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Articles 5011 - 5040 of 7290
Full-Text Articles in Engineering
Adaptive Feature Extraction And Svm Classification For Real-Time Fault Diagnosis Of Drivetrain Gearboxes, Dingguo Lu, Wei Qiao
Adaptive Feature Extraction And Svm Classification For Real-Time Fault Diagnosis Of Drivetrain Gearboxes, Dingguo Lu, Wei Qiao
Department of Electrical and Computer Engineering: Faculty Publications
Drivetrain gearboxes play an important role in many modern industrial applications. This paper presents a novel method consisting of adaptive feature extraction and support vector machine (SVM)-based classification for condition monitoring and fault diagnosis of drivetrain gearboxes operating in variable-speed conditions. An adaptive signal resampling algorithm, a frequency tracker, and a feature generation algorithm are integrated in the proposed method for effective extraction of the features of gearbox faults from the stator current signal of the AC electric machine connected to the gearbox. A radial basis function kernel-SVM classifier is designed to identify the fault in the gearbox according to …
Achievable Throughput Regions Of Fading Broadcast And Interference Channels Under Qos Constraints, Deli Qiao, Mustafa Cenk Gursoy, Senem Velipasalar
Achievable Throughput Regions Of Fading Broadcast And Interference Channels Under Qos Constraints, Deli Qiao, Mustafa Cenk Gursoy, Senem Velipasalar
Department of Electrical and Computer Engineering: Faculty Publications
Transmission over fading broadcast and interference channels in the presence of quality of service (QoS) constraints is studied. Effective capacity, which provides the maximum constant arrival rate that a given service process can support while satisfying statistical QoS constraints, is employed as the performance metric. In the broadcast scenario, the effective capacity region achieved with superposition coding and successive interference cancellation is identified and is shown to be convex. Subsequently, optimal power control policies that achieve the boundary points of the effective capacity region are investigated, and an algorithm for the numerical computation of the optimal power adaptation schemes for …
Adaptive Threshold Displacement Algorithm For Removing Hidden Information From Digital Images, Fahimeh Rezaei, Michael Hempel, Tao Ma, Pradhumna Lal Shrestha, Dongming Peng, Hamid Sharif
Adaptive Threshold Displacement Algorithm For Removing Hidden Information From Digital Images, Fahimeh Rezaei, Michael Hempel, Tao Ma, Pradhumna Lal Shrestha, Dongming Peng, Hamid Sharif
Department of Electrical and Computer Engineering: Faculty Publications
The growth of the Internet and online social media, especially in recent years, also gave rise to a proliferation of online multimedia content creation and distribution. The use of modern steganography methods – the art of hiding information within multimedia – presents an unprecedented opportunity for malicious uses of these materials. Therefore, developing an effective technique to avoid the distribution of secret data is a significant problem that is addressed in this paper for digital images. We introduce a novel algorithm to remove the steganography information embedded in an image without changing the quality of the image and with no …
Adaptive Channel Allocation And Routing In Cognitive Radio Networks, Zhihui Shu, Jiazhen Zhou, Yi Qian, Rose Qingyang Hu
Adaptive Channel Allocation And Routing In Cognitive Radio Networks, Zhihui Shu, Jiazhen Zhou, Yi Qian, Rose Qingyang Hu
Department of Electrical and Computer Engineering: Faculty Publications
One of the biggest challenges in multi-hop cognitive radio networking is the dynamic change of channel availability to secondary users which could cause the breaking of routes and thus communications. To address this challenge, we propose an adaptive channel allocation and routing scheme in this paper. Our scheme is flexible so that it can react to the dynamic change of channel availability, and it can maximize the throughput by exploiting network coding opportunities. First, we model the primary users’ activity, channel availability and the interference among the secondary users in a cognitive radio network environment, and show how to implement …
Effect Of Aviation Fuel Type And Fuel Injection Conditions On The Spray Characteristics Of Pressure Swirl And Hybrid Air Blast Fuel Injectors, Rick Thomas Feddema
Effect Of Aviation Fuel Type And Fuel Injection Conditions On The Spray Characteristics Of Pressure Swirl And Hybrid Air Blast Fuel Injectors, Rick Thomas Feddema
Open Access Theses
Feddema, Rick T. M.S.M.E., Purdue University, December 2013. Effect of Aviation Fuel Type and Fuel Injection Conditions on the Spray Characteristics of Pressure Swirl and Hybrid Air Blast Fuel Injectors. Major Professor: Dr. Paul E. Sojka, School of Mechanical Engineering
Spray performance of pressure swirl and hybrid air blast fuel injectors are central to combustion stability, combustor heat management, and pollutant formation in aviation gas turbine engines. Next generation aviation gas turbine engines will optimize spray atomization characteristics of the fuel injector in order to achieve engine efficiency and emissions requirements.
