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Authors: Mustafa M. Donma, Orkide Donma, Murat Aydin, Muhammet Demirkol, Burcin Nalbantoglu, Aysin Nalbantoglu, Birol Topcu

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Childhood obesity is an ever increasing global health problem, affecting both developed and developing countries. Accurate evaluation of obesity in children requires difficult and detailed investigation. In our study, obesity in children was evaluated using new body fat ratios and indices. Assessment of anthropometric measurements, as well as some ratios, is important because of the evaluation of gender differences particularly during the late periods of obesity. A total of 239 children; 168 morbid obese (MO) (81 girls and 87 boys) and 71 normal weight (NW) (40 girls and 31 boys) children, participated in the study. Informed consent forms signed by the parents were obtained. Ethics Committee approved the study protocol. Mean ages (years)±SD calculated for MO group were 10.8±2.9 years in girls and 10.1±2.4 years in boys. The corresponding values for NW group were 9.0±2.0 years in girls and 9.2±2.1 years in boys. Mean body mass index (BMI)±SD values for MO group were 29.1±5.4 kg/m² and 27.2±3.9 kg/m² in girls and boys, respectively. These values for NW group were calculated as 15.5±1.0 kg/m² in girls and 15.9±1.1 kg/m² in boys. Groups were constituted based upon BMI percentiles for age-and-sex values recommended by WHO. Children with percentiles >99 were grouped as MO and children with percentiles between 85 and 15 were considered NW. The anthropometric measurements were recorded and evaluated along with the new ratios such as trunk-to-appendicular fat ratio, as well as indices such as Index-I and Index-II. The body fat percent values were obtained by bio-electrical impedance analysis. Data were entered into a database for analysis using SPSS/PASW 18 Statistics for Windows statistical software. Increased waist-to-hip circumference (C) ratios, decreased head-to-neck C, height ‘to’ ‘two’-‘to’-waist C and height ‘to’ ‘two’-‘to’-hip C ratios were observed in parallel with the development of obesity (p≤0.001). Reference value for height ‘to’ ‘two’-‘to’-hip ratio was detected as approximately 1.0. Index-II, based upon total body fat mass, showed much more significant differences between the groups than Index-I based upon weight. There was not any difference between trunk-to-appendicular fat ratios of NW girls and NW boys (p≥0.05). However, significantly increased values for MO girls in comparison with MO boys were observed (p≤0.05). This parameter showed no difference between NW and MO states in boys (p≥0.05). However, statistically significant increase was noted in MO girls compared to their NW states (p≤0.001). Trunk-to-appendicular fat ratio was the only fat-based parameter, which showed gender difference between NW and MO groups. This study has revealed that body ratios and formula based upon body fat tissue are more valuable parameters than those based on weight and height values for the evaluation of morbid obesity in children.

Keywords: Anthropometry, childhood obesity, gender, Morbid obesity.

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Authors: Anna Słupik, Krzysztof Jaworski, Anna Mosiołek, Dariusz Białoszewski

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Background: Maintaining the correct body balance is essential in the prevention of falls in the elderly, which is especially important for women because of postmenopausal osteoporosis and the serious consequences of falls. One of the exercise methods which is very popular among adults, and which may affect body balance in the positive way is the Pilates method. The aim of the study was to evaluate the effect of regular Pilates exercises on the ability to maintain body balance in static conditions in adult healthy women. Material and methods: The study group consisted of 20 healthy women attending Pilates twice a week for at least 1 year. The control group consisted of 20 healthy women physically inactive. Women in the age range from 35 to 50 years old without pain in musculoskeletal system or other pain were only qualified to the groups. Body balance was assessed using MatScan VersaTek platform with Sway Analysis Module based on Matscan Clinical 6.7 software (Tekscan Inc., U.S.A). The balance was evaluated under the following conditions: standing on both feet with eyes open, standing on both feet with eyes closed, one-leg standing (separately on the right and left foot) with eyes open. Each test lasted 30 seconds. The following parameters were calculated: estimated size of the ellipse of 95% confidence, the distance covered by the Center of Gravity (COG), the size of the maximum shift in the sagittal and frontal planes and load distribution between the left and right foot, as well as between rear- and forefoot. Results: It was found that there is significant difference between the groups in favor of the study group in the size of the confidence ellipse and maximum shifts of COG in the sagittal plane during standing on both feet, both with the eyes open and closed (p <0.05). While standing on one leg both on the right and left leg, with eyes opened there was a significant difference in favor of the study group, in terms of the size of confidence ellipse, the size of the maximum shifts in the sagittal and in the frontal plane (p <0.05). There were no differences between the distribution of load between the right and left foot (standing with both feet), nor between fore- and rear foot (in standing with both feet or one-leg). Conclusions: 1. Static balance in women exercising regularly by Pilates method is better than in inactive women, which may in the future prevent falls and their consequences. 2. The observed differences in maintaining balance in frontal plane in one-leg standing may indicate a positive impact of Pilates exercises on the ability to maintain global balance in terms of reduced support surface. 3. Pilates method can be used as a form preventive therapy for all people who are expected to have problems with body balance in the future, for example in chronic neurological disorders or vestibular problems. 4. The results have shown that, further prospective randomized research on a larger and more representative group is needed.

