Search results for: numerical calculations CFD

Authors: Thanh-Phong Dao, Shyh-Chour Huang

Abstract:

This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism

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Authors: HyunSu Seo, HoYoung Son, Sungjin Kim, WooYoung Jung

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In order to understand the seismic behavior of steel frame structure with infill FRP composite panel, simple models for simulation on the steel frame with the panel systems were developed in this study. To achieve the simple design method of the steel framed structure with the damping panel system, 2-D finite element analysis with the springs and dashpots models was conducted in ABAQUS. Under various applied spring stiffness and dashpot coefficient, the expected hysteretic energy responses of the steel frame with damping panel systems we re investigated. Using the proposed simple design method which decides the stiffness and the damping, it is possible to decide the FRP and damping materials on a steel frame system.

Keywords: numerical analysis, FEM, infill, GFRP, damping

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Authors: P. M. Keshtiban, M. Zadshakoyan

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One of the important factors that alter different process and geometrical parameters on metal forming processes is friction between contacting surfaces. Some important factors that effected directly by friction are: stress, strain, required load, wear of surfaces and then geometrical parameters. In order to control friction effects permanent lubrication is necessary. In this article, the friction coefficient is elicited by the most effective method, ring compression tests. The tests were done by both finite element method and practical tests. Different friction curves that extracted by finite element simulations and has good conformity with published results, used for obtaining final friction coefficient. In this study Mos2 is used as the lubricant and Al5754 alloy used as the specimens material.

Keywords: experiment, FEM, friction coefficient, ring compression

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Authors: Hassina Gheribi, Salim Boukebbab

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The measurement of the parts manufactured on CMM (coordinate measuring machine) is based on the association of a surface of perfect geometry to the group of dots palpated via a mathematical calculation of the distances between the palpated points and itself surfaces. Surfaces not being never perfect, they are measured by a number of points higher than the minimal number necessary to define them mathematically. However, the central problems of three-dimensional metrology are the estimate of, the orientation parameters, location and intrinsic of this surface. Including the numerical uncertainties attached to these parameters help the metrologist to make decisions to be able to declare the conformity of the part to specifications fixed on the design drawing. During this paper, we will present a data-processing model in Visual Basic-6 which makes it possible automatically to determine the whole of these parameters, and their uncertainties.

Keywords: coordinate measuring machines (CMM), associated surface, uncertainties of measurement, acquisition and modeling

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Authors: S. Al Dandachli, F. Perales, Y. Monerie, F. Jamin, M. S. El Youssoufi, C. Pelissou

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The goal of this research is to study the fracture process and mechanical behavior of concrete under I–II mixed-mode stress, which is essential for ensuring the safety of concrete structures. For this purpose, two-dimensional simulations of three-point bending tests under variable load and geometry on notched cement paste samples of composite samples (cement paste/siliceous aggregate) are modeled by employing Cohesive Zone Models (CZMs). As a result of experimental validation of these tests, the CZM model demonstrates its capacity to predict fracture propagation at the local scale.

Keywords: cement paste, interface, cohesive zone model, fracture, three-point flexural test bending

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Authors: Amit Kumar, Rajdeep Chakrabarty, Ganesh Gupta

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This paper illustrates the detailed accreditation process of Accreditation Board of Engineering and Technology (ABET) for accrediting engineering and Technology programs. ABET is a non-governmental agency that accredits engineering and technology, applied and natural sciences, and computing sciences programs. ABET was founded on 10th May 1932 and was founded by Institute of Electrical and Electronics Engineering. International industries accept ABET accredited institutes having the highest standards in their academic programs. In this accreditation, there are eight criteria in general; criterion 1 describes the student outcome evaluations, criteria 2 measures the program's educational objectives, criteria 3 is the student outcome calculated from the marks obtained by students, criteria 4 establishes continuous improvement, criteria 5 focus on curriculum of the institute, criteria 6 is about faculties of this institute, criteria 7 measures the facilities provided by the institute and finally, criteria 8 focus on institutional support towards staff of the institute. In this paper, we focused on the calculative part of each criterion with equations and suitable examples, the files and documentation required for each criterion, and the total workflow of the process. The references and the values used to illustrate the calculations are all taken from the samples provided at ABET's official website. In the final section, we also discuss the criterion-wise score weightage followed by evaluation with timeframe and deadlines.