Fuel injector spray atomization performance is affected by the …
Microstructural Evolution During Stress Relaxation Of Gold Thin Films, Luthfia Amra Syarbaini
Microstructural Evolution During Stress Relaxation Of Gold Thin Films, Luthfia Amra Syarbaini
Open Access Theses
Microstructure evolution in metal thin films for use in microelectronic devices was studied due to the formation of defects such as whiskers and hillocks that may cause problems in electrical circuits. Thin film stress relaxation can occur through a variety of processes. Understanding such mechanisms and the conditions under which certain mechanism dominate can potentially lead to the improved control of thin film stability. Studies of the 3D microstructural changes in Au thin films on silicon and other substrates with different thermal expansion coefficients aid us in understanding thin film relaxation phenomena such as hillock/whisker formation. Techniques such as in-situ …
Developing A Holistic Modeling Approach For Search-Based System Architecting, Renzhong Wang, Cihan H. Dagli
Developing A Holistic Modeling Approach For Search-Based System Architecting, Renzhong Wang, Cihan H. Dagli
Engineering Management and Systems Engineering Faculty Research & Creative Works
This paper proposes a holistic modeling approach that combines the capabilities of Object Process Methodology (OPM), Colored Petri Net (CPN), and feature model. The resultant holistic model not only can capture the structural, behavioral, and dynamic aspects of a system, allowing simulation and strong analysis methods to be applied, it can also specify the architectural design space. This modeling approach is developed to facilitate the implementation of search-based system architecting where search algorithms are used to explore design trade space for good architecture alternatives. Such architecting approach integrates certain model construction, alternative generation, simulation, and assessment processes into a coherent …
Minimum-Mass Panels Under Probabilistic Aeroelastic Flutter Constraints, Bret Stanford, Philip Beran
Minimum-Mass Panels Under Probabilistic Aeroelastic Flutter Constraints, Bret Stanford, Philip Beran
United States Air Force: Publications
Aeroelastic flutter is a dangerous failure mode, and aircraft structural components are designed under a deterministic flutter margin. Meeting this safety factor may result in overly-conservative structures, however, an alternative approach incorporates uncertainties into the computational models, and imposes a maximum allowable flutter probability during the optimization process. This technique is demonstrated for the variable-thickness design of an elastic panel subjected to supersonic flow. A performance measure approach based on the first -order reliability method incorporates probabilistic flutter constraints during the search for a minimum-mass panel. Optimization results are given for uncertainties in the panel's boundary conditions, and for non-deterministic …
Social Pervasive Systems: The Integration Of Social Networks And Pervasive Systems, Soumaia Al Ayyat
Social Pervasive Systems: The Integration Of Social Networks And Pervasive Systems, Soumaia Al Ayyat
Papers, Posters, and Presentations
Sensor technology embedded in smart mobile devices branded such devices as candidates for building innovative context-aware pervasive applications. On a parallel front, the notable evolution in the shape and form of social networking and their seamless accessibility from mobile devices founded a goldmine of contextual information. Utilizing an ecosystem that combines both mobile smart devices and a big data like environment in the form of social networks allows for the creation of an elitist set of services and applications that merge the two domains. In this paper, and following the footsteps of similar research efforts that attempted to combine both …
Multi-Scale Characterization Of Nanostructured Sodium Aluminum Hydride, Shathabish Narasegowda
Multi-Scale Characterization Of Nanostructured Sodium Aluminum Hydride, Shathabish Narasegowda
Doctoral Dissertations
