Search results for: settlement equations

Authors: Youb Said, Fourar Ali

Abstract:

To describe the influence of bottom roughness on the free surface flows by numerical modeling, a two-dimensional model was developed. The equations of continuity and momentum (Naviers Stokes equations) are solved by the finite volume method. We considered a turbulent flow in an open channel with a bottom roughness. For our simulations, the K-ε model was used. After setting the initial and boundary conditions and solve the equations set, we were able to achieve the following results: vortex forming in the hollow causing substantial energy dissipation in the obstacle areas that form the bottom roughness. The comparison of our results with experimental ones shows a good agreement in terms of the results in the rough area. However, in other areas, differences were more or less important. These differences are in areas far from the bottom, especially the free surface area just after the bottom. These disagreements are probably due to experimental constants used by the k-ε model.

Keywords: modeling, free surface flow, turbulence, bottom roughness, finite volume, K-ε model, energy dissipation

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

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Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Kevin T. Inks

Abstract:

India’s Brahmaputra River Valley has, since independence, experienced consistent low-intensity guerrilla warfare between ethnic and religious groups. These groups are often organized around perceived ethnic territoriality, and target civilians, communities, and especially migrants belonging to other ethnic and religious groups. Intense flooding and erosion have led to widespread displacement, and disaster relief funds are largely tied to legal land tenure. Displaced residents of informal settlements receive little or no resettlement aid, and their subsequent migration strategies and risk from guerrilla violence are poorly understood. Semi-structured interviews and comprehensive surveys focused on perceptions of risk, efficacy of disaster relief, and migration and adaptation strategies were conducted with households identified as being ‘at-risk’ of catastrophic flooding and erosion in Majuli District, Assam. Interviews with policymakers and government workers were conducted to assess disaster relief efforts in informal settlements, and remote sensing methods were used to identify informal settlement and hydrogeomorphic change. The results show that various ethnic and religious groups have differential strategies and preferences for resettlement. However, these varying strategies are likely to lead to differential levels of risk from guerrilla violence. Members of certain ethnic groups residing in informal settlements, in the absence of resettlement assistance, are more likely to seek out unofficial settlement on land far from the protection of the state and experience greater risk of becoming victims of political violence. As climate change and deforestation are likely to increase the severity of the displacement crisis in the Brahmaputra River Valley, more comprehensive disaster relief and surveying efforts are vital for limiting migration and informal settlement in potential sites of guerrilla warfare.

Keywords: climate, displacement, flooding, India, violence

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

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In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: elastic foundation, impact, moving load, thick plate

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique that is capable of regularizing the shocks and sharp interfaces simultaneously in the shock-interface interaction simulations. The direct numerical simulation of flows involving shocks has been investigated for many years and a lot of numerical methods were developed to capture the shocks. However, most of these methods rely on the numerical dissipation to regularize the shocks. Moreover, in high Reynolds number flows, the nonlinear terms in hyperbolic Partial Differential Equations (PDE) dominates, constantly generating small scale features. This makes direct numerical simulation of shocks even harder. The same difficulty happens in two-phase flow with sharp interfaces where the nonlinear terms in the governing equations keep sharpening the interfaces to discontinuities. The main idea of the proposed technique is to average out the small scales that is below the resolution (observable scale) of the computational grid by filtering the convective velocity in the nonlinear terms in the governing PDE. This technique is named “observable method” and it results in a set of hyperbolic equations called observable equations, namely, observable Navier-Stokes or Euler equations. The observable method has been applied to the flow simulations involving shocks, turbulence, and two-phase flows, and the results are promising. In the current paper, the observable method is examined on the performance of regularizing shocks and interfaces at the same time in shock-interface interaction problems. Bubble-shock interactions and Richtmyer-Meshkov instability are particularly chosen to be studied. Observable Euler equations will be numerically solved with pseudo-spectral discretization in space and third order Total Variation Diminishing (TVD) Runge Kutta method in time. Results are presented and compared with existing publications. The interface acceleration and deformation and shock reflection are particularly examined.

