Dissertations / Theses: 'Analytical mechanics'

1

Lindberg, Martin, and Anders Pärlstrand. "Analytical Mechanics with Computer Algebra." Thesis, KTH, Mekanik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-148947.

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In this project we have been studying two different advanced mechanical pendulums, which are close to impossible to solve by hand. The theory behind our method is Lagrange’s equations which lead to the system's equations of motion. These equations of motion are solved with Sophia, a program package to the symbolic programming language Maple. The solution is given on a general analytic form and can be specified with numerical parameters which allow us to visualize the particle animation and also plot the generalized coordinates.
I det här projektet har vi studerat två olika avancerade mekaniska pendlar som i stort sett inte går att behandla med papper och penna. Teorin vi har använt oss av är Lagranges ekvationer som leder till systemets rörelseekvationer. Dessa rörelseekvationer löses sedan medelst Sophia, ett programpaket till det symbolhanterande programmeringsspråket Maple. Lösningen ges på generell analytisk form och kan sedan preciseras med numeriska parametrar så att partikelbanor och plottar för lägeskoordinater kan överskådas.

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2

Strand, Filip, and Jakob Arnoldsson. "Analytical Mechanics with Computer Algebra." Thesis, KTH, Mekanik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-232119.

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Classical mechanics is the branch of physics concerned with describing the motion of bodies. The subject is based on three simple axioms relating forces and movement. These axioms were first postulated by Newton in the 17th century and are known as his three laws of motion. Lagrangian mechanics is a restatement of the Newtonian formulation. It deals with energy quantities and paths-of-motion instead of forces. This often makes it simpler to use when working with non-trivial mechanical systems. In this thesis, we use the Lagrangian method to model two such systems; A rotating torus and a variant of the classical double pendulum. It soon becomes clear that the complexity of these systems make them difficult to attack by hand. For this reason, we take a computer-based approach. We use a software-package called Sophia which is a plug-in to the computer algebra system Maple. Sofia was developed at the Department of Mechanics at KTH for the specific purpose of modeling mechanical problems using Lagrange’s method. We demonstrate that this method can be successfully applied to the analysis of motion of complex mechanical systems. The complete equations of motion are derived in a symbolic form and then integrated numerically. The motion of the system is finally visualized by means of 3D graphics software Blender.

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3

Barry, Matthew M. "Analytical and experimental studies of thermoelectric devices and materials." Thesis, University of Pittsburgh, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10183683.

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Interest in thermoelectric devices (TEDs) for waste-heat recovery applications has recently increased due to a growing global environmental consciousness and the potential economic benefits of increasing cycle efficiency. Unlike conventional waste-heat recovery systems like the organic Rankine cycle, TEDs are steady-state, scalable apparatus that directly convert a temperature difference into electricity using the Seebeck effect. The benefits of TEDS, namely steady-state operation and scalability, are often outweighed by their low performance in terms of thermal conversion efficiency and power output. To address the issue of poor device performance, this dissertation takes a multi-faceted approach focusing on device modeling, analysis and design and material processing.

First, a complete one-dimensional thermal resistance network is developed to analytically model a TED, including heat exchangers, support structures and thermal and electrical contact resistances. The purpose of analytical modeling is twofold: to introduce an optimization algorithm of the thermoelectric material geometry based upon the realized temperature difference to maximize thermal conversion efficiency and power output; and to identify areas within the conventional TED that can be restructured to allow for a greater temperature difference across the junction and hence increased performance. Additionally, this model incorporates a component on the numerical resolution of radiation view factors within a TED cavity to properly model radiation heat transfer. Results indicate that geometric optimization increases performance upwards of 30% and the hot-side ceramic diminishes realized temperature difference. The resulting analytical model is validated with published numerical and comparable analytical models, and serves as a basis for experimental studies.

Second, an integrated thermoelectric device is presented. The integrated TED is a restructured TED that eliminates the hot-side ceramic and directly incorporates the hot-side heat exchanger into the hot-side interconnector, reducing the thermal resistance between source and hot-side junction. A single-state and multi-stage pin-fin integrated TED are developed and tested experimentally, and the performance characteristics are shown for a wide range of operating fluid temperatures and flow rates. Due to the eliminated to thermal restriction, the integrated TED shows unique performance characteristics in comparison to conventional TED, indicating increased performance.

Finally, a grain-boundary engineering approach to material processing of bulk bismuth telluride (Bi₂Te₃) is presented. Using uniaxial compaction and sintering techniques, the preferred crystallographic orientation (PCO) and coherency of grains, respectively, are controlled. The effect of sintering temperature on thermoelectric properties, specifically Seebeck coefficient, thermal conductivity and electrical resistivity, are determined for samples which exhibited the highest PCO. It is shown the performance of bulk Bi₂Te₃ produced by the presented method is comparable to that of nano-structured materials, with a maximum figure of merit of 0.40 attained at 383 K.

