Cellular core structures are the state-of-the-art technology for light weight structures in the aerospace industry. In an aerospace product, sandwich panels with cellular core represent the primary structural component as a given aerospace product may contain a large number of sandwich panels. This reveals the necessity of understanding the mechanical behavior of the cellular core and the impact of that behavior on the overall structural behavior of the sandwich panel, and hence the final aerospace product. As the final aerospace product must go through multiple qualification tests to achieve a final structure that is capable of withstanding all environments possible, analyzing the structure prior to testing is very important to avoid any possible failures and to ensure that the final design is indeed capable of withstanding the loads. To date, due to the lack of full understanding of the mechanical behavior of cellular cores and hence the sandwich panels, there still remains a significant lack of analytical capability to predict the proper behavior of the final product and failures may still occur even with significant effort spent on pre-test analyses. Analyzing cellular core to calculate the equivalent material properties of this type of structure is the only way to properly design the core for sandwich enhanced stiffness to weight ratio of the sandwich panels. A detailed literature review is first conducted to access the current state of development of this research area based on experiment and analysis. Then, one of the recently developed homogenization schemes is chosen to investigate the mechanical behavior of heavy, non-corrugated square cellular core with a potential application in marine structures. The mechanical behavior of the square cellular core is then calculated by applying the displacement approach to a representative unit cell finite element model. The mechanical behavior is then incorporated into sandwich panel finite element model and in an in-house code to test the predicted mechanical properties by comparing the center-of-panel displacement from all analyses to that of a highly detailed model. The research is then expanded to cover three cellular core shapes, hexagonal cores made of corrugated sheets, square cores made of corrugated sheets, and triangular cores. The expansion covers five different cell sizes and twenty one different core densities for each of the core shapes considering light cellular cores for space applications, for a total of 315 detailed studies. The accuracy of the calculated properties for all three core shapes is checked against highly detailed finite element models of sandwich panels. Formulas are then developed to calculate the mechanical properties of the three shapes of cellular cores studied for any core density and any of the five cell sizes. An error analysis is then performed to understand the quality of the predicted equivalent properties considering the panel size to cell size ratio as well as the facesheet thickness to core thickness ratio. The research finally expanded to understand the effect of buckling of the unit cell on the equivalent mechanical property of the cellular core. This part of the research is meant to address the impact of the local buckling that may occur due to impact of any type during the manufacturing, handling or assembly of the sandwich panels. The variation of the equivalent mechanical properties with the increase in transverse compression load, until the first folding of the unit cell is complete, is calculated for each of the three core shapes under investigation. / Ph. D.

The solutions to many problems in structural design and analysis are quite laborious and time-consuming. This fact has motivated the search for analogies that might lead to quicker, yet accurate solutions. Fortunately, the laws governing structural behavior find many parallels among the laws of electricity and, therefore, it is conceivable that electrical circuits may be devised which are equivalent to certain structural problems. It is the purpose of this thesis to set up several equivalent circuits and to present solutions using accepted methods of analysis. Only statistical loadings are considered. Information about necessary equipment for experimental work is given. Examples given show which analogs are best suited to certain structural problems. It is hoped that the foregoing will stimulate more investigation in the field of electrical analogies for structural problems. A discussion follows which will present the work which has previously been done in this field. This will help to acquaint the reader with the subject and show the need for further development. / Master of Science

As compared to traditional cloud computing, edge computing provides computational, sensor, and storage resources co-located with client requests, thereby reducing network transmission and providing context-awareness. While server farms can allocate cloud computing resources on demand at runtime, edge-based heterogeneous devices, ranging from stationary servers to mobile, IoT, and energy harvesting devices are not nearly as reliable and abundant. As a result, edge application developers face the following obstacles: 1) heterogeneous devices provide hard-to-access resources, due to dissimilar capabilities, operating systems, execution platforms, and communication interfaces; 2) unreliable resources cause high failure rates, due to device mobility, low energy status, and other environmental factors; 3) resource scarcity hinders the performance; 4) the dissimilar and dynamic resources across edge environments make QoS impossible to guarantee. Edge environments are characterized by the prevalence of equivalent functionalities, which satisfy the same application requirements by different means. The thesis of this research is that equivalent functionalities can be exploited to improve the reliability, efficiency, and adaptiveness of edge-based services. To prove this thesis, this dissertation comprises three key interrelated research thrusts: 1) create a system architecture and programming support for providing edge services that run on heterogeneous and ever changing edge devices; 2) introduce programming abstractions for executing equivalent functionalities; 3) apply equivalent functionalities to improve the reliability, efficiency, and adaptiveness of edge services. We demonstrate how the connected devices with unreliable, dynamic, and scarce resources can automatically form a reliable, adaptive, and efficient execution environment for sensing, computing, and other non-trivial tasks. This dissertation is based on 5 conference papers, presented at ICDCS'20, ICWS'19, EDGE'19, CLOUD'18, and MobileSoft'18 / Doctor of Philosophy / As mobile and IoT devices are generating ever-increasing volumes of sensor data, it has become impossible to transfer this data to remote cloud-based servers for processing. As an alternative, edge computing coordinates nearby computing resources that can be used for local processing. However, while cloud computing resources are abundant and reliable, edge computing ones are scarce and unreliable. This dissertation research introduces novel execution strategies that make it possible to provide reliable, efficient, and flexible edge-based computing services in dissimilar edge environments.

