Search results for: geometric nonlinearity

Authors: Siddegowda, Y. A. Sathish, G. Krishnegowda, T. M. Mohan Kumar

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Road accidents are a human tragedy. They involve high human suffering and monetary costs in terms of untimely death, injuries and social problems. India had earned the dubious distinction of having more number of fatalities due to road accidents in the world. Road safety is emerging as a major social concern around the world especially in India because of infrastructure project works. A case study was taken on NH – 07 which connects to various major cities and industries. The study shows that major cases of fatalities are due to bus, trucks and high speed vehicles. The main causes of accidents are due to high density, non-restriction of speed, use of mobile phones, lack of board signs on road parking, visibility restriction, improper geometric design, road use characteristics, environmental aspects, social aspects etc. Data analysis and preventive measures are enlightened in this paper.

Keywords: accidents, environmental aspects, fatalities, geometric design, road user characteristics

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Parth Gupta, Ujjawal Singh, Shashank Kumar, Mansi Chandra, Arnab Sarkar

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Microfluidic devices have emerged as indispensable tools across various scientific disciplines, offering precise control and manipulation of fluids at the microscale. Their efficacy in flow-based research, spanning engineering, chemistry, and biology, relies heavily on the geometric design of microfluidic channels. This work introduces a novel approach to optimise these channels through Response Surface Methodology (RSM), departing from the conventional practice of addressing one parameter at a time. Traditionally, optimising microfluidic channels involved isolated adjustments to individual parameters, limiting the comprehensive understanding of their combined effects. In contrast, our approach considers the simultaneous impact of multiple parameters, employing RSM to efficiently explore the complex design space. The outcome is an innovative microfluidic channel that consumes an optimal sample volume and minimises flow time, enhancing overall efficiency. The relevance of geometric parameter optimization in microfluidic channels extends significantly in biomedical engineering. The flow characteristics of porous materials within these channels depend on many factors, including fluid viscosity, environmental conditions (such as temperature and humidity), and specific design parameters like sample volume, channel width, channel length, and substrate porosity. This intricate interplay directly influences the performance and efficacy of microfluidic devices, which, if not optimized, can lead to increased costs and errors in disease testing and analysis. In the context of biomedical applications, the proposed approach addresses the critical need for precision in fluid flow. it mitigate manufacturing costs associated with trial-and-error methodologies by optimising multiple geometric parameters concurrently. The resulting microfluidic channels offer enhanced performance and contribute to a streamlined, cost-effective process for testing and analyzing diseases. A key highlight of our methodology is its consideration of the interconnected nature of geometric parameters. For instance, the volume of the sample, when optimized alongside channel width, length, and substrate porosity, creates a synergistic effect that minimizes errors and maximizes efficiency. This holistic optimization approach ensures that microfluidic devices operate at their peak performance, delivering reliable results in disease testing. A key highlight of our methodology is its consideration of the interconnected nature of geometric parameters. For instance, the volume of the sample, when optimized alongside channel width, length, and substrate porosity, creates a synergistic effect that minimizes errors and maximizes efficiency. This holistic optimization approach ensures that microfluidic devices operate at their peak performance, delivering reliable results in disease testing. A key highlight of our methodology is its consideration of the interconnected nature of geometric parameters. For instance, the volume of the sample, when optimized alongside channel width, length, and substrate porosity, creates a synergistic effect that minimizes errors and maximizes efficiency. This holistic optimization approach ensures that microfluidic devices operate at their peak performance, delivering reliable results in disease testing.

Keywords: microfluidic device, minitab, statistical optimization, response surface methodology

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Authors: Aarushi Agarwal, Tara Singh, Anju Lata Singh, Trayambak Tiwari, Indramani Lal Singh

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The existing interdependent relationship between attention and consciousness has been put to debate since long. To testify the nature, dual-task paradigm has been used to simultaneously manipulate awareness and attention. With central discrimination task which is attentional demanding, participants also perform simple discrimination task in the periphery in near absence of attention. Individual-based analysis of performance accuracy in single and dual condition showed and above chance level performance i.e. more than 80%. In order to widen the understanding of extent of discrimination carried in near absence of attention, natural image and its geometric equivalent shape were presented in the periphery; synthetic objects accounted to lower level of performance than natural objects in dual condition. The gaze plot and heatmap indicate that peripheral performance do not necessarily involve saccade every time, verifying the discrimination in the periphery was in near absence of attention. Thus our studies show an interdependent nature of attention and awareness.