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4

Brown, Ainsmar Xavier. "Inflatable wing UAV experimental and analytical flight mechanics." Thesis, Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39492.

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The field of man portable UASs (Unmanned Aerial Systems) is currently a key area in improving the fielded warrior's capabilities. Pressurized aerostructures that can perform with similar results of solid structures can potentially change how this objective may be accomplished now and in the future. Construction with high density polymers and other composites is currently part of active inflatable vehicle research. Many shape forming techniques have also been adapted from the airship and balloon manufacturing industry. Additional research includes modeling techniques so that these vehicles may be included in simulation packages. A flight dynamics simulation with reduced-order aeroelastic effects derived with Lagrangian and Eulerian dynamics approaches were developed and optimized to predict the behavior of inflatable flexible structures in small UASs. The models are used to investigate the effects of significant structural deflections (warping) on aerodynamic surfaces. The model also includes compensation for large buoyancy ratios. Existing literature documents the similarity in structural dynamics of rigid beams and inflatable beams before wrinkling. Therefore, wing bending and torsional modes are approximated with the geometrically exact ntrinsic beam equations using NATASHA (Nonlinear Aeroelastic Trim And Stability for HALE Aircraft) code. An approach was also suggested for inclusion of unique phenomena such as wrinkling during flight. A simplified experimental setup will be designed to examine the most significant results observed from the simulation model. These methods may be suitable for specifying limits on flight maneuvers for inflatable UASs.

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5

Panneerselvam, Dinesh. "Mechanics of Asphalt Concrete: Analytical and Computational Studies." online version, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=case1106341613.

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6

García, Aragón Juan Antonio. "Experimental and analytical investigations of granular-fluid mixtures down inclines." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41021.

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Granular-fluid mixtures flowing down an incline in the grain-inertia regime were studied experimentally and analytically. The equations of motion are based on the kinetic theory for granular flow. The boundary conditions are formulated following two methods. The first is a simple mechanical approach based on the energy exchange at the wall. The other is based on the kinetic theory for granular flow. Solutions for dry granular flow down a chute are studied in order to compare both methods. The extension of the kinetic theory presented here, includes drag forces resulting from the interstitial fluid that cushions interparticle collisions and particle-wall collisions. Frictional stresses, produced when long term contacts are present, and fluid turbulent fluctuations are introduced in the model.
The results are compared with measurements from an experimental chute in which the inclination, the solids flow rate and fluid flow rate are all varied. The theory is found to give a good qualitative account of the observed behaviour. Finally an application of the model to the description of the mechanical behaviour of the Nevado del Ruiz 1985 debris flow is attempted.

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7

Jacob, David. "Analytical analysis of absorption cycles." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/16094.

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8

Abou, Jaoudé Abdo. "Advanced Analytical Model for the Prognostic of Industrial Systems Subject to Fatigue." Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00874624.

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This thesis is dedicated to the prognostic evaluation of dynamic systems. The work presented here aims at developing an advanced tool to treat the prognostic evaluation in linear and nonlinear deterministic context in a first part as well as in the stochastic context in a second part. Our purpose is to prepare a general prognostic tool that can be capable of well predicting the RUL of a system based on an analytical damage accumulation law in either a deterministic or a stochastic context.

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9

Kaufmann, Matthew Vernon 1969. "Finite element and analytical methods for analyzing interfacial thermal resistance." Thesis, The University of Arizona, 1993. http://hdl.handle.net/10150/278334.

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In this thesis, the phenomena of thermal contact resistance is examined from both an analytical and numerical standpoint. Strong emphasis is made on the differentiation between the macroscopic and microscopic mechanisms and their separate effects on the thermal resistance at the interface of two unbonded materials. Of particular interest is the interface between two dissimilar materials. A full analysis of the macroscopic influence of thermal strains on the deformations at the interface is presented. The dependence of interfacial thermal resistance on the direction of heat flow is explained. The theory of microscopic-based contact resistance is also reviewed. A computer code enabling coupled thermal-mechanical finite element analyses of models was developed to investigate the complex interplay between thermal strains, interface separation, and contact conductance. The program is used to examine past and current methods of experimentally determining thermal contact resistance. A unique procedure, based on observed interfacial phenomena, for experimentally measuring true thermal contact resistance is presented and numerically verified. Finally, the technology developed in this thesis is used to analyze some interface problems in electronic packages.

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10

Garapati, Sri Harsha. "Analytical and Numerical Modeling of Assembly Procedures of Steel Fulcra of Bascule Bridges." Thesis, University of South Florida, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3557075.

