• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.515-528
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• 2006

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.

• Steel and Composite Structures
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• v.19 no.4
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• pp.829-841
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equilibrium equations are derived from the principle of virtual displacements. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• 한국연소학회:학술대회논문집
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• 2000.05a
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• pp.35-44
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• 2000

It was numerically studied that NOx emission characteristics of confined $CH_{4}$ jet flames with the variation of the diameter of inner fuel nozzle, the flow rate of $CH_{4}$ and equivalence ratio. Parabolic type equations were adopted in the calculation and GRI-2.1I mechanism was used for the chemical reaction. NOx emission index (EINOx) was introduced to evaluate NOx emission quantitatively in parametrically varied flames and the contribution of Thermal and Prompt NO mechanism was discussed. The results showed that Total EINOx varied sensitively with the variation of the flow rate of$CH_{4}$ but it was not sensitive to the variation of the diameter of inner fuel nozzle. Thermal EINOx showed the similar tendency to total EINOx and Prompt EINOx showed insensitivity to the variation of the diameter of inner fuel nozzle and the flow rate of $CH_{4}$.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.39-48
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• 1995

The ADI method was introduced by Peaceman and Rachford [6] in 1955, to solve the discretized boundary value problems for elliptic and parabolic PDEs. The finite difference discretization of the model elliptic problem $$ (1) -\Delta u = f, \Omega = [0, 1] \times [0, 1] $$ $$ u = 0 on \delta \Omega $$ with 5-point centered finite difference discretization, with n +2 mesh-points in the x - direction and m + 2 points in the y direction, leads to the solution of a linear system of equations of the form $$ (2) Au = b $$ where A is a matrix of dimension $N = n \times m$. Without loss of generality and for the sake of simplicity, we will assume for the remainder of this paper that m = n, so that $N = n^2$.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.

• Journal of ILASS-Korea
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• v.12 no.2
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• pp.79-85
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• 2007

In this study, the effect of jet velocity profile on the thickness and velocity of the liquid sheet formed by two impinging low speed jets was investigated. To predict the distribution of thickness and velocity of liquid sheet theoretically, the jet velocity profile which was measured experimentally was adopted in addition to the constant jet velocity as well as Poiseuille's parabolic profile. For three cases, the distribution of thickness and velocity of liquid sheet was analytically predicted by solving conservation equations including stagnation point. The predicted results were compared with previous experimental results. The jet velocity profile definitely affected the resulting characteristics of liquid sheet. The distribution of thickness and velocity of liquid sheet was more close to the measured results compared with that which was predicted by the assumption of constant jet velocity.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.10
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• pp.735-741
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• 2007

An axial F.R.P. fan model for cooling tower is developed. The fan is designed using the equations for one dimensional inviscid flow through the fan blade. Fan shape is swept forward with a parabolic function. Calculations of the three dimensional turbulent flow around the fan are carried out to investigate performance of the fan. Data of the total pressure rise and hydraulic efficiency can be obtained for the various setting angles. Calculated values of the total pressure rise and hydraulic efficiency at the design point are less than those of the design specification. The prototype of the F.R.P. fan is made by laminating of the fiberglass and epoxy resins on the mold of fan shape.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.46-49
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• 2008

This paper deals with the free vibrations of elastica shaped arches with constant arc length. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, in-plane vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged end constraints. The effects of rotatory inertia, rise to span length ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica and parabolic shaped arches are compared. Also, typical mode shapes are presented in figures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.394.2-394
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• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in the rectangular coordinates rather than in polar coordinates, in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. (omitted)