• Journal of the Korean Mathematical Society
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• v.29 no.2
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• pp.281-295
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• 1992

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.838-848
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• 1992

The objective of the study is to provide a theoretical tools for analyzing the fracture of leyered composites with a center crack. It is assumed that the composite is composed of successive accumulation of the fiber layer and resin layer with the fiber layer being perfectly bonded to the resin layer except the region of a center crack. In-plane shear loading (Mode II) and the anti-plane shear loading (Mode III) are considered separately. Boundary value problems are formulated by using a plane theory of elasticity and governing equations are reduced to a Fredholm integral equation of a second kind. The equation is solved numerically and the stress intensity factors are obtained. The normalized Mode II and Mode III stress intensity factors are evaluated for various combinations of material properties and for various geometrical parametes.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.181-210
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• 2009

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of isotropic flat plates. The so-called exact finite strip is assumed to be simply supported out-of-plane at the loaded ends. The strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. It is noted that in the present method, only one of the calculated out-of-plane buckling deflection modes, corresponding to the lowest buckling load, i.e., the first mode is used for the initial post-buckling study. Thus, the postbuckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman's compatibility equation governing the behavior of isotropic flat plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial postbuckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.361-371
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• 1983

The turbulent structures of the free plane jet and two dimensional impinging jet are investigated experimentally. In order to get the two dimensional jet, the contour of the cubic equation suggested by Morel is used for a contracting nozzle. A linearized constant-temperature hot-wire anemometer is used for measurement. Mean velocities and turbulent intensities are measured along the centerline of the jet. Jet halp width spatial double velocity correlation coefficients and integral length scales are obtained. It is established that the free plane jet is truly self-preserving about 40 slot widths downstream of the nozzle. The experiments for the impinging jet are carried out at four different impingement wall locations within the self-preserving region of the free plane jet, and comparing the results with that of free plane jet, the mean velocity is changed in the region of 0.25H and turbulent intensities are affected in the region of 0.2H from the wall, respectively, where H means the distance between the nozzle exit and the wall.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.241-251
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• 2005

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.107-109
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• 2003

We propose a wall distance free one-equation turbulence model. The model is organized in an extremely simple form. Only a few model constants were introduced into the model. The model is numerically tough and easy-of-use. The model also demonstrated the ability to simulate the laminar to turbulent flow transition. The model has been applied to the channel flow, the plane jet, the backward facing step flow, the flat plate boundary layer, as well as the flow around the 2D airfoil at large angles of attack, which obtained satisfactory results.

• Journal of the Korean Society of Clothing and Textiles
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• v.20 no.3
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• pp.519-526
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• 1996

To investigate the relationship between plane and side drape coefficient, the drape tester designed in which coordinate of projected outline of draped specimen could be recorded. By using this drape tester, the three dimensional shape, plane and side drape coefficient were obtained from coordinate of plane projected shape, and furthermore examined the tendency in changes of drape coefficient in terms of diameter of specimen, deflection angle, and bending rigidity. The side drape coefficients were constant regardless of changes in diameter of specimen. The plane drape coefficients, however, made a little difference according to changes in diameter of specimen. The experimental drape coefficient agreed well with the theoretical drape coefficient according to deflection angle. In the meanwhile, when the plane drape coefficients were regressed with the side drape coefficents, regression equation was $y=0.375x-0.002x^2+6.9\times10^{-5}x^3$. When the $\overline{\theta_s}$ is mean of deflection angle of selected points which have the longest and shortest distance from center point in the node, the theoretical drape coefficient calculated from $\overline{\theta_s}$ has high correlation with experimental drape coefficient. The plane and side drape coefficient changed linearly with increasing the bending length, $\sqrt[3]{EI/w}$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.89-96
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• 2007

A volume integral equation method (VIEM) is applied for the effective analysis of plane elastostatic problems in unbounded solids containing single isotropic inclusion of two different shapes considering composite fiber volume fraction. Single cylindrical inclusion and single square cylindrical inclusion are considered in the composites with six different fiber volume fractions (0.25, 0.30, 0.35, 0.40, 0.45, 0.50). Using the rule of mixtures, the effective material properties are calculated according to the corresponding composite fiber volume fraction. The analysis of plane elastostatic problems in the unbounded effective material containing single fiber that covers an area corresponding to the composite fiber volume fraction in the bounded matrix material are carried out. Thus, single fiber, matrix material with a finite region, and the unbounded effective material are used in the VIEM models for the plane elastostatic analysis. A detailed analysis of stress field at the interface between the matrix and the inclusion is carried out for single cylindrical or square cylindrical inclusion. Next, the stress field is compared to that at the interface between the matrix and the single inclusion in unbounded isotropic matrix with single isotropic cylindrical or square cylindrical inclusion. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of inclusions. Through the analysis of plane elastostatic problems, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing inclusions considering composite fiber volume fraction.

• Ocean Systems Engineering
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• v.13 no.2
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• pp.123-146
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• 2023

In this paper, Moore-Gibson-Thompson theory of thermoelasticity is considered to investigate the fundamental solution and vibration of plane wave in an isotropic photothermoelastic solid. The governing equations are made dimensionless for further investigation. The dimensionless equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. Also some preliminary properties of the solution are explored. In the second part, the vibration of plane waves are examined by expressing the governing equation for two dimensional case. It is found that for the non-trivial solution of the equation yield that there exist three longitudinal waves which advance with the distinct speed, and one transverse wave which is free from thermal and carrier density response. The impact of various models (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (ii) Lord and Shulman's (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv) Green and Naghdi type-III(GN-III)(1992) on the attributes of waves i.e., phase velocity, attenuation coefficient, specific loss and penetration depth are elaborated by plotting various figures of physical quantities. Various particular cases of interest are also deduced from the present investigations. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.