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To model shrink-fitting in metal components, an analytical model for two long compound cylinders with temperature dependent material properties and interference between them is developed for calculating transient temperatures and stresses. A finite element model is developed for the same geometry which incorporated the temperature dependent material properties. A convergence study is performed on the finite element and analytical model. The finite element model is validated by comparing the approximations of finite element model with the analytical solution.

In an assembly procedure of fulcrums for bascule bridges, called AP1, the trunnion is shrink-fitted into a hub, followed by shrink fitting the trunnion-hub assembly into the girder of the bridge. In another assembly procedure called AP2, the hub is shrink-fitted into the girder, followed by shrink-fitting the trunnion in the hub-girder assembly. A formal design of experiments (DOE) study is conducted on both AP1 and AP2 using the finite element model to find the influence of geometrical parameters such as radial thickness of the hub, radial interference, and various shrink-fitting methods on the design parameter of overall minimum critical crack length (OMCCL)—a measure of likelihood of failure by cracking. Using the results of DOE study conducted on both the assembly procedures, AP1 and AP2 are quantitatively compared for the likelihood of fracture during assembly.

For single-staged shrink-fitting methods, for high and low hub radial thickness to hub inner diameter ratio, assembly procedure AP1 and AP2 are recommended, respectively. For fulcra with low hub radial thickness to hub inner diameter ratio and where staged shrink-fitting methods are used, for AP2, cooling the trunnion in dry-ice/alcohol and heating the girder, and for AP1, cooling the trunnion-hub assembly in dry-ice/alcohol followed by immersion in liquid nitrogen is recommended. For fulcra with high hub radial thickness to hub inner diameter ratio and where staged shrink-fitting methods are used, cooling the components in dry-ice/alcohol and heating the girder is recommended for both AP1 and AP2.

Due to the limitations of AP2, assembly procedures by heating the girder with heating coils instead of dipping an already stressed trunnion-hub assembly in liquid nitrogen are studied for decreasing the likelihood of failure by cracking and yielding. In an assembly procedure called AP3-A, only the girder is heated to shrink-fit the trunnion-hub assembly in the girder. This assembly procedure AP3-A is found to be infeasible because the girder fails by yielding if heating is expected to be completed in a reasonable amount of time. An alternative assembly procedure called AP3-B is suggested for shrink-fitting where the heating of the girder is combined with cooling the trunnion-hub assembly in dry-ice/alcohol mixture. This assembly procedure AP3-B is found to be feasible. A complete DOE study is conducted on AP3-B to find the influence of parameters like hub radial thickness and radial interference at trunnion-hub interface on the design parameter of overall minimum critical crack length. The design parameter, OMCCL values during the assembly procedure AP3-B are quantitatively compared with the widely used assembly procedures (AP1 single-stage shrink-fitting and AP1 multi-staged shrink fitting). The results of this work suggest that increasing the hub radial thickness decreases the likelihood of fracture significantly. For hubs with large radial thickness, heating the girder combined with cooling the trunnion-hub in dry-ice/alcohol mixture (AP3-B) is recommended but for hubs with low radial thickness, multistage cooling of the trunnion-hub assembly in dry-ice/alcohol mixture followed by dipping in liquid nitrogen (AP1- multistage cooling) is recommended.

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11

Driessen, Brian James. "Analytical and numerical studies in nonholonomic dynamical systems." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/17338.

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12

Goyal, Vinay K. "Analytical Modeling of the Mechanics of Nucleation and Growth of Cracks." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/30006.

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With the traditional fracture mechanics approaches, an initial crack and self-similar progression of cracks are assumed. In this treatise, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in fracture mechanics as Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracture based crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and lower surface connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of fracture is determined by the critical energy release rate. The material between two adjacent laminae of a laminated composite structure or the material between the adherend and the adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The proper work-conjugacy relations between the stress and deformation measures are identified for the interfacial surface theory. In the principle of virtual work, the interfacial cohesive-decohesive tractions are conjugate to the displacement jumps across the upper and lower surfaces. A finite deformation kinematics theory is developed for the description of the upper and lower surface such that the deformation measures are invariant with respect to superposed rigid body translation and rotation. Various mechanical softening constitutive laws thermodynamically consistent with damage mechanics are postulated that relate the interfacial tractions to the displacement jump. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. In addition, interfacial constitutive laws are developed to describe the contact-friction behavior. Interface elements applicable to two dimensional and three dimensional analyses are formulated for the analyses of contact, friction, and delamination problems. The consistent form of the interface element internal force vector and the tangent stiffness matrix are considered in the formulation. We investigate computational issues related to interfacial interpenetration, mesh sensitivity, the number of integrations points and the integration scheme, mathematical form of the softening constitutive law, and the convergence characteristics of the nonlinear solution procedure when cohesive-decohesive constitutive laws are used. To demonstrate the predictive capability of the interface finite element formulation, steadystate crack growth is simulated for quasi-static loading of various fracture test configurations loaded under Mode I, Mode II, Mode III, and mixed-mode loading. The finite element results are in agreement with the analytical results available in the literature and those developed in this work. A progressive failure methodology is developed and demonstrated to simulate the initiation and material degradation of a laminated panel due to intralaminar and interlaminar failures. Initiation of intralaminar failure can be by a matrix-cracking mode, a fiber-matrix shear mode, and a fiber failure mode. Subsequent material degradation is modeled using damage parameters for each mode to selectively reduce lamina material properties. The interlaminar failure mechanism such as delamination is simulated by positioning interface elements between adjacent sublaminates. The methodology is validated with respect to experimental data available in the literature on the response and failure of quasi-isotropic panels with centrally located circular cutouts. Very good agreement between the progressive failure analysis and the experiments is achieved if the failure analyses includes the interaction of intralaminar and interlaminar failures in the postbuckling response of the panels. In addition, ideas concerning the implementation of a fatigue model incorporated with a cohesive zone model are discussed.
Ph. D.