Keywords: attention, awareness, dual task paradigm, natural and geometric images

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Authors: Vladimir Simovic, Matija Varga, Robert Svetlacic

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Scientific work analytically explores and demonstrates techniques that can animate objects and geometric characters using CSS3 language by applying proper formatting and positioning of elements. This paper presents examples of optimum application of the CSS3 descriptive language when generating general web animations (e.g., billiards and movement of geometric characters, etc.). The paper presents analytically, the optimal development and animation design with the frames within which the animated objects are. The originally developed content is based on the upgrading of existing CSS3 descriptive language animations with more complex syntax and project-oriented work. The purpose of the developed animations is to provide an overview of the interactive features of CSS3 descriptive language design for computer games and the animation of important analytical data based on the web view. It has been analytically demonstrated that CSS3 as a descriptive language allows inserting of various multimedia elements into websites for public and internal sites.

Keywords: web animation recording, KML GML HTML5 forms, Cascading Style Sheets 3, Google Earth Professional

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Authors: H. Loumi-Fergane, A. Belaidi

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The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qⁱ, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: conservation laws, field theories, multisymplectic geometry, relativistic mechanics

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Authors: Ayda Kurtulus

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Heydar Aliyev Centre and Quéops Pyramid are two contrasting examples of sacred geometry perceived as metaphorical alchemy by linking cosmos and earth. Zaha Hadid’s modern building has a wave-like shape and semi-circular alternations that show fluidity and movement, while The Great Pyramid of Giza is triangular. The centre is reminding of the shape of planets, an attempt to regain the balance lost in the modern-day capitalist world, while the Great Pyramid of Giza represents a vortex of energy that connects heaven and earth, harmony and balance. The sacred geometric shapes link the past and the future through God and Ra, humanism and spiritualism in an architectural evolution continuum, mind and spirit into one. An analysis of two geometrical forms, a semi-circle, and a triangle, were carried out through a comprehensive literature review, indicating that behind the materialistic perceptual beauty of buildings, ancient and contemporary, there are mathematical and sacred geometrical constructions that add value to one superficiality can interpret.

Keywords: architectural shapes, The Great Pyramid of Giza, Heydar Aliyev Centre, sacred geometry, philosophy

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Authors: Mariya V. Yanyukina, Michael A. Bolotov

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Assembling accuracy is the degree of accordance between the actual values of the parameters obtained during assembly, and the values specified in the assembly drawings and technical specifications. However, the assembling accuracy depends not only on the quality of the production process but also on the correctness of the assembly process. Therefore, preliminary calculations of assembly stages are carried out to verify the correspondence of real geometric parameters to their acceptable values. In the aviation industry, most calculations involve interacting dimensional chains. This greatly complicates the task. Solving such problems requires a special approach. The purpose of this article is to carry out the problem of improving the technology of assembly of aviation units by use of computer calculations. One of the actual examples of the assembly unit, in which there is an interacting dimensional chain, is the turbine wheel of gas turbine engine. Dimensional chain of turbine wheel is formed by geometric parameters of disk and set of blades. The interaction of the dimensional chain consists in the formation of two chains. The first chain is formed by the dimensions that determine the location of the grooves for the installation of the blades, and the dimensions of the blade roots. The second dimensional chain is formed by the dimensions of the airfoil shroud platform. The interaction of the dimensional chain of the turbine wheel is the interdependence of the first and second chains by means of power circuits formed by a plurality of middle parts of the turbine blades. The timeliness of the calculation of the dimensional chain of the turbine wheel is the need to improve the technology of assembly of this unit. The task at hand contains geometric and mathematical components; therefore, its solution can be implemented following the algorithm: 1) research and analysis of production errors by geometric parameters; 2) development of a parametric model in the CAD system; 3) creation of set of CAD-models of details taking into account actual or generalized distributions of errors of geometrical parameters; 4) calculation model in the CAE-system, loading of various combinations of models of parts; 5) the accumulation of statistics and analysis. The main task is to pre-simulate the assembly process by calculating the interacting dimensional chains. The article describes the approach to the solution from the point of view of mathematical statistics, implemented in the software package Matlab. Within the framework of the study, there are data on the measurement of the components of the turbine wheel-blades and disks, as a result of which it is expected that the assembly process of the unit will be optimized by solving dimensional chains.

