Search results for: newton raphson

Authors: H. Abaal, R. Skouri

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A power flow analysis is a steady-state study of power grid. The goal of power flow analysis is to determine the voltages, currents, and real and reactive power flows in a system under a given load conditions. In this paper, the load flow analysis program by Newton Raphson polar coordinates Method is developed. The effectiveness of the developed program is evaluated through a simple 5-IEEE test system bus by simulations using MATLAB.

Keywords: power flow analysis, Newton Raphson polar coordinates method

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Authors: Daniel Fundi Murithi

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Data from economic, social, clinical, and industrial studies are in some way incomplete or incorrect due to censoring. Such data may have adverse effects if used in the estimation problem. We propose the use of Maximum Likelihood Estimation (MLE) under a progressive type-II censoring scheme to remedy this problem. In particular, maximum likelihood estimates (MLEs) for the location (µ) and scale (λ) parameters of two Parameter Rayleigh distribution are realized under a progressive type-II censoring scheme using the Expectation-Maximization (EM) and the Newton-Raphson (NR) algorithms. These algorithms are used comparatively because they iteratively produce satisfactory results in the estimation problem. The progressively type-II censoring scheme is used because it allows the removal of test units before the termination of the experiment. Approximate asymptotic variances and confidence intervals for the location and scale parameters are derived/constructed. The efficiency of EM and the NR algorithms is compared given root mean squared error (RMSE), bias, and the coverage rate. The simulation study showed that in most sets of simulation cases, the estimates obtained using the Expectation-maximization algorithm had small biases, small variances, narrower/small confidence intervals width, and small root of mean squared error compared to those generated via the Newton-Raphson (NR) algorithm. Further, the analysis of a real-life data set (data from simple experimental trials) showed that the Expectation-Maximization (EM) algorithm performs better compared to Newton-Raphson (NR) algorithm in all simulation cases under the progressive type-II censoring scheme.

Keywords: expectation-maximization algorithm, maximum likelihood estimation, Newton-Raphson method, two-parameter Rayleigh distribution, progressive type-II censoring

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Authors: Kusum Tharani, Ratna Dahiya

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This paper aims to analyze the power flow of a grid connected 100-kW Photovoltaic(PV) array connected to a 25-kV grid via a DC-DC boost converter and a three-phase three-level Voltage Source Converter (VSC). Maximum Power Point Tracking (MPPT) is implemented in the boost converter bymeans of a Simulink model using the 'Perturb & Observe' technique. First, related papers and technological reports were extensively studied and analyzed. Accordingly, the system is tested under various loading conditions. Power flow analysis is done using the Newton-Raphson method in Matlab environment. Finally, the system is subject to Single Line to Ground Fault and Three Phase short circuit. The results are simulated under the grid-connected operating model.

Keywords: grid connected PV Array, Newton-Raphson Method, power flow analysis, three phase fault

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: T. Martini, J. M. Martínez

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An algorithmic acceleration strategy based on quasi-Newton (or secant) methods is displayed for address the practical problem of accelerating the convergence of the Newton-Lagrange method in the case of convergence to critical multipliers. Since the Newton-Lagrange iteration converges locally at a linear rate, it is natural to conjecture that quasi-Newton methods based on the so called secant equation and some minimal variation principle, could converge superlinearly, thus restoring the convergence properties of Newton's method. This strategy can also be applied to accelerate the convergence of algorithms applied to fixed-points problems. Computational experience is reported illustrating the efficiency of this strategy to solve fixed-point problems with linear convergence rate.

Keywords: algorithmic acceleration, fixed-point problems, nonlinear programming, quasi-newton method

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Authors: Aymen Laadhari

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We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: finite element method, level set, Newton, membrane

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

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Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken.

