Search results for: least squares nonlinear

Authors: Germán Díaz Flórez, Carlos Alberto Olvera Olvera, Domingo José Gómez Meléndez, Francisco Eneldo López Monteagudo

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In recent decades, population growth has exerted great pressure on natural resources. Two of the most scarce and difficult to obtain resources, arable land, and water, are closely interrelated, to the satisfaction of the demand for food production. In Mexico, the agricultural sector uses more than 70% of water consumption. Therefore, maximize the efficiency of current production systems is inescapable. It is essential to utilize techniques and tools that will enable us to the significant savings of water, labor and fertilizer. In this study, we present a production module of hydroponic green forage (HGF), which is a viable alternative in the production of livestock feed in the semi-arid and arid zones. The equipment in addition to having a forage production module, has a climate and irrigation control system that operated with photovoltaics. The climate control, irrigation and power management is based on fuzzy control techniques. The fuzzy control provides an accurate method in the design of controllers for nonlinear dynamic physical phenomena such as temperature and humidity, besides other as lighting level, aeration and irrigation control using heuristic information. In this working, firstly refers to the production of the hydroponic green forage, suitable weather conditions and fertigation subsequently presents the design of the production module and the design of the controller. A simulation of the behavior of the production module and the end results of actual operation of the equipment are presented, demonstrating its easy design, flexibility, robustness and low cost that represents this equipment in the primary sector.

Keywords: fuzzy, climate control system, hydroponic green forage, forage production module

Procedia PDF Downloads 373

Authors: Wajih Abbassi, Zouhaier Ben Khelifa

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The present research points towards the empirical validation of three options valuation models, the ad-hoc Black-Scholes model as proposed by Berkowitz (2001), the constant elasticity of variance model of Cox and Ross (1976) and the Kou jump-diffusion model (2002). Our empirical analysis has been conducted on a sample of 26,974 options written on three indexes, the S&P 500, Nasdaq 100 and the Russell 2000 that were negotiated during the year 2007 just before the sub-prime crisis. We start by presenting the theoretical foundations of the models of interest. Then we use the technique of trust-region-reflective algorithm to estimate the structural parameters of these models from cross-section of option prices. The empirical analysis shows the superiority of the Kou jump-diffusion model. This superiority arises from the ability of this model to portray the behavior of market participants and to be closest to the true distribution that characterizes the evolution of these indices. Indeed the double-exponential distribution covers three interesting properties that are: the leptokurtic feature, the memory less property and the psychological aspect of market participants. Numerous empirical studies have shown that markets tend to have both overreaction and under reaction over good and bad news respectively. Despite of these advantages there are not many empirical studies based on this model partly because probability distribution and option valuation formula are rather complicated. This paper is the first to have used the technique of nonlinear curve-fitting through the trust-region-reflective algorithm and cross-section options to estimate the structural parameters of the Kou jump-diffusion model.

Keywords: jump-diffusion process, Kou model, Leptokurtic feature, trust-region-reflective algorithm, US index options

Procedia PDF Downloads 407

Authors: Hari Krishnan K. P., Anil Kumar M. V.

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The Direct Strength Method (DSM) is used for the computation of the design strength of members whose behavior is governed by any form of buckling. DSM based semiempirical equations have been successfully used for cold-formed steel (CFS) members subjected to compression, bending, and shear. The DSM equations for the strength of a CFS member are based on the parameters accounting for strength [yield load (Py), yield moment (My), and shear yield load (Vy) for compression, bending, and shear respectively] and stability [buckling load (Pcr), buckling moment (Mcr), and shear buckling load (Vcr) for compression, bending and shear respectively]. The buckling of column and beam shall be governed by local, distortional, or global buckling modes and their interaction. Recently DSM-based methods are extended for the web crippling strength of CFS beams also. Numerous DSM-based expressions were reported in the literature, which is the function of loading case, cross-section shape, and boundary condition. Unlike members subjected to axial load, bending, or shear, no unified expression for the design web crippling strength irrespective of the loading case, cross-section shape, and end boundary conditions are available yet. This study, based on nonlinear finite element analysis results, shows that the slenderness of the web, which shall be represented either using web height to thickness ratio (h=t) or Pcr has negligible contribution to web crippling strength. Hence, the results in this paper question the suitability of DSM based approach for the web crippling strength of CFS beams.

Keywords: cold-formed steel, beams, DSM-based procedure, interior two flanged loading, web crippling

Procedia PDF Downloads 74

Authors: Oleg Ye Sysoyev, Artem Yu Dobryshkin, Nyein Sitt Naing

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Cylindrical shells are widely used in the construction of buildings and structures, as well as in the air structure. Thin-walled casings made of aluminum alloys are an effective substitute for reinforced concrete and steel structures in construction. The correspondence of theoretical calculations and the actual behavior of aluminum alloy structures is to ensure their trouble-free operation. In the laboratory of our university, "Building Constructions" conducted an experimental study to determine the effect of the system of attached masses on the natural oscillations of shallow cylindrical shells of aluminum alloys, the results of which were compared with theoretical calculations. The purpose of the experiment is to measure the free oscillations of an open, sloping cylindrical shell for various variations of the attached masses. Oscillations of an open, slender, thin-walled cylindrical shell, rectangular in plan, were measured using induction accelerometers. The theoretical calculation of the shell was carried out on the basis of the equations of motion of the theory of shallow shells, using the Bubnov-Galerkin method. A significant splitting of the flexural frequency spectrum is found, influenced not only by the systems of attached маsses but also by the values of the wave formation parameters, which depend on the relative geometric dimensions of the shell. The correspondence of analytical and experimental data is found, using the example of an open shell of alloy D19, which allows us to speak about the high quality of the study. A qualitative new analytical solution of the problem of determining the value of the oscillation frequency of the shell, carrying a system of attached masses is shown.