Keywords: accuracy, assembly, interacting dimension chains, turbine

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Authors: Jaan-Willem Simon, Bertram Stier, Brett Bednarcyk, Evan Pineda, Stefanie Reese

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Textile composites, in which the reinforcing fibers are woven or braided, have become very popular in numerous applications in aerospace, automotive, and maritime industry. These textile composites are advantageous due to their ease of manufacture, damage tolerance, and relatively low cost. However, physics-based modeling of the mechanical behavior of textile composites is challenging. Compared to their unidirectional counterparts, textile composites introduce additional geometric complexities, which cause significant local stress and strain concentrations. Since these internal concentrations are primary drivers of nonlinearity, damage, and failure within textile composites, they must be taken into account in order for the models to be predictive. The macro-scale approach to modeling textile-reinforced composites treats the whole composite as an effective, homogenized material. This approach is very computationally efficient, but it cannot be considered predictive beyond the elastic regime because the complex microstructural geometry is not considered. Further, this approach can, at best, offer a phenomenological treatment of nonlinear deformation and failure. In contrast, the mesoscale approach to modeling textile composites explicitly considers the internal geometry of the reinforcing tows, and thus, their interaction, and the effects of their curved paths can be modeled. The tows are treated as effective (homogenized) materials, requiring the use of anisotropic material models to capture their behavior. Finally, the micro-scale approach goes one level lower, modeling the individual filaments that constitute the tows. This paper will compare meso- and micro-scale approaches to modeling the deformation, damage, and failure of textile-reinforced polymer matrix composites. For the mesoscale approach, the woven composite architecture will be modeled using the finite element method, and an anisotropic damage model for the tows will be employed to capture the local nonlinear behavior. For the micro-scale, two different models will be used, the one being based on the finite element method, whereas the other one makes use of an embedded semi-analytical approach. The goal will be the comparison and evaluation of these approaches to modeling textile-reinforced composites in terms of accuracy, efficiency, and utility.

Keywords: multiscale modeling, continuum damage model, damage interaction, textile composites

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Authors: Yasmeen A. S. Essawy, Khaled Nassar

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With the rapid increase of complexity in the building industry, professionals in the A/E/C industry were forced to adopt Building Information Modeling (BIM) in order to enhance the communication between the different project stakeholders throughout the project life cycle and create a semantic object-oriented building model that can support geometric-topological analysis of building elements during design and construction. This paper presents a model that extracts topological relationships and geometrical properties of building elements from an existing fully designed BIM, and maps this information into a directed acyclic Elemental Graph Data Model (EGDM). The model incorporates BIM-based search algorithms for automatic deduction of geometrical data and topological relationships for each building element type. Using graph search algorithms, such as Depth First Search (DFS) and topological sortings, all possible construction sequences can be generated and compared against production and construction rules to generate an optimized construction sequence and its associated schedule. The model is implemented in a C# platform.

Keywords: building information modeling (BIM), elemental graph data model (EGDM), geometric and topological data models, graph theory

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Authors: Watchareeporn Chaimongkol

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In this paper, we compare the statistical measures accuracy of composite forecasting model to estimate automobile customer demand in Thailand. A modified simple exponential smoothing and autoregressive integrate moving average (ARIMA) forecasting model is built to estimate customer demand of passenger cars, instead of using information of historical sales data. Our model takes into account special characteristic of the Thai automobile market such as sales promotion, advertising and publicity, petrol price, and interest rate for loan. We evaluate our forecasting model by comparing forecasts with actual data using six accuracy measurements, mean absolute percentage error (MAPE), geometric mean absolute error (GMAE), symmetric mean absolute percentage error (sMAPE), mean absolute scaled error (MASE), median relative absolute error (MdRAE), and geometric mean relative absolute error (GMRAE).