Keywords: Engineering Accreditation Committee, Computing Accreditation Committee, performance indicator, Program Educational Objective, ABET Criterion 1 to 7, IEEE, National Board of Accreditation, MOOCS, Board of Studies, stakeholders, course objective, program outcome, articulation, attainment, CO-PO mapping, CO-PO-SO mapping, PDCA cycle, degree certificates, course files, course catalogue

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Authors: I. Mnafeg, A. Abichou, L. Beji

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Traditional mechanical control systems in thrust vectoring are efficient in rocket thrust guidance but their costs and their weights are excessive. The fluidic injection in the nozzle divergent constitutes an alternative procedure to achieve the goal. In this paper, we present a 3D analytical model for fluidic injection in a supersonic nozzle integrating an orifice. The fluidic vectoring uses a sonic secondary injection in the divergent. As a result, the flow and interaction between the main and secondary jet has built in order to express the pressure fields from which the forces and thrust vectoring are deduced. Under various separation criteria, the present analytical model results are compared with the existing numerical and experimental data from the literature.

Keywords: flow separation, fluidic thrust vectoring, nozzle, secondary jet, shock wave

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Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

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In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed and illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, multivariate Bayesian control

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Authors: Saowanit Sukparungsee

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Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: number of defects, exponentially weighted moving average, average run length, square root transformations

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Authors: P. Kooche Baghy, S. Eskandari, E.javanmard

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Neural network has been used as a predictive means of cold rolling force in this dissertation. Thus, imposed average force on rollers as a mere input and five pertaining parameters to its as a outputs are regarded. According to our study, feed-forward multilayer perceptron network has been selected. Besides, Bayesian algorithm based on the feed-forward back propagation method has been selected due to noisy data. Further, 470 out of 585 all tests were used for network learning and others (115 tests) were considered as assessment criteria. Eventually, by 30 times running the MATLAB software, mean error was obtained 3.84 percent as a criteria of network learning. As a consequence, this the mentioned error on par with other approaches such as numerical and empirical methods is acceptable admittedly.

Keywords: artificial neural network, Bayesian, cold rolling, force evaluation

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Authors: Mao-Sheng Su, Santhanamoorthi Nachimuthu, Jyh-Chiang Jiang

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Climate change is widely recognized as a global crisis, with anthropogenic CO₂ emissions from fossil fuel combustion and industrial processes being major contributors. To address this challenge, carbon capture and sequestration (CCS) technology has emerged as a key strategy for selectively capturing CO₂ from flue gas streams. Among the various solid adsorbents, metal–organic frameworks (MOFs) are notable for their extensive surface area and controllable pore chemistry. The porous MOF structure is comprised of metal ions or clusters coordinated to organic linker compounds. In particular, the pore parameters of MOFs are readily tunable, making them promising materials for CO₂ capture applications. Among these, amine-functionalized MOFs have demonstrated exceptional CO₂ capture abilities because their high uptake capacity and selectivity. In this study, we have investigated the CO₂ capture abilities and adsorption mechanisms of the diamine-appended framework N-Ethylethylenediamine-Mg₂(4,4’-dioxidobiphenyl-3,3’-dicarboxylate) (e-2-Mg₂(dobpdc)) using density functional theory (DFT) calculations. Previous studies have suggested that CO₂ can be captured via both outer- and inner-amine binding sites. Our findings reveal that CO₂ adsorption at the outer amine site is kinetically more favorable compared to the inner amine site, with a lower energy barrier of 1.34 eV for CO₂ physisorption to chemisorption compared to the inner amine, which has an activation barrier of 1.60 eV. Furthermore, we find that CO₂ adsorption is significantly enhanced in an alkaline environment, as deprotonation of the diamine molecule reduces the energy barrier to 0.24 eV. This theoretical study provides detailed insights into CO₂ adsorption in diamine-appended e-2-Mg₂(dobpdc) MOF, offering a deeper understanding of CO₂ capture mechanisms and valuable information for the advancement of effective CO₂ sequestration technologies.

Keywords: DFT, MOFs, CO₂ capture, catalyst

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Authors: Mohd Salmi Md Noorani, Ghada Al-Mahbashi, Sakhinah Abu Bakar

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This paper investigates projective lag synchronization (PLS) behavior in drive response dynamical networks (DRDNs) model with identical nodes. A hybrid feedback control method is designed to achieve the PLS with mismatch and without mismatch terms. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

Keywords: drive-response dynamical network, projective lag synchronization, hybrid feedback control, stability theory

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Authors: Ram Narayan Khare, Adhyatma Khare, Aradhna Shrivastava

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In this study, numerical modeling of ‘Lime Surkhi’ masonry building has been carried out for a prototype ancient building situated at seismic zone III using the Finite Element Method by Abaqus software. The model is designed in order to get the failure envelope and then decide the best method of retrofitting the structure so that the structure is made to withstand more decades, given its historical background. Previously, due to a lack of technologies, it was difficult to determine the mode of failure. Present technological development can predict the mode of failure, and subsequently, the structure can be refabricated accordingly. The study makes an important addition to the understanding of retrofitting ancient and old buildings based on the results of FEM modeling.