Keywords: open hollow shell, nonlinear oscillations, associated mass, frequency

Procedia PDF Downloads 269

Authors: Ziying Wu, Danfeng Yan

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Multi-Access Edge Computing (MEC) is one of the key technologies of the future 5G network. By deploying edge computing centers at the edge of wireless access network, the computation tasks can be offloaded to edge servers rather than the remote cloud server to meet the requirements of 5G low-latency and high-reliability application scenarios. Meanwhile, with the development of IOV (Internet of Vehicles) technology, various delay-sensitive and compute-intensive in-vehicle applications continue to appear. Compared with traditional internet business, these computation tasks have higher processing priority and lower delay requirements. In this paper, we design a 5G-based Vehicle-Aware Multi-Access Edge Computing Network (VAMECN) and propose a joint optimization problem of minimizing total system cost. In view of the problem, a deep reinforcement learning-based joint computation offloading and task migration optimization (JCOTM) algorithm is proposed, considering the influences of multiple factors such as concurrent multiple computation tasks, system computing resources distribution, and network communication bandwidth. And, the mixed integer nonlinear programming problem is described as a Markov Decision Process. Experiments show that our proposed algorithm can effectively reduce task processing delay and equipment energy consumption, optimize computing offloading and resource allocation schemes, and improve system resource utilization, compared with other computing offloading policies.

Keywords: multi-access edge computing, computation offloading, 5th generation, vehicle-aware, deep reinforcement learning, deep q-network

Procedia PDF Downloads 84

Authors: Jin Woo Hwang, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

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As greenhouse effect has been recognized as serious environmental problem of the world, interests in carbon dioxide (CO₂) emission which comprises major part of greenhouse gas (GHG) emissions have been increased recently. Since construction industry takes a relatively large portion of total CO₂ emissions of the world, extensive studies about reducing CO₂ emissions in construction and operation of building have been carried out after the 2000s. Also, performance based design (PBD) methodology based on nonlinear analysis has been robustly developed after Northridge Earthquake in 1994 to assure and assess seismic performance of building more exactly because structural engineers recognized that prescriptive code based design approach cannot address inelastic earthquake responses directly and assure performance of building exactly. Although CO₂ emissions and PBD approach are recent rising issues on construction industry and structural engineering, there were few or no researches considering these two issues simultaneously. Thus, the objective of this study is to minimize the CO₂ emissions and cost of building designed by PBD approach in structural design stage considering structural materials. 4 story and 4 span reinforced concrete building optimally designed to minimize CO₂ emissions and cost of building and to satisfy specific seismic performance (collapse prevention in maximum considered earthquake) of building satisfying prescriptive code regulations using non-dominated sorting genetic algorithm-II (NSGA-II). Optimized design result showed that minimized CO₂ emissions and cost of building were acquired satisfying specific seismic performance. Therefore, the methodology proposed in this paper can be used to reduce both CO₂ emissions and cost of building designed by PBD approach.

Keywords: CO2 emissions, performance based design, optimization, sustainable design

Procedia PDF Downloads 390

Authors: A. Bahmanpour, I. Eames, C. Klettner, A. Dimakopoulos

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We develop a new set of diagnostic tools to analyze inundation into a model district using three-dimensional CFD simulations, with a view to generating a database against which to test simpler models. A three-dimensional model of Oregon city with different-sized groups of building next to the coastline is used to run calculations of the movement of a long period wave on the shore. The initial and boundary conditions of the off-shore water are set using a nonlinear inverse method based on Eulerian spatial information matching experimental Eulerian time series measurements of water height. The water movement is followed in time, and this enables the pressure distribution on every surface of each building to be followed in a temporal manner. The three-dimensional numerical data set is validated against published experimental work. In the first instance, we use the dataset as a basis to understand the success of reduced models - including 2D shallow water model and reduced 1D models - to predict water heights, flow velocity and forces. This is because models based on the shallow water equations are known to underestimate drag forces after the initial surge of water. The second component is to identify critical flow features, such as hydraulic jumps and choked states, which are flow regions where dissipation occurs and drag forces are large. Finally, we describe how future tsunami inundation models should be modified to account for the complex effects of buildings through drag and blocking.Financial support from UCL and HR Wallingford is greatly appreciated. The authors would like to thank Professor Daniel Cox and Dr. Hyoungsu Park for providing the data on the Seaside Oregon experiment.

Keywords: computational fluid dynamics, extreme events, loading, tsunami

Procedia PDF Downloads 94

Authors: Sanjai Sureshkumar, Sathish G. Kumar, P. V. V. Sathyanarayana

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For e-gear drivetrain, the transmission error and the resulting variation in mesh stiffness is one of the main source of excitation in High performance Electric Vehicle. These vibrations are transferred through the shaft to the bearings and then to the e-Gear drive housing eventually radiating noise. A parametrical model developed in 1-D system simulation by optimizing the micro and macro geometry along with bearing properties and oil filtration to achieve least transmission error and high contact ratio. Histogram analysis is performed to condense the actual road load data into condensed duty cycle to find the bearing forces. The structural vibration generated by these forces will be simulated in a nonlinear solver obtaining the normal surface velocity of the housing and the results will be carried forward to Acoustic software wherein a virtual environment of the surrounding (actual testing scenario) with accurate microphone position will be maintained to predict the sound pressure level of radiated noise and directivity plot of the e-Gear Drive. Order analysis will be carried out to find the root cause of the vibration and whine noise. Broadband spectrum will be checked to find the rattle noise source. Further, with the available results, the design will be optimized, and the next loop of simulation will be performed to build a best e-Gear Drive on NVH aspect. Structural analysis will be also carried out to check the robustness of the e-Gear Drive.

Keywords: 1-D system simulation, contact ratio, e-Gear, mesh stiffness, micro and macro geometry, transmission error, radiated noise, NVH

Procedia PDF Downloads 135

Authors: K. Meera Saheb, K. Krishna Bhaskar

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Complex structures used in many fields of engineering are made up of simple structural elements like beams, plates etc. These structural elements, sometimes carry concentrated masses at discrete points, and when subjected to severe dynamic environment tend to vibrate with large amplitudes. The frequency amplitude relationship is very much essential in determining the response of these structural elements subjected to the dynamic loads. For Timoshenko beams, the effects of shear deformation and rotary inertia are to be considered to evaluate the fundamental linear and nonlinear frequencies. A commonly used method for solving vibration problem is energy method, or a finite element analogue of the same. In the present Coupled Displacement Field method the number of undetermined coefficients is reduced to half when compared to the famous Rayleigh Ritz method, which significantly simplifies the procedure to solve the vibration problem. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. The prime objective of the present paper here is to study, in detail, the effect of a central concentrated mass on the large amplitude free vibrations of uniform shear flexible beams. Accurate closed form expressions for linear frequency parameter for uniform shear flexible beams with a central concentrated mass was developed and the results are presented in digital form.

