Norton Model Research Articles

Creep analysis of a cylinder subjected to 2D thermoelasticity loads and boundary conditions with inner heat generation source

This paper presents an in-depth investigation of the creep behavior of a thick-walled cylinder subjected to thermomechanical loads with internal heat generation under various boundary conditions. The cylinder is subjected to internal pressure with the incoming heat flux in the inner layer and the outgoing heat flux from the outer layer accompanied by heat generation. The displacement field follows the kinematics of the first-order shear deformation theory (FSDT). Simultaneously, the temperature field is treated as two-dimensional, exhibiting variations both along the thickness and the length of the cylinder, with a linear temperature gradient across the cylinder's thickness. Using the energy method, the equilibrium equations and general boundary conditions are derived for the cylinder. Norton's model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. The redistribution, displacements, strains and stresses over time have been obtained by the semi-analytical iteration method. Moreover, the effectiveness of the proposed method in addressing axisymmetric cylindrical shells under various boundary conditions and thermo-mechanical loading is demonstrated. A parametric study on the creep behavior has also been carried out which reveals critical insights. Notably, the study demonstrates that effective stress and radial displacement during creep can be effectively managed by optimizing the external cooling profile or the internal heating profile. Furthermore, the investigation reveals that the presence of a heat source markedly influences the effective stress and displacement within structure, highlighting the interplay between thermal and mechanical factors in determining the structural integrity. To validate the findings of this study, the finite element method was employed, with the results indicating good agreement between the two approaches.

Influence of constitutive equation and friction on measurement of creep strain rate based on small specimen testing technique

AbstractTwo stress regime‐dependent creep constitutive equations, that is, two‐regime Norton (2RN) model and Sin‐hyperbolic (Sinh) model, are adopted to numerically investigate the influence of constitutive equation and friction on the measurement of steady‐state creep strain rate based on five types small specimens. Results show that the influence of constitutive equation and friction depends strongly on the type of small specimen. A measurement error of more than 19 times may occur if the 2RN model is used, while the use of the Sinh model is able to generate a consistently lower measurement error. Of all small specimens, the cantilever beam testing (CaBT) is revealed to exhibit the best comprehensive performance in terms of measurement error and response to friction. To validate numerical findings, creep tests on the CaBT specimen of P91 steel are conducted at 600°C. Finally, recommendations on the choice of small specimen for obtaining creep strain rate are made.

Evaluation of Harmonic Currents and Network Impedance using Norton Model in an Unidentified Network Configuration

This paper presents a study that focuses on the evaluation of the analysis of harmonic currents emitted by loads and the harmonic impedance of a real electrical network using the Norton model. The primary advantage of employing this model lies in its ability to address scenarios where the complete network configuration, particularly from the distribution side, is not known. By calculating currents and voltages at the supply-side for two different operating conditions, the harmonic current content and the network impedance can be evaluated. To induce variations in operating conditions, a switching shunt capacitor is utilized. The results show that the fifth and the seventh harmonics clearly appear with values of 189.382 A and 135.073 A, respectively, while the other harmonics have values close to zero. The harmonic impedance also shows the presence of the fifth and the seventh harmonics with values of 1865.681 Ω and 4289.3 Ω, respectively. The main contribution of this paper focuses on converting the real electrical network into numerical data that can be accepted by the software. The components of the network model have to be carefully selected to understand the harmonic analysis and to success the simulation, which is conducted using the EMTP-ATPDraw program. The results of this investigation can be used as a database for electrical transmission and distribution companies in case of making any changes in the network, such as installation of new loads or cables, or in case of making measurements.

