• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.145-159
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• 2011

The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.4
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• pp.118-125
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• 1992

Theoretical equations for hoop stress, longitudinal or meridian stress and Von Mises stress of an axismmetric conical pressure vessel and a frustum of conical pressure velle, both of which are pressuized by hydrostatic loading, are derived from equilibrium equations. The membrane stresses conputed by theoretical equations for a conical pressure vessel and a frustum of conical pressure vessel are compared with the values obtained from finite elelment method. Based on the fact that the computational values by theoretical equations are well agreed with the finite element results, derived equations are proved to be valid and it is possible for those equations to be conveniently used for structural analysis or design of frustum of conical pressure vessel which is a part of silo body.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.653-660
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.21 no.4
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• pp.1-10
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• 2013

This paper addresses the derivation of 6-DOF equation of Tanker and Receiver's aircraft for aerial refueling. The new set of nonlinear equations are derived in terms of the relative translational and rotational motion of receiver aircraft respect to the tanker aircraft body frame. Further the wind effect terms due to the tanker's turbulence are included. The derivation of absolute dynamic equation for tanker aircraft written in the inertial frame is calculated from the relative dynamics equations of receiver. The derived relative and absolute equations are implemented the simulation in the same flight conditions to verify the relative motion and compare the trim results by using the MATLAB/SIMULINK program.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.31-44
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• 2011

Partial differential equations on a Riemannain manifold is one of the most important areas in differential geometry. In this article, we survey the role of parabolic equations on some of the main results of differential geometry and topology, especially in the modern mathematical history. Also, we introduce some recent research in this area.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05a
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• pp.443-446
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• 2005

The shear strength equations of the joint with RC column and steel beam are used the proposed equations of ASCE, Kanno and AIJ but there are not applied variable joint details. Until now the variable experimental studies are practiced but the studies of predicted shear strength equation are not integrated and only the applicable equations to each case are proposed. The purpose of this study is statistical analysis for the proposed equations applied existing experiments. The proposed equations are ASCE, Kanno, M-Kanno, AIJ and M-AIJ. The 47 of shear failure experiments are used in this study The consequence is that the Kanno's equation is very analogized with the experimental result but ASCE equation underestimates about 42$\%$. AIJ and M-AIJ are not proper equations for estimating the shear strength of RCS joint.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.52-60
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• 1996

Existing equations of bed load transport are reviewed mainly considering the meaning and. role of variables used in the equations. The development of several equations and the problems of each equation are investigated by comparing their computed results against field or laboratory data. On the basis of the review remedies of each equation are suggested, and modified forms of existing equations are developed for wider application and improvement in the accuracy. Empirical parameters introduced in each equation are determined by testing them against Brownlie(1985)'s collected data, and discrepancy ranges of the refined equations are shown to see their degrees of accuracy.

• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.2
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• pp.122-130
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• 2013

Rail geometries such as cant, grade and curvature can be easily represented by means of a track coordinate system. In this analysis, in order to derive a dynamic and constraint equation of a wheelset, the track coordinate system is used as an intermediate stage. Dynamic and constraint equations of railway vehicle bodies except the wheelset are written in the Cartesian coordinate system as a conventional method. Therefore, whole dynamic equations of a railway vehicle are derived by combining wheelset dynamic equations and dynamic equations of railway vehicle bodies. Constraint equations and constraint Jacobians are newly derived for the track coordinate system. A process for numerical analysis is suggested for the derived dynamic and constraint equations of a railway vehicle. The proposed dynamic analysis of a railway vehicle is validated by comparison against results obtained from VI-RAIL analysis.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.