Keywords: coupled displacement field, coupling equation, large amplitude vibrations, moderately thick plates

Procedia PDF Downloads 205

Authors: W. Hamaidia, T. Zebbiche

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This paper presents the design of axisymmetric supersonic nozzles, in order to accelerate a supersonic flow to the desired Mach number and that having a small weight, in the same time gives a high thrust. The concerned nozzle gives a parallel and uniform flow at the exit section. The nozzle is divided into subsonic and supersonic regions. The supersonic portion is independent to the upstream conditions of the sonic line. The subsonic portion is used to give a sonic flow at the throat. In this case, nozzle gives a uniform and parallel flow at the exit section. It’s named by minimum length Nozzle. The study is done at high temperature, lower than the dissociation threshold of the molecules, in order to improve the aerodynamic performances. Our aim consists of improving the performances both by the increase of exit Mach number and the thrust coefficient and by reduction of the nozzle's mass. The variation of the specific heats with the temperature is considered. The design is made by the Method of Characteristics. The finite differences method with predictor-corrector algorithm is used to make the numerical resolution of the obtained nonlinear algebraic equations. The application is for air. All the obtained results depend on three parameters which are exit Mach number, the stagnation temperature, the chosen mesh in characteristics. A numerical simulation of nozzle through Computational Fluid Dynamics-FASTRAN was done to determine and to confirm the necessary design parameters.

Keywords: flux supersonic flow, axisymmetric minimum length nozzle, high temperature, method of characteristics, calorically imperfect gas, finite difference method, trust coefficient, mass of the nozzle, specific heat at constant pressure, air, error

Procedia PDF Downloads 133

Authors: Gulcan Ozerim, Gunay Anlas

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In shape memory alloys, upon loading, stress increases around crack tip and a martensitic phase transformation occurs in early stages. In many studies the stress distribution in the vicinity of the crack tip is represented by using linear elastic fracture mechanics (LEFM) although the pseudo-elastic behavior results in a nonlinear stress-strain relation. In this study, the HRR singularity (Hutchinson, Rice and Rosengren), that uses Rice’s path independent J-integral, is tried to formulate the stress distribution around the crack tip. In HRR approach, the Ramberg-Osgood model for the stress-strain relation of power-law hardening materials is used to represent the elastic-plastic behavior. Although it is recoverable, the inelastic portion of the deformation in martensitic transformation (up to the end of transformation) resembles to that of plastic deformation. To determine the constants of the Ramberg-Osgood equation, the material’s response is simulated in ABAQUS using a UMAT based on ZM (Zaki-Moumni) thermo-mechanically coupled model, and the stress-strain curve of the material is plotted. An edge cracked shape memory alloy (Nitinol) plate is loaded quasi-statically under mode I and modeled using ABAQUS; the opening stress values ahead of the cracked tip are calculated. The stresses are also evaluated using the asymptotic equations of both LEFM and HRR. The results show that in the transformation zone around the crack tip, the stress values are much better represented when the HRR singularity is used although the J-integral does not show path independent behavior. For the nodes very close to the crack tip, the HRR singularity is not valid due to the non-proportional loading effect and high-stress values that go beyond the transformation finish stress.

Keywords: crack, HRR singularity, shape memory alloys, stress distribution

Procedia PDF Downloads 307

Authors: Salah R. Al Zaidee, Ali S. Mahdi

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Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R², in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: meta-modal, objective function, steel frames, seismic analysis, design

Procedia PDF Downloads 223

Authors: Carlos Minguez, Christian F. Sagbay, Erika E. Ordoñez

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Guinea pigs (Cavia porcellus) play prominent roles as experimental models for medical research and as pets. However, in developing countries like South America, the Philippines, and sub-Saharan Africa, the meat of guinea pigs is an economic source of animal protein for the poor and malnourished humans because guinea pigs are mainly fed with forage and do not compete directly with human beings for food resources, such as corn or wheat. To achieve efficient production of guinea pigs, it is essential to provide insurance against vitamin C deficiency. The objective of this research was to investigate the effect of the partial replacement of alfalfa with fresh citrus pulp (Citrus sinensis) in a diet of guinea pigs on the growth performance, slaughter traits and mortality during the fattening period (between 20 and 74 days of age). A total of 300 guinea pigs were housed in collective cages of about ten animals (2 x 1 x 0.4 m) and were distributed into two completely randomized groups. Guinea pigs in both groups were fed ad libitum, with a standard commercial pellet diet (10 MJ of digestible energy/kg, 17% crude protein, 11% crude fiber, and 4.5% crude fat). Control group was supplied with fresh alfalfa as forage. In the treatment group, 30% of alfalfa was replaced by fresh citrus pulp. Growth traits, including body weight (BW), average daily gain (ADG), feed intake (FI), and feed conversion ratio (FCR), were measured weekly. On day 74, the animals were slaughtered, and slaughter traits, including live weight at slaughter (LWS), full gastrointestinal tract weight (FGTW), hot carcass weight (with head; HCW), cold carcass weight (with head; CCW), drip loss percentage (DLP) and dressing out carcass yield percentage (DCY), were evaluated. Contrasts between groups were obtained by calculated generalized least squares values. Mortality was evaluated by Fisher's exact test due to low numbers in some cells. In the first week, there were significant differences in the growth traits BW, ADG, FI, and FCR, which were superior in control group. These differences may have been due to the origin of the young guinea pigs, which, before weaning, were all raised without fresh citrus pulp, and they were not familiarized with the new supplement. In the second week, treatment group had significantly increased ADG compared with control group, which may have been the result of a process of compensatory growth. During subsequent weeks, no significant differences were observed between animals raised in the two groups. Neither were any significant differences observed across the total fattening period. No significant differences in slaughter traits or mortality rate were observed between animals from the two groups. In conclusion, although there were no significant differences in growth performance, slaughter traits, or mortality, the use of fresh citrus pulp is recommended. Fresh citrus pulp is a by-product of orange juice industry and it is cheap or free. Forage made with fresh citrus pulp could reduce about of 30 % the quantity of alfalfa in guinea pig for meat and as consequence, reduce the production costs.