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13

Schultze, John Francis. "Evaluation of analytical and experimental methods to predict constrained layer damping behavior." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-09122009-040317/.

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14

Perkins, John T. "ANALYTICAL STRIP METHOD FOR THIN CYLINDRICAL SHELLS." UKnowledge, 2017. http://uknowledge.uky.edu/ce_etds/57.

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The Analytical Strip Method (ASM) for the analysis of thin cylindrical shells is presented in this dissertation. The system of three governing differential equations for the cylindrical shell are reduced to a single eighth order partial differential equation (PDE) in terms of a potential function. The PDE is solved as a single series form of the potential function, from which the displacement and force quantities are determined. The solution is applicable to isotropic, generally orthotropic, and laminated shells. Cylinders may have simply supported edges, clamped edges, free edges, or edges supported by isotropic beams. The cylindrical shell can be stiffened with isotropic beams in the circumferential direction placed anywhere along the length of the cylinder. The solution method can handle any combination of point loads, uniform loads, hydrostatic loads, sinusoidal loads, patch loads, and line loads applied in the radial direction. The results of the ASM are compared to results from existing analytical solutions and numerical solutions for several examples; the results for each of the methods were in good agreement. The ASM overcomes limitations of existing analytical solutions and provides an alternative to approximate numerical and semi-numerical methods.

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15

Liu, Ren. "A numerical and analytical study of internal waves in stratified fluids." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257314.

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16

Prucz, Jacky C. "Analytical and experimental methodology for evaluating passively damped structural joints." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/11987.

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17

Sirivolu, Dushyanth. "An Analytical Model for High-Velocity Impact of Composite Sandwich Panels." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1227548412.

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18

Stewart, John. "Physical and analytical aspects of projection operators in non equilibrium statistical mechanics." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248591.

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19

Homer, Eric Richards. "Recovering Grain Boundary Inclination Parameters Through Oblique Double-Sectioning." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1544.pdf.

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20

Gastebled, Olivier J. "Fracture in reinforced concrete : computational and analytical studies." Thesis, Heriot-Watt University, 1999. http://hdl.handle.net/10399/1238.

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21

Kaya, Yasemin. "Analytical And Numerical Solutions To Rotating Orthotropic Disk Problems." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608868/index.pdf.

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Analytical and numerical models are developed to investigate the effect of orthotropy on the stress distribution in variable thickness solid and annular rotating disks. The plastic treatment is based on Hill&rsquo
s quadratic yield criterion, total deformation theory, and Swift&rsquo
s hardening law. The elastic-plastic stress distributions, residual stresses and radial displacement distributions are obtained after having analysed the cases of rotating solid disk, annular disk with rigid inclusion, annular disk subjected to either internal or external pressure. Thermal loading is also considered for the annular disk with rigid inclusion. Effects of different values of elastic and plastic orthotropy parameters are investigated. It is observed that the elastic orthotropy significantly affects the residual stresses in disks. The most remarkable effect of the plastic orthotropy is observed on the disk with rigid inclusion.

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22

Wertz, John Nicholas. "An Energy-Based Experimental-Analytical Torsional Fatigue Life-Prediction Method." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275400649.

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23

Xin, Xudong. "An analytical and numerical analysis of dynamic failure based on the multi-physics involved /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025668.

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24

Airey, K. "An electrochemical and analytical study of iron corrosion inhibitors." Thesis, University of Newcastle Upon Tyne, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303326.