Keywords: Lagrange interpolation, linear complexity, monomial matrix, Newton interpolation

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Authors: Aymen Laadhari, Gábor Székely

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This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: finite element method, implicit, level set, membrane, Newton method

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Authors: Puneet Chawla, Balwinder Singh

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Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper, P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton-Raphson method. Using Q-V curves, the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: voltage stability, reactive power, power flow, weakest bus, STATCOM

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Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim

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In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Al Omari Moahmmed Ahmed

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In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

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Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

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Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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Authors: Mai Abdul Latif, Yuntian Feng

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Applied Element Method (AEM) is a method that was developed to aid in the analysis of the collapse of structures. Current available methods cannot deal with structural collapse accurately; however, AEM can simulate the behavior of a structure from an initial state of no loading until collapse of the structure. The elements in AEM are connected with sets of normal and shear springs along the edges of the elements, that represent the stresses and strains of the element in that region. The elements are rigid, and the material properties are introduced through the spring stiffness. Nonlinear dynamic analysis has been widely modelled using the finite element method for analysis of progressive collapse of structures; however, difficulties in the analysis were found at the presence of excessively deformed elements with cracking or crushing, as well as having a high computational cost, and difficulties on choosing the appropriate material models for analysis. The Applied Element method is developed and coded to significantly improve the accuracy and also reduce the computational costs of the method. The scheme works for both linear elastic, and nonlinear cases, including elasto-plastic materials. This paper will focus on elastic and elasto-plastic material behaviour, where the number of springs required for an accurate analysis is tested. A steel cantilever beam is used as the structural element for the analysis. The first modification of the method is based on the Gaussian Quadrature to distribute the springs. Usually, the springs are equally distributed along the face of the element, but it was found that using Gaussian springs, only up to 2 springs were required for perfectly elastic cases, while with equal springs at least 5 springs were required. The method runs on a Newton-Raphson iteration scheme, and quadratic convergence was obtained. The second modification is based on adapting the number of springs required depending on the elasticity of the material. After the first Newton Raphson iteration, Von Mises stress conditions were used to calculate the stresses in the springs, and the springs are classified as elastic or plastic. Then transition springs, springs located exactly between the elastic and plastic region, are interpolated between regions to strictly identify the elastic and plastic regions in the cross section. Since a rectangular cross-section was analyzed, there were two plastic regions (top and bottom), and one elastic region (middle). The results of the present study show that elasto-plastic cases require only 2 springs for the elastic region, and 2 springs for the plastic region. This showed to improve the computational cost, reducing the minimum number of springs in elasto-plastic cases to only 6 springs. All the work is done using MATLAB and the results will be compared to models of structural elements using the finite element method in ANSYS.

Keywords: applied element method, elasto-plastic, Gaussian springs, nonlinear

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Authors: Geetanjali Panda, Suvrakanti Chakraborty

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In this paper, Newton-like descent methods are proposed for unconstrained optimization problems, which use q-derivatives of the gradient of an objective function. First, a local scheme is developed with alternative sufficient optimality condition, and then the method is extended to a global scheme. Moreover, a variant of practical Newton scheme is also developed introducing a real sequence. Global convergence of these schemes is proved under some mild conditions. Numerical experiments and graphical illustrations are provided. Finally, the performance profiles on a test set show that the proposed schemes are competitive to the existing first-order schemes for optimization problems.

Keywords: Descent algorithm, line search method, q calculus, Quasi Newton method

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Authors: Nicholas Jensen

Abstract:

As the effort to create new drugs to treat rare conditions cost-effectively intensifies, there is a need to ensure maximum efficiency in the manufacturing process. This includes the creation of ultracompact treatment forms, which can best be achieved via applications of fundamental laws of physics. This paper reports an experiment exploring the relationship between the forms of Newton's 2ⁿᵈ Law appropriate to linear motion and to transversal architraves. The moment of inertia of three discs was determined by experiments and compared with previous data derived from a theoretical relationship. The method used was to attach the discs to a moment arm. Comparing the results with those obtained from previous experiments, it is found to be consistent with the first law of thermodynamics. It was further found that Newton's 2ⁿᵈ law violates the second law of thermodynamics. The purpose of this experiment was to explore the relationship between the forms of Newton's 2nd Law appropriate to linear motion and to apply torque to a twisting force, which is determined by position vector r and force vector F. Substituting equation alpha in place of beta; angular acceleration is a linear acceleration divided by radius r of the moment arm. The nevrological analogy of Newton's 2nd Law states that these findings can contribute to a fuller understanding of thermodynamics in relation to viscosity. Implications for the pharmaceutical industry will be seen to be fruitful from these findings.