Binaural simulation is the recreation of a three-dimensional audio environment around a listener's head. The binaural simulation of structural acoustic data would open new opportunities in virtual prototyping and simulation. By modeling the structure as an array of vibrating monopoles and applying Head Related Transfer Functions (HRTFs) to each of the sources, a binaural simulation of this type can be created. Unfortunately, this simulation method requires an extensive amount of computer power and speed for real-time simulation, more so than is available with current technology. The objective of this research is to reduce the number of computations required in the binaural simulation of structural acoustic data. This thesis details two methods of reducing the number of real-time calculations required in this binaural analysis: singular value decomposition (SVD), and equivalent source reduction (ESR). The SVD method reduces the complexity of the HRTF computations by breaking the HRTFs into dominant singular values and vectors. The ESR method reduces the number of sources to be analyzed in real-time by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. The ESR and SVD reduction methods can be combined to provide an estimated computation time reduction of 99.4%. In addition, preliminary tests show that there is a 97% correlation between the results of the combined reduction methods and the results found with current binaural simulation techniques. / Master of Science

<p>This thesis investigates simulation of synchronous machines using a novel Magnetic Equivalent Circuit (MEC) model. The proposed model offers sufficient detail richness for design calculations, while still keeping the simulation time acceptably short.</p><p>Different modeling methods and circuit alternatives are considered. The selected approach is a combination of several previous methods added with some new features. A detailed description of the new model is given. The flux derivative is chosen as the magnetic flow variable which enables a description with standard circuit elements. The model is implemented in dq-coordinates to reduce complexity and simulation time. A new method to reflect winding harmonics is introduced.</p><p>Extensive measurements have been made to estimate the traditional dq-model parameters. These in combination with analytical calculations are used to determine the parameters for the new MEC model.</p><p>The model is implemented using the Dymola simulation program. The results are evaluated by comparison with measurements and FEM simulations. Three different operation cases are investigated; synchronous operation, asynchronous start and inverter fed operation. The agreement with measurements and FEM simulations varies, but it is believed that it can be improved by more work on the parameter determination.</p><p>The overall conclusion is that the MEC method is a useful approach for detailed simulation of synchronous machines. It enables proper modeling of magnetic saturation, and promises sufficiently detailed results to enable accurate loss calculations. However, the experience is that the complexity of the circuits should be kept at a reasonable low level. It is believed that the practical problems with model structure, parameter determination and the simulation itself will otherwise be difficult to master.</p>

<p>The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass.</p><p>The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation.</p><p>Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study.</p><p>The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis.</p><p><b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN)</p>

The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass. The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation. Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study. The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis. <b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN) / NR 20140805

The aim of this thesis is to expand on parts of the work of Björn–Björn–Shanmugalingam [2] and in particular on the construction and properties of hyperbolic fillings of nonempty bounded metric spaces. In light of [2], we introduce two new parameters λ and ξ to the construction while relaxing a specific maximal-condition. With these modifications we obtain a slightly more flexible model that generates a larger family of hyperbolic fillings. We then show that every hyperbolic filling in this family possess the desired property of being Gromov hyperbolic. Next, we uniformize an arbitrary hyperbolic filling of this type and show that, under fairly weak conditions, the boundary of the uniformization is snowflake-equivalent to the completion of the metric space it corresponds to. Finally, we show that this unifomized hyperbolic filling is a uniform space. In summary, our construction generates hyperbolic fillings which satisfy the necessary conditions for it to serve its intended purpose of an analytical tool for further studies in [2, Chapters 9-13 ] or similar. As such, it can be regarded as an improvement to the reference model.

<p> Some aspects of the nucleon-nucleon interaction are investigated. Phase-equivalent families of rank-two separable potentials are derived by inverting the on- shell phaseshifts. The off-shell properties of these potentials are examined and shown to be well behaved. These and additiona l pairs of phase-equivalent local and separable potentials are included in a proton-proton bremsstrahlung calculation. In particular, the off-shell dependence of the cross sections is shown to be small. </p> / Thesis / Doctor of Philosophy (PhD)

Transmission line reactance is an important parameter in carrying out stability studies. The model proposed here utilizes available real time synchrophasor data and information about the generation in the ERCOT grid to determine the Thevenin equivalent reactance of a line. Synchrophasors provide the advantage of synchronized measurements of phase angles which are essential in determining the transmission line reactance. This thesis provides the results of applying this model to estimate the Thevenin equivalent line reactance between McDonald Observatory in West Texas and The University of Texas at Austin. / text