• Advances in nano research
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• v.10 no.2
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• pp.175-189
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• 2021

In this article, frequency characteristics, and sensitivity analysis of a size-dependent laminated composite cylindrical nanoshell under bi-directional thermal loading using Nonlocal Strain-stress Gradient Theory (NSGT) are presented. The governing equations of the laminated composite cylindrical nanoshell in thermal environment are developed using Hamilton's principle. The thermodynamic equations of the laminated cylindrical nanoshell are obtained using First-order Shear Deformation Theory (FSDT) and Fourier-expansion based Generalized Differential Quadrature element Method (FGDQM) is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The novelty of the current study is to consider the effects of bi-directional temperature loading and sensitivity parameter on the critical temperature and frequency characteristics of the laminated composite nanostructure. Apart from semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the laminated cylindrical shell. The results created from finite element simulation illustrates a close agreement with the semi-numerical method results. Finally, the influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature, sensitivity, and frequency of the laminated composite nanostructure are investigated, in details.

• Journal of the Korean Society of Safety
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• v.22 no.5
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• pp.41-49
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• 2007

In general, the curved structures have the engineering efficiency as well as a fine view compared with straight member. Also, composite materials are composed of two or more different materials to produce desirable properties for structural strength as compared to single ones. Shell structures with composite materials have many advantages in strength and weight reduction. Therefore, composite laminated conical shells are analyzed in this study. To solve differential equations of conical shells, this paper used finite difference method. Various parametric study according to the change of radius ratio, vertex angle and subtended angle are examined. The change of radius ratio, vertex angle and subtended angle mean the change from conical shells to cylindrical shells, conical shells to circular plates and open shells closed shells, respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1338-1346
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• 1994

The objective of this study is to investigate the effect of various parameters, such as temperature, mean current density and voltage on the performance of phosphoric acid fuel cell (PAFC) by numerical analysis. Two types of flow passages, which are Z-parallel type and Z-counter type, are evaluated to obtain the best current density and temperature distribution. Parametric studies and sensitivity analysis of the PAFC system's operation in single cell are accomplished. A steady state simulation of the entire system is developed using nonlinear ordinary differential equations. The finite difference method and trial and error procedures are used to obtain a solution.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.57-62
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• 2013

Because of high torque and easiness of speed control, Direct Current(DC) motors have been used for a long time. But, its applications are limited in circumstance and performance, since they contained brush and commutator. The commutation characteristic gives effect to life and performance of the DC motor. Naturally, the commutation characteristic analysis is strongly required. In this paper, With the result of finite element analysis, The inductance is calculated each rotor position and applied to the voltage equations coupled with commutation equation. Also, contact resistances of brush/commutator assembly are considered using contact area and brush width converted with commutator segments. The time derivative term in the differential equation is solved in time difference method. This algorithm was applied to 2-pole shunt DC motor. We considered commutation characteristic by changing contact resistance between brush and commutator segment.

• Journal of Welding and Joining
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• v.16 no.3
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• pp.141-147
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• 1998

Design sensitivity analysis of a vehicle system is an essential tool for design optimization and trade-off studies. Most optimization algorithms require the derivatives of cost and constraint function with respect to design in order to calculate the next improved design. This paper presents an efficient algorithm application for the design sensitivity analysis, using the direct differentiation method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method. A mounting area of suspension that welded on chassis frame is analyzed to show the validity and the efficiency of the proposed method.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.289-298
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• 2010

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.779-787
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• 2007

This paper presents a highly efficient moving least squares finite difference method (MLS FDM) for a heat transfer problem of bi-material with interfacial boundary. The MLS FDM directly discretizes governing differential equations based on a node set without a grid structure. In the method, difference equations are constructed by the Taylor polynomial expanded by moving least squares method. The wedge function is designed on the concept of hyperplane function and is embedded in the derivative approximation formula on the moving least squares sense. Thus interfacial singular behavior like normal derivative jump is naturally modeled and the merit of MLS FDM in fast derivative computation is assured. Numerical experiments for heat transfer problem of bi-material with different heat conductivities show that the developed method achieves high efficiency as well as good accuracy in interface problems.