Complex metal hydrides are the most promising candidate materials for onboard hydrogen storage. The practicality of this class of materials is counter-poised on three critical attributes: reversible hydrogen storage capacity, high hydrogen uptake/release kinetics, and favorable hydrogen uptake/release thermodynamics. While a majority of modern metallic hydrides that are being considered are those that meet the criteria of high theoretical storage capacity, the challenges lie in addressing poor kinetics, thermodynamics, and reversibility. One emerging strategy to resolve these issues is via nanostructuring or nano-confinement of complex hydrides. By down-sizing and scaffolding them to retain their nano-dimensions, these materials are expected to …
Mercury Concentrations In Tropical Resident And Migrant Songbirds On Hispaniola, Jason M. Townsend, Christopher C. Rimmer, Charles T. Driscoll, Kent P. Mcfarland, Eduardo E. Inigo-Elias
Mercury Concentrations In Tropical Resident And Migrant Songbirds On Hispaniola, Jason M. Townsend, Christopher C. Rimmer, Charles T. Driscoll, Kent P. Mcfarland, Eduardo E. Inigo-Elias
Civil and Environmental Engineering - All Scholarship
Despite growing concerns over mercury (Hg) exposure to humans and wildlife on a global scale, little is known about Hg bioaccumulation in the New World tropics. From 2005 to 2011, we monitored Hg concentrations in blood of nine avian species occupying a geographic range of tropical wet broadleaf sites on the island of Hispaniola, including eight passerines (two Nearctic- Neotropical migrant and six resident species) and one top order predatory accipiter. Invertivorous songbirds were further differentiated by foraging guild, with six species of groundforagers and two species of foliage-gleaners. Blood Hg concentrations were orders of magnitude higher in birds sampled …
Some Insights For The Prediction Of Near-Wall Turbulence, Farid Karimpour, Subhas K. Venayagamoorthy
Some Insights For The Prediction Of Near-Wall Turbulence, Farid Karimpour, Subhas K. Venayagamoorthy
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
In this paper, we revisit the eddy viscosity formulation to highlight a number of important issues that have direct implications for the prediction of near-wall turbulence. For steady wall-bounded turbulent flows, we make the equilibrium assumption between rates of production (P) and dissipation (ε) of turbulent kinetic energy (κ) in the near-wall region to propose that the eddy viscosity should be given by vt ε/S2, where S is the mean shear rate. We then argue that the appropriate velocity scale is given by (STL)-1/2 k1/2 where TL = k ε is the turbulence (decay) time scale. The …
Metrology Of Volume Chirped Bragg Gratings Recorded In Photo-Thermo-Refractive Glass For Ultrashort Pulse Stretching And Compressing, Christopher Lantigua
Metrology Of Volume Chirped Bragg Gratings Recorded In Photo-Thermo-Refractive Glass For Ultrashort Pulse Stretching And Compressing, Christopher Lantigua
Electronic Theses and Dissertations
Chirped Bragg gratings (CBGs) recorded in photo-thermo-refractive (PTR) glass provide a very efficient and robust way to stretch and compress ultra-short laser pulses. These gratings offer the ability to stretch pulses from hundreds of femtoseconds, to the order of 1 ns and then recompress them. However, in order to achieve pulse stretching of this magnitude, 100 mm thick CBGs are needed. Using these CBGs to both stretch, and re-compress the pulse thus requires propagation through 200 mm of optical glass. This therefore demands perfect control of the glass homogeneity, as well as the holographic recording process of the CBG. In …
Nano-Silicon/Graphene Composite Anodes For Enhanced Performance Lithium Ion Batteries, Rhet Joseph Caballes De Guzman
Nano-Silicon/Graphene Composite Anodes For Enhanced Performance Lithium Ion Batteries, Rhet Joseph Caballes De Guzman
Wayne State University Dissertations
The ever evolving technological applications such as with portable electronics and electric vehicles have led to increasing energy demands that have proven the existing commercial LIB capacity insufficient. Recently, the most promising anode material to substitute the traditional graphite is Si. As an anode Si has low discharge potential and theoretical the highest known theoretical capacity (>10 fold of graphite). However, due to the increased accommodated Li+ during charge-discharge reactions, silicon's volume varies up to 400%, causing pulverization and loss of electrical contact.