Experimental Investigation and Prediction for Bending Creep of Glass Fiber-Reinforced Polymer Pultruded Tube

This study experimentally investigates the bending creep behavior of a pultruded tube made of glass fiber-reinforced polymer (GFRP) and provides the corresponding fitting model as well as the life prediction equation. In the experiment process, the static bending test is performed first to determine the ultimate load-bearing capacities. Then, the creep experiments lasting 3000 h are conducted for GFRP pultruded tubes with 50%, 55%, 60%, and 65% fiber contents, subjected to four different load levels, i.e., 20%, 32.5%, 45%, 57.5%, and 70%, of the ultimate load-bearing capacity. The results indicate that the creep behavior exhibits linear viscoelasticity for load levels below 45%, while the specimens under load levels of 57.5% and 70% experienced creep failure before 1500 h. The test results indicate that for GFRP tubes, the higher the load level, the more pronounced the creep deformation, and specimens with a higher fiber content exhibit better creep resistance compared to those with lower fiber content. When the load level is less than 45%, the creep behavior appears as linear viscoelasticity. However, at a load level of 57.5%, the specimens experience shear failure, and at a load level of 70%, the specimens undergo overall bending failure. In addition, the prediction equation of creep deflection for GFRP pultruded tubes in linear viscoelasticity is developed by utilizing the Bailey–Norton model and the Findley model, and the prediction equation of creep life is acquired by fitting the experimental data with an exponential function.

A new constitutive model for salt rock under cyclic loadings based on state variables

Underground salt rock caverns are ideal for national strategic energy storage, compressed air energy storage, and CO2 storage. Operation periods of salt cavern storage can be affected by periodic injection of gases during production/charging and discharging activities, thus causing fatigue damage to surrounding rock. It is therefore necessary to establish a model that can accurately characterize the evolution process of fatigue damage in salt rock under cyclic loading. This is a necessary input into the design of salt cavern storage systems and for the evaluation of their operation and safety. Relying on the rheological properties and cracks of salt rock and their effects on the bearing capacity of materials, this paper establishes a fatigue damage constitutive model of salt rock, using the rheological characteristics of rock and the deformation–crack expansion relationship. First, the time-varying state variable is introduced through the classical Norton model to characterize the degree of hardening; this is in order to modify the relationship between the stress deformation rate and the correlation of the historical path of loading and unloading of salt rock. Then, based on the relationship between crack damage and effective stress development under deformation conditions, a fatigue damage constitutive model of salt rock is established. Finally, using cyclic loading and unloading data of salt rock under different stress ratios or confining pressures, we verify and compare the model parameters. The results show that: (1) The model can accurately predict the fatigue deformation characteristics of salt rock under different cyclic loading and unloading paths and can better characterize the interaction between deformation and stress path; (2) In this model, parameter a affects stage II while parameter b affects stage I of salt rock fatigue deformation. This can be understood as the factor representing the relationship between stress and deformation rate of salt rock; (3) Parameter d0 characterizing the initial nucleation area and parameter μd representing crack growth rate factor jointly affect/modify the stress–strain relationship in the critical failure stage or stage III of the model.

Performance Analysis of a Backward/Forward Algorithm Adjusted to a Distribution Network with Nonlinear Loads and a Photovoltaic System

Context: The backward/forward (BF) algorithm is a sweep-type technique that has recently been used as a strategy for the power flow analysis of ill-conditioned networks. The purpose of this study is to evaluate the performance of the BF algorithm compared to that of a computational tool such as Simulink, with both strategies adjusted to the operating conditions of a distribution network with nonlinear components (loads and photovoltaic system), unbalanced loads, and harmonic distortion in the voltage and current signals. Method: The study case is a low-voltage distribution network with a radial topology, unbalanced loads, and nonlinear components. The BF algorithm is adjusted to consider two approaches of the Norton model: a coupled admittance matrix and a decoupled admittance matrix. The latter is also used in the network model created in Simulink. The performance of the algorithm is evaluated by analyzing 18 operation scenarios defined according to the presence and use intensity of the loads and solar irradiance levels (low and high). Results: In general, the three strategies could successfully determine the waveform and RMS values of the voltage signals with errors of less than 0,8 and 1,3%, respectively. However, the performance of the strategies for the estimation of current signals and power parameters shows errors of 5-300% depending on the level of solar irradiance at which the photovoltaic system operates. Conclusions: The results show that the BF strategy can be used to analyze unbalanced power grids with increasing penetration of renewable generation and the integration of nonlinear devices, but the performance of this strategy depends on the load model applied to represent the behavior of nonlinear devices and generation systems.