Keywords: fresh citrus, growth, Guinea pig, mortality

Procedia PDF Downloads 172

Authors: Andrea Ghermandi

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Natural treatment systems such as constructed wetlands and waste stabilization ponds are increasingly used to treat water and wastewater from a variety of sources, including stormwater and polluted surface water. The provision of ancillary benefits in the form of cultural ecosystem services makes these systems unique among water and wastewater treatment technologies and greatly contributes to determine their potential role in promoting sustainable water management practices. A quantitative analysis of these benefits, however, has been lacking in the literature. Here, a critical assessment of the recreational and educational benefits in natural treatment systems is provided, which combines observed public use from a survey of managers and operators with estimated public use as obtained using geotagged photos from social media as a proxy for visitation rates. Geographic Information Systems (GIS) are used to characterize the spatial boundaries of 273 natural treatment systems worldwide. Such boundaries are used as input for the Application Program Interfaces (APIs) of two popular photo-sharing websites (Flickr and Panoramio) in order to derive the number of photo-user-days, i.e., the number of yearly visits by individual photo users in each site. The adequateness and predictive power of four univariate calibration models using the crowdsourced data as a proxy for visitation are evaluated. A high correlation is found between photo-user-days and observed annual visitors (Pearson's r = 0.811; p-value < 0.001; N = 62). Standardized Major Axis (SMA) regression is found to outperform Ordinary Least Squares regression and count data models in terms of predictive power insofar as standard verification statistics – such as the root mean square error of prediction (RMSEP), the mean absolute error of prediction (MAEP), the reduction of error (RE), and the coefficient of efficiency (CE) – are concerned. The SMA regression model is used to estimate the intensity of public use in all 273 natural treatment systems. System type, influent water quality, and area are found to statistically affect public use, consistently with a priori expectations. Publicly available information regarding the home location of the sampled visitors is derived from their social media profiles and used to infer the distance they are willing to travel to visit the natural treatment systems in the database. Such information is analyzed using the travel cost method to derive monetary estimates of the recreational benefits of the investigated natural treatment systems. Overall, the findings confirm the opportunities arising from an integrated design and management of natural treatment systems, which combines the objectives of water quality enhancement and provision of cultural ecosystem services through public use in a multi-functional approach and compatibly with the need to protect public health.

Keywords: constructed wetlands, cultural ecosystem services, ecological engineering, waste stabilization ponds

Procedia PDF Downloads 163

Authors: Zhongmin Wang, Wudong Fan, Hengshan Zhang, Yimin Zhou

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In data-driven prognostic methods, the prediction accuracy of the estimation for remaining useful life of bearings mainly depends on the performance of health indicators, which are usually fused some statistical features extracted from vibrating signals. However, the existing health indicators have the following two drawbacks: (1) The differnet ranges of the statistical features have the different contributions to construct the health indicators, the expert knowledge is required to extract the features. (2) When convolutional neural networks are utilized to tackle time-frequency features of signals, the time-series of signals are not considered. To overcome these drawbacks, in this study, the method combining convolutional neural network with gated recurrent unit is proposed to extract the time-frequency image features. The extracted features are utilized to construct health indicator and predict remaining useful life of bearings. First, original signals are converted into time-frequency images by using continuous wavelet transform so as to form the original feature sets. Second, with convolutional and pooling layers of convolutional neural networks, the most sensitive features of time-frequency images are selected from the original feature sets. Finally, these selected features are fed into the gated recurrent unit to construct the health indicator. The results state that the proposed method shows the enhance performance than the related studies which have used the same bearing dataset provided by PRONOSTIA.

Keywords: continuous wavelet transform, convolution neural net-work, gated recurrent unit, health indicators, remaining useful life

Procedia PDF Downloads 109

Authors: M. A. Askari, M. A. Nazari, P. Perrier, Y. Payan

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Growth and remodeling of biological structures have gained lots of attention over the past decades. Determining the response of the living tissues to the mechanical loads is necessary for a wide range of developing fields such as, designing of prosthetics and optimized surgery operations. It is a well-known fact that biological structures are never stress-free, even when externally unloaded. The exact origin of these residual stresses is not clear, but theoretically growth and remodeling is one of the main sources. Extracting body organs from medical imaging, does not produce any information regarding the existing residual stresses in that organ. The simplest cause of such stresses is the gravity since an organ grows under its influence from its birth. Ignoring such residual stresses might cause erroneous results in numerical simulations. Accounting for residual stresses due to tissue growth can improve the accuracy of mechanical analysis results. In this paper, we have implemented a computational framework based on fixed-point iteration to determine the residual stresses due to growth. Using nonlinear continuum mechanics and the concept of fictitious configuration we find the unknown stress-free reference configuration which is necessary for mechanical analysis. To illustrate the method, we apply it to a finite element model of healthy human face whose geometry has been extracted from medical images. We have computed the distribution of residual stress in facial tissues, which can overcome the effect of gravity and cause that tissues remain firm. Tissue wrinkles caused by aging could be a consequence of decreasing residual stress and not counteracting the gravity. Considering these stresses has important application in maxillofacial surgery. It helps the surgeons to predict the changes after surgical operations and their consequences.