Keywords: seismic retrofitting, Abaqus, FEM, historic building, Lime Surkhi masonry

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Authors: Martín Felipe García Romero, Nancy Mondragón Escamilla, Ismael Araujo Vargas, Viviana Basurto Rios, Kevin Cano Pulido, Pedro Enrique Velázquez Elisondo

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This paper presents a preliminary prototype of an 83 kW all-electric motorbike since, nowadays, electric motorbikes have advanced drastically in their technology in such a way that lately, there has been a boom in the field of competition of medium power electric vehicles. The field of electric vehicle racing mainly pursues the aim of obtaining an optimal performance of all the motorbike components in order to obtain a safe racing vehicle fast enough while looking for the stability of all the systems onboard. A general description of the project is given up to date, detailing the parts of the system, integration, numerical estimations, and a rearrangement proposal of the actual prototype with the aim to mechanically and thermally improve the vehicle.

Keywords: electric motorcycle, thermal analysis, mechanic analysis, electric vehicle

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Authors: Ozden Saygili, Eser Cakti

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Mosques and minarets can be severely damaged as a result of earthquakes. Non-linear behavior of minarets of Mihrimah Sultan and Süleymaniye Mosques and the minaret of St. Sophia are analyzed to investigate seismic response, damage and failure mechanisms of minarets during earthquake. Selected minarets have different height and diameter. Discrete elements method was used to create the numerical minaret models. Analyses were performed using sine waves. Two parameters were used for evaluating the results: the maximum relative dislocation of adjacent drums and the maximum displacement at the top of the minaret. Both parameters were normalized by the drum diameter. The effects of minaret geometry on seismic behavior were evaluated by comparing the results of analyses.

Keywords: discrete element method, earthquake safety, nonlinear analysis, masonry structures

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Authors: Arthur Thirion

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Auxetic geometries allow the generation of a negative Poisson ratio (NPR) in conventional materials. This behaviour allows materials to have certain improved mechanical properties, including impact resistance and altered synclastic behaviour. This means these structures have significant potential when it comes to applications as chronic wound dressings. To this end, 6 different "perforated sheet" structure types were 3D printed. These structures all had variations of key geometrical features included cell length and angle. These were tested in compression and tension to assess their Poisson ratio. Both a positive and negative Poisson ratio was generated by the structures depending on the loading. The a/b ratio followed by θ has been shown to impact the Poisson ratio significantly. There is still a significant discrepancy between modelled and observed behaviour.

Keywords: auxetic materials, 3D printing, negative Poisson's ratio, tunable Poisson's ratio

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Authors: Terada Pinyo

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This study is the survey research, designed to find out the threshold competency of graduate students in terms of knowledge excellency and professional skills proficiency based on Thai Qualifications Framework for Higher Education (TQF). The sample group consisted of 240 students. The results were collected by stratified sampling, using study programs for each stage. The results were analysed and calculated by computer program. Statistics used during analysing were percentage, mean, and standard deviation. From the study, the threshold competency of graduate students were in very high score range in both overall and specific category. The top category which received the most score was interpersonal skills and responsibility, following by ethics and morality, knowledge and skills, and numerical communication and information technology.

Keywords: threshold competency, Thai qualifications framework for higher education, graduate school

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Authors: Mahbube Eghtesad

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For a number of years, the problem of simultaneous detection and tracking of a target has been one of the most relevant and challenging issues in a wide variety of military and civilian systems. We develop methods for detecting and tracking a target using an orthogonal frequency division multiplexing (OFDM) based radar. As a preliminary step we introduce the target trajectory and Gaussian noise model in discrete time form. Then resorting to match filter and Kalman filter we derive a detector and target tracker. After that we propose an OFDM radar in order to achieve further improvement in tracking performance. The motivation for employing multiple frequencies is that the different scattering centers of a target resonate differently at each frequency. Numerical examples illustrate our analytical results, demonstrating the achieved performance improvement due to the OFDM signaling method.