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25

Schwarzer, Norbert. "Modelling of the contact mechanics of thin films using analytical linear elastic approaches." Doctoral thesis, N. Schwarzer: Arbitrary load distribution on a layered half space, ASME Journal of Tribology, Vol. 122, No. 4, October 2000, 672-681, ISSN 0742-4787; N. Schwarzer, F. Richter, G. Hecht: ”Elastic Field in a Coated Half Space under Hertzian pressure distribution”, J. of Surface & Coatings Technology 114 (1999) 292-304, ISSN 0257-8972; N. Schwarzer, Th. Chudoba, D. Billep, F. Richter: ”Investigation of coating substrate compounds using inclined spherical indentation”, J. of Surface & Coatings Technology 116 – 119 (1999) 244-252, ISSN 0257-8972, 2003. https://monarch.qucosa.de/id/qucosa%3A18161.

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In this work the author presents simulation procedures (mathematical models) with the aim to help determining and analysing the mechanical properties of coating-substrate-systems and finding an optimal coating structure which should protect the compound from inelastic deformation under a given range of load conditions. Such procedures may be used as a tool to minimise the search field for experimental work. For this purpose one would need a mathematical model which allows one to calculate the complete elastic field with all its displacement and stress components within a multilayer film on a substrate under given mechanical loading and intrinsic stress conditions. Due to copyright restrictions the author is not allowed to publish the Part II of his habilitation thesis at this place. It concerns the references in meta data.
In der Arbeit werden mathematische Modelle zur Berechnung der mechanischen Eigenschaften geschichtet aufgebauter Materialien unter unterschiedlichsten Lastbedingungen (Kontakt- und intrinsische Beanspruchung) vorgestellt und diskutiert. Auf Grund von Schutzrechtsbestimmungen ist eine Veröffentlichung der in der Habilitation angegebenen Literatur im Teil II an dieser Stelle nicht möglich. Der interessierte Leser wird gebeten die Arbeiten in den entsprechenden Journalen einzusehen. Dies betrifft die in den Metadaten angegebenen Veröffentlichungen des Autors.

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Schwarzer, Norbert. "Modelling of the contact mechanics of thin films using analytical linear elastic approaches." Doctoral thesis, [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11244005.

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27

Baska, David A. "An analytical/empirical model for prediction of lateral spread displacements /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/10182.

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28

Yellin, Jessica M. "An analytical and experimental analysis for a one-dimensional passive stand-off layer damping treatment /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/7030.

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29

Walker, Rohan. "Analytical solutions for modeling soft soil consolidation by vertical drains." Access electronically, 2006. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20060725.102120/index.html.

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30

Pearce, Helen A(Helen Annette) 1971. "Experimental and analytical investigation into the shear behaviour of rock joints." Monash University, Dept. of Civil Engineering, 2001. http://arrow.monash.edu.au/hdl/1959.1/8267.

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31

Jain, Nitesh. "Experiment and analytical evaluation of dynamic fracture in graded multifunctional materials /." View online ; access limited to URI, 2005. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/AAI3188059.

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32

Kong, Dali. "Analytical and numerical studies of several fluid mechanical problems." Thesis, University of Exeter, 2012. http://hdl.handle.net/10036/3651.

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In this thesis, three parts, each with several chapters, are respectively devoted to hydrostatic, viscous and inertial fluids theories and applications. In the hydrostatics part, the classical Maclaurin spheroids theory is generalized, for the first time, to a more realistic multi-layer model, which enables the studies of some gravity problems and direct numerical simulations of flows in fast rotating spheroidal cavities. As an application of the figure theory, the zonal flow in the deep atmosphere of Jupiter is investigated for a better understanding of the Jovian gravity field. High viscosity flows, for example Stokes flows, occur in a lot of processes involving low-speed motions in fluids. Microorganism swimming is such typical a case. A fully three dimensional analytic solution of incompressible Stokes equation is derived in the exterior domain of an arbitrarily translating and rotating prolate spheroid, which models a large family of microorganisms such as cocci bacteria. The solution is then applied to the magnetotactic bacteria swimming problem and good consistency has been found between theoretical predictions and laboratory observations of the moving patterns of such bacteria under magnetic fields. In the analysis of dynamics of planetary fluid systems, which are featured by fast rotation and very small viscosity effects, three dimensional fully nonlinear numerical simulations of Navier-Stokes equations play important roles. A precession driven flow in a rotating channel is studied by the combination of asymptotic analyses and fully numerical simulations. Various results of laminar and turbulent flows are thereby presented. Computational fluid dynamics requires massive computing capability. To make full use of the power of modern high performance computing facilities, a C++ finite-element analysis code is under development based on PETSc platform. The code and data structures will be elaborated, along with the presentations of some preliminary results.

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33

Hahn, Steven Eric. "An experimental/analytical investigation of combined shear/end loaded compression strength testing of unidirectional composites." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-12232009-020534/.