Keywords: compressible flow simulation, inviscid regularization, Richtmyer-Meshkov instability, shock-bubble interactions.

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Authors: Edson Ephraim Sanga

Abstract:

This paper stems to explore possible places used for recreation in unplanned settlements in order to avail knowledge on how to create and shape urban spaces essential for recreation and leisure. The context of unplanned settlements is spatially characterized compactness and congestions of buildings developed by residents without professional inputs. These characteristics surpass greenery landscapes such as parks and squares essential for health, happiness and wellbeing. The lack of recreational greenery landscape arises a question on how possible can recreation take places in the settlements? This study used qualitative methods mainly observation and in-depth interview to explore the recreational situation in Manzese informal settlements as an instrumental case and found that ordinary spaces are re-configured into recreational spaces and used as ‘parks’ and ‘squares’ in the settlements. The spaces are diverse and complex as they possess different spatial characteristics based on their physical attributes and the way they are used and interpreted by respective users. This paper argues that the re-configuration processes of ordinary spaces should not be taken for granted because they portray the appropriation of spaces from quotidian dimensions in a particular context.

Keywords: ordinary spaces, recreation, unplanned settlement, urban spaces

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Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: Sayantani Neogi, Sean Taylor, Julia Budka

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This paper presents the results of the investigations of soil/sediment sequences associated with the New Kingdom town at Sai Island, Sudan. During the course of this study, geoarchaeological surveys have been undertaken in the vicinity of this Pharaonic town within the island and the soil block samples for soil micromorphological analysis were accordingly collected. The intention was to better understand the archaeological site in its environmental context and the nature of the land surface prior to the establishment of the settlement. Soil micromorphology, a very powerful geoarchaeological methodology, is concerned with the description, measurement and interpretation of soil components and pedological features at a microscopic scale. Since soil profiles themselves are archives of their own history, soil micromorphology investigates the environmental and cultural signatures preserved within buried soils and sediments. A study of the thin sections from these soils/sediments has been able to provide robust data for providing interesting insights into the various nuances of this site, for example, the nature of the topography and existent environmental condition during the time of Pharaonic site establishment. These geoarchaeological evaluations have indicated that there is a varied hidden landscape context for this pharaonic settlement, which indicates a symbiotic relationship with the Nilotic environmental system.

Keywords: geoarchaeology, New Kingdom, Nilotic environment, soil micromorphology

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Authors: Ali H. Mahfouz, Hossam E. M. Sallam, Abdulwali Wazir, Hamod H. Kharezi

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The soil profile at site of the bridge project includes soft fine grained soil layer located between 5.0 m to 11.0 m in depth, it has high water content, low SPT no., and low bearing capacity. The clay layer induces high settlement due to surcharge application of earth embankment at ramp T1, ramp T2, and ramp T3 especially at heights from 9m right 3m. Calculated settlement for embankment heights less than 3m may be accepted regarding Saudi Code for soil and foundation. The soil and groundwater at the project site comprise high contents of sulfates and chlorides of high aggressively on concrete and steel bars, respectively. Regarding results of the study, it has been recommended to use stone column piles or new technology named PCC piles as soil improvement to improve the bearing capacity of the weak layer. The new technology is cast in-situ thin wall concrete pipe piles (PCC piles), it has economically advantageous and high workability. The technology can save time of implementation and cost of application is almost 30% of other types of piles.