Non-contact gravitational energy harvesting from solid spheres using a two-stage triboelectric nanogenerator

Off-grid connected objects are widely used for environmental monitoring applications such as air and water quality, soil salinity, weather forecasting and more. In recent studies, mechanical energy harvesting using triboelectric nanogenerators (TENGs) have gained in efficiency, even though the design of these TENGs was kept simple. In this context, the durability of the mechanical contact between triboelectric materials is challenged. This is why, free-standing balls have been proposed to reduce the friction in TENGs instead of foils, which are commonly used. Thus, a non-contact gravitational TENG at state-of-the-art performances is proposed in this work. This two-stage design is based on free-standing balls in a rotor and a contactless capacitive coupler. The power generation has been investigated for these two stages according to analytical models. A new methodology to extract the Norton model parameters from a moving TENG is suggested. Through an optimized interdigitated design of the capacitive coupler, a 27-fold increase of the primary stage power is demonstrated and a state-of-the-art peak output power density of 24.45 W m−2 is reached. This study is a leading-edge example of how TENGs could be adopted to power small remote apparatus, in addition of battery.

Creep behaviors of HTPE propellants

AbstractIn this paper, creep tests were carried out on HTPE/AP/Al/RDX propellant specimens to investigate the effects of stress level and temperature on their creep behavior and to investigate the creep mechanism. Higher stresses and temperature can cause greater creep strain in the propellant, ultimately leading to its destruction. On this basis, the creep master curve was further obtained based on the Time‐Temperature Superposition Principle (TTSP), extending the creep investigation time range to 1010 s. Based on previous experience, some explorations have been made on constitutive equations. The burgers model fits the creep behavior under different conditions more closely, while the Norton model has higher stress sensitivity.

Harmonic Impedance Model of Multiple Utility-Interactive Multilevel Photovoltaic Inverters

An important requirement of the power grid with high penetration of renewable energy sources is the mitigation of potential harmonic interactions between different distributed large grid-tie inverters and the mains. This work presents the harmonic interaction between multiple multilevel photovoltaic (PV) inverters based on the well-known T-type neutral-point-clamped inverter (3L-TNPC). The multiple 3L-TNPC is connected in parallel to a common ac bus by using distribution voltage feeders. The analysis is performed by using the Norton equivalence model of each power circuit, its admittance matrix modeling, and the potential overall impedance resonances with the ac grid. The main contribution of this work is the development of a current harmonic injection model of the system operating under a polluted voltage grid for harmonic analysis, while overall filtering design restrictions due to impedance limits based on current and voltage standards are considered. The proposed impedance Norton model is compared with the electromagnetic transient model (EMT model) by using comprehensive simulations, showing good match between both models.

Research on thermomechanical fatigue life prediction of regenerative cooling thrust chamber

The ratcheting effect of the liner wall structure in the thrust chamber of liquid rocket engine under cyclic load is studied, and its service life is predicted. Firstly, the 3-D heat transfer analysis of the wall of the thrust chamber is carried out while explaining the mechanism of its "dog room" failure. Based on the results of the heat transfer analysis, the stress-strain evolution of the structure under cyclic load is analyzed by nonlinear plane strain finite element method. According to the finite element analysis results, the ratcheting effect of the liner wall structure is described and the ratcheting damage is calculated. The low cycle fatigue damage is calculated by using modified Morrow model, and the creep damage is also calculated using Norton model. Finally, the total damage of thrust chamber liner wall is calculated by using Miner linear cumulative damage law and the thermomechanical fatigue life of the structure is estimated. The result shows that the middle point of the lower surface of the liner wall will fail first, and the calculated service life is 33 times, which is good agreement with its actual service life. In the total damage of the weak point, ratcheting damage, creep damage and low cycle fatigue damage account for 52%, 32% and 16% respectively, indicating that the ratcheting effect is the main reason for the failure of the thrust chamber structure. The research results of this paper provide important engineering reference for the structural optimization design and rapid life prediction of regenerative cooling thrust chamber of liquid rocket engine and the future reusable aerospace power.

