the demand facing Turkish dried fig processors is inelastic. Moreover also the producer-level dried fig price elasticity has inelastic structure. The study also finds evidence of a complementary structure between fig products apart from fresh fig.

Polyvinyl alcohol (PVA) desize effluent is a high COD contributor to towel manufacturing plant's Primary Oxygenation Treatment of Water operation, and being non-biodegradable, is a threat to the environment. When all-PVA/wax size is used in weaving, significant incentives exist to recover the synthetic polymer material from the desize wash water stream and reuse it. A new technology that would eliminate the disadvantages of the current Reverse Osmosis Ultrafiltration (UF) PVA recovery process is Vacuum Flash Evaporation (VFE). This research adapts the VFE process to the recovery and reuse of all-PVA size emanating from towel manufacturing, and compares the economics of its implementation in a model plant to current plant systems that use PVA/starch blend sizes with no materials/water recovery. After bench scale research optimized the VFE PVA recovery process from the desize effluent and determined the mass of virgin PVA that was required to be added to the final, recycled PVA size formulations. The physical changes in the recycled size film and yarn composite properties from those of the initial (conventional) slashing were determined using a number of characterization techniques, including DSC, TGA, SEM, tensile testing, viscometry, number of abrasion cycles to first yarn breaks, microscopy and contact angle measurements. Cotton chemical impurities extracted from the yarns during desizing played an important role in the recovered PVA film physical properties. The recovered PVA improved the slashed yarn weave ability. Along with recovered PVA, pure hot water was recovered from the VFE. Virgin wax adds to the final, recycled size formulations were determined to be unnecessary, as the impurities extracted into the desize effluent stream performed the same functions in the size as the wax. Using the bench results, the overall VFE process was optimized and demonstrated to be technically viable through six cycles, proof-of-concept trials conducted on a Webtex Continuous Pilot Slasher. Based on the pilot scale trials, comparative economics were developed. Incorporation of the VFE technology for PVA size recovery and recycling resulted in ~$3.2M/year in savings over the conventional PVA/starch/wax process, yielding a raw ROI of less than one year based on a $3M turnkey capital investment.