Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Fracture Mechanics Investigation of Structures with Defects

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities. This dissertation, concentrates on some of the fractural aspects of shaft and composite which have being increasingly used in modern structures, consists four chapters within two parts. Chapters 1 to 4 are included in part 1. In the first chapter, the basic knowledge about the stress and displacement fields in the vicinity of a crack tip is introduced. A review involves the general methods of calculating stress intensity factors are presented. In Chapter 2, two simple engineering methods for a fast and close approximation of stress intensity factors of cracked or notched beams under tension, bending moment, shear force, as well as torque are presented. New formulae for calculating the stress intensity factors are proposed. One of the methods named Section Method is improved and applied to the three dimensional analysis of cracked circular section for calculating stress intensity factors. The comparisons between the present results and the solutions calculated by ABAQUS for single mode and mixed mode are studied. In chapter 3, fracture criteria for a crack subjected to mixed mode loading of two-dimension and three-dimension are reviewed. The crack extension angle for single mode and mixed mode, and the critical loading domain obtained by SEDF and MTS are compared. The effects of the crack depth and the applied force ratio on the crack propagation angle and the critical loading are investigated. Three different methods calculating the crack initiation angle for three-dimension analysis of various crack depth and crack position are compared. It should be noted that the stress intensity factors used in the criteria are calculated in section 2.1.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Local dynamics and bending mechanics of mesostructured materials

Die vorliegende Arbeit behandelt die Anwendung der Rasterkraftmikroskopie auf die Untersuchung mesostrukturierter Materialien. Mesostrukturierte Materialien setzen sich aus einzelnen mesoskopen Bausteinen zusammen. Diese Untereinheiten bestimmen im Wesentlichen ihr charakteristisches Verhalten auf äußere mechanische oder elektrische Reize, weshalb diesen Materialien eine besondere Rolle in der Natur sowie im täglichen Leben zukommt. Ein genaues Verständnis der Selbstorganisation dieser Materialien und der Wechselwirkung der einzelnen Bausteine untereinander ist daher von essentieller Bedeutung zur Entwicklung neuer Synthesestrategien sowie zur Optimierung ihrer Materialeigenschaften. Die Charakterisierung dieser mesostrukturierten Materialien erfolgt üblicherweise mittels makroskopischer Analysemethoden wie der dielektrischen Breitbandspektroskopie, Thermogravimetrie sowie in Biegungsexperimenten. In dieser Arbeit wird gezeigt, wie sich diese Analysemethoden mit der Rasterkraftmikroskopie verbinden lassen, um mesostrukturierte Materialien zu untersuchen. Die Rasterkraftmikroskopie bietet die Möglichkeit, die Oberfläche eines Materials abzubilden und zusätzlich dazu seine quantitativen Eigenschaften, wie die mechanische Biegefestigkeit oder die dielektrische Relaxation, zu bestimmen. Die Übertragung makroskopischer Analyseverfahren auf den Nano- bzw. Mikrometermaßstab mittels der Rasterkraftmikroskopie erlaubt die Charakterisierung von räumlich sehr begrenzten Proben bzw. von Proben, die nur in einer sehr kleinen Menge (<10 mg) vorliegen. Darüberhinaus umfasst das Auflösungsvermögen eines Rasterkraftmikroskops, welche durch die Größe seines Federbalkens (50 µm) sowie seines Spitzenradius (5 nm) definiert ist, genau den Längenskalenbereich, der einzelne Atome mit der makroskopischen Welt verbindet, nämlich die Mesoskala. In dieser Arbeit werden Polymerfilme, kolloidale Nanofasern sowie Biomineralien ausführlicher untersucht.rnIm ersten Projekt werden mittels Rasterkraftmikroskopie dielektrische Spektren von mischbaren Polymerfilmen aufgenommen und mit ihrer lokalen Oberflächenstruktur korreliert. Im zweiten Projekt wird die Rasterkraftmikroskopie eingesetzt, um Biegeexperimente an kolloidalen Nanofasern durchzuführen und so ihre Brucheigenschaften genauer zu untersuchen. Im letzten Projekt findet diese Methode Anwendung bei der Charakterisierung der Biegeeigenschaften von Biomineralien. Des Weiteren erfolgt eine Analyse der organischen Zusammensetzung dieser Biomineralien. Alle diese Projekte demonstrieren die vielseitige Einsetzbarkeit der Rasterkraftmikroskopie zur Charakterisierung mesostrukturierter Materialien. Die Korrelation ihrer mechanischen und dielektrischen Eigenschaften mit ihrer topographischen Beschaffenheit erlaubt ein tieferes Verständnis der mesoskopischen Materialien und ihres Verhaltens auf die Einwirkung äußerer Stimuli.rn

Predictability in Social Science, The statistical mechanics approach.

The subject of this work concerns the study of the immigration phenomenon, with emphasis on the aspects related to the integration of an immigrant population in a hosting one. Aim of this work is to show the forecasting ability of a recent finding where the behavior of integration quantifiers was analyzed and investigated with a mathematical model of statistical physics origins (a generalization of the monomer dimer model). After providing a detailed literature review of the model, we show that not only such a model is able to identify the social mechanism that drives a particular integration process, but it also provides correct forecast. The research reported here proves that the proposed model of integration and its forecast framework are simple and effective tools to reduce uncertainties about how integration phenomena emerge and how they are likely to develop in response to increased migration levels in the future.

Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using Complete Basis Set and Gaussian-n Models combined with CPCM Continuum Solvation Methods

Complete basis set and Gaussian-n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pKa values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol, to calculate pKa values with cycle 1. The complete basis set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Accurate pKa Calculations for Carboxylic Acids Using Complete Basis Set and Gaussian-n Models Combined with CPCM Continuum Solvation Methods”

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pKa values for six carboxylic acids. An experimental value of −264.61 kcal/mol for the free energy of solvation of H+, ΔGs(H+), was combined with a value for Ggas(H+) of −6.28 kcal/mol to calculate pKa values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pKa values accurate to less than half a pKa unit.

Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.