The Cost of Change: How Ideological Shifts Impact Afghans' Investment in Learning English

AbstractThe role of English in Afghanistan has always been contentious, but in 2001 English acquired symbolic capital that provided people with a motive to invest in learning the language. To better understand this investment, this study employed Darvin and Norton's Model of Investment along with the notion of Linguistic Entrepreneurship to investigate how dynamic shifts in the global era can influence people's willingness to invest in a new language, and how this investment is tied to issues of ideology, capital, and identity. Narrative data were collected via frames and interviews to present the experiences of people who had lived through a relatively prosperous time in Afghanistan's recent history, yet who also faced uncertainty due to the sudden shift in power that threatened the conditions which had allowed them to align themselves with more global ambitions. The study reveals how government and western support was influential in Afghans investing in English, which allowed them to accrue economic, cultural, and social capital, transforming them into linguistic entrepreneurs. However, recent events mean this support has been marginalized, diminishing the ability of Afghans to invest in English and leaving the participants in this study in a precarious position as new ideologies which promote opposition to western influence take hold of the country.

A Practical Harmonic Admittance Matrix Derivation Approach for Fluctuating Power Photovoltaic Systems

Due to a range of economic incentives and policy supports, distributed photovoltaic (PV) systems are accelerating their penetration into the distribution network at all voltage levels. However, the PV systems are connected to the grid via power electronic converters, which are nonlinear devices characterized by inherent harmonic emission, and their cumulative harmonic injection into the grid is detrimental to the grid power quality. Although the existing literature proves that harmonic admittance matrix (HAM)-based models can represent well the supply voltage dependence of harmonics, the conventional HAM derivation approach is based on the harmonic sensitivity tests conducted under laboratory conditions, making it infeasible for infield implementation. To address this issue, this paper starts with investigating the harmonic emission and grid interaction mechanisms of PV systems analytically, followed by analyzing the power dependency of HAMs experimentally. Based on the findings, a HAM derivation and self-tuning approach is proposed for fluctuating power PV systems, where only the infield measurements at the point of connection are needed. The model accuracy is compared against the widely used constant current source model and harmonic Norton model, while its integration approach for harmonic power flow analysis is demonstrated via the simulated European low voltage test feeder.

The Implementation of SST as the System of Room Reservation for Students’ Organization at Atma Jaya BSD Campus

The implementation of SST in any organization activity can create a positive outcome and bring less negative response if the system failed. The bureau of students, alumni, and student career counselling at Atma Jaya has difficulties managing a room booking process for the student’s organization. The current method of room booking is done manually, and it has taken a lot of costs, especially from time, human resources, and the process itself. This research focuses on developing the SST system that can help the bureau manage the room booking process. The system itself will be developed on a web-based platform using Laravel as the framework. The room booking system will be developed using an SDLC model with five general processes: planning, analysing, design, implementation, and testing. This research will also measure user satisfaction while using the system using Kaplan and Norton Model. The result of this study is a web-based system for a room booking process for students’ organizations in Atma Jaya BSD Campus. Based on the evaluation of user satisfaction, this system has an average score of 4.56, which indicates the user is very satisfied using this system for the room reservation.