Keywords: soft foundation soil, bearing capacity, bridge ramps, soil improvement, geogrid, PCC piles

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Authors: Salim H. Al Salmani, Kevin Tansey, Mohammed S. Ozigis

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The study of the growth of built-up areas and settlement expansion is a major exercise that city managers seek to undertake to establish previous and current developmental trends. This is to ensure that there is an equal match of settlement expansion needs to the appropriate levels of services and infrastructure required. This research aims at demonstrating the potential of satellite image processing technique, harnessing the utility of single feature probability-object based image analysis technique in assessing the urban growth dynamics of the Muscat Governorate in Oman for the period 1990, 2002 and 2013. This need is fueled by the continuous expansion of the Muscat Governorate beyond predicted levels of infrastructural provision. Landsat Images of the years 1990, 2002 and 2013 were downloaded and preprocessed to forestall appropriate radiometric and geometric standards. A novel approach of probability filtering of the target feature segment was implemented to derive the spatial extent of the final Built-Up Area of the Muscat governorate for the three years period. This however proved to be a useful technique as high accuracy assessment results of 55%, 70%, and 71% were recorded for the Urban Landcover of 1990, 2002 and 2013 respectively. Furthermore, the Normalized Differential Built – Up Index for the various images were derived and used to consolidate the results of the SFP-OBIA through a linear regression model and visual comparison. The result obtained showed various hotspots where urbanization have sporadically taken place. Specifically, settlement in the districts (Wilayat) of AL-Amarat, Muscat, and Qurayyat experienced tremendous change between 1990 and 2002, while the districts (Wilayat) of AL-Seeb, Bawshar, and Muttrah experienced more sporadic changes between 2002 and 2013.

Keywords: urban growth, single feature probability, object based image analysis, landcover change

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Authors: Nima Farshidfar, Navid Daryasafar

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In this paper, the seismic stability of reinforced soil slopes is studied using pseudo-dynamic analysis. Equilibrium equations that are applicable to the every kind of failure surface are written using Horizontal Slices Method. In written equations, the balance of the vertical and horizontal forces and moment equilibrium is fully satisfied. Failure surface is assumed to be log-spiral, and non-linear equilibrium equations obtained for the system are solved using Newton-Raphson Method. Earthquake effects are applied as horizontal and vertical pseudo-static coefficients to the problem. To solve this problem, a code was developed in MATLAB, and the critical failure surface is calculated using genetic algorithm. At the end, comparing the results obtained in this paper, effects of various parameters and the effect of using pseudo - dynamic analysis in seismic forces modeling is presented.

Keywords: soil slopes, pseudo-dynamic, genetic algorithm, optimization, limit equilibrium method, log-spiral failure surface

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Authors: Dhiaadin Bahaadin Noory

Abstract:

This research involves the effect of both sizes of reinforced zone and the amount of polypropylene fiber reinforcement on the structural behavior of model-reinforced sand loaded by square footing. The ratio of the side of the square reinforced zone to the footing width (W/B) and the ratio of the square reinforced zone depth to footing width (H/B) has been varied from one to six and from one to three, respectively. The tests were carried out on a small-scale laboratory model in which uniform-graded sand was used as a fill material. It was placed in a highly dense state by hitting a thin wooden board placed on the sand surface with a hammer. The sand was reinforced with randomly oriented discrete fibrillated polypropylene fibers. The test results indicated a significant increase in the bearing capacity and stiffness of the subgrade and a modification of load–the settlement behavior of sand with the size of the reinforced zone and amount of fiber reinforcement. On the basis of the present test results, the optimal side width and depth of the reinforced zone were 4B and 2B, respectively, while the optimal percentage of fibers was 0.4%.

Keywords: square footing, polypropylene fibers, bearing capacity, stiffness, load settlement behavior, relative density

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Authors: Mustapha Kamel Mihoubi, Hocine Dahmani

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The purpose of work is to study the phenomenon of agitation of storm waves at basin caused by different directions of waves relative to the current provision thrown numerical model based on the equation in shallow water using Boussinesq model MIKE 21 BW. According to the diminishing effect of penetration of a wave optimal solution will be available to be reproduced in reduced model. Another alternative arrangement throws will be proposed to reduce the agitation and the effects of the swell reflection caused by the penetration of waves in the harbor.

