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In this paper, some applications of the Method of Least Squares (MLS) for the solution of various problems in electromagnetics engineering is briefly reviewed. Here, MLS is employed for the solution of various problems such as solution of equations, curve fitting to measured data, generalized Fourier coefficients, linear operator equations, inegro-differential equations, electrostatics and magnetostatics problems, boundary value problems (by the Least Square Boundary Residual Method LSBRM), design of impedance transformers and matching by step and tapered lines, optimum design of multihole directional couplers, coupled-line couplers, branch line couplers, ring couplers, analysis of wire antennas, antenna pattern synthesis, array synthesis and scattering. In this study, it becomes clear that MLS can be applied to devise effective numerical algorithms for the analysis and design of problems in the subject areas of radiation, scattering, antennas, microwaves, engineering mathematic, etc. Some papers and books published in the area of MLS applications for the analysis and design of problems in electromagnetics engineering are grouped and presented in references.

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Ballasted track are of the most common species of railway in our country. The aim of this paper is study of three-dimensional models suitable for railway ballasted track and Dynamic analysis of those using numerical method Runge-Kutta 4th Order Method, after the dynamic analysis is performed and finally responses related to railway components be determined. To analyze the effect of passing under the railway train, a function of loading time on the railway line is applied and the effect of dynamic response under loading is evaluated. Previous researchers in the field activities of the railway system modeling and analysis of the dynamics on the two-dimensional models have been done. But this article is trying to consider the transverse nodes, on previous models and comes in three-dimensional dynamic analysis of the numerical method to be done. In other words, a new perspective in this article, consider nodes for transverse railroad modeling and numerical analysis of it. Brief description of the numerical methods mentioned along with the solving algorithm is mentioned in this article. In this research, simulation and modeling for rails, tie, connections and railway superstructure layers, is considered as elements of lump mass, spring and damper is used. Traditional methods used for the design of rail lines, based on static loading and quasi-dynamic analysis, the line components are analyzed, but in this article, according to the theories discussed in relation to rail component vibration, and study of dynamic load effects on track components into the issue to be more realistic. Responses obtained from dynamic analysis can be as input and issues designed to optimize rail components.

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The present study proposes a novel numerical method for fatigue life prediction under non-proportional loading. This method is employed for fatigue life estimation of different materials including 1045 Steel, 30CrNiMo8HH, Titanium TC4, extracted AZ31B Magnesium and Aluminum alloy 6061 under both proportional and non-proportional loadings. Basis of the method is developed in the framework of two numerical modifications. The first modification modifies fatigue damage parameters by correlating damages quantities of non-proportional loading to the proportional one. The second modification uses the same equation as the first one, but the corresponding damage coefficient is replaced by the additional hardening coefficient. In addition, these modifications are applied to fatigue damage parameters including maximum shear strain, SWT, Fatemi-Socie, and Babaei-Ghasemi model and also verified against experimental observations available in literature. Furthermore, the obtained results are discussed in details and also are compared to the non-modified findings. Moreover, the variation of the fatigue life prediction error is calculated for the aforementioned models. Finally, the results show considering and implementation of these modifications significantly improves the accuracy of the predicted fatigue lives for all the studied cases.

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Partial differential equations are needed in most of the engineering fields. Analytical solutions to these equations cannot be derived except in some very special cases, making numerical methods more important. Alongside advances in science and technology, new methods have been proposed for solution of partial differential equations, such as meshless methods. Recently, the generalized exponential basis function (GEBF) meshless method has been introduced. In this method the unknown function is approximated as a linear combination of exponential basis functions. In linear problems, the unknown coefficients are calculated such that the homogenous form of main differential equation is satisfied in all points of the grid. In order to solve nonlinear equations, Newton-Kantorovich scheme is first used to linearize them. The linearized equations are then solved iteratively to obtain the result. In this paper, time dependent problems in solid mechanics have been investigated. In order to examine performance of the proposed method, linear and non-linear problems in solid mechanics are considered and the results are compared with analytical solutions. The results show good accuracy (less than 1 percentage error) of the presented method.

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One of the important ways for improving performance of diesel engines is selecting of a proper and efficient fuel injection pattern. In this study six different patterns of fuel injection have been considered and performance of a diesel engine by using these patterns of fuel injection have been investigate numerically by employing AVL Fire. An annulus nozzle have been consider for the fuel injection system. It is expected that considering an annulus nozzle lead to increase of spry cone angle and proper distribution of the fuel inside the combustion chamber. Results show that employing proper and efficient patterns of fuel injection lead to increase of engine power and decrease of exhaust pollutants gases. Results also show that by employing a quasi-triangle fuel injection pattern, the diesel engine has better performance in competition with the case of using a constant fuel injection. It is found that by employing a quasi-triangle pattern of fuel injection, SFC reduces to 0.2043 kg/kJ, while the engine power increased by 27.5% and the magnitude of NO increases slightly. In the case of employing a constant-decreasing fuel injection pattern, the magnitude of SFC reduces to 0.2029kg/kJ whereas the magnitude of NO increases in comparison with the case of using constant fuel injection pattern. Numerical results show that by employing a constant-increasing pattern of fuel injection, the engine power is approximately equal to the engine’s power in the case of using a constant fuel injection pattern. But in this case the magnitude of NO reduces considerably.