Economic injury level of date spider mite, Oligonychus afrasiaticus (Acari: Tetranychidae) on six commercial date cultivars

The date spider mite, Oligonychus afrasiaticus (McGregor) (Acari: Tetranychidae) is a destructive pest on date palm trees, causing high economic losses. Here, we investigated the relationship between population density of O. afrasiaticus and the extent of its injury level as well as the relation between rate of damage and date yield losses indices on six commercial date cultivars in five date palm growing provinces including Khuzestan (Sayer and Berhee), Hormozgan (Pyarum), Kerman (Mazafati), Bushehr (Kabkab), and Sistan and Baluchestan (Rabi) of Iran. The experiment was conducted in a complete randomized block design with five treatments and three replications. To this end, in each replication, four date clusters were selected from four different geographical directions, in each of them, 25 fruits were checked randomly to unveil the number of healthy and infested fruits. The sampling was repeated at seven-day intervals from late May to early September. Finally, the Norton model was used to estimate the economic injury level (EIL) under both biological and chemical control conditions. The highest value of EIL in 2019 was estimated for Sayer in the chemical control method (1827 Mite-day) and the lowest one was estimated for Pyarum in the biological control method (25.5 mite-day). Our results also revealed that the cost of biological control was significantly lower than chemical control. The highest and lowest rate of date injury (symptoms of the pest feeding) were observed on Berhee and Mazafati cultivars, respectively. Also, the highest and lowest rate of date loss were observed on Kabkab and Sayer cultivars, respectively. On the other hand, the cost of chemical control in both years was higher than that of biological control.

Feasibility of Black-Box Time Domain Modeling of Single-Phase Photovoltaic Inverters Using Artificial Neural Networks

This paper introduces a new black-box approach for time domain modeling of commercially available single-phase photovoltaic (PV) inverters in low voltage networks. An artificial neural network is used as a nonlinear autoregressive exogenous model to represent the steady state behavior as well as dynamic changes of the PV inverter in the frequency range up to 2 kHz. The data for the training and the validation are generated by laboratory measurements of a commercially available inverter for low power applications, i.e., 4.6 kW. The state of the art modeling approaches are explained and the constraints are addressed. The appropriate set of data for training is proposed and the results show the suitability of the trained network as a black-box model in time domain. Such models are required, i.e., for dynamic simulations since they are able to represent the transition between two steady states, which is not possible with classical frequency-domain models (i.e., Norton models). The demonstrated results show that the trained model is able to represent the transition between two steady states and furthermore reflect the frequency coupling characteristic of the grid-side current.

Comparison of Static and Long-term Creep Behaviors between Balau Wood and Glass Fiber Reinforced Polymer Composite for Cross-arm Application

Cross arms are mainly made up of wood (conventional) and pultruded glass fiber reinforced polymer composite (modern) installed in suspension tower. However, the creep response of both materials has not been fully covered in many literatures to explain the long-term durability of the current cross arm design. Thus, it is necessary to find the creep trends and models to evaluate the behavior in the tropical outdoor environment. The creep properties of Balau wood and pultruded composite at load of 10, 20 and 30 % of ultimate flexural stress were evaluated from quasi-static flexural test results. Using several creep numerical models, the creep properties of wood and composite cross arms were modelled. The results showed that the GFRP had a significant value of flexural strength, while Balau wood performed better in flexural modulus. In terms of creep properties, GFRP specimen exhibited high creep resistance with greater stability during transition from elastic to viscoelastic phase. From numerical modelling perspective, the simulated creep trends from Burger and Norton models were deviated from the experimental data. Subsequently, the most suitable creep model to forecast the creep behavior for wood and composite specimens was Findley model. All in all, pultruded composite is the most appropriate durable material to be applied in cross arms, while Findley model is a suitable model to represent creep performance of anisotropic materials.