Keywords: agitation, Boussinesq equations, combination, harbor

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Authors: Mary Cruz

Abstract:

Founded from 1496 to 1502, Santo Domingo is the oldest European settlement in the Americas, inhabited without any discontinuity and was the first seat of Spanish power in the new world. Capital of the country since 1932.In this text, we discover Santo Domingo as an international tourist center, Urban Structure, Eco-tourism, Contamination and other issues related to tourism and development of this city. Founded from 1496 to 1502, Santo Domingo is the oldest European settlement in the Americas, inhabited without any discontinuity and was the first seat of Spanish power in the new world. Capital of the country since 1932. Encouraged by the United Nations and the World Bank, many Caribbean governments have encouraged tourism from the 1950s to boost their Third World economies. In this text, we discover Santo Domingo as an international tourist center, Urban Structure, Eco-tourism, Contamination and challenges of the first tourist destination in the Caribbean.

Keywords: eco-tourism, urban structure, contamination, development

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

Abstract:

The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Anna Avramenko, Heikki Haario

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This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

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Authors: Sateesh Kumar Pisini, Swetha Priya Pisini

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Granular piles are becoming popular as a technique of deep ground improvement not only in soft cohesive soils but also in loose cohesionless deposits. The present experimental study has been carried out on granular piles in sand (loose sand and medium dense sand i.e. relative density at 15% and 30%) with geogrid reinforcement. In this experimental study, a group of five piles installed in sand (at different spacing i.e s = 2d, 3d and 4d) the length and diameter of the pile (L = 0.4 m and d= 50 mm) kept as same for all series of experiments. Geogrid reinforcement is provided on granular piles with a limited number of laboratory tests. It has been conducted in laboratory to study the behavior of a granular pile with reinforced geogrid layers supporting a square footing at different s/d ratios. The influence of geogrid layers providing on granular piles investigated through model tests. In this paper the experimental study carried out results in significant increase in load carrying capacity and decrease in settlement reduction of the weak cohesionless soil. Also, the behavior of load carrying capacity and settlement with changing the s/d ratio has been carried out through a parametric study.

Keywords: granular piles, cohesionless soil, geogrid reinforcement, load carrying capacity

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: DucTho Le, Duy Kien Dao, Quoc Tinh Bui, Haidang Phan

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The article is concerned with the motion of ultrasonic guided waves in a unidirectional fiber-reinforced composite plate under acoustic sources. Such unidirectional composite material has orthotropic elastic properties as it is very stiff along the fibers and rather compliant across the fibers. The dispersion equations of free Lamb waves propagating in an orthotropic layer are derived that results in the dispersion curves. The connection of these equations to the Rayleigh-Lamb frequency relations of isotropic plates is discussed. By the use of reciprocity in elastodynamics, closed-form solutions of elastic wave motions subjected to time-harmonic loads in the layer are computed in a simple manner. We also consider the problem of Lamb waves generated by a set of time-harmonic sources. The obtained computations can be very useful for developing ultrasound-based methods for nondestructive evaluation of composite structures.

Keywords: lamb waves, fiber-reinforced composite plates, dispersion equations, nondestructive evaluation, reciprocity theorems

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: Kausar Ali

Abstract:

There are several ground treatment techniques which may meet the twin objectives of increasing the bearing capacity with simultaneous reduction of settlements, but the use of stone columns is one of the most suited techniques for flexible structures such as embankments, oil storage tanks etc. that can tolerate some settlement and used worldwide. However, when the stone columns in very soft soils are loaded; stone columns undergo excessive settlement due to low lateral confinement provided by the soft soil, leading to the failure of the structure. The poor performance of stone columns under these conditions can be improved by encasing the columns with a suitable geosynthetic. In this study, the effect of reinforcement on bearing capacity of composite soil has been investigated by conducting laboratory model tests on floating and end bearing long stone columns with l/d ratio of 12. The columns were reinforced by providing geosynthetic encasement over varying column length (upper 25%, 50%, 75%, and 100% column length). In this study, a group of columns has been used instead of single column, because in the field, columns used for the purpose always remain in groups. The tests indicate that the encasement over the full column length gives higher failure stress as compared to the encasement over the partial column length for both floating and end bearing long columns. The performance of end-bearing columns was found much better than the floating columns.