This dissertation focuses on a systematic approach in developing effective means to utilize Si for improved …
Development And Implementation Of A Proactive Safety Performance Evaluation System For General Contractors, Ahmet Selim Alpmen
Development And Implementation Of A Proactive Safety Performance Evaluation System For General Contractors, Ahmet Selim Alpmen
Wayne State University Dissertations
Construction safety is an essential aspect of the construction industry and measuring safety performance has been of continuing concern. Most of the preceding studies concentrated on two widely used metrics in industry to evaluate and improve safety performance, EMR and incidence rates. However, it is recognized that these metrics have shortcomings, such as being reactive and not proactive, or representing a macroscopic approach and not microscopic approach, or disregarding the events that lead to accidents and only being result-oriented. Improving safety is one aspect of a research but using an appropriate safety measure is as important. Using these parameters comes …
Performance Qualification And Raman Investigation On Cell Behavior And Aging Of Lifepo₄ Cathodes In Lithium-Ion Batteries, Amir Salehi
Material Science and Engineering Theses - Archive
This thesis explores the ability of Raman spectroscopy to understand the complex chemistry taking place in LiFePO₄ cathodes of Li ion batteries. The performance of Li ion batteries was optimized through electrode fabrication and assembling procedures. Various amounts of Timcal Super P carbon were used to construct a conductive network of C-LiFePO₄ particles and the performance of the cathodes was examined during battery cycling. Raman spectroscopy along with electrochemical characterization such as charge/ discharge curves, electrochemical impedance spectroscopy and Cyclic Voltammetry was employed for detailed investigation of battery performance and aging. It is found that both quantity and quality of …
Effects Of Surface Plasmon Excitations On Photoluminescence By Cdse/Zns Quantum Dots, Ankit Kumar Singh
Effects Of Surface Plasmon Excitations On Photoluminescence By Cdse/Zns Quantum Dots, Ankit Kumar Singh
Material Science and Engineering Theses - Archive
The influence of localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs) on the photoluminescence (PL) spectra of core/shell type CdSe/ZnS quantum dots (QDs) has been studied. Thin film samples of these QDs were deposited on glass slides, irradiated by 514 nm polarized beam from an Argon-ion laser, and PL spectra were measured using a high-resolution 1250M JY-Horiba spectrometer equipped with liquid-nitrogen cooled CCD detector. In the first set of experiments, PL spectra were measured on QDs and QDs-Au NPs mixture as a functions of the intensity of the 514 nm laser beam. In the second set of experiments, PL …
Synthesis Of Silver-Diamond Like Carbon Thin Films By Magnetron Sputtering, Venkatesh Majji
Synthesis Of Silver-Diamond Like Carbon Thin Films By Magnetron Sputtering, Venkatesh Majji
Material Science and Engineering Theses - Archive
Diamond-like carbon thin films are been used in wide range of applications due to their attractive tribological properties. Metal-doped DLC films have significant properties which make them compatible to use in larger variety of applications. The present study examines the dispersion and their effect on various tribological properties when Ag is incorporated into the DLC thin films. These Ag-DLC nanocomposite films were synthesized by a hybrid CVD and magnetron sputtering process in a discharge composed of CH4, and Ar atmosphere. These DLC and Ag-DLC films were characterized by Transmission Electron Microscopy (TEM), Fourier Transform Infrared Spectroscopy (FTIR), X-ray Photoelectron Spectroscopy …
Effects Of Strain Energy Release Rate On Delamination In Temperature Environment, Venkata Naga Ravitej Sankarabatla
Effects Of Strain Energy Release Rate On Delamination In Temperature Environment, Venkata Naga Ravitej Sankarabatla
Mechanical and Aerospace Engineering Theses - Archive
Delamination is the weakest and major failure mode in laminated composites. Extensive efforts on initiation and growth of delamination under mechanical load have been investigated. A little emphasis was made earlier to account for the delamination in laminates under temperature loading. Strain energy release rate, a fracture mechanics parameter has been widely accepted to use for study the characteristics of delamination growth. In order to conduct a quick assessment of delamination growth, a closed form expression is developed to quantify the strain energy release rate of the laminate subjected to temperature environment. A finite element model is also developed to …
Role Of Engine Age And Lubricant Chemistry On The Characteristics Of Egr Soot, Olusanmi Adeniji Adeniran
Role Of Engine Age And Lubricant Chemistry On The Characteristics Of Egr Soot, Olusanmi Adeniji Adeniran
Material Science and Engineering Theses - Archive
Exhaust products of Diesel Engines serves as an environmental hazard, and to curtail this problem a Tier 3 emission standard was introduced which involves change in engine designs and introduction of EGR systems in Diesel engines. EGR systems, however has the challenge of generating soot which are abrasive and are major causes of wear in Diesel engines. This work has studied the characteristics of EGR soot formed in different range of engine age and in different lubricant chemistries of Mineral and Synthetic based diesel Oils. It is found that lubricant degradation is encouraged by less efficient combustion as engine age …