Keywords: matched filter, target trashing, OFDM radar, Kalman filter

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Authors: Mina Esmi Jahromi, Mehdi Khiadani

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Plunging water jets discharging into turbulent crossflows are capable of providing efficient air water interfacial area, which is desirable for the process of mass transfer. Although several studies have been dedicated to the air entrainment by water jets impinging into stagnant water, very few studies have focused on the water jets in crossflows. This study investigates development of the two-phase flow as a result of the jet impingements into crossflows by means of image processing technique and CFD simulations. Investigations are also conducted on the oxygen transfer and a correlation is established between the aeration properties and the oxygenation capacity of water jets in crossflows. This study helps the optimal design and the effective operation of the industrial and the environmental equipment incorporating water jets in crossflows.

Keywords: air entrainment, CFD simulation, image processing, jet in crossflow, oxygen transfer, two-phase flow

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Authors: Zied Guidara, Alexander Morgenstern, Aref Younes Maalej

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In this paper, a desiccant solar unit for air conditioning and desalination is presented first. Secondly, a dynamic modelling study of the desiccant wheel is developed. After that, a simulation study and an experimental investigation of the behaviour of desiccant wheel are developed. The experimental investigation is done in the chamber of commerce in Freiburg-Germany. Indeed, the variations of calculated and measured temperatures and specific humidity of dehumidified and rejected air are presented where a good agreement is found when comparing the model predictions with experimental data under the considered range of operating conditions. Finally, the study of the compartments of desalination and water condensation shows that the unit can produce an acceptable quantity of water at the same time of the air conditioning operation.

Keywords: air conditioning, desalination, condensation, design, desiccant wheel

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Authors: S. Som-Am, B. Grechuk

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Moser’s worm problem is the unsolved problem in geometry which asks for the minimal area of a convex region on the plane which can cover all curves of unit length, assuming that curves may be rotated and translated to fit inside the region. We study a version of this problem asking for a minimal convex cover for closed unit curves. By combining geometric methods with numerical box’s search algorithm, we show that any such cover should have an area at least 0.0975. This improves the best previous lower bound of 0.096694. In fact, we show that the minimal area of convex hull of circle, equilateral triangle, and rectangle of perimeter 1 is between 0.0975 and 0.09763.

Keywords: Moser’s worm problem, closed arcs, convex cover, minimal-area cover

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Authors: F. Louati, H. Trabelsi, M. Jamei

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Desiccation cracks following drainage-humidification cycles. With water loss, mainly due to evaporation, suction in the soil increases, producing volumetric shrinkage and tensile stress. When the tensile stress reaches tensile strength, the soil cracks. Desiccation cracks networks can directly control soil hydraulic properties. The aim of this study was for quantifying the hydraulic properties for examples the water retention curve, the saturated hydraulic conductivity, the unsaturated hydraulic conductivity function, the shrinkage dynamics in Tibar soil- clay soil in the Northern of Tunisia. Then a numerical simulation of unsaturated hydraulic properties for a crack network has been attempted. The finite elements code ‘CODE_BRIGHT’ can be used to follow the hydraulic distribution in cracked porous media.

Keywords: desiccation, cracks, permeability, unsaturated hydraulic flow, simulation

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Authors: Adedayo Oke Adelakun

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The chaotic dynamics of periodically forced oscillators with smooth potential has been extensively investigated via theoretical, numerical and experimental simulations. With the advent of the study of chaotic dynamics by means of method of multiple time scale analysis, Melnikov theory, bifurcation diagram, Poincare's map, bifurcation diagrams and Lyapunov exponents, it has become necessary to seek for a better understanding of nonlinear oscillator with noisy term. In this paper, we examine the influence of noise on complex dynamical behaviour of periodically forced F6 - Duffing oscillator for specific choice of noisy parameters. The inclusion of noisy term improves the dynamical behaviour of the oscillator which may have wider application in secure communication than smooth potential.

