• Journal of the Microelectronics and Packaging Society
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• v.7 no.4
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• pp.17-22
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• 2000

In this paper, methods to analyze wire sweep during the semiconductor chip encapsulation have been studied. The wire sweep analysis is used to analyze the deformation of bonding wires that connect the chip to the leadframe during encapsulation. The analysis is done using either analytical solutions or numerical simulation. The analytical solution is used for rough but fast calculation of wire sweep. The results from the numerical simulation are closest to the experimental results.

• Journal of Korean Society for Atmospheric Environment
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• v.7 no.3
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• pp.189-196
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• 1991

In recent years spectral methods have been found to be a powerful tool for the numerical solution of hynamic differential equations. The main attraction of spectral method is accuracy even though it is generally difficult to implement and solve the complex problems using spectral method. We introduced diffusion equations describing the state of air pollution and solved by pseutospectral method in dimensionless form. The results were compared with both those of other numerical methods and analytical solutions. Comparing with finite difference method and finite element method, spectral method shows the highest accuracy for one dimension problem in this study. Also, the results of two dimensional diffusion problems show good agreement with analytical solutions.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.34 no.1
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• pp.27-32
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• 2018

This work provides the analytical methods to represent the updated form of stiffness or flexibility matrices using the measurements of the first few natural frequencies and the corresponding mode shapes. This study derives the mathematical forms on the variance of stiffness or flexibility matrices to minimize the performance index in the satisfaction of the eigen-function including the residual force depending on the measured data. The proposed methods can be utilized in detecting damage and updating the parameter matrices deviated from the analytical parameter matrices. The validity of the proposed methods is investigated in a numerical experiment of truss structure and the numerical results of stiffness-based and flexibility-based methods are compared. The sensitivity to the external noise is also examined for applying to the practical work.

• Journal of Korean Association for Spatial Structures
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• v.2 no.3 s.5
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• pp.115-122
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• 2002

It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.

• Steel and Composite Structures
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• v.24 no.6
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• pp.671-677
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• 2017

In this paper, two powerful analytical methods called Variational Approach (VA) and Hamiltonian Approach (HA) are used to solve high nonlinear non-Natural vibration problems. The presented approaches are works well for the whole range of amplitude of the oscillator. The first iteration of the approaches leads us to high accurate solution. Numerical results are also presented by using Runge-Kutta's [RK] algorithm. The full comparison between the presented approaches and the numerical ones are shown in figures. The effects of important parameters on the response of nonlinear behavior of the systems are studied completely. Finally, the results show that the Variational Approach and Hamiltonian approach are strong enough to prepare easy analytical solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.97-109
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• 1998

A comparison of the two dimensional heat loss, computed using the analytical method and the finite difference method in two models(i.e. one is a parabolic fin whose parabolic curves meet at the fin center line and the other is a transformed parabolic fin whose tip cuts vertically), is made assuming the analytical method is correct. For these methods, the root temperature and surrounding convection coefficients of these fins are assumed as constants. The results show that the relative errors of the heat loss between the two methods for the parabolic fin whose tip cuts vertically are smaller than those for the one whose tip does not cut. In case of Bi=0.01, the values of the heat loss obtained using a finite difference method are close to those values obtained using the analytical method for both models. The values of the heat loss from both models calculated by using the analytical method are almost the same for given range of non-dimensional fin length in case of Bi = 0.01 and 0.1.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1350-1358
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• 2001

During the last decade, a number of experiments and numerical analyses had been performed in conjunction with the development of simplified analytical methods to estimate the fracture behavior of cracked piping in nuclear power plant. However, the necessity of further investigation for the analytical methods was issued because of the discrepancies with the experimental data. The objective of this paper is to find out the optimum methods to evaluate the load-carrying capacities for cracked pipes. To do this, numerous analytical and finite element analyses were carried out for various pipe and crack geometries and materials. These results were synthesized for crack shapes and can be used as basic data for leak before analyses and risk informed inspections.

• Journal of the Korean Wood Science and Technology
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• v.35 no.3
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• pp.1-9
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• 2007

To analyze the behavior of multiple bolted connection with analytical method, there was a major problem in terms of the number of bolt as two. Multiple bolted connection is wrong in other way, that is impossible to analyze the behavior of connection with various types. So the numerical analysis model was developed to analyze the behavior of connection with various types, and to overcome the limitation of number of bolt. The optimum values for analysis the behavior of multiple bolted connection with numerical methods were obtained as, r=0.35, Kx=137.5, and Ky=257.4. The numerical analysis method was developed in this study showed high efficiency for the existing methods in the behavior analysis of connection.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.185-223
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• 2022

The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases' molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = h^m(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1883-1890
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• 2017

Transformers are one of the most precious elements of the electric power system. Stability and reliability of the electric power network mainly depend on the working of the transformer. Leakage reactance of the transformer is one of the important factors and accurate calculation of the leakage reactance is necessary for the transformer designers and electric distributors. Leakage reactance of the transformer depends on the geometry of the transformer. There are many different methods for the calculations of the leakage reactance however mostly are usable when the axial heights of the high voltage and low voltage windings are equal. When the axial heights of high voltage and low voltage windings are asymmetric most of the analytical methods are not reliable. In this study, a new analytical method is introduced for the calculation of the leakage reactance. Fourteen different transformers are investigated in this study and four of them are presented in this paper. The results of the new analytical method are compared with the experimental results. Other analytical and numerical methods are also compared with this new method. Results show that this method is more reliable and accurate as compared to the other analytical methods. The maximum relative error between short-circuit test and proposed method for these fourteen transformers was less than 2.8%.