Cold Plasma Treatment Of Magnetic Nanoparticles, Ke Wang
Cold Plasma Treatment Of Magnetic Nanoparticles, Ke Wang
Material Science and Engineering Theses - Archive
This thesis investigates the application of cold plasma to remove the oleic acid bonded on magnetic nanoparticles: SmCo5 nanoflakes prepared via surfactant assisted high energy ball milling and CoFe2O4 nanoparticles prepared via chemical synthesis. Oleic acid molecules bonded on nanoparticles are in the carboxylate form which could not be washed away by organic solvents in ultrasonic bath; only free oleic acid molecules left on the nanoparticle surface after ball milling can be washed away through ultrasonic bath. High temperature annealing method works for removing oleic acid but nanoparticles would be damaged because of oxidation and decomposition.The RF cold plasma has …
Investigation Of Side Wall Effects On An Inward Scramjet Inlet At Mach Number 8.6, Tiago Cavalcanti Rolim
Investigation Of Side Wall Effects On An Inward Scramjet Inlet At Mach Number 8.6, Tiago Cavalcanti Rolim
Mechanical and Aerospace Engineering Dissertations - Archive
Experimental and computational studies were conducted to evaluate the performance of a scramjet inlet as the side cowl length is changed. A slender inward turning inlet with a total length of 304.8 mm, a span of 50.8 mm with a top and a bottom compression ramp each at 11.54 deg and a compression ratio of 4.79 was used. The side cowl lengths were of 0, 50.8 and 76.2 mm. The UTA Hypersonic Shock Tunnel facility was used in the reflected mode to test the inlet model. The model was instrumented with nine piezoelectric pressure transducers, for static and total pressure …
Development Of Artificial Neural Network Based Black Box Model Of A Data Center As A Temperature Predicting Tool As A Function Of Server Location, Dissipating Server Heat And Crac Fan Speed, Chinmay N. Date
Mechanical and Aerospace Engineering Theses - Archive
Modern data centers consume an astonishing 1.3\% power all around the world. As the number of data centers continue to grow, there is an increasing need and demand to develop new ways to reduce the power footprint. Several approaches are being made to achieve this. One of such several approaches is to develop control systems that would keep the data centers running energy efficiently. Various control theories have been developed throughout the world to achieve the optimal energy efficient state. However, during the synthesis of such control schemes, the CFD simulations take up excessive time for plotting the thermal map …
Development Of Multi-Element Active Aerodynamics For The Formula Sae Car, James Patrick Merkel
Development Of Multi-Element Active Aerodynamics For The Formula Sae Car, James Patrick Merkel
Mechanical and Aerospace Engineering Theses - Archive
This thesis focuses on the design, development, and implementation of an active aerodynamics system on 2013 Formula SAE car. The aerodynamics package itself consists of five element front and rear wings as well as an under body diffuser. Five element wings produce significant amounts of drag which is a compromise between the cornering ability of the car and the acceleration capability on straights. The active aerodynamics system allows for the wing angle of attack to dynamically change their configuration on track based on sensory data to optimize the wings for any given scenario. The wings are studied using computational fluid …
Compaction Physics Of Solid Additive Blends : A Thermal Properties Study, Amy Brown
Compaction Physics Of Solid Additive Blends : A Thermal Properties Study, Amy Brown
Material Science and Engineering Theses - Archive
Compacted solid additive blends have attracted the interest of the polymers industry due to their ability to improve processability. However, limited research has been performed to analyze the thermal properties that these additives have during pelletization.This research studies the reaction behavior of erucamide and silica, when in a pure and mixed form, with each other when thermal conductivity and frictional heating experiments are conducted. During the thermal conductivity study, it was found that pure erucamide had a thermal conductivity of 0.37 W/mK. The thermal conductivity of pure silica could not be found since silica will not compact to itself. Therefore, …
The Samara Spacecraft: Design And Development Of A Self-Stabilizing, Auto-Rotating, Distributed Sensing System, Amit Desai Lalloobhai
The Samara Spacecraft: Design And Development Of A Self-Stabilizing, Auto-Rotating, Distributed Sensing System, Amit Desai Lalloobhai
Mechanical and Aerospace Engineering Theses - Archive
The scope of this research is the design and development of a self-stabilizing re-entry vehicle that closely resembles naturally occurring seeds in nature. It was hypothesized that a femto-satellite with a shape of a samara could self stabilize and passively generate lift, as well as transmit a signal during its descent through the atmosphere. The research included a conceptual design phase and a preliminary design phase that entailed analytic simulations, and an experimental demonstration. The goal was to investigate the feasibility of developing the above-mentioned femto-vehicle that could increase the range capability of its descent to maximize data capture.