Keywords: hierarchical structure, periodically forced oscillator, noisy parameters, dynamical behaviour, F6 - duffing oscillator

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Amare Setegn Enyew, Bikila Teklu Wodajo

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The primary aim of flexible pavement design is to ensure the development of economical and safe road infrastructure. However, failures can still occur due to improper or erroneous structural design. In Ethiopia, the design of flexible pavements relies on doing calculations manually and selecting pavement structure from catalogue. The catalogue offers, in eight different charts, alternative structures for combinations of traffic and subgrade classes, as outlined in the Ethiopian Roads Authority (ERA) Pavement Design Manual 2001. Furthermore, design modification is allowed in accordance with the structural number principles outlined in the AASHTO 1993 Guide for Design of Pavement Structures. Nevertheless, the manual calculation and design process involves the use of nomographs, charts, tables, and formulas, which increases the likelihood of human errors and inaccuracies, and this may lead to unsafe or uneconomical road construction. To address the challenge, a software called AASHERA has been developed for AASHTO 1993 and ERA design methods, using MATLAB language. The software accurately determines the required thicknesses of flexible pavement surface, base, and subbase layers for the two methods. It also digitizes design inputs and references like nomographs, charts, default values, and tables. Moreover, the software allows easier comparison of the two design methods in terms of results and cost of construction. AASHERA's accuracy has been confirmed through comparisons with designs from handbooks and manuals. The software can aid in reducing human errors, inaccuracies, and time consumption as compared to the conventional manual design methods employed in Ethiopia. AASHERA, with its validated accuracy, proves to be an indispensable tool for flexible pavement structure designers.

Keywords: flexible pavement design, AASHTO 1993, ERA, MATLAB, AASHERA

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Authors: M. A. Sadeghian, J. Yang, Q. F. Liu

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Steel extended end plate bolted connections are recommended to be widely utilized in special moment-resisting frame subjected to monotonic loading. Improper design of steel beam to column connection can lead to the collapse and fatality of structures. Therefore comprehensive research studies of beam to column connection design should be carried out. Also the performance and effect of corrugated on the strength of beam column end plate connection up to failure under monotonic loading in horizontal direction is presented in this paper. The non-linear elastic–plastic behavior has been considered through a finite element analysis using the multi-purpose software package LUSAS. The effect of vertically and horizontally types of corrugated web was also investigated.

Keywords: corrugated beam, monotonic loading, finite element analysis, end plate connection

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Authors: Rong-Tsorng Wang

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In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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Authors: Guillaume Craveur

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The evaluation of the passenger exchange time is necessary for railway operators in order to optimize and dimension rail traffic. Several influential parameters are identified and studied. Each parameter leads to a modeling completed with the buildingEXODUS software. The objective is the modelling of passenger exchanges measured by passenger counting. Population size is dimensioned using passenger counting files which are a report of the train service and contain following useful informations: number of passengers who get on and leave the train, exchange time. These information are collected by sensors placed at the top of each train door. With passenger counting files it is possible to know how many people are engaged in the exchange and how long is the exchange, but it is not possible to know passenger flow of the door. All the information about observed exchanges are thus not available. For this reason and in order to minimize inaccuracies, only short exchanges (less than 30 seconds) with a maximum of people are performed.

Keywords: passengers exchange, numerical tools, rolling stock, platforms

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Authors: Maher Agi, Hardik Soni

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This paper presents a deterministic model for optimized control of the inventory of a perishable product subject to both physical deterioration and degradation of its freshness condition. The demand for the product depends on its current inventory level and freshness condition. Our model allows for any positive amount of end of cycle inventory. Some useful conditions that characterize the optimal solution of the model are derived and an algorithm is presented for finding the optimal values of the price, the inventory cycle, the end of cycle inventory level and the order quantity. Numerical examples are then given. Our work shows how the product freshness in conjunction with the inventory deterioration affects the inventory management decisions.

Keywords: inventory management, lot sizing, perishable products, deteriorating inventory, age-dependent demand, stock-dependent demand

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Authors: Karim Akkouche

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Many methods have been developed for characterizing the behavior of bolted joints. However, in the presence of a certain model of stiffeners, no orientation was given in relation to their modeling. To this end, multitude of coarse errors can arise in the reproduction of the propagation of efforts and in representation of the modes of deformations. Considering these particularities, a numerical investigation was carried out in our laboratory. In this paper we will present a comparative study between three types of assemblies. A non-linear 3D modeling was chosen, given that it takes into consideration geometric and material non-linearity, using the Finite Element calculation code ABAQUS. Initially, we evaluated the influence of the presence of each stiffener on the "global" behavior of the assemblies, this by analyzing their Moment-Rotation curves, also by referring to the classification system proposed by NF EN 1993- 1.8 which is based on the resisting moment Mj-Rd and the initial stiffness Sj.int. In a second step, we evaluated the "local" behavior of their components by referring to the stress-strain curves.

Keywords: assembly, post-beam, end plate, nonlinearity

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