• Smart Structures and Systems
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• v.21 no.4
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• pp.469-477
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• 2018

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

• Steel and Composite Structures
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• v.39 no.5
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• pp.565-581
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• 2021

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

• Bulletin of the Korean Chemical Society
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• v.13 no.6
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• pp.665-669
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• 1992

We consider the problem of a random walker on a one-dimensional lattice (N sites) confronting a centrally-located deep trap (trapping probability, T=1) and N-1 adjacent sites at each of which there is a nonzero probability s(0 < s < 1) of the walker being trapped. Exact analytic expressions for < n > and the average number of steps required for trapping for arbitrary s are obtained for two types of finite boundary conditions (confining and reflecting) and for the infinite periodic chain. For the latter case of boundary condition, Montroll's exact result is recovered when s is set to zero.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.355-360
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• 1996

When the operational strains of a structure can not be directly measured in order to predict the life of the structure due to the problem of the attachment, those must be obtained indirectly. Since the displacement and the strain are interrelated, the strain can be predicted from the measured displacement and displacement-strain transformation matrix. The transformation matrix is dependent on the boundary condition, unfortunately, and it is also difficult to know exactly that of the operational system. In this study, for the structure with arbitrary boundary condition under the operation, the approximate method is proposed in order to predict the operational strains using the transformation matrix obtained by using free boundary conditions. And the method is applied to predict the strains of leads of surface mount component under the vibration of the printed circuit board.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.628-633
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• 2003

An analysis on the steady-state has been made of flow of a compressible fluid rapidly-rotating in a pipe. The flow is induced by an small arbitrary azimuthally-varying thermal forcing added on the basic state of rigid body isothermal rotation. The system Ekman number is assumed to be very small value. Analytic solutions have been obtained for axisymmetric and non-axisymmetric types, in which the axisymmetric solution comes from the azimuthally-averaged wall boundary condition and the non-axisymmetric solution from fluctuating wall boundary condition.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3463-3473
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• 1996

The characteristics of wave propagation along a catenary depend on various impedance conditions; i.e., spatial impedance of catenary, impedance of boundaries. In this study, wave propagation along a simple catenary system is studied with arbitrary impedance conditions such as impedance of pantograph, boundary, catenary etc. Seven coupled equations which determine the characteristics of wave propagation along catenary system have been derived and numerically solved. Results demonstrate the role of each impedance condition in the dynamics of catenary system, i.e. the way in which the conditions affect waves on catenary as well as contact force of pantograph. The formulation and suggested solution method can be certainly used for desinging an optimal catenary system for a given pantograph.

• Structural Engineering and Mechanics
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• v.6 no.2
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• pp.173-183
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• 1998

In the shape design of flexible structures, it is useful to predict the initial shape from the desirable large deformed shapes under some loading conditions. In this paper, we present a numerical procedure of an initial shape determination problem for hyperelastic materials which enables us to calculate an initial shape corresponding to the prescribed deformed shape and boundary condition. The present procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) finite element method for hyperelasticity, in which arbitrary change of shapes in both the initial and deformed states can be treated by considering the variation of geometric mappings in the equilibrium equation. Then the determination problem of the initial shape can be formulated as a nonlinear problem to solve the unknown initial shape for the specified deformed shape that satisfies the equilibrium equation. The present approach can be implemented easily to the finite element method by employing the isoparametric hypothesis. Some basic numerical results are also given to characterize the present procedure.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.5
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• pp.430-436
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• 2011

The purpose of this study is to analyze the vibration and sound generation characteristics of the sandwich panel. Two thick panels were assumed to be separated by a compliant viscoelastic core. The transverse vibration induced by an external impact was analyzed using the Rayleigh-Ritz method. For applying arbitrary boundary condition of the panels, the edges were assumed to be supported by the translational and rotational springs. The beam functions were used as the trial functions. The effect of the boundary condition and viscoelastic core on the resulting vibration characteristics was investigated. The radiated sound power was analyzed using the proposed numerical model and the Rayleigh integral. The dynamic properties of the core and the mass-stiffness-mass resonance frequency had significant influence on the impact sound.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.997-1008
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• 1994

Heat transfer by laminar oscillating flow in a circular pipe has been studied analytically. The general solution with respect to the arbitrary wall boundary condition is obtained by superposing the fluid temperatures with the sinusoidal wall temperature distributions. The fulid temperature distributions are two dimensional, but uniform flow assumption is used to simplify the velocity distribution. The heat transfer characteristics in the thermally developing regions are analyzed by applying the general solution to the two cases of thermal boundary conditions in which the wall temperature and wall heat flux distributions have a square-wave form, respectively. The results show that the length of the thermally developing region becomes larger in proportion to the oscillation frequency at slow oscillation and eventually approaches to the value comparable to the swept distance as the frequency increases. The time and cross-section averaged Nusselt number in the developing region is inversely proportional to the square root of the distance from the position where the wall boundary condition is changed suddenly. In the developed region, Nusselt number is only determined by the oscillation frequency.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.5 no.3
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• pp.14-21
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• 1994

In this paper, a numerical method to be obtain the radar cross section(RCS) of three- dimensional bodies with arbitrary geometry and material compositions on the electromagnetic field with arbitrary incident angle is described. The RCS is obtained by solving the individual surface integral equation about multilayers scatterer using the three-dimensional bonudary element method(BEM). To show propriety and usefulness as to the three-dimensional BEM in this paper, the choice of a geometry is a multi-regular hexahedron and multi-right-angled hexahedron out of oblique incident electric field, and is considered to apply to every condition with loss sufficiently.