Impact of inverter digital time delay on the harmonic characteristics of grid‐connected large‐scale photovoltaic system

The digitally controlled inverter is widely applied to the photovoltaic (PV) plant, however, the effects of inverter digital time delay on the harmonic characteristic of PV system which directly influences the power quality and even the stability of the system, have not been investigated yet. This study investigates the harmonic characteristic of a grid-connected large-scale PV system based on the equivalent Norton model of the system with considering the digital time delay of the inverter. According to the system equivalent model, the series harmonic resonance circuit and the parallel harmonic resonance circuit are divided to study the impacts of digital time delay in the cases of the inverter output harmonic exist and the grid voltage harmonic exit, respectively. Then, the harmonic resonance mechanism of a grid-connected large-scale PV system is studied and the effects of digital time delay on the harmonic characteristic of system output current is quantitatively analysed by defining the harmonic magnification coefficient. It turns out that frequency and magnitude of harmonic magnification points in the grid-side current of the system are increased as the digital time delay increases. Reference to the actual 20 MWp grid-connected PV system, a simulation model is built to verify the theoretical analysis results.

Canadian Immersion Students’ Investment in French

AbstractFrench second language education, including the option of one‐way French immersion, is mandated for majority‐language Anglophone children in New Brunswick, Canada's only officially bilingual province. Language ideological debates in the province surrounding official English–French bilingualism led us to investigate adolescent majority‐language immersion students’ investment in French, the co‐official minority language, using Darvin and Norton's tripartite (capital, ideology, identity) model. We discuss 3 student profiles, drawing on data collected from multimodal focus groups conducted among 8th‐grade French immersion students. Our analysis reveals a dominance of neoliberal ideologies in these students’ investment in French, rendering it imbalanced and largely driven by imagined access to future economic capital. Language as cultural or social capital figures inconsistently in their investment. Drawing on our data, we conclude by proposing that Darvin and Norton's model, with a balanced focus on each kind of capital within the model, may be used conceptually by educators in program development. The model used in such a way would enable educators to give equal priority to students’ identity and intercultural development as to their preparation for participation in economic marketplaces, thus potentially expanding majority‐language students’ investment in their co‐official minority second language.

Extended coupled Norton model of modern power‐electronic devices for large‐scale harmonic studies in distribution networks

The increasing application of non-linear power-electronic based devices in low voltage networks might have a negative impact on power quality, particularly on harmonics. To estimate the harmonic levels or to identify possible resonances, respective network simulations involving a large number of power electronic devices are necessary. These require realistic device models, which need to represent both the harmonic emission and the input admittance characteristic, as otherwise simulations might not converge or result in unrealistic results. While many proposals exist for harmonic emission models, not much approaches can be found regarding the input admittance. This study intends to fill this gap and presents a modelling approach combining the harmonic emission and the input admittance characteristic in a single model. Therefore, the classic Norton model is extended by a generic circuit-based part, which consists of linear, passive components and is parameterised based on measurements. The extended Norton model is applied to six photovoltaic inverters and 18 electric vehicle chargers and its application are demonstrated in a harmonic simulation.

Power, Ideology and Identity in Digital Literacy: A Sociolinguistic Study

This study investigates the significance of digital media in terms of social implications. It draws its theoretical insights from the Darvin and Norton model of investment (2015) as it gives purely a new dimension to the concept of digital literacy. The study is designed in order to evaluate some important aspects of Social media, particularly Facebook, as an important digital literacy practice. Firstly, the study examines the way power is operated in the digital mediated construction of social identities. Certain social identities position other identities and accord or refuse them power. These even shape social ideologies and identities as English-language speakers hold a privileged position in society while Urdu-language speakers are marginalized all over the world. Secondly, it explores the role of digital media in the investment of language and digital literacy practices to represent social ideologies at three different angles of marriage, adulthood and family. Having established a sampling frame consisting of nine Facebook pictorial postings from three Facebook pages, the findings suggested that the text and visual representations of Facebook postings use various linguistic features like literary devices that are playing an evident role in the representation of social ideologies.