Keywords: composite forecasting, simple exponential smoothing model, autoregressive integrate moving average model selection, accuracy measurements

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Authors: T. S. Shashikumar

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Radon is a radioactive gas emitted from radium, a daughter product of uranium that occurs naturally in rocks and soil. Radon, together with its decay products, emits alpha particles that can damage lung tissue. The activity concentration of ²²²Ra has been analyzed in water samples collected from borewells and rivers in and around Hassan city, Karnataka State, India. The measurements were performed by Emanometry technique. The concentration of ²²²Rn in borewell waters varies from 18.49±1.89 to 397.26±12.3 Bql^-1 with geometric mean 120.48±12.87 Bql^-1 and in river waters it varies from 92.63±9.31 to 93.98±9.51 Bql^-1 with geometric mean of 93.16±9.33 Bql^-1. In the present study, the radon concentrations are higher in Adarshanagar and Viveka Nagar which are found to be 397.26±12.3 Bql^-1 and 325.78±32.56 Bql^-1. Most of the analysed samples show a ²²²Rn concentration more than 100 Bql^-1 and this can be attributed to the geology of the area where the ground waters are located, which is predominantly of granitic characteristic. The average inhalation dose and ingestion dose in the borewell water are found to be 0.405 and 0.033 µSvy^-1; and in river water it is found to be 0.234 and 0.019 µSvy^-1, respectively. The average total effective dose rate in borewell waters and river waters are found to be 0.433 and 0.253 µSvy^-1, which does not cause any health risk to the population of Hassan region.

Keywords: borewell, effective dose, emanometry, 222Rn

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Authors: Christopher B. Obida, George A. Blackburn, James D. Whyatt, Kirk T. Semple

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In many regions of the world, especially in developing countries, river network data are outdated or completely absent, yet such information is critical for supporting important functions such as flood mitigation efforts, land use and transportation planning, and the management of water resources. In this study, a method was developed for delineating river networks using Sentinel 1 imagery. Unsupervised classification was applied to multi-temporal Sentinel 1 data to discriminate water bodies from other land covers then the outputs were combined to generate a single persistent water bodies product. A thinning algorithm was then used to delineate river centre lines, which were converted into vector features and built into a topologically structured geometric network. The complex river system of the Niger Delta was used to compare the performance of the Sentinel-based method against alternative freely available water body products from United States Geological Survey, European Space Agency and OpenStreetMap and a river network derived from a Shuttle Rader Topography Mission Digital Elevation Model. From both raster-based and vector-based accuracy assessments, it was found that the Sentinel-based river network products were superior to the comparator data sets by a substantial margin. The geometric river network that was constructed permitted a flow routing analysis which is important for a variety of environmental management and planning applications. The extracted network will potentially be applied for modelling dispersion of hydrocarbon pollutants in Ogoniland, a part of the Niger Delta. The approach developed in this study holds considerable potential for generating up to date, detailed river network data for the many countries where such data are deficient.

Keywords: Sentinel 1, image processing, river delineation, large scale mapping, data comparison, geometric network

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Authors: Hadjoui Abdelhamid, Saimi Ahmed

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The hybrid h-p finite element method for the dynamic behavior of nonlinear rotors is described in this paper. The standard h-version method of discretizing the problem is retained, but modified to allow the use of polynomially-enriched beam elements. A hierarchically enriching element will thus not affect the nodal displacement and rotation, but will influence the values of the nodal bending moment and shear force is used. The deterministic movements of rotation and translation of the support which are coupled to the excitations due to unbalance are also taken into account. We study also the geometric dissymmetry of the shaft and the disc, thus the equations of motion of the rotor contain variable parametric coefficients over time that can lead to a lateral dynamic instability. The effects of movements combined support for bearings are analyzed and discussed through Campbell diagrams and spectral analyses. A program is made in Matlab. After validation of the program, several examples are studied. The influence of physical and geometric parameters on the natural frequencies of the shaft is determined through the study of these examples. Among these parameters, we include the variation in the diameter and the thickness of the rotor, the position of the disc.

