• Steel and Composite Structures
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• v.26 no.5
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.137-162
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• 2017

The Chinese algebraic method, the tian yuan shu, was developed during Song period (960-1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the Siku quanshu and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call 'equation'.

• Proceeding of EDISON Challenge
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• 2016.11a
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• pp.101-105
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• 2016

Prandtl's Lifting-line theory is the classical theory of calculating aerodynamic properties. Though it is classical method, it predicts the aerodynamic properties well. By lifting-line theory, high aspect ratio is critical factor to decrease induced drag. And 'elliptic-similar' wing also makes the minimum induced drag. But due to the problem of manufacturing, tapered wing is preferred and have been utilized. In this Paper, by using Edison CFD, verifying the classical lifting-line theory. To consider induced drag only, using Euler equation as governing equation instead of full Navier-Stokes equation. Refer to the theory, optimum taper ratio which makes the minimum induced drag is 0.3. Utilizing the CFD results, plotting oswald factor over various taper ratio and investigating whether the consequences are valid or not. As a result, solving Euler equation by EDISON CFD cannot guarantee the theoretical values because it is hard to set the proper grid to solve. Results are divided into two cases. One is the values are decreased gradually and another seems to following tendency, but values are all negative number.

• Journal of the Korean Society of Tobacco Science
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• v.35 no.1
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• pp.1-6
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• 2013

Near InfraRed Spectroscopy(NIRS) is a quick and accurate analytical method to measure multiple components in tobacco manufacturing process. This study was carried out to develop calibration equation of near infrared spectroscopy for the prediction of the amount of chemical components and hot water solubles(HWS) of reconstituted tobacco leaf. Calibration samples of reconstituted tobacco leaf were collected from every lot produced during one year. The calibration equation was formulated as modified partial least square regression method (MPLS) by analyzing laboratory actual values and mathematically pre-treated spectra. The accuracy of the acquired equation was confirmed with the standard error of prediction(SEP) of chemical components in reconstituted tobacco leaf samples, indicated as coefficient of determination($R^2$) and prediction error of sample unacquainted, followed by the verification of model equation of laboratory actual values and these predicted results. As a result of monitoring, the standard error of prediction(SEP) were 0.25 % for total sugar, 0.03 % for nicotine, 0.03 % for chlorine, 0.16 % for nitrate, and 0.38 % for hot water solubles. The coefficient of determination($R^2$) were 0.98 for total sugar, 0.97 for nicotine, 0.96 for chlorine, 0.98 for nitrate and 0.92 for hot water solubles. Therefore, the NIRS calibration equation can be applicable and reliable for determination of chemical components of reconstituted tobacco leaf, and NIRS analytical method could be used as a rapid and accurate quality control method.

• Water for future
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• v.28 no.5
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• pp.151-162
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• 1995

A two-dimensional stream tube dispersion model is developed to simulate accurately transverse dispersion processes of pollutants in natural channels. Two distinct features of the stream tube dispersion model derived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in a natural coordinate system which follows the general direction of the channel flow. In the model studied, Eulerian-Lagrangian method is used to solve the stream tube dispersion equation. The stream tube dispersion equation is decoupled into two components by the operator-splitting approach; one is governing advection and the other is governing dispersion. The advection equation has been solved using the method of characteristics and the results are interpolated onto Eulerian grid on which the dispersion equation is solved by centered difference method. In solving the advection equation, cubic spline interpolating polynomials is used. In the present study, the results of the application of this model to a natural channel are compared with a steady-state flow measurements. Simulation results are in good accordance with measured data.

• Structural Engineering and Mechanics
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• v.41 no.1
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• pp.67-81
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• 2012

Differential Quadrature Method (DQM) is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. In this study the governing equation which represents the free vibration of coupled shear walls is solved using the DQM method. A one-dimensional model has been used in this study. At the end of study various examples are presented to verify the accuracy of the method.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.215-230
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• 2001

In this paper, an asymptotic two-scale method is developed for solving vibration problem of long periodic structures. Such eigenmodes appear as a slow modulations of a periodic one. For those, the present method splits the vibration problem into two small problems at each order. The first one is a periodic problem and is posed on a few basic cells. The second is an amplitude equation to be satisfied by the envelope of the eigenmode. In this way, one can avoid the discretisation of the whole structure. Applying the Floquet method, the boundary conditions of the global problem are determined for any order of the asymptotic expansions.

• Journal of computational fluids engineering
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• v.2 no.2
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• pp.35-43
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• 1997

An efficient inverse method for 1.he supersonic/hypersonic axisymmetric body design is developed for the parabolized Navier-Stokes equations. The developed method is examined numerically for three extreme testcases in the supersonic(M/sub ∞/=3.0) and hypersonic(M/sub ∞/=6.28) speeds. The first one is a negative pressure distribution near a vacuum pressure and the second one is a positive pressure distribution over the whole region of the body. The last one is the case of abrupt change of pressure distribution to zero in the forward region of the body. These testcases show the robustness of the method. By introducing a regular-falsi method and by using a not-fully converged inverse solution, the convergence behavior was greatly improved.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.808-813
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• 2004

The stress analysis on orthotropic composite cylindrical shells with one circular or one elliptical cutout subjected to an axial force is carried out by using an analytical and experimental method. The composite cylindrical shell governing equation of the Donnell's type is applied to this study and all results are presented by the stress concentration factor. The stress concentration factor is defined as the ratio of the stress on the region around a cutout to the nominal stress of the shell. The stress concentration factor is classified into the circumferential stress concentration factors and the radial stress concentration factors due to the cylindrical coordinate of which the origin is the center of a cutout. The considered loading condition is only axial tension loading condition. In this study, thus, the maximum stress is induced on perpendicular region against axial direction, on the coordinate. Various cutout sizes are expressed using the radius ratio, (equation omitted), which is the radius of a cutout over one of the cylindrical shell. Experimental results are obtained using strain gages, which are attached around a cutout of the cylindrical shell. As the result from this study, the stress concentration around a cutout can be predicted by using the analytical method for an orthotropic composite cylindrical shell having a circular or an elliptical cutout.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.12
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• pp.626-633
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• 2004

In this paper, we present a time domain combined field integral equation (TD-CFIE) formulation to analyze the transient electromagnetic response from three-dimensional dielectric objects. The solution method in this paper is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. A set of the RWG (Rao, Wilton, Glisson) functions Is used for spatial expansion of the equivalent electric and magnetic current densities and a combination of RWG and its orthogonal component is used as spatial testing. We also investigate spatial testing procedures for the TD-CFIE to select the proper testing functions that are derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable enables one to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are presented and compared with the solutions of the frequency domain combined field integral equation (FD-CFIE).