Development And Operation Of An Integrated Sampling Probe And Gas Analyzer For Turbulent Mixing Studies In Complex Supersonic Flows, John D. Wiswall
Development And Operation Of An Integrated Sampling Probe And Gas Analyzer For Turbulent Mixing Studies In Complex Supersonic Flows, John D. Wiswall
Mechanical and Aerospace Engineering Theses - Archive
For many aerospace applications, mixing enhancement between co-flowing streams has been identified as a critical and enabling technology. Due to short fuel residence times in scramjet combustors, combustion is limited by the molecular mixing of hydrogen (fuel) and air. Determining the mixedness of fuel and air in these complex supersonic flowfields is critical to the advancement of novel injection schemes currently being developed at UTA in collaboration with NASA Langley and intended to be used on a future two-stage to orbit (~Mach 16) hypersonic air-breathing vehicle for space access.Expanding on previous work, an instrument has been designed, fabricated, and tested …
Numerical Study Of Incompressible Fluid Flow In A Vertically Dropping Pool With And Without End Sill, Vimal Ramanuj
Numerical Study Of Incompressible Fluid Flow In A Vertically Dropping Pool With And Without End Sill, Vimal Ramanuj
Mechanical and Aerospace Engineering Theses - Archive
The study involves numerical analysis of flow field for three different flow regimes taking place in a vertically dropping pool. In general, a vertically dropping flow generates a skimming flow regime with one recirculation zone along with a developing shear layer. The presence of an obstacle (end sill) results in the formation of another recirculation zone downstream of the impinging jet. Based on the nature of these zones, the flow is categorized as napped, periodically oscillatory and skimming. The type of flow regime depends on the flow parameters like velocity and depth of flow which are controlled by Froude number. …
3-D Fracture Study Of The Beol Cu/Low-K Stack To Assess And Mitigate The Cpi Risk During The Reflow Process, Zaeem Baig
3-D Fracture Study Of The Beol Cu/Low-K Stack To Assess And Mitigate The Cpi Risk During The Reflow Process, Zaeem Baig
Mechanical and Aerospace Engineering Theses - Archive
As scaling of components continues, using SiO2 as a dielectric in the Back-End-Of-Line (BEoL) is no longer a viable option and can be replaced with low-k and ultralow-k (ULK) dielectric materials for advanced integrated circuits (IC) packaging solutions. The low-k materials improve performance by reducing parasitic capacitance and crosstalk between adjacent metal lines. However, low-k dielectrics have lower modulus, lower fracture toughness, higher coefficient of thermal expansion (CTE), and poor adhesion as compared to SiO2. Thus, low-k dielectric integration in the contemporary IC packages poses a significant reliability challenge. Delamination along the metal-dielectric interfaces and crack propagation in the dielectric …
A Novel Approach For Two-Dimensional Inclusion/Hole Problems Using The Airy Stress Function Method, Manikandan Madhavan
A Novel Approach For Two-Dimensional Inclusion/Hole Problems Using The Airy Stress Function Method, Manikandan Madhavan
Mechanical and Aerospace Engineering Theses - Archive
This thesis demonstrates the application of the Airy stress function in solving plane elasticity problems. An Airy stress function is determined for two-dimensional infinite plates containing a circular inclusion embedded with a circular hole subjected to tensile loading and the traction and displacement functions for various boundary conditions satisfy the equilibrium and continuity conditions. Mathematica was useful for solving the complex expressions and to calculate the elastic fields for a variety of elastic problems in this study.