Keywords: Campbell diagram, critical speeds, nonlinear rotor, version h-p of FEM

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Authors: Hatem Mrad, Alban Notin, Mohamed Bouazara

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Sheet metal forming process has a multiple successive steps starting from sheets fixation to sheets evacuation. Often after forming operation, the sheet has defects requiring additional corrections steps. For example, in the drawing process, the formed sheet may have several defects such as springback, localized thinning and bends. All these defects are directly dependent on process, geometric and material parameters. The prediction and elimination of these defects requires the control of most sensitive parameters. The present study is concerned with a reliable parametric study of deep forming process in order to control the localized thinning. The proposed approach will be based on stochastic finite element method. Especially, the polynomial Chaos development will be used to establish a reliable relationship between input (process, geometric and material parameters) and output variables (sheet thickness). The commercial software Abaqus is used to conduct numerical finite elements simulations. The automatized parametrical modification is provided by coupling a FORTRAN routine, a PYTHON script and input Abaqus files.

Keywords: sheet metal forming, reliability, localized thinning, parametric simulation

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Authors: Alexandru Dumitrache, Florin Frunzulica, Octavian Preotu

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The flow mitigation detachment problem near solid surfaces, resulting in improved globally aerodynamic performance by exploiting the Coanda effect on surfaces, has been addressed extensively in the literature, since 1940. The research is carried on and further developed, using modern means of calculation and new experimental methods. In this paper, it is shown interest in the detailed behavior of a classical interior ejector assisted by the Coanda effect, used in propulsion systems. For numerical investigations, an implicit formulation of RANS equations for axisymmetric flow with a shear stress transport k- ω (SST model) turbulence model is used. The obtained numerical results emphasize the efficiency of the ejector, depending on the physical parameters of the flow and the geometric configuration. Furthermore, numerical investigations are carried out regarding the evolution of the Reynolds number when the jet is attached to the wall, considering three geometric configurations: sudden expansion, open cavity and sudden expansion with divergent at the inlet. Therefore, further insight into complexities involving issues such as the variety of flow structure and the related bifurcation and flow instabilities are provided. Thus, the conditions and the limits within which one can benefit from the advantages of Coanda-type flows are determined.

Keywords: Coanda effect, Coanda ejector, CFD, stationary bifurcation, sudden expansion

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Authors: Chiung-Ju Huang

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This study examines whether the Taiwan’s public debt is sustainable utilizing an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. The empirical results show that Taiwan’s public debt appears as a nonlinear series and is stationary in regime 1 but not in regime 2. This result implies that while Taiwan’s public debt was mostly sustainable over the 1996 to 2013 period examined in the study, it may no longer be sustainable in the most recent two years as the public debt ratio has increased cumulatively to 3.618%.

Keywords: nonlinearity, public debt, sustainability, threshold autoregressive model

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Authors: Qian Yi Ooi

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At present, airfoil parameters are still designed and optimized according to the scale of conventional aircraft, and there are still some slight deviations in terms of scale differences. However, insufficient parameters or poor surface mesh quality is likely to occur if these small deviations are embedded in a future civil aircraft with a size that is quite different from conventional aircraft, such as a blended-wing-body (BWB) aircraft with future potential, resulting in large deviations in geometric similarity in computational fluid dynamics (CFD) simulations. To avoid this situation, the study on the CFD calculation on the geometric similarity of airfoil parameters and the quality of the surface mesh is conducted to obtain the ability of different parameterization methods applied on different airfoil scales. The research objects are three airfoil scales, including the wing root and wingtip of conventional civil aircraft and the wing root of the giant hybrid wing, used by three parameterization methods to compare the calculation differences between different sizes of airfoils. In this study, the constants including NACA 0012, a Reynolds number of 10 million, an angle of attack of zero, a C-grid for meshing, and the k-epsilon (k-ε) turbulence model are used. The experimental variables include three airfoil parameterization methods: point cloud method, B-spline curve method, and class function/shape function transformation (CST) method. The airfoil dimensions are set to 3.98 meters, 17.67 meters, and 48 meters, respectively. In addition, this study also uses different numbers of edge meshing and the same bias factor in the CFD simulation. Studies have shown that with the change of airfoil scales, different parameterization methods, the number of control points, and the meshing number of divisions should be used to improve the accuracy of the aerodynamic performance of the wing. When the airfoil ratio increases, the most basic point cloud parameterization method will require more and larger data to support the accuracy of the airfoil’s aerodynamic performance, which will face the severe test of insufficient computer capacity. On the other hand, when using the B-spline curve method, average number of control points and meshing number of divisions should be set appropriately to obtain higher accuracy; however, the quantitative balance cannot be directly defined, but the decisions should be made repeatedly by adding and subtracting. Lastly, when using the CST method, it is found that limited control points are enough to accurately parameterize the larger-sized wing; a higher degree of accuracy and stability can be obtained by using a lower-performance computer.