Keywords: growth, soft tissue, residual stress, finite element method

Procedia PDF Downloads 333

Authors: Ashis Mallick, Rajeev Ranjan

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The closed form solution for thermal stresses in an annular fin with hyperbolic profile is derived using Adomian decomposition method (ADM). The conductive-convective fin with variable thermal conductivity is considered in the analysis. The nonlinear heat transfer equation is efficiently solved by ADM considering insulated convective boundary conditions at the tip of fin. The constant of integration in the solution is to be estimated using minimum decomposition error method. The solution of temperature field is represented in a polynomial form for convenience to use in thermo-elasticity equation. The non-dimensional thermal stress fields are obtained using the ADM solution of temperature field coupled with the thermo-elasticity solution. The influence of the various thermal parameters in temperature field and stress fields are presented. In order to show the accuracy of the ADM solution, the present results are compared with the results available in literature. The stress fields in fin with hyperbolic profile are compared with those of uniform thickness profile. Result shows that hyperbolic fin profile is better choice for enhancing heat transfer. Moreover, less thermal stresses are developed in hyperbolic profile as compared to rectangular profile. Next, Nelder-Mead based simplex search method is employed for the inverse estimation of unknown non-dimensional thermal parameters in a given stress fields. Owing to the correlated nature of the unknowns, the best combinations of the model parameters which are satisfying the predefined stress field are to be estimated. The stress fields calculated using the inverse parameters give a very good agreement with the stress fields obtained from the forward solution. The estimated parameters are suitable to use for efficient and cost effective fin designing.

Keywords: Adomian decomposition, inverse analysis, hyperbolic fin, variable thermal conductivity

Procedia PDF Downloads 305

Authors: V. Churkin, M. Lopatin

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The purpose of the paper is to estimate the US small wind turbines market potential and forecast the small wind turbines sales in the US. The forecasting method is based on the application of the Bass model and the generalized Bass model of innovations diffusion under replacement purchases. In the work an exponential distribution is used for modeling of replacement purchases. Only one parameter of such distribution is determined by average lifetime of small wind turbines. The identification of the model parameters is based on nonlinear regression analysis on the basis of the annual sales statistics which has been published by the American Wind Energy Association (AWEA) since 2001 up to 2012. The estimation of the US average market potential of small wind turbines (for adoption purchases) without account of price changes is 57080 (confidence interval from 49294 to 64866 at P = 0.95) under average lifetime of wind turbines 15 years, and 62402 (confidence interval from 54154 to 70648 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 90,7%, while in the second - 91,8%. The effect of the wind turbines price changes on their sales was estimated using generalized Bass model. This required a price forecast. To do this, the polynomial regression function, which is based on the Berkeley Lab statistics, was used. The estimation of the US average market potential of small wind turbines (for adoption purchases) in that case is 42542 (confidence interval from 32863 to 52221 at P = 0.95) under average lifetime of wind turbines 15 years, and 47426 (confidence interval from 36092 to 58760 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 95,3%, while in the second –95,3%.

Keywords: bass model, generalized bass model, replacement purchases, sales forecasting of innovations, statistics of sales of small wind turbines in the United States

Procedia PDF Downloads 331

Authors: David C. Ni

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Contemporary models for N-body systems are based on temporal, two-body, and mass point representation of Newtonian mechanics. Other mainstream models include 2D and 3D Ising models based on local neighborhood the lattice structures. In Quantum mechanics, the theories of collective modes are for superconductivity and for the long-range quantum entanglement. However, these models are still mainly for the specific phenomena with a set of designated parameters. We are therefore motivated to develop a new construction directly from the complex-variable N-body systems based on the extended Blaschke functions (EBF), which represent a non-temporal and nonlinear extension of Lorentz transformation on the complex plane – the normalized momentum spaces. A point on the complex plane represents a normalized state of particle momentums observed from a reference frame in the theory of special relativity. There are only two key parameters, normalized momentum and nonlinearity for modelling. An algorithm similar to Jenkins-Traub method is adopted for solving EBF iteratively. Through iteration, the solution sets show a form of σ + i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various distributions, such as 1-peak, 2-peak, and 3-peak etc. distributions and some of them are analog to the canonical distributions. The results of the numerical analysis demonstrate continuum-to-discreteness transitions, evolutional invariance of distributions, phase transitions with conjugate symmetry, etc., which manifest the construction as a potential candidate for the unification of statistics. We hereby classify the observed distributions on the finite convergent domains. Continuous and discrete distributions both exist and are predictable for given partitions in different regions of parameter-pair. We further compare these distributions with canonical distributions and address the impacts on the existing applications.

Keywords: blaschke, lorentz transformation, complex variables, continuous, discrete, canonical, classification

Procedia PDF Downloads 286

Authors: Didier Auroux, Vladimir Groza

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This work is part of STEEP Marie-Curie ITN project, and it focuses on the identification of unknown parameters of the proposed generic Abrasive WaterJet Milling (AWJM) PDE model, that appears as an ill-posed inverse problem. The necessity of studying this problem comes from the industrial milling applications where the possibility to predict and model the final surface with high accuracy is one of the primary tasks in the absence of any knowledge of the model parameters that should be used. In this framework, we propose the identification of model parameters by minimizing a cost function, measuring the difference between experimental and numerical solutions. The adjoint approach based on corresponding Lagrangian gives the opportunity to find out the unknowns of the AWJM model and their optimal values that could be used to reproduce the required trench profile. Due to the complexity of the nonlinear problem and a large number of model parameters, we use an automatic differentiation software tool (TAPENADE) for the adjoint computations. By adding noise to the artificial data, we show that in fact the parameter identification problem is highly unstable and strictly depends on input measurements. Regularization terms could be effectively used to deal with the presence of data noise and to improve the identification correctness. Based on this approach we present results in 2D and 3D of the identification of the model parameters and of the surface prediction both with self-generated data and measurements obtained from the real production. Considering different types of model and measurement errors allows us to obtain acceptable results for manufacturing and to expect the proper identification of unknowns. This approach also gives us the ability to distribute the research on more complex cases and consider different types of model and measurement errors as well as 3D time-dependent model with variations of the jet feed speed.