Keywords: Newtonian physics, inertia, viscosity, pharmaceutical applications

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

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The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability

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Authors: Anubhav Shrivastava, Lakshya Bhat, Shivarudraswamy

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Distributed Generation is the need of the hour. With current advancements in the DG technology, there are some major issues that need to be tackled in order to make this method of generation of energy more efficient and feasible. Among other problems, the control in voltage is the major issue that needs to be addressed. This paper focuses on control of voltage using reactive power control of DGs with the help of fuzzy logic. The membership functions have been defined accordingly and the control of the system is achieved. Finally, with the help of simulation results in Matlab, the control of voltage within the tolerance limit set (+/- 5%) is achieved. The voltage waveform graphs for the IEEE 14 bus system are obtained by using simple algorithm with MATLAB and then with fuzzy logic for 14 bus system. The goal of this project was to control the voltage within limits by controlling the reactive power of the DG using fuzzy logic.

Keywords: distributed generation, fuzzy logic, matlab, newton raphson, IEEE 14 bus, voltage regulation, radial network

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Authors: M. Abdelmalek

Abstract:

In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

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Authors: Byung Ho Jung, Dong Hoon Lim

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Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. Logistic regression is used extensively in numerous disciplines, including the medical and social science fields. In this paper, we address the problem of estimating parameters in the logistic regression based on MapReduce framework with RHadoop that integrates R and Hadoop environment applicable to large scale data. There exist three learning algorithms for logistic regression, namely Gradient descent method, Cost minimization method and Newton-Rhapson's method. The Newton-Rhapson's method does not require a learning rate, while gradient descent and cost minimization methods need to manually pick a learning rate. The experimental results demonstrated that our learning algorithms using RHadoop can scale well and efficiently process large data sets on commodity hardware. We also compared the performance of our Newton-Rhapson's method with gradient descent and cost minimization methods. The results showed that our newton's method appeared to be the most robust to all data tested.

Keywords: big data, logistic regression, MapReduce, RHadoop

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Authors: Prashant G. Metri

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A numerical model is developed to study nano liquid film flow over an unsteady stretching sheet in the presence of hydromagnetic have been investigated. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness β and the unsteadiness parameter S is found, the effect of unsteadiness parameter S, and the hydromagnetic parameter S, on the velocity and temperature distributions are presented. The present analysis shows that the combined effect of magnetic field and viscous dissipation has a significant influence in controlling the dynamics of the considered problem. Comparison with known results for certain particular cases is in excellent agreement.

Keywords: boundary layer flow, nanoliquid, thin film, unsteady stretching sheet

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Authors: Abbas Moradi, Mohsen Safajoy, Reza Yazdanparast

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Analysis of blade-disc dovetail joints is one of the biggest challenges facing designers of aero-engines. To avoid comparatively expensive experimental full-scale tests, numerical methods can be used to simulate loaded disc-blades assembly. Mortar method provides a powerful and flexible tool for solving frictional contact problems. In this study, 2D frictional contact in dovetail has been analysed based on the mortar algorithm. In order to model the friction, the classical law of coulomb and moving friction cone algorithm is applied. The solution is then obtained by solving the resulting set of non-linear equations using an efficient numerical algorithm based on Newton–Raphson Method. The numerical results show that this approach has better convergence rate and accuracy than other proposed numerical methods.

Keywords: computational contact mechanics, dovetail joints, nonlinear FEM, mortar approach

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

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A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Nur Rokhman

Abstract:

A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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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: Tania Sharmin Khaleque, Mohammad Ferdows

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The flow and heat transfer characteristics of a convection with temperature-dependent viscosity and thermal diffusivity along a vertical plate with internal heat generation effect have been studied. The plate temperature is assumed to follow a power law of the distance from the leading edge. The resulting governing two-dimensional equations are transformed using suitable transformations and then solved numerically by using fifth order Runge-Kutta-Fehlberg scheme with a modified version of the Newton-Raphson shooting method. The effects of the various parameters such as variable viscosity parameter β_1, the thermal diffusivity parameter β_2, heat generation parameter c and the Prandtl number Pr on the velocity and temperature profiles, as well as the local skin- friction coefficient and the local Nusselt number are presented in tabular form. Our results suggested that the presence of internal heat generation leads to increase flow than that of without exponentially decaying heat generation term.

Keywords: free convection, heat generation, thermal diffusivity, variable viscosity

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