Keywords: airfoil, computational fluid dynamics, geometric similarity, surface mesh quality

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Authors: M. Orefice, V. Di Vito

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This paper provides a description of a Collision Avoidance algorithm that has been developed starting from the mathematical modeling of the flight of insects, in terms of spirals and conchospirals geometric paths. It is able to calculate a proper avoidance manoeuver aimed to prevent the infringement of a predefined distance threshold between ownship and the considered intruder, while minimizing the ownship trajectory deviation from the original path and in compliance with the aircraft performance limitations and dynamic constraints. The algorithm is designed in order to be suitable for real-time applications, so that it can be considered for the implementation in the most recent airborne automatic collision avoidance systems using the traffic data received through an ADS-B IN device. The presented approach is able to take into account the rules-of-the-air, due to the possibility to select, through specifically designed decision making logic based on the consideration of the encounter geometry, the direction of the calculated collision avoidance manoeuver that allows complying with the rules-of-the-air, as for instance the fundamental right of way rule. In the paper, the proposed collision avoidance algorithm is presented and its preliminary design and software implementation is described. The applicability of this method has been proved through preliminary simulation tests performed in a 2D environment considering single intruder encounter geometries, as reported and discussed in the paper.

Keywords: ADS-B Based Application, Collision Avoidance, RPAS, Spiral Geometry.

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Authors: Tu-Chieh Hung, Wei-Mon Yan, Xiao-Dong Wang, Yu-Xian Huang

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This work employs a combined optimization procedure including a simplified conjugate-gradient method and a three-dimensional fluid flow and heat transfer model to study the optimal geometric parameter design of double-layered microchannel heat sinks. The overall thermal resistance RT is the objective function to be minimized with number of channels, N, the channel width ratio, β, the bottom channel aspect ratio, αb, and upper channel aspect ratio, αu, as the search variables. It is shown that, for the given bottom area (10 mm×10 mm) and heat flux (100 W cm-2), the optimal (minimum) thermal resistance of double-layered microchannel heat sinks is about RT=0.12 ℃/m2W with the corresponding optimal geometric parameters N=73, β=0.50, αb=3.52, and, αu= 7.21 under a constant pumping power of 0.05 W. The optimization process produces a maximum reduction by 52.8% in the overall thermal resistance compared with an initial guess (N=112, β=0.37, αb=10.32 and, αu=10.93). The results also show that the optimal thermal resistance decreases rapidly with the pumping power and tends to be a saturated value afterward. The corresponding optimal values of parameters N, αb, and αu increase while that of β decrease as the pumping power increases. However, further increasing pumping power is not always cost-effective for the application of heat sink designs.

Keywords: optimization, double-layered microchannel heat sink, simplified conjugate-gradient method, thermal resistance

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Golak Bihari Mahanta, Bibhuti Bhusan Biswal, B. B. V. L. Deepak, Amruta Rout, Gunji Balamurali

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Robots are widely used in the manufacturing industry for rapid production with higher accuracy and precision. With the help of End-of-Arm Tools (EOATs), robots are interacting with the environment. Robotic grippers are such EOATs which help to grasp the object in an automation system for improving the efficiency. As the robotic gripper directly influence the quality of the product due to the contact between the gripper surface and the object to be grasped, it is necessary to design and optimize the gripper mechanism configuration. In this study, geometric and kinematic modeling of the parallel gripper is proposed. Grey wolf optimizer algorithm is introduced for solving the proposed multiobjective gripper optimization problem. Two objective functions developed from the geometric and kinematic modeling along with several nonlinear constraints of the proposed gripper mechanism is used to optimize the design variables of the systems. Finally, the proposed methodology compared with a previously proposed method such as Teaching Learning Based Optimization (TLBO) algorithm, NSGA II, MODE and it was seen that the proposed method is more efficient compared to the earlier proposed methodology.

