• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.949-966
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• 2016

The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.778-785
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• 2006

In this paper, two possible ways for mode shape expansion are proposed and opened for discussion for future use. The first method minimizes the modal flexibility error between the experimental and analytical mode shapes corresponding to the measured DOFs to find the multiplication matrix which can be treated as the least-squares minimization problem. In the second method, Normalized Modal Difference (NMD) is used to calculate multiplication matrix using the analytical DOFs corresponding to measured DOfs. This matrix is then used to expand the measured mode shape to unmeasured DOFs. A simulated simply supported beam is used to demonstrate the performance of the methods. These methods are then compared with two most promising existing methods namely Kidder dynamic expansion and Modal expansion methods. It is observed that the performance of the modal flexibility method is comparable with existing methods. NMD also have the potential to expand the mode shapes though it is seen more sensitive to the distribution of error between FEM and actual test data.

• Journal of KSNVE
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• v.9 no.2
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• pp.340-347
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• 1999

The acoustic performance of reactive type single expansion chamber can be calculated theoretically by plane wave theory. But higher order model should be considered to widen the frequency range. Mode matching method has been developed to consider higher order modes, but very complicated algebra should be used. Munjal suggested a numerical collocation method, which can overcome the shortcomings of mode matching method, using the compatibility conditions for acoustic pressure and particle velocity at the junctions of area discontinuities. But the restriction of Munjal's method is that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In this paper, the new method was suggested to overcome the shortcomings of Munjal's method. The predictions by this method was also compared with those by the finite element method and Munjal's method in order to demonstrate the accuracy of the modified method presented here.

• Journal of Hydrogen and New Energy
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• v.18 no.3
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• pp.256-264
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• 2007

In order to calculate the relation between the hydrogen and the hydrogen absorption metals in the atomic level, Embedded Atom Method(EAM) is recommended. In this study, we had constructed the EAM programs from constitutive formulas and parameters of the hydrogen and palladium for the purpose of predicting the expansion behavior on hydrogen absorbing in the geometric shape of hydrogen absorption metals, as palladium bars and plates. And the EAM analyses data were compared with the experiment data by using electrochemical method. As results, it is note that the expansion rate in thickness of the palladium plate model by EAM analyses is about 4 times larger than width and length, be similar to experiment results. Also, in the microscopic and macroscopic level the expansion behavior through EAM analyses show good agreement with experiment data.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.3
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• pp.11-18
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• 1990

The Kelvin's method of stationary phase breaks down at the cusp point and yields a nonuniform expansion near it. By making use of the nonuniform expansion, we derive a uniform expansion near the cusp point.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.253-264
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• 2012

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).

• Journal of KSNVE
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• v.9 no.5
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• pp.914-921
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• 1999

There are many theoretical investigations to analyze higher order mode of reactive type single expansion chambers with offset inlet/outlet locations. But the conventional method has the restriction that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In the paper, a new method was suggested to apply the Kim's method to silencer with circular cross-section. Not only the offset location but also the magnitude of cross-section area of inlet/outlet pipe can be considered by the suggested method. The predictions by this new method also compared with those by the finite element method and Munjal's method in order to verify the accuracy of the suggested method presented here.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1110-1115
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• 2006

Cold expansion of fastener holes has been successfully used for many years to impart beneficial compressive residual stresses. Beneficial compressive residual stress of fastener hole that has been cold expanded before is reduced by using of materials for a long time. As a result, fatigue life of material is reduced. So, compressive residual stresses of material have to regenerate by re-cold expansion method. In this paper, it was carried out a finite element analysis about variation of residual stress due to tensile stress and residual stress distribution that was regenerated by re-cold expansion method in the fastener hole. Here, a diversity tensile stress was used. Also, it was performed a finite element analysis according to cold expansion rate of re cold expansion in order to obtain a beneficial compressive residual stress.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.204-210
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• 1998

A method is developed to include the effect of volume expansion in the description of the flame dynamics using G-equation. Line volume-source is used to represent the effect of the exothermic process of combustion with source strength determined by the density difference between the burned and the unburned region. Volume expansion adjusts the flow field to accommodate the increased volume flow rate crossing the flame front. Test result predicted the measured velocity field qualitatively. The method was applied to study the interaction of vortex and premixed flame. Increased volume expansion did not change the initial growth rate of flame area. However, the residence time and flame surface area increased with higher expansion ratios.