Keywords: Balance exercises, body balance, Pilates, pressure distribution, women.

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Authors: Natasha Bhate

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Contraception is important in helping to reduce maternal and infant mortality rates by allowing women to control the number and spacing in-between their children. It also reduces the need for unsafe abortions. Women worldwide use contraception; however, the contraceptive prevalence rate is still relatively low in Central American countries like Guatemala. There is also an unmet need for contraception in Guatemala, which is more significant in rural, indigenous women due to barriers preventing contraceptive use. The study objective was to investigate and analyse the current barriers women face, in Guatemala, Panajachel and the surrounding areas, in using contraception, with a view of identifying ways to overcome these barriers. This included exploring the contraceptive barriers women believe exist and the influence of males in contraceptive decision making. The study took place at a charity in Panajachel, Guatemala, and had a cross-sectional, qualitative design to allow an in-depth understanding of information gathered. This particular study design was also chosen to help inform the charity with qualitative research analysis, in view of their intent to create a local reproductive health programme. A semi-structured interview design, including photo facilitation to improve cross-cultural communication, with interpreter assistance, was utilized. A pilot interview was initially conducted with small improvements required. Participants were recruited through purposive and convenience sampling. The study host at the charity acted as a gatekeeper; participants were identified through attendance of the charity’s women’s-initiative programme workshops. 20 participants were selected and agreed to study participation with two not attending; a total of 18 participants were interviewed in June 2017. Interviews were audio-recorded and data were stored on encrypted memory sticks. Framework analysis was used to analyse the data using NVivo11 software. The University of Leeds granted ethical approval for the research. Religion, language, the community, and fear of sickness were examples of existing contraceptive barrier themes recognized by many participants. The influence of men was also an important barrier identified, with themes of machismo and abuse preventing contraceptive use in some women. Women from more rural areas were believed to still face barriers which some participants did not encounter anymore, such as distance and affordability of contraceptives. Participants believed that informative workshops in various settings were an ideal method of overcoming existing contraceptive barriers and allowing women to be more empowered. The involvement of men in such workshops was also deemed important by participants to help reduce their negative influence in contraceptive usage. Overall, four recommendations following this study were made, including contraceptive educational courses, a gender equality campaign, couple-focused contraceptive workshops, and further qualitative research to gain a better insight into men’s opinions regarding women using contraception.

Keywords: Barrier, contraception, machismo, religion.

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Authors: Delphine Mukaneza, Lin Qiao, Wang Pengxin, Li Yan, Chen Yingyi

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Human activities on land use make the land-cover gradually change or transit. In this study, we examined the use of Landsat TM data to detect the land use change of Kigali between 1987 and 2009 using remote sensing techniques and analysis of data using ENVI and ArcGIS, a GIS software. Six different categories of land use were distinguished: bare soil, built up land, wetland, water, vegetation, and others. With remote sensing techniques, we analyzed land use data in 1987, 1999 and 2009, changed areas were found and a dynamic situation of land use in Kigali city was found during the 22 years studied. According to relevant Landsat data, the research focused on land use change in accordance with the role of remote sensing in the process of urbanization. The result of the work has shown the rapid increase of built up land between 1987 and 1999 and a big decrease of vegetation caused by the rebuild of the city after the 1994 genocide, while in the period of 1999 to 2009 there was a reduction in built up land and vegetation, after the authority of Kigali city established, a Master Plan where all constructions which were not in the range of the master Plan were destroyed. Rwanda's capital, Kigali City, through the expansion of the urban area, it is increasing the internal employment rate and attracts business investors and the service sector to improve their economy, which will increase the population growth and provide a better life. The overall planning of the city of Kigali considers the environment, land use, infrastructure, cultural and socio-economic factors, the economic development and population forecast, urban development, and constraints specification. To achieve the above purpose, the Government has set for the overall planning of city Kigali, different stages of the detailed description of the design, strategy and action plan that would guide Kigali planners and members of the public in the future to have more detailed regional plans and practical measures. Thus, land use change is significantly the performance of Kigali active human area, which plays an important role for the country to take certain decisions. Another area to take into account is the natural situation of Kigali city. Agriculture in the region does not occupy a dominant position, and with the population growth and socio-economic development, the construction area will gradually rise and speed up the process of urbanization. Thus, as a developing country, Rwanda's population continues to grow and there is low rate of utilization of land, where urbanization remains low. As mentioned earlier, the 1994 genocide massacres, population growth and urbanization processes, have been the factors driving the dramatic changes in land use. The focus on further research would be on analysis of Rwanda’s natural resources, social and economic factors that could be, the driving force of land use change.