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34

Murcia, A. J. (Armando J. ). "Analytical modelling of the performance of a snow deposit under plate loading." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64057.

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35

Beuth, Jack L. "An analytical and experimental study of crack extension in center- notched composites." Thesis, Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/101161.

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The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally in order to evaluate its validity. The theory is applied within a macroscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line crack to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation around the border of an actual rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Predictions of the normal stress ratio theory are obtained for the problems of a unidirectional tensile coupon with a horizontal center notch and a unidirectional losipescu shear specimen with a vertical center notch, each with an arbitrary fiber orientation. These predictions are subsequently compared to experimental results. It is shown that the normal stress ratio theory exhibits a strong ability to correctly predict crack extension direction. Predicted critical stresses correlated well with experimental stresses at crack initiation. Use of the elliptical flaw analysis resulted in significant agreement with observed locations of crack extension, while still providing correct crack extension direction predictions. It is suggested that future analytical studies include application of the normal stress ratio theory as a predictor of critical stresses and its application within a rounded notch tip analysis. Also, future experimental efforts should include performing the critical shear tests identified in this study which could not be performed using the Iosipescu specimen.
M.S.

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36

Taha, Haithem Ezzat Mohammed. "Mechanics of Flapping Flight: Analytical Formulations of Unsteady Aerodynamics, Kinematic Optimization, Flight Dynamics and Control." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/24428.

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A flapping-wing micro-air-vehicle (FWMAV) represents a complex multi-disciplinary system whose analysis invokes the frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, non-conventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, non-autonomous dynamical system. Furthermore, the stringent weight and size constraints that are always imposed on FWMAVs invoke design with minimal actuation. In addition to the numerous motivating applications, all these features of FWMAVs make it an interesting research point for engineers. In this Dissertation, some challenging points related to FWMAVs are considered. First, an analytical unsteady aerodynamic model that accounts for the leading edge vortex contribution by a feasible computational burden is developed to enable sensitivity and optimization analyses, flight dynamics analysis, and control synthesis. Second, wing kinematics optimization is considered for both aerodynamic performance and maneuverability. For each case, an infinite-dimensional optimization problem is formulated using the calculus of variations to relax any unnecessary constraints induced by approximating the problem as a finite-dimensional one. As such, theoretical upper bounds for the aerodynamic performance and maneuverability are obtained. Third, a design methodology for the actuation mechanism is developed. The proposed actuation mechanism is able to provide the required kinematics for both of hovering and forward flight using only one actuator. This is achieved by exploiting the nonlinearities of the wing dynamics to induce the saturation phenomenon to transfer energy from one mode to another. Fourth, the nonlinear, time-periodic flight dynamics of FWMAVs is analyzed using direct and higher-order averaging. The region of applicability of direct averaging is determined and the effects of the aerodynamic-induced parametric excitation are assessed. Finally, tools combining geometric control theory and averaging are used to derive analytic expressions for the textit{Symmetric Products}, which are vector fields that directly affect the acceleration of the averaged dynamics. A design optimization problem is then formulated to bring the maneuverability index/criterion early in the design process to maximize the FWMAV maneuverability near hover.
Ph. D.

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37

Putnam, Zachary Reed. "Improved analytical methods for assessment of hypersonic drag-modulation trajectory control." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53555.

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During planetary entry, a vehicle uses drag generated from flight through the planetary atmosphere to decelerate from hyperbolic or orbital velocity. To date, all guided entry systems have utilized lift-modulation trajectory control. Deployable aerodynamic devices enable drag-modulation trajectory control, where a vehicle controls its energy and range during entry by varying drag area. Implementation of conventional lift-modulation systems is challenging for deployable systems. In contrast, drag-modulation trajectory control may be simpler and lower-cost than current state-of-the-art lift-modulation systems. In this investigation, a survey of analytical methods for computing planetary entry trajectories is presented and the approximate analytical solution to the entry equations of motion originally developed by Allen and Eggers is extended to enable flight performance evaluation of drag-modulation trajectory control systems. Results indicate that significant range control authority is available for vehicles with modestly sized decelerators. The extended Allen-Eggers solution is closed-form and enables rapid evaluation of nonlifting entry trajectories. The solution is utilized to develop analytical relationships for discrete-event drag-modulation systems. These relationships have direct application to onboard guidance and targeting systems. Numerical techniques were used to evaluate drag-modulation trajectory control for precision landing and planetary aerocapture missions, including development of prototype real-time guidance and targeting algorithms. Results show that simple, discrete-event drag-modulation trajectory control systems can provide landed accuracies competitive with the current state of the art and a more benign aerothermal environment during entry for robotic-scale exploration missions. For aerocapture, drag-modulation trajectory control is shown to be feasible for missions to Mars and Titan and the required delta-V for periapsis raise is insensitive to the particular method of drag modulation. Overall, results indicate that drag-modulation trajectory control is feasible for a subset of planetary entry and aerocapture missions. To facilitate intelligent system selection, a method is proposed for comparing lift and drag-modulation trajectory control schemes. This method applies nonlinear variational techniques to closed-form analytical solutions of the equations of motion, generating closed-form expressions for variations of arbitrary order. This comparative method is quantitative, performance-based, addresses robustness, and applicable early in the design process. This method is applied to steep planetary entry trajectories and shows that, in general, lift and drag-modulation systems exhibit similar responses to perturbations in environmental and initial state perturbations. However, significant differences are present for aerodynamic perturbations and results demonstrate that drag systems may be more robust to uncertainty in aerodynamic parameters. Finally, the results of these contributions are combined to build a set of guidelines for selecting lift or drag-modulation for a Mars Science Laboratory-class planetary entry mission.