Keywords: Abrasive Waterjet Milling, inverse problem, model parameters identification, regularization

Procedia PDF Downloads 294

Authors: Daniel Panario, Daniel Santana de Freitas, Brett Stevens

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Almost Perfect Nonlinear (APN) permutations with optimal resistance against differential cryptanalysis can be found in several domains. The permutation used in the standard for symmetric cryptography (the AES), for example, is based on a special kind of inversion in GF(28). Although very close to APN (2-uniform), this permutation still contains one number 4 in its differential spectrum, which means that, rigorously, it must be classified as 4-uniform. This fact motivates the search for fully APN permutations in other domains of definition. The extremely high complexity associated to this kind of problem precludes an exhaustive search for an APN permutation with 256 elements to be performed without the support of a suitable mathematical structure. On the other hand, in principle, there is nothing to indicate which mathematically structured domains can effectively help the search, and it is necessary to test several domains. In this work, the search for APN permutations in rings ℤ2×ℤ2k is investigated. After a full, exhaustive search with k=2 and k=3, all possible APN permutations in those rings were recorded, together with their differential profiles. Some very promising heuristics in these cases were collected so that, when used as a basis to prune backtracking for the same search in ℤ2×ℤ8 (search space with size 16! ≅244), just a few tenths of a second were enough to produce an APN permutation in a single CPU. Those heuristics were empirically extrapolated so that they could be applied to a backtracking search for APNs over ℤ2×ℤ16 (search space with size 32! ≅2117). The best permutations found in this search were further refined through Simulated Annealing, with a definition of neighbors suitable to this domain. The best result produced with this scheme was a 3-uniform permutation over ℤ2×ℤ16 with only 24 values equal to 3 in the differential spectrum (all the other 968 values were less than or equal 2, as it should be the case for an APN permutation). Although far from being fully APN, this result is technically better than a 4-uniform permutation and demanded only a few seconds in a single CPU. This is a strong indication that the use of mathematically structured domains, like the rings described in this work, together with heuristics based on smaller cases, can lead to dramatic cuts in the computational resources involved in the complexity of the search for APN permutations in extremely large domains.

Keywords: APN permutations, heuristic searches, symmetric cryptography, S-box design

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Authors: Darren A. Whitaker, Dan Palmer, Jens Wesholowski, James Flaherty, John Mack, Ahmad B. Albadarin, Gavin Walker

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Traditional mechanosynthesis has been performed by either ball milling or manual grinding. However, neither of these techniques allow the easy application of process control. The temperature may change unpredictably due to friction in the process. Hence the amount of energy transferred to the reactants is intrinsically non-uniform. Recently, it has been shown that the use of Twin-Screw extrusion (TSE) can overcome these limitations. Additionally, TSE enables a platform for continuous synthesis or manufacturing as it is an open-ended process, with feedstocks at one end and product at the other. Several materials including metal-organic frameworks (MOFs), co-crystals and small organic molecules have been produced mechanochemically using TSE. The described advantages of TSE are offset by drawbacks such as increased process complexity (a large number of process parameters) and variation in feedstock flow impacting on product quality. To handle the above-mentioned drawbacks, this study utilizes UV-Vis spectrophotometry (InSpectroX, ColVisTec) as an online tool to gain real-time information about the quality of the product. Additionally, this is combined with real-time process information in an Advanced Process Control system (PharmaMV, Perceptive Engineering) allowing full supervision and control of the TSE process. Further, by characterizing the dynamic behavior of the TSE, a model predictive controller (MPC) can be employed to ensure the process remains under control when perturbed by external disturbances. Two reactions were studied; a Knoevenagel condensation reaction of barbituric acid and vanillin and, the direct amidation of hydroquinone by ammonium acetate to form N-Acetyl-para-aminophenol (APAP) commonly known as paracetamol. Both reactions could be carried out continuously using TSE, nuclear magnetic resonance (NMR) spectroscopy was used to confirm the percentage conversion of starting materials to product. This information was used to construct partial least squares (PLS) calibration models within the PharmaMV development system, which relates the percent conversion to product to the acquired UV-Vis spectrum. Once this was complete, the model was deployed within the PharmaMV Real-Time System to carry out automated optimization experiments to maximize the percentage conversion based on a set of process parameters in a design of experiments (DoE) style methodology. With the optimum set of process parameters established, a series of PRBS process response tests (i.e. Pseudo-Random Binary Sequences) around the optimum were conducted. The resultant dataset was used to build a statistical model and associated MPC. The controller maximizes product quality whilst ensuring the process remains at the optimum even as disturbances such as raw material variability are introduced into the system. To summarize, a combination of online spectral monitoring and advanced process control was used to develop a robust system for optimization and control of two TSE based mechanosynthetic processes.

Keywords: continuous synthesis, pharmaceutical, spectroscopy, advanced process control

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong

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Earthquake is one of the main loads threatening dam safety. Once the dam is damaged, it will bring huge losses of life and property to the country and people. Therefore, it is very important to research the seismic safety of the dam. Due to the complex foundation conditions, high fortification intensity, and high scientific and technological content, it is necessary to adopt reasonable methods to evaluate the seismic safety performance of concrete arch dams built and under construction in strong earthquake areas. Structural seismic vulnerability analysis can predict the probability of structural failure at all levels under different intensity earthquakes, which can provide a scientific basis for reasonable seismic safety evaluation and decision-making. In this paper, the response surface method (RSM) is applied to the seismic vulnerability analysis of arch dams, which improves the efficiency of vulnerability analysis. Based on the central composite test design method, the material-seismic intensity samples are established. The response surface model (RSM) with arch crown displacement as performance index is obtained by finite element (FE) calculation of the samples, and then the accuracy of the response surface model (RSM) is verified. To obtain the seismic vulnerability curves, the seismic intensity measure ??(?1) is chosen to be 0.1~1.2g, with an interval of 0.1g and a total of 12 intensity levels. For each seismic intensity level, the arch crown displacement corresponding to 100 sets of different material samples can be calculated by algebraic operation of the response surface model (RSM), which avoids 1200 times of nonlinear dynamic calculation of arch dam; thus, the efficiency of vulnerability analysis is improved greatly.