Keywords: gripper optimization, metaheuristics, , teaching learning based algorithm, multi-objective optimization, optimal gripper design

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Authors: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: Jiunde Lee, Meng-Yu Wun

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The present study attempted to explore how the range differences of ‘Geometric Field of Vision’ (GFOV) and differences in camera control in 3D simulation games, OMSI—The Bus Simulator of the 2013 PC version, affected players’ cognitive load, anxiety, and task performances. The study employed a between-subjects factorial experimental design. A total of 80 subjects completed experiment whose data were eligible for further analysis. The results of this study showed that in the difference of field of view, players had better task performances in a spacious view. Although cognitive resources consumed more of the players’ ‘mental demand,’ ‘physical demand’, and ‘temporal demand’, they had better performances in the experiment, and their anxiety was effectively reduced. On the other hand, in the narrow GFOV, players thought they spent more cognitive resources on ‘effort’ and ‘frustration degree,’ and had worse task performances, but it was not significant enough to reduce their anxiety. In terms of difference of camera control, players had worse performances since the fixed lens restricted their dexterous control. However, there was no significant difference in the players’ subjective cognitive resources or anxiety. The results further illustrated that task performances were affected by the interaction of GFOV and camera control.

Keywords: geometric field of view, camera lens, cognitive load, anxiety

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Authors: Seyedehsomayeh Hosseini

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Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: Jeron Maheswaran, Sudath C. Siriwardane

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In fatigue analysis, the structural detail of tubular joint has taken great attention among engineers. The DNV-RP-C203 is covering this topic quite well for simple and clear joint cases. For complex joint and geometry, where joint classification isn’t available and limitation on validity range of non-dimensional geometric parameters, the challenges become a fact among engineers. The classification of joint is important to carry out through the fatigue analysis. These joint configurations are identified by the connectivity and the load distribution of tubular joints. To overcome these problems to some extent, this paper compare the fatigue life of tubular joints in offshore jacket according to the stress concentration factors (SCF) in DNV-RP-C203 and finite element method employed Abaqus/CAE. The paper presents the geometric details, material properties and considered load history of the jacket structure. Describe the global structural analysis and identification of critical tubular joints for fatigue life estimation. Hence fatigue life is determined based on the guidelines provided by design codes. Fatigue analysis of tubular joints is conducted using finite element employed Abaqus/CAE [4] as next major step. Finally, obtained SCFs and fatigue lives are compared and their significances are discussed.

Keywords: fatigue life, stress-concentration factor, finite element analysis, offshore jacket structure

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Authors: Brouri Adil, Giri Fouad

Abstract:

The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Praveen Huded, Suresh Dash

Abstract:

Pile foundations are one of the most preferred deep foundation system for high rise or heavily loaded structures. In many instances, the failure of the pile founded structures in liquefiable soils had been observed even in many recent earthquakes. Recent centrifuge and shake table experiments on two layered soil system have credibly shown that failure of pile foundation can occur because of buckling, as the pile behaves as an unsupported slender structural element once the surrounding soil liquefies. However the buckling capacity depends on largely on the depth of soil liquefied and its residual strength. Hence it is essential to check the pile against the possible buckling failure. Beam on non-linear Winkler Foundation is one of the efficient method to model the pile-soil behavior in liquefiable soil. The pile-soil interaction is modelled through p-y springs, different author have proposed different types of p-y curves for the liquefiable soil. In the present paper the influence two such p-y curves on the buckling capacity of pile foundation is studied considering initial geometric and non-linear behavior of pile foundation. The proposed method is validated against experimental results. Significant difference in the buckling capacity is observed for the two p-y curves used in the analysis. A parametric study is conducted to understand the influence of pile diameter, pile flexural rigidity, different initial geometric imperfections, and different soil relative densities on buckling capacity of pile foundation.

Keywords: Pile foundation , Liquefaction, Buckling load, non-linear py curve, Opensees

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Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn

Abstract:

The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

Procedia PDF Downloads 688