Search results for: gauss-%20bonnet

Authors: I. V. Singh, A. Singh

Abstract:

In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.

Keywords: Meshless, EFG method, potential flow, Lagrange multiplier method, penalty method, penalty parameter and scaling parameter

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Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: M. Fakharian, M. I. Khodakarami

Abstract:

In this paper, a new trend for improvement in semianalytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific subparametric elements. Mapping functions are uses as a class of higherorder Lagrange polynomials, special shape functions, Gauss-Lobatto- Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.

Keywords: 2D Elastodynamic Problems, Lagrange Polynomials, G-L-Lquadrature, Decoupled SBFEM.

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Authors: A. A. Sharma, B. J. N. Sharma

Abstract:

This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers’ diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: Quasilongitudinal, reflection and transmission, semiconductors, acoustics.

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Authors: A. Bahmanikashkouli, O.R. Bahadori Nezhad

Abstract:

In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

Keywords: Generalized Differential Quadrature method, Nonlinear consolidation, Nonlinear system of equations, Time-varied drainage

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Authors: U. Prasopchingchana

Abstract:

The temperature distribution and the heat transfer rates through a multi-layer door of a furnace were investigated. The inside of the door was in contact with hot air and the other side of the door was in contact with room air. Radiation heat transfer from the walls of the furnace to the door and the door to the surrounding area was included in the problem. This work is a two dimensional steady state problem. The Churchill and Chu correlation was used to find local convection heat transfer coefficients at the surfaces of the furnace door. The thermophysical properties of air were the functions of the temperatures. Polynomial curve fitting for the fluid properties were carried out. Finite difference method was used to discretize for conduction heat transfer within the furnace door. The Gauss-Seidel Iteration was employed to compute the temperature distribution in the door. The temperature distribution in the horizontal mid plane of the furnace door in a two dimensional problem agrees with the one dimensional problem. The local convection heat transfer coefficients at the inside and outside surfaces of the furnace door are exhibited.

Keywords: Conduction, heat transfer, multi-layer door, natural convection

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Authors: Sheela Tiwari, R. Naresh, R. Jha

Abstract:

The paper presents an investigation in to the effect of neural network predictive control of UPFC on the transient stability performance of a multimachine power system. The proposed controller consists of a neural network model of the test system. This model is used to predict the future control inputs using the damped Gauss-Newton method which employs ‘backtracking’ as the line search method for step selection. The benchmark 2 area, 4 machine system that mimics the behavior of large power systems is taken as the test system for the study and is subjected to three phase short circuit faults at different locations over a wide range of operating conditions. The simulation results clearly establish the robustness of the proposed controller to the fault location, an increase in the critical clearing time for the circuit breakers, and an improved damping of the power oscillations as compared to the conventional PI controller.

Keywords: Identification, Neural networks, Predictive control, Transient stability, UPFC.

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

Abstract:

Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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Authors: Assem M. F. Sallam, Ah. El-S. Makled

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In this paper, there is an implementation, verification, and graphical demonstration of a software application, which can be used swiftly over different preliminary orbit determination methods. A passive orbit determination method is used in this study to determine the location of a satellite or a flying body. It is named a passive orbit determination because it depends on observation without the use of any aids (radio and laser) installed on satellite. In order to understand how these methods work and how their output is accurate when compared with available verification data, the built models help in knowing the different inputs used with each method. Output from the different orbit determination methods (Gibbs, Lambert, and Gauss) will be compared with each other and verified by the data obtained from Satellite Tool Kit (STK) application. A modified model including all of the orbit determination methods using the same input will be introduced to investigate different models output (orbital parameters) for the same input (azimuth, elevation, and time). Simulation software is implemented using MATLAB. A Graphical User Interface (GUI) application named OrDet is produced using the GUI of MATLAB. It includes all the available used inputs and it outputs the current Classical Orbital Elements (COE) of satellite under observation. Produced COE are then used to propagate for a complete revolution and plotted on a 3-D view. Modified model which uses an adapter to allow same input parameters, passes these parameters to the preliminary orbit determination methods under study. Result from all orbit determination methods yield exactly the same COE output, which shows the equality of concept in determination of satellite’s location, but with different numerical methods.

Keywords: Orbit determination, STK, MATLAB-GUI, satellite tracking.

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Authors: R .Lassoued, M. Guenfoud

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An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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Authors: Thanida Sujarittham, Narumon Emarat, Jintawat Tanamatayarat, Kwan Arayathanitkul, Suchai Nopparatjamjomras

Abstract:

Electric field is an important fundamental concept in electrostatics. In high-school, generally Thai students have already learned about definition of electric field, electric field due to a point charge, and superposition of electric fields due to multiple-point charges. Those are the prerequisite basic knowledge students holding before entrancing universities. In the first-year university level, students will be quickly revised those basic knowledge and will be then introduced to a more complicated topic—electric field due to continuous charged distributions. We initially found that our freshman students, who were from the Faculty of Science and enrolled in the introductory physic course (SCPY 158), often seriously struggled with the basic physics concepts—superposition of electric fields and inverse square law and mathematics being relevant to this topic. These also then resulted on students’ understanding of advanced topics within the course such as Gauss's law, electric potential difference, and capacitance. Therefore, it is very important to determine students' understanding of electric field due to continuous charged distributions. The open-ended question about sketching net electric field vectors from a uniformly charged insulating rod was administered to 260 freshman science students as pre- and post-tests. All of their responses were analyzed and classified into five levels of understandings. To get deep understanding of each level, 30 students were interviewed toward their individual responses. The pre-test result found was that about 90% of students had incorrect understanding. Even after completing the lectures, there were only 26.5% of them could provide correct responses. Up to 50% had confusions and irrelevant ideas. The result implies that teaching methods in Thai high schools may be problematic. In addition for our benefit, these students’ alternative conceptions identified could be used as a guideline for developing the instructional method currently used in the course especially for teaching electrostatics.

Keywords: Electrostatics Electric field due to continuous charged distributions, inverse square law, superposition principle, levels of student understandings.

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Authors: K. Karuppasamy

Abstract:

In this paper, analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill-poor soil system overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behaviour of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedal iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil–foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include magnitude of applied load, velocity of load, damping, ultimate resistance of poor soil and granular fill layer. Range of values of parameters has been considered as per Indian Railway conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil–foundation system.

Keywords: Infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load, nonlinear behavior of poor soil.

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