Keywords: high concrete arch dam, performance index, response surface method, seismic vulnerability analysis, vector-valued intensity measure

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Authors: Iacopo Odoardi, Emanuele Felice, Dario D'Ingiullo

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We investigate the role of human capital in the Chinese inland-coastal inequality and how the consequences of the 2007-2008 crisis may induce China to refocus its development path on human capital. We compare panel data analyses for two periods for the richer/coastal and the relatively poor/inland provinces. Considering the rapid evolution of the Chinese economy and the changes forced by the international crisis, we wonder if these events can lead to rethinking local development paths, fostering greater attention on the diffusion of higher education. We expect that the consequences on human capital may, in turn, have consequences on the inland/coastal dualism. The focus on human capital is due to the fact that the growing differences between inland and coastal areas can be explained by the different local endowments. In this respect, human capital may play a major role and should be thoroughly investigated. To assess the extent to which human capital has an effect on economic growth, we consider a fixed-effects model where differences among the provinces are considered parametric shifts in the regression equation. Data refer to the 31 Chinese provinces for the periods 1998-2008 and 2009-2017. Our dependent variable is the annual variation of the provincial gross domestic product (GDP) at the prices of the previous year. Among our regressors, we include two proxies of advanced human capital and other known factors affecting economic development. We are aware of the problem of conceptual endogeneity of variables related to human capital with respect to GDP; we adopt an instrumental variable approach (two-stage least squares) to avoid inconsistent estimates. Our results suggest that the economic strengths that influenced the Chinese take-off and the dualism are confirmed in the first period. These results gain relevance in comparison with the second period. An evolution in local economic endowments is taking place: first, although human capital can have a positive effect on all provinces after the crisis, not all types of advanced education have a direct economic effect; second, the development path of the inland area is changing, with an evolution towards more productive sectors which can favor higher returns to human capital. New strengths (e.g., advanced education, transport infrastructures) could be useful to foster development paths of inland-coastal desirable convergence, especially by favoring the poorer provinces. Our findings suggest that in all provinces, human capital can be useful to promote convergence in growth paths, even if investments in tertiary education seem to have a negative role, most likely due to the inability to exploit the skills of highly educated workers. Furthermore, we observe important changes in the economic characteristics of the less developed internal provinces. These findings suggest an evolution towards more productive economic sectors, a greater ability to exploit both investments in fixed capital and the available infrastructures. All these aspects, if connected with the improvement in the returns to human capital (at least at the secondary level), lead us to assume a better reaction (i.e., resilience) of the less developed provinces to the crisis effects.

Keywords: human capital, inland-coastal inequality, Great Recession, China

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Authors: Satish Kumar, Spandan Sahu, Sarjati Sahoo, K. K. Khatua

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An experimental investigation has been carried out in a tilting flume of 2 m wide, 13 m long, and 0.3 m deep to study the effect of flow on the formation of braided channel pattern. Sediment flow is recirculated through the flume, which passes from the headgate to the sediment/water collecting tank through the tailgate. Further, without altering the geometry of the sand bed channel, the discharge is varied to study the effect of the formation of the braided pattern with time. Then the flow rate is varied to study the effect of flow on the formation of the braided pattern. Sediment transport rate is highly variable and was found to be a nonlinear function of flow rate, aspect ratio, longitudinal slope, and time. Total braided intensity (BIT) for each discharge case is found to be more than the active braided intensity (BIA). Both the parameters first increase and then decrease as the time progresses following a similar pattern for all the observed discharge cases. When the flow is increased, the movement of sediment also increases since the active braided intensity is found to adjust quickly. The measurement of velocity and boundary shear helps to study the erosion and sedimentation processes in the channel and formation of small meandering channels and then the braided channel for different discharge conditions of a sediment river. Due to regime properties of rivers, both total braided Intensity and active braided intensity become stable for a given channel and flow conditions. In the present case, the trend of the ratio of BIA to BIT is found to be asymptotic against the time with a value of 0.4. After the particular time elapses off the flow, new small channels are also found to be formed with changes in the sinuosity of the active channels, thus forming the braided network. This is due to the continuous erosion and sedimentation processes occurring for the flow process for the flow and sediment conditions.

Keywords: active braided intensity, bed load, sediment transport, shear stress, total braided intensity

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Authors: Hsiao-Tien Pao, Yi-Ying Li, Hsin-Chia Fu

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This paper addressed the impacts of energy consumption, economic growth, financial development, and population size on environmental degradation using grey relational analysis (GRA) for China, where foreign direct investment (FDI) inflows is the proxy variable for financial development. The more recent historical data during the period 2004–2011 are used, because the use of very old data for data analysis may not be suitable for rapidly developing countries. The results of the GRA indicate that the linkage effects of energy consumption–emissions and GDP–emissions are ranked first and second, respectively. These reveal that energy consumption and economic growth are strongly correlated with emissions. Higher economic growth requires more energy consumption and increasing environmental pollution. Likewise, more efficient energy use needs a higher level of economic development. Therefore, policies to improve energy efficiency and create a low-carbon economy can reduce emissions without hurting economic growth. The finding of FDI–emissions linkage is ranked third. This indicates that China do not apply weak environmental regulations to attract inward FDI. Furthermore, China’s government in attracting inward FDI should strengthen environmental policy. The finding of population–emissions linkage effect is ranked fourth, implying that population size does not directly affect CO₂ emissions, even though China has the world’s largest population, and Chinese people are very economical use of energy-related products. Overall, the energy conservation, improving efficiency, managing demand, and financial development, which aim at curtailing waste of energy, reducing both energy consumption and emissions, and without loss of the country’s competitiveness, can be adopted for developing economies. The GRA is one of the best way to use a lower data to build a dynamic analysis model.

Keywords: China, CO₂ emissions, foreign direct investment, grey relational analysis

Procedia PDF Downloads 378

Authors: Pradeepa Teegala, Ramreddy Chitteti

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This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

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Authors: Sumedha Weerasekara, Morgan Miles, Mark Morrison, Branka Krivokapic-Skoko