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38

Tryggeson, Henrik. "Analytical vortex solutions to Navier-Stokes equation." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1282.

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Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.

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39

Mello, Frank James. "Weak formulations in analytical dynamics, with applications to multi-rigid-body systems, using time finite elements." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/32854.

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40

Mo, Pin-Qiang. "Centrifuge modelling and analytical solutions for the cone penetration test in layered soils." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14319/.

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The interpretation of measurements from the cone penetration test is still predominately based on empirical correlations, which can be attributed to the lack of understanding of penetration mechanisms, that involve severe stress-strain and shear dilatancy close to the probe. Even so, it remains one of the most widely used in-situ tools for site characterisation, and several methods for displacement pile design have been developed using CPT data. This research investigates the response of penetrometers and the behaviour of layered soils during installation of probes using geotechnical centrifuge modelling and cavity expansion analysis. Two series of centrifuge tests were performed in stratum configurations of silica sand in a half-cylindrical axisymmetric model, allowing the observation of the induced soil deformation through a Perspex window. The variations of penetration resistance and soil deformation with penetration depth, soil density, stress level and soil layering are examined from the results of the centrifuge tests. The quantified soil displacements and the resulting strains in the axisymmetric model have provided an effective approach for investigation of penetration mechanisms with soil element trajectories, strain paths and rotations of principal strain rate. The effects of layering on both resistance and soil deformation are shown with dependence of the relative soil properties and profiles. The results presented also serve as a base for applications of cavity expansion solutions, back analyses and further studies. Analytical solutions for cavity expansion in two concentrically arranged regions of soil are developed using a non-associated Mohr-Coulomb yield criterion for large strain analysis of both spherical and cylindrical cavities. The solutions are validated against finite element simulations and a detailed parametric study of the layered effects on the pressure-expansion curves is performed. To apply the proposed solutions to penetration problems, a simplified combination approach is suggested to eliminate the discrepancy between concentric layering and horizontal layering. The analytical study of penetration in two-layered and multi-layered soils is therefore achieved, with comparisons to elastic solutions and numerical simulations provided. The back analyses based on the resistance and soil deformation emphasise the influences of small-strain stiffness, soil-probe interface friction angle, and relative density/state parameter. The correlation between the cone tip resistance and the pile bearing capacity is also discussed, and the scale effects are examined through the ground surface effect and the layering effect by the developed cavity expansion solutions. The penetration mechanisms are summarised from the aspects of soil stress-strain history, particle breakage, soil patterns, and penetration in layered soils. The layered effects emphasised in this research indicate that the penetration resistance is strongly dependent on the soil properties within the influence zones above and below the probe tip, and also related to the in-situ stress gradient along the penetration path. It is also suggested that correlations from calibration chamber tests using uniform soil and a constant stress field may not be suitable for direct interpretation of CPT data. Finally, the averaging technique for pile design is suggested based on the transition curve of tip resistance in layered soils with consideration of the scale effects.

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41

Li, Lin. "A semi-analytical self-similar solution of a bent-over jet in crossflow /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20353029.

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42

Deglaire, Paul. "Analytical Aerodynamic Simulation Tools for Vertical Axis Wind Turbines." Doctoral thesis, Uppsala universitet, Elektricitetslära, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-132073.