Keywords: geosynthetic, ground improvement, soft clay, stone column

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Authors: Thang Minh Le, Hadi Khabbaz

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The coefficient of consolidation is a parameter governing the rate at which saturated soil particularly clay undergoes consolidation when subjected to an increase in pressure. The rate and amount of compression in soil varies with the rate that pore water is lost; and hence depends on soil permeability. Over many years, various methods have been proposed to determine the coefficient of consolidation, cv, which is an indication of the rate of foundation settlement on soft ground. However, defining this parameter is often problematic and heavily relies on graphical techniques, which are subject to some uncertainties. This paper initially presents an overview of many well-established methods to determine the vertical coefficient of consolidation from the incremental loading consolidation tests. An array of consolidation tests was conducted on the undisturbed clay samples, collected at various depths from a site in Nakdong river delta, Busan, South Korea. The consolidation test results on these soft sensitive clay samples were employed to evaluate the targeted methods to predict the settlement rate of Busan clay. In relationship of time-displacement-velocity, a total of 3 method groups from 10 common procedures were classified and compared together. Discussions on study results will be also provided.

Keywords: Busan clay, coefficient of consolidation, constant rate of strain, incremental loading

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Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

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Authors: Vuyayo Tsheleza, Simbarashe Ndhleve, Christopher Mpundu Musampa

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Mismanagement of waste is continuously emerging as a rising malpractice in most developing countries, especially in fast growing cities. Household solid waste in Mthatha has been reported to be one of the problems facing the city and is overwhelming local authorities, as it is beyond the environment and management capacity of the existing waste management system. This study estimates per capita waste generation, quantity of different waste types generated by inhabitants of formal and informal settlements in Mthatha as well as waste management practices in the aforementioned socio-economic stratums. A total of 206 households were systematically selected for the study using stratified random sampling categorized into formal and informal settlements. Data on household waste generation rate, composition, awareness, and household waste management behaviour and practices was gathered through mixed methods. Sampled households from both formal and informal settlements with a total of 684 people generated 1949kg per week. This translates to 2.84kg per capita per week. On average, the rate of solid waste generation per capita was 0.40 kg per day for a person living in informal settlement and 0.56 kg per day person living in formal settlement. When recorded in descending order, the proportion food waste accounted for the most generated waste at approximately 23.7%, followed by disposable nappies at 15%, papers and cardboards 13.34%, glass 13.03%, metals at 11.99%, plastics at 11.58%, residue at 5.17, textiles 3.93%, with leather and rubber at 2.28% as the least generated waste type. Different waste management practices were reported in both formal and informal settlements with formal settlements proving to be more concerned about environmental management as compared to their counterparts, informal settlement. Understanding attitudes and perceptions on waste management, waste types and per capita solid waste generation rate can help evolve appropriate waste management strategies based on the principle of reduce, re-use, recycle, environmental sound disposal and also assist in projecting future waste generation rate. These results can be utilized as input when designing growing cities’ waste management plans.

Keywords: awareness, characterisation, per capita, quantification

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Authors: C. Recommandé, J. C. Blind, A. Clavel, R. Gourichon, V. Le Gal

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Simulations are developed in this paper with usual DSGE model equations. The model is based on simplified version of Smets-Wouters equations in use at European Central Bank which implies 10 macro-economic variables: consumption, investment, wages, inflation, capital stock, interest rates, production, capital accumulation, labour and credit rate, and allows take into consideration the banking system. Throughout the simulations, this model will be used to evaluate the impact of rate shocks recounting the actions of the European Central Bank during 2008.

Keywords: CC-LM, Central Bank, DSGE, liquidity shock, non-standard intervention

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