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This paper is aimed at exploring the interrelationships among entrepreneurial ecosystem factors and entrepreneurial cognition in regional and metropolitan ecosystems. Entrepreneurial ecosystem factors examined include: culture, infrastructure, access to finance, informal networks, support services, access to universities, and the depth and breadth of the talent pool. Using a multivariate approach we explore the impact of these ecosystem factors or elements on entrepreneurial cognition. In doing so, the existing body of knowledge from the literature on entrepreneurial ecosystem and cognition have been blended to explore the relationship between entrepreneurial ecosystem factors and cognition in a way not hitherto investigated. The concept of the entrepreneurial ecosystem has received increased attention as governments, universities and communities have started to recognize the potential of integrated policies, structures, programs and processes that foster entrepreneurship activities by supporting innovation, productivity and employment growth. The notion of entrepreneurial ecosystems has evolved and grown with the advancement of theoretical research and empirical studies. Importance of incorporating external factors like culture, political environment, and the economic environment within a single framework will enhance the capacity of examining the whole systems functionality to better understand the interaction of the entrepreneurial actors and factors within a single framework. The literature on clusters underplays the role of entrepreneurs and entrepreneurial management in creating and co-creating organizations, markets, and supporting ecosystems. Entrepreneurs are only one actor following a limited set of roles and dependent upon many other factors to thrive. As a consequence, entrepreneurs and relevant authorities should be aware of the other actors and factors with which they engage and rely, and make strategic choices to achieve both self and also collective objectives. The study uses stratified random sampling method to collect survey data from 12 different regions in regional and metropolitan regions of NSW, Australia. A questionnaire was administered online among 512 Small and medium enterprise owners operating their business in selected 12 regions in NSW, Australia. Data were analyzed using descriptive analyzing techniques and partial least squares - structural equation modeling. The findings show that even though there is a significant relationship between each and every entrepreneurial ecosystem factors, there is a weak relationship between most entrepreneurial ecosystem factors and entrepreneurial cognition. In the metropolitan context, the availability of finance and informal networks have the largest impact on entrepreneurial cognition while culture, infrastructure, and support services having the smallest impact and the talent pool and universities having a moderate impact on entrepreneurial cognition. Interestingly, in a regional context, culture, availability of finance, and the talent pool have the highest impact on entrepreneurial cognition, while informal networks having the smallest impact and the remaining factors – infrastructure, universities, and support services have a moderate impact on entrepreneurial cognition. These findings suggest the need for a location-specific strategy for supporting the development of entrepreneurial cognition.

Keywords: academic achievement, colour response card, feedback

Procedia PDF Downloads 124

Authors: Desere Kokt

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Hospitality establishments worldwide are bearing the brunt of the effects of Covid-19. As the hospitality industry is looking to recover, emphasis is placed on rejuvenating the industry. This is especially pertinent for economic development in areas of high unemployment, such as the Free State province of South Africa. The province is not a main tourist area and thus depends on the influx of tourists. The province has great scenic beauty with many accommodation establishments that provide job opportunities to the local population. The two main economic hubs of the Free State province namely Bloemfontein and Clarens, were the focus of the investigation. The emphasis was on graded accommodation establishments as they must adhere to the quality principles of the Tourism Grading Council of South Africa (TGCSA) to obtain star grading. The hospitality industry is known for being labour intensive, and employees need to be available to cater for the needs of paying customers. This is referred to as ‘emotional labour’ and implies that employees need to manage their feelings and emotions as part of performing their jobs. The focus of this study was thus on psychological factors related to working in the hospitality industry – specifically psychological contract and psychological capital and its impact on the commitment of employees in graded accommodation establishments. Employee commitment can be explained as a psychological state that binds the individual to the organisation and involves a set of psychological relationships that include affective (emotions), normative (perceived obligation) and continuance (staying with the organisation) dimensions. Psychological contract refers to the reciprocal beliefs and expectations between the employer and the employee and consists of transactional and rational contracts. Transactional contracts are associated with the economic exchange, and contractional issues related to the employment contract and rational contracts relate to the social exchange between the employee and the organisation. Psychological capital refers to an individual’s positive psychology state of development that is characterised by self-efficiency (having confidence in doing one’s job), optimism (being positive and persevering towards achieving one’s goals), hope (expectations for goals to succeed) and resilience (bouncing back to attain success when beset by problems and adversity). The study employed a quantitative research approach, and a structured questionnaire was used to gather data from respondents. The study was conducted during the Covid-19 pandemic, which hampered the data gathering efforts of the researchers. Many accommodation establishments were either closed or temporarily closed, which meant that data gathering was an intensive and laborious process. The main researcher travelled to the various establishments to collect the data. Nine hospitality establishments participated in the study, and around 150 employees were targeted for data collection. Ninety-two (92) questionnaires were completed, which represents a response rate of 61%. Data were analysed using descriptive and inferential statistics, and partial least squares structural equation modelling (PLS-SEM) was applied to examine the relationship between the variables.

Keywords: employee commitment, hospitality industry, psychological contract, psychological capital

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Authors: Carla Maria Costa Ferreira, Maria Helena Freitas Melao Barros

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The rules implemented in Europe regarding structural design are termed Structural Eurocodes and deal with the several materials available for construction. Particularly regarding the very used in Europe concrete with steel reinforcement, it is named the Eurocode 2 – Design of Concrete Structures, usually known as EC2. The need of tables and abacuses to help in the design of reinforced concrete was due to the fact that the evolution and the study of new procedures and higher strength concrete showed that the previous tables needed to be improved. Reinforced concrete structures have particular aspects in the design that come from the nonlinear behavior of the concrete and steel and, in the case of concrete, also by the very low tensile strength. The design of reinforced concrete structures is made in terms of evaluating the ultimate strength and how it behaves under service conditions. As a matter of fact, the use of higher-strength concrete and steel classes showed that these serviceability design that was important for prestressed structures may be relevant in reinforced concrete structures. For these aspects, there are tables and design charts used for the ultimate limit design of reinforced concrete sections under bending moments and axial forces, and also auxiliary design diagrams able to evaluate the stress of the steel and the concrete at a section and the ductility for service limit states verification. For practical use, here are presented tables and design charts for the ultimate limit design of reinforced concrete sections and also auxiliary interaction diagrams for verification of the serviceability conditions. These kinds of aid for design were only available to engineers before the development of computers and, nowadays, yet an important tool in the universities for the students' use. Usually, in the reinforced concrete design, it is needed to obtain the area of the steel longitudinal reinforcement to be placed in the structure. The quantity and the position of the steel area may have different solutions and these tables and abacuses permit to obtain many possibilities in order to optimize the solution in economic or ductility terms.

Keywords: design examples, Eurocode 2, reinforced concrete, section design

Procedia PDF Downloads 47