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Wind power is a renewable energy source that is today the fastest growing solution to reduce CO2 emissions in the electric energy mix. Upwind horizontal axis wind turbine with three blades has been the preferred technical choice for more than two decades. This horizontal axis concept is today widely leading the market. The current PhD thesis will cover an alternative type of wind turbine with straight blades and rotating along the vertical axis. A brief overview of the main differences between the horizontal and vertical axis concept has been made. However the main focus of this thesis is the aerodynamics of the wind turbine blades. Making aerodynamically efficient turbines starts with efficient blades. Making efficient blades requires a good understanding of the physical phenomena and effective simulations tools to model them. The specific aerodynamics for straight bladed vertical axis turbine flow are reviewed together with the standard aerodynamic simulations tools that have been used in the past by blade and rotor designer. A reasonably fast (regarding computer power) and accurate (regarding comparison with experimental results) simulation method was still lacking in the field prior to the current work. This thesis aims at designing such a method. Analytical methods can be used to model complex flow if the geometry is simple. Therefore, a conformal mapping method is derived to transform any set of section into a set of standard circles. Then analytical procedures are generalized to simulate moving multibody sections in the complex vertical flows and forces experienced by the blades. Finally the fast semi analytical aerodynamic algorithm boosted by fast multipole methods to handle high number of vortices is coupled with a simple structural model of the rotor to investigate potential aeroelastic instabilities. Together with these advanced simulation tools, a standard double multiple streamtube model has been developed and used to design several straight bladed rotor ranging from 2 kW to 20 kW.
Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 704

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43

Li, Lin, and 李琳. "A semi-analytical self-similar solution of a bent-over jet in crossflow." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31221373.

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44

Littell, Justin. "The Experimental and Analytical Characterization of the Macromechanical Response for Triaxial Braided Composite Materials." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1224164770.

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45

El-Hajjar, Rani Fayez. "Experimental study and analytical modeling of translayer fracture in pultruded FRP composites." Diss., Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-03152004-230942/unrestricted/elhajjar%5Frani%5Ff%5F200405%5Fphd.pdf.

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Thesis (Ph. D.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2004.
Dr. Zureick, Abdul-Hamid, Committee Member; Dr. White, Donald, Committee Member; Dr. Saxena, Ashok, Committee Member; Dr. Jacobs, Laurence, Committee Member; Dr. Haj-Ali, Rami, Committee Chair; Dr. Armanios, Erian, Committee Member. Vita. Includes bibliographical references (leaves 164-172).

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46

Ebrahimpour, Mohammad Reza. "An analytical study of the power flow equations with applications to systems with multiple close solutions." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/15746.

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47

Tinker, John Andrew. "Development of an Ultra-Lightweight Buckling-Restrained Brace Using Analytical and Numerical Methods." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/447.

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An ultra-lightweight buckling-restrained brace (ULWBRB) is developed using a highly ductile aluminum core and FRP restrainer. Utilization of lightweight materials results in a BRB that is 25% the weight of traditional mortar-filled tube varieties allowing easy installation in small to medium sized buildings requiring seismic retrofit without the need for heavy equipment. Construction utilizes commonly stocked materials able to be customized for required strength, drift, and geometry limitations. Analytical single degree of freedom (SDOF) and Euler buckling models are compared with published equations to determine the required restrainer stiffness (RRS). SDOF models yield RRS values 200% higher than the Euler model. Applied end moments due to frame deformation are incorporated into a modified design method that gives RRS values 50% higher than Euler model without eccentricity. RRS is provided using a bundled and wrapped FRP tube configuration using a developed shear flow method considering composite action. Uniaxial low-cycle fatigue (LCF) testing of a 6061-T6 candidate alloy provides data for a constitutive model using combined kinematic-isotropic hardening. LCF testing of round short gage coupons indicates the candidate alloy is capable of stable cycling to 2%, 3%, and 4% total strain with excellent ductility. Early fracture of specimens at 24, 18, and 11 cycles, respectively, also indicates that other candidate alloys should be examined for improved fatigue life. However, inconsistency is noted between similar tests of 6061-T6 that were able to achieve up to 76 cycles at 2.5% total strain. ULWBRB FEA models loaded monotonically consistently give higher RRS values as compared to the analytical methods. This is due to assignment of initial imperfections, longer more realistic unbraced length, higher axial loads achieved through the post-yield region, and plastic hinging potential. Cyclic simulations of braces with the same RRS values are also able to achieve reliable and stable hysteretic behavior through 21 cycles. If a less stiff restrainer is used, cumulative energy dissipation potential is reduced considerably due to pinched hysteresis loops and strain ratcheting. Applied end moments are found to have a linear effect on the RRS that can be modeled by superposition of the buckling effect plus end moment.

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Yang, Shuilong. "Experimental and analytical investigation of the effect of autofrettage on fatique damage development in blocks containing crossbores under cyclic internal pressure /." Access abstract and link to full text, 1995. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9528551.

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LI, JUNSHAN. "The Development of Semi-Analytical Solutions for 3-D Contact Problems." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1092069082.

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Goodpaster, Benjamin A. "Analytical Modeling and Impedance Characterization of Nonlinear, Steady-State Structural Dynamics in Thermomechanical Loading Environments." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524063139635613.

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Dissertations / Theses on the topic 'Analytical mechanics'

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