• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.619-628
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• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.289-294
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• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• Journal of Power System Engineering
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• v.5 no.2
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• pp.79-86
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• 2001

A method is presented for generating the path which significantly reduces residual vibration of the redundant, flexible robot manipulator in the presence of obstacles. The desired path is optimally designed so that the system completes the required move with minimum residual vibration, avoiding obstacles. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinate, called VLCS, to represent the link flexibility. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables. A planar three-link manipualtor is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate path, in the presence of obstacles.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.157-166
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• 2006

In order to model blending surfaces with curvature continuity, in this paper we apply sixth order partial differential equations (PDEs), which are solved with a composite power series based method. The proposed composite power series based approach meets boundary conditions exactly, minimises the errors of the PDEs, and creates almost as accurate blending surfaces as those from the closed form solution that is the most accurate but achievable only for some simple blending problems. Since only a few unknown constants are involved, the proposed method is comparable with the closed form solution in terms of computational efficiency. Moreover, it can be used to construct 3- or 4-sided patches through the satisfaction of continuities along all edges of the patches. Therefore, the developed method is simpler and more efficient than numerical methods, more powerful than the analytical methods, and can be implemented into an effective tool for the generation and manipulation of complex free-form surfaces.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1632-1642
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• 1992

When a blind hole of small diameter is drilled in the field of residual stress, strain relieved around the hole is function of magnitude of stress, patterns of stress distribution and hole geometry of diameter and depth. Relieved strain coefficients can be calculated from FEM analysis of relieved strain and actual stress. These relieved strain coefficients make it possible to measure residual stress which vary along the depth in the subsurface of stressed material. In this study, the calibration tests of residual stress measurement are carried out by drilling a hole incrementally on the cantilever or on the tensile test bar. Residual stresses can be determined from measured strains around a shallow hole by application of power series method. For the sake of reliable measurement of residual stress, much efforts should be done to measure relieved strains and hole depth more accurately comparing with conventional procedures of gage subject to the external load. Otherwise linear equations converting strains into stresses may yield erratic residual stresses because of ill-conditions of linear equations. With accurate measurements of relieved strains, residual stress even if varying along the depth can be measured. It is also possible to measure residual stress in the thin film of material by drilling a shallow hole.

• East Asian Journal of Business Economics (EAJBE)
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• v.3 no.3
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• pp.14-26
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• 2015

A wind speed forecast is a crucial and sophisticated task in a wind farm for planning turbines and corresponds to an estimate of the expected production of one or more wind turbines in the near future. By production is often meant available power for wind farm considered (with units KW or MW depending on both the wind speed and direction. Such forecasts can also be expressed in terms of energy, by integrating power production over each time interval. In this study, we technically focused on mathematical modeling of wind speed and direction forecast based on locally data set gathered from Aghdasiyeh station in Tehran. The methodology is set on using most common techniques derived from literature review. Hence we applied the most sophisticated forecasting methods to embed seasonality, trend, and irregular pattern for wind speed as an angular variables. Through this research, we carried out the most common techniques such as the Box and Jenkins family, VARMA, the component method, the Weibull function and the Fourier series. Finally, the best fit for each forecasting method validated statistically based on white noise properties and the final comparisons using residual standard errors and mean absolute deviation from real data.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.1988-1997
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• 2005

This study is concerned with structural integrity evaluations for the interference-fit flywheels in reactor coolant pumps (RCPs) of nuclear power plants. Stresses in the flywheel due to the shrinkage loads and centrifugal loads at the RCP normal operation speed, design overspeed and joint-release speed are obtained using the finite element method (FEM), where release of the deformation-controlled stresses as a result of structural interactions during rotation is considered. Fracture mechanics evaluations for a series of cracks assumed to exist in the flywheel are conducted, considering ductile (fatigue) and non-ductile fracture, and stress intensity factors are obtained for the cracks using the finite element alternating method (FEAM). From analysis results, it is found that fatigue crack growth rates calculated are negligible for smaller cracks. Meanwhile, the material resistance to non-ductile fracture in terms of the critical stress intensity factor (K$_{IC}$) and the nil-ductility transition reference temperature (RT$_{NDT}$) are governing factors for larger cracks.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.41 no.3
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• pp.227-233
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• 2005

In order to estimate the effective horse power(EHP) in towing net of a bottom trawl ship, the ship's resistance was calculated by using a series data of Yamagata and Wigley formula. Also the effective horse power for a ship(EHPs) was estimated versus the ship speed in sailing and the propulsive efficiency was calculated with the brake horse power and the effective horse power. Then the effective horse power for a ship and a trawl net were estimated in the application of the propulsive efficiency in towing net. The total effective horse power($EHP_T$) was average 187.6kW and the effective horse power for a 1.awl net($EHP_n$) was average 176.7kW at a smooth sea state in towing net. The ratio of $EHP_n$ to $EHP_T$ was about 94.0% and the value was higher slightly than was already informed at a smooth sea state. The power for keeping up a townet speed was required more about 20% of a maximum continuous power at a rather rough sea state than a smooth sea state. In the future, if the residual resistance is considered with a sea state, $EHP_n$ will be estimated more correctly Also the data of EHP estimated by this method will be used as the basic data to design a trawl net.

• Steel and Composite Structures
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• v.36 no.1
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• pp.75-86
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• 2020

The grid structures with welded hollow spherical joint (WHSJ) have gained increasing popularity for use in industrial buildings with suspended cranes, and usually welded with steel tube (ST). The fatigue performance of steel tube-welded hollow spherical joint (ST-WHSJ) is however not yet well characterized, and there is little research on fatigue life prediction methods of ST-WHSJ. In this study, based on previous fatigue tests, three series of specimen fatigue data with different design parameters and stress ratios were compared, and two fatigue failure modes were revealed: failure at the weld toe of the ST and the WHSJ respectively. Then, S-N curves of nominal stress were uniformed. Furthermore, a finite element model (FEM) was validated by static test, and was introduced to assess fatigue behavior with the hot spot stress method (HSSM) and the effective notch stress method (ENSM). Both methods could provide conservative predictions, and these two methods had similar results. However, ENSM, especially when using von Mises stress, had a better fit for the series with a non- positive stress ratio. After including the welding residual stress and mean stress, analyses with the local stress method (LSM) and the critical distance method (CDM, including point method and line method) were carried out. It could be seen that the point method of CDM led to more accurate predictions than LSM, and was recommended for series with positive stress ratios.