Keywords: Land use change, urbanization, Kigali City, Landsat.

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Authors: Anna Costanza Russo, Daniele Landi, Michele Germani

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Nowadays, the European Ecodesign Directive has emerged as a new approach to integrate environmental concerns into the product design and related processes. Ecodesign aims to minimize environmental impacts throughout the product life cycle, without compromising performances and costs. In addition, the recent Ecodesign Directives require products which are increasingly eco-friendly and eco-efficient, preserving high-performances. It is very important for producers measuring performances, for electric cooking ranges, hobs, ovens, and grills for household use, and a low power consumption of appliances represents a powerful selling point, also in terms of ecodesign requirements. The Ecodesign Directive provides a clear framework about the sustainable design of products and it has been extended in 2009 to all energy-related products, or products with an impact on energy consumption during the use. The European Regulation establishes measures of ecodesign of ovens, hobs, and kitchen hoods, and domestic use and energy efficiency of a product has a significant environmental aspect in the use phase which is the most impactful in the life cycle. It is important that the product parameters and performances are not affected by ecodesign requirements from a user’s point of view, and the benefits of reducing energy consumption in the use phase should offset the possible environmental impact in the production stage. Accurate measurements of cooking appliance performance are essential to help the industry to produce more energy efficient appliances. The development of ecodriven products requires ecoinnovation and ecodesign tools to support the sustainability improvement. The ecodesign tools should be practical and focused on specific ecoobjectives in order to be largely diffused. The main scope of this paper is the development, implementation, and testing of an innovative tool, which could be an improvement for the sustainable design of induction hobs. In particular, a prototypical software tool is developed in order to simulate the energy performances of the induction hobs. The tool is focused on a multiphysics model which is able to simulate the energy performances and the efficiency of induction hobs starting from the design data. The multiphysics model is composed by an electromagnetic simulation and a thermal simulation. The electromagnetic simulation is able to calculate the eddy current induced in the pot, which leads to the Joule heating of material. The thermal simulation is able to measure the energy consumption during the operational phase. The Joule heating caused from the eddy currents is the output of electromagnetic simulation and the input of thermal ones. The aims of the paper are the development of integrated tools and methodologies of virtual prototyping in the context of the ecodesign. This tool could be a revolutionary instrument in the field of industrial engineering and it gives consideration to the environmental aspects of product design and focus on the ecodesign of energy-related products, in order to achieve a reduced environmental impact.

Keywords: Ecodesign, induction hobs, virtual prototyping, energy efficiency.

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Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

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The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: Computing experiment, hydroelasticity, physical experiment, vibration.

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Authors: S. Aziz, B. Alexander, C. Gengnagel, S. Weinzierl

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This paper explores a generative design, simulation, and optimization workflow for the integration of acoustical diffuser and/or absorber geometry with embedded coupled Helmholtz-resonators for full scale 3D printed building components. Large-scale additive manufacturing in conjunction with algorithmic CAD design tools enables a vast amount of control when creating geometry. This is advantageous regarding the increasing demands of comfort standards for indoor spaces and the use of more resourceful and sustainable construction methods and materials. The presented methodology highlights these new technological advancements and offers a multimodal and integrative design solution with the potential for an immediate application in the AEC-Industry. In principle, the methodology can be applied to a wide range of structural elements that can be manufactured by additive manufacturing processes. The current paper focuses on a case study of an application for a biaxial load-bearing beam grillage made of reinforced concrete, which allows for a variety of applications through the combination of additive prefabricated semi-finished parts and in-situ concrete supplementation. The semi-prefabricated parts or formwork bodies form the basic framework of the supporting structure and at the same time have acoustic absorption and diffusion properties that are precisely acoustically programmed for the space underneath the structure. To this end, a hybrid validation strategy is being explored using a digital and cross-platform simulation environment, verified with physical prototyping. The iterative workflow starts with the generation of a parametric design model for the acoustical geometry using the algorithmic visual scripting editor Grasshopper3D inside the Building Information Modeling (BIM) software Revit. Various geometric attributes (i.e., bottleneck and cavity dimensions) of the resonator are parameterized and fed to a numerical optimization algorithm which can modify the geometry with the goal of increasing absorption at resonance and increasing the bandwidth of the effective absorption range. Using Rhino.Inside and LiveLink for Revit the generative model was imported directly into the Multiphysics simulation environment COMSOL. The geometry was further modified and prepared for simulation in a semi-automated process. The incident and scattered pressure fields were simulated from which the surface normal absorption coefficients were calculated. This reciprocal process was repeated to further optimize the geometric parameters. Subsequently the numerical models were compared to a set of 3D concrete printed physical twin models which were tested in a .25 m x .25 m impedance tube. The empirical results served to improve the starting parameter settings of the initial numerical model. The geometry resulting from the numerical optimization was finally returned to grasshopper for further implementation in an interdisciplinary study.

Keywords: Acoustical design, additive manufacturing, computational design, multimodal optimization.

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Authors: M. Keshavarzi

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Grasslands of Iran are encountered with a vast desertification and destruction. Some legumes are plants of forage importance with high palatability. Studied legumes in this project are Onobrychis, Medicago sativa (alfalfa) and Trifolium repens. Seeds were cultivated in research field of Kaboutarabad (33 km East of Isfahan, Iran) with an average 80 mm. annual rainfall. Plants were cultivated in a split plot design with 3 replicate and two water treatments (weekly irrigation, and under stress with same amount per 15 days interval). Water entrance to each plots were measured by Partial flow. This project lasted 20 weeks. Destructive samplings (1m2 each time) were done weekly. At each sampling plants were gathered and weighed separately for each vegetative parts. An Area Meter (Vista) was used to measure root surface and leaf area. Total shoot and root fresh and dry weight, leaf area index and soil coverage were evaluated too. Dry weight was achieved in 750c oven after 24 hours. Statgraphic and Harvard Graphic software were used to formulate and demonstrate the parameters curves due to time. Our results show that Trifolium repens has affected 60 % and Medicago sativa 18% by water stress. Onobrychis total fresh weight was reduced 45%. Dry weight or Biomass in alfalfa is not so affected by water shortage. This means that in alfalfa fields we can decrease the irrigation amount and have some how same amount of Biomass. Onobrychis show a drastic decrease in Biomass. The increases in total dry matter due to time in studied plants are formulated. For Trifolium repens if removal or cattle entrance to meadows do not occurred at perfect time, it will decrease the palatability and water content of the shoots. Water stress in a short period could develop the root system in Trifolium repens, but if it last more than this other ecological and soil factors will affect the growth of this plant. Low level of soil water is not so important for studied legume forges. But water shortage affect palatability and water content of aerial parts. Leaf area due to time in studied legumes is formulated. In fact leaf area is decreased by shortage in available water. Higher leaf area means higher forage and biomass production. Medicago and Onobrychis reach to the maximum leaf area sooner than Trifolium and are able to produce an optimum soil cover and inhibit the transpiration of soil water of meadows. Correlation of root surface to Total biomass in studied plants is formulated. Medicago under water stress show a 40% decrease in crown cover while at optimum condition this amount reach to 100%. In order to produce forage in areas without soil erosion Medicago is the best choice even with a shortage in water resources. It is tried to represent the growth simulation of three famous Forage Legumes. By growth simulation farmers and range managers could better decide to choose best plant adapted to water availability without designing different time and labor consuming field experiments.

Keywords: Ecological parameters, Medicago, Onobrychis, Trifolium.

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Authors: Kari Björn

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Introduction of games has expanded the application area of computer-aided learning tools to wide variety of age groups of learners. Serious games engage the learners into a real-world -type of simulation and potentially enrich the learning experience. Institutional background of a Bachelor’s level engineering program in Information and Communication Technology is introduced, with detailed focus on one of its majors, Health Technology. As part of a Customer Oriented Software Application thematic semester, one particular course of “eHealth Business and Solutions” is described and reflected in a gamified framework. Learning a consistent view into vast literature of business management, strategies, marketing and finance in a very limited time enforces selection of topics relevant to the industry. Health Technology is a novel and growing industry with a growing sector in consumer wearable devices and homecare applications. The business sector is attracting new entrepreneurs and impatient investor funds. From engineering education point of view the sector is driven by miniaturizing electronics, sensors and wireless applications. However, the market is highly consumer-driven and usability, safety and data integrity requirements are extremely high. When the same technology is used in analysis or treatment of patients, very strict regulatory measures are enforced. The paper introduces a course structure using gamification as a tool to learn the most essential in a new market: customer value proposition design, followed by a market entry game. Students analyze the existing market size and pricing structure of eHealth web-service market and enter the market as a steering group of their company, competing against the legacy players and with each other. The market is growing but has its rules of demand and supply balance. New products can be developed with an R&D-investment, and targeted to market with unique quality- and price-combinations. Product cost structure can be improved by investing to enhanced production capacity. Investments can be funded optionally by foreign capital. Students make management decisions and face the dynamics of the market competition in form of income statement and balance sheet after each decision cycle. The focus of the learning outcome is to understand customer value creation to be the source of cash flow. The benefit of gamification is to enrich the learning experience on structure and meaning of financial statements. The paper describes the gamification approach and discusses outcomes after two course implementations. Along the case description of learning challenges, some unexpected misconceptions are noted. Improvements of the game or the semi-gamified teaching pedagogy are discussed. The case description serves as an additional support to new game coordinator, as well as helps to improve the method. Overall, the gamified approach has helped to engage engineering student to business studies in an energizing way.

Keywords: Engineering education, integrated curriculum, learning experience, learning outcomes.

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Authors: Vaso K. Kapnopoulou, Piero Caridis

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The fatigue of ship structural details is of major concern in the maritime industry as it can generate fracture issues that may compromise structural integrity. In the present study, a fatigue analysis of the lower hopper knuckle connection of a bulk carrier was conducted using the Finite Element Method by means of ABAQUS/CAE software. The fatigue life was calculated using Miner’s Rule and the long-term distribution of stress range by the use of the two-parameter Weibull distribution. The cumulative damage ratio was estimated using the fatigue damage resulting from the stress range occurring at each load condition. For this purpose, a cargo hold model was first generated, which extends over the length of two holds (the mid-hold and half of each of the adjacent holds) and transversely over the full breadth of the hull girder. Following that, a submodel of the area of interest was extracted in order to calculate the hot spot stress of the connection and to estimate the fatigue life of the structural detail. Two hot spot locations were identified; one at the top layer of the inner bottom plate and one at the top layer of the hopper plate. The IACS Common Structural Rules (CSR) require that specific dynamic load cases for each loading condition are assessed. Following this, the dynamic load case that causes the highest stress range at each loading condition should be used in the fatigue analysis for the calculation of the cumulative fatigue damage ratio. Each load case has a different effect on ship hull response. Of main concern, when assessing the fatigue strength of the lower hopper knuckle connection, was the determination of the maximum, i.e. the critical value of the stress range, which acts in a direction normal to the weld toe line. This acts in the transverse direction, that is, perpendicularly to the ship's centerline axis. The load cases were explored both theoretically and numerically in order to establish the one that causes the highest damage to the location examined. The most severe one was identified to be the load case induced by beam sea condition where the encountered wave comes from the starboard. At the level of the cargo hold model, the model was assumed to be simply supported at its ends. A coarse mesh was generated in order to represent the overall stiffness of the structure. The elements employed were quadrilateral shell elements, each having four integration points. A linear elastic analysis was performed because linear elastic material behavior can be presumed, since only localized yielding is allowed by most design codes. At the submodel level, the displacements of the analysis of the cargo hold model to the outer region nodes of the submodel acted as boundary conditions and applied loading for the submodel. In order to calculate the hot spot stress at the hot spot locations, a very fine mesh zone was generated and used. The fatigue life of the detail was found to be 16.4 years which is lower than the design fatigue life of the structure (25 years), making this location vulnerable to fatigue fracture issues. Moreover, the loading conditions that induce the most damage to the location were found to be the various ballasting conditions.

Keywords: Lower hopper knuckle, high cycle fatigue